LMFDB - Embedded newform 201.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,2,Mod(1,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, 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("201.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	201.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:	$1.60499308063$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.48119$ of defining polynomial
Character	$\chi$	$=$	201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.67513 q^{2} -1.00000 q^{3} +5.15633 q^{4} -1.48119 q^{5} -2.67513 q^{6} +0.193937 q^{7} +8.44358 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.67513 q^{2} -1.00000 q^{3} +5.15633 q^{4} -1.48119 q^{5} -2.67513 q^{6} +0.193937 q^{7} +8.44358 q^{8} +1.00000 q^{9} -3.96239 q^{10} -0.156325 q^{11} -5.15633 q^{12} -6.15633 q^{13} +0.518806 q^{14} +1.48119 q^{15} +12.2750 q^{16} +3.76845 q^{17} +2.67513 q^{18} -7.50659 q^{19} -7.63752 q^{20} -0.193937 q^{21} -0.418190 q^{22} +3.09332 q^{23} -8.44358 q^{24} -2.80606 q^{25} -16.4690 q^{26} -1.00000 q^{27} +1.00000 q^{28} -5.92478 q^{29} +3.96239 q^{30} +7.57452 q^{31} +15.9502 q^{32} +0.156325 q^{33} +10.0811 q^{34} -0.287258 q^{35} +5.15633 q^{36} +4.11871 q^{37} -20.0811 q^{38} +6.15633 q^{39} -12.5066 q^{40} +8.98778 q^{41} -0.518806 q^{42} -1.00000 q^{43} -0.806063 q^{44} -1.48119 q^{45} +8.27504 q^{46} +5.58181 q^{47} -12.2750 q^{48} -6.96239 q^{49} -7.50659 q^{50} -3.76845 q^{51} -31.7440 q^{52} -2.41327 q^{53} -2.67513 q^{54} +0.231548 q^{55} +1.63752 q^{56} +7.50659 q^{57} -15.8496 q^{58} +13.3757 q^{59} +7.63752 q^{60} +6.73084 q^{61} +20.2628 q^{62} +0.193937 q^{63} +18.1187 q^{64} +9.11871 q^{65} +0.418190 q^{66} +1.00000 q^{67} +19.4314 q^{68} -3.09332 q^{69} -0.768452 q^{70} -1.11871 q^{71} +8.44358 q^{72} -13.3127 q^{73} +11.0181 q^{74} +2.80606 q^{75} -38.7064 q^{76} -0.0303172 q^{77} +16.4690 q^{78} +12.9624 q^{79} -18.1817 q^{80} +1.00000 q^{81} +24.0435 q^{82} -0.936996 q^{83} -1.00000 q^{84} -5.58181 q^{85} -2.67513 q^{86} +5.92478 q^{87} -1.31994 q^{88} -15.8192 q^{89} -3.96239 q^{90} -1.19394 q^{91} +15.9502 q^{92} -7.57452 q^{93} +14.9321 q^{94} +11.1187 q^{95} -15.9502 q^{96} -3.64244 q^{97} -18.6253 q^{98} -0.156325 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 5 q^{4} + q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 3 * q^3 + 5 * q^4 + q^5 - 3 * q^6 + q^7 + 9 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 5 q^{4} + q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 3 q^{9} - q^{10} + 10 q^{11} - 5 q^{12} - 8 q^{13} + 7 q^{14} - q^{15} + 5 q^{16} + 3 q^{18} - 2 q^{19} - 7 q^{20} - q^{21} + 3 q^{23} - 9 q^{24} - 8 q^{25} - 18 q^{26} - 3 q^{27} + 3 q^{28} + 4 q^{29} + q^{30} + 11 q^{31} + 11 q^{32} - 10 q^{33} - 2 q^{34} + 5 q^{35} + 5 q^{36} - 9 q^{37} - 28 q^{38} + 8 q^{39} - 17 q^{40} + q^{41} - 7 q^{42} - 3 q^{43} - 2 q^{44} + q^{45} - 7 q^{46} + 18 q^{47} - 5 q^{48} - 10 q^{49} - 2 q^{50} - 32 q^{52} + 7 q^{53} - 3 q^{54} + 12 q^{55} - 11 q^{56} + 2 q^{57} - 4 q^{58} + 15 q^{59} + 7 q^{60} - 2 q^{61} + 3 q^{62} + q^{63} + 33 q^{64} + 6 q^{65} + 3 q^{67} + 16 q^{68} - 3 q^{69} + 9 q^{70} + 18 q^{71} + 9 q^{72} - 19 q^{73} + 5 q^{74} + 8 q^{75} - 42 q^{76} + 2 q^{77} + 18 q^{78} + 28 q^{79} - 29 q^{80} + 3 q^{81} + 29 q^{82} - 7 q^{83} - 3 q^{84} - 18 q^{85} - 3 q^{86} - 4 q^{87} + 4 q^{88} - 6 q^{89} - q^{90} - 4 q^{91} + 11 q^{92} - 11 q^{93} + 36 q^{94} + 12 q^{95} - 11 q^{96} - 8 q^{97} - 14 q^{98} + 10 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 5 * q^4 + q^5 - 3 * q^6 + q^7 + 9 * q^8 + 3 * q^9 - q^10 + 10 * q^11 - 5 * q^12 - 8 * q^13 + 7 * q^14 - q^15 + 5 * q^16 + 3 * q^18 - 2 * q^19 - 7 * q^20 - q^21 + 3 * q^23 - 9 * q^24 - 8 * q^25 - 18 * q^26 - 3 * q^27 + 3 * q^28 + 4 * q^29 + q^30 + 11 * q^31 + 11 * q^32 - 10 * q^33 - 2 * q^34 + 5 * q^35 + 5 * q^36 - 9 * q^37 - 28 * q^38 + 8 * q^39 - 17 * q^40 + q^41 - 7 * q^42 - 3 * q^43 - 2 * q^44 + q^45 - 7 * q^46 + 18 * q^47 - 5 * q^48 - 10 * q^49 - 2 * q^50 - 32 * q^52 + 7 * q^53 - 3 * q^54 + 12 * q^55 - 11 * q^56 + 2 * q^57 - 4 * q^58 + 15 * q^59 + 7 * q^60 - 2 * q^61 + 3 * q^62 + q^63 + 33 * q^64 + 6 * q^65 + 3 * q^67 + 16 * q^68 - 3 * q^69 + 9 * q^70 + 18 * q^71 + 9 * q^72 - 19 * q^73 + 5 * q^74 + 8 * q^75 - 42 * q^76 + 2 * q^77 + 18 * q^78 + 28 * q^79 - 29 * q^80 + 3 * q^81 + 29 * q^82 - 7 * q^83 - 3 * q^84 - 18 * q^85 - 3 * q^86 - 4 * q^87 + 4 * q^88 - 6 * q^89 - q^90 - 4 * q^91 + 11 * q^92 - 11 * q^93 + 36 * q^94 + 12 * q^95 - 11 * q^96 - 8 * q^97 - 14 * q^98 + 10 * 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 $

$2$	2.67513	1.89160	0.945802	−	0.324745i	$-0.105279\pi$
$2$	2.67513	1.89160	0.945802	+	0.324745i	$0.105279\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.15633	2.57816
$5$	−1.48119	−0.662410	−0.331205	−	0.943559i	$-0.607455\pi$
$5$	−1.48119	−0.662410	−0.331205	+	0.943559i	$0.607455\pi$
$6$	−2.67513	−1.09212
$7$	0.193937	0.0733011	0.0366506	−	0.999328i	$-0.488331\pi$
$7$	0.193937	0.0733011	0.0366506	+	0.999328i	$0.488331\pi$
$8$	8.44358	2.98526
$9$	1.00000	0.333333
$10$	−3.96239	−1.25302
$11$	−0.156325	−0.0471338	−0.0235669	−	0.999722i	$-0.507502\pi$
$11$	−0.156325	−0.0471338	−0.0235669	+	0.999722i	$0.507502\pi$
$12$	−5.15633	−1.48850
$13$	−6.15633	−1.70746	−0.853729	−	0.520718i	$-0.825664\pi$
$13$	−6.15633	−1.70746	−0.853729	+	0.520718i	$0.825664\pi$
$14$	0.518806	0.138657
$15$	1.48119	0.382443
$16$	12.2750	3.06876
$17$	3.76845	0.913984	0.456992	−	0.889471i	$-0.348927\pi$
$17$	3.76845	0.913984	0.456992	+	0.889471i	$0.348927\pi$
$18$	2.67513	0.630534
$19$	−7.50659	−1.72213	−0.861065	−	0.508496i	$-0.830202\pi$
$19$	−7.50659	−1.72213	−0.861065	+	0.508496i	$0.830202\pi$
$20$	−7.63752	−1.70780
$21$	−0.193937	−0.0423204
$22$	−0.418190	−0.0891585
$23$	3.09332	0.645002	0.322501	−	0.946569i	$-0.395476\pi$
$23$	3.09332	0.645002	0.322501	+	0.946569i	$0.395476\pi$
$24$	−8.44358	−1.72354
$25$	−2.80606	−0.561213
$26$	−16.4690	−3.22983
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−5.92478	−1.10020	−0.550102	−	0.835098i	$-0.685411\pi$
$29$	−5.92478	−1.10020	−0.550102	+	0.835098i	$0.685411\pi$
$30$	3.96239	0.723430
$31$	7.57452	1.36042	0.680212	−	0.733016i	$-0.261888\pi$
$31$	7.57452	1.36042	0.680212	+	0.733016i	$0.261888\pi$
$32$	15.9502	2.81962
$33$	0.156325	0.0272127
$34$	10.0811	1.72889
$35$	−0.287258	−0.0485554
$36$	5.15633	0.859388
$37$	4.11871	0.677112	0.338556	−	0.940946i	$-0.390061\pi$
$37$	4.11871	0.677112	0.338556	+	0.940946i	$0.390061\pi$
$38$	−20.0811	−3.25758
$39$	6.15633	0.985801
$40$	−12.5066	−1.97747
$41$	8.98778	1.40366	0.701828	−	0.712347i	$-0.252368\pi$
$41$	8.98778	1.40366	0.701828	+	0.712347i	$0.252368\pi$
$42$	−0.518806	−0.0800535
$43$	−1.00000	−0.152499	−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000	−0.152499	−0.0762493	+	0.997089i	$0.524294\pi$
$44$	−0.806063	−0.121519
$45$	−1.48119	−0.220803
$46$	8.27504	1.22009
$47$	5.58181	0.814191	0.407095	−	0.913386i	$-0.366542\pi$
$47$	5.58181	0.814191	0.407095	+	0.913386i	$0.366542\pi$
$48$	−12.2750	−1.77175
$49$	−6.96239	−0.994627
$50$	−7.50659	−1.06159
$51$	−3.76845	−0.527689
$52$	−31.7440	−4.40210
$53$	−2.41327	−0.331488	−0.165744	−	0.986169i	$-0.553002\pi$
$53$	−2.41327	−0.331488	−0.165744	+	0.986169i	$0.553002\pi$
$54$	−2.67513	−0.364039
$55$	0.231548	0.0312219
$56$	1.63752	0.218823
$57$	7.50659	0.994272
$58$	−15.8496	−2.08115
$59$	13.3757	1.74136	0.870681	−	0.491848i	$-0.163679\pi$
$59$	13.3757	1.74136	0.870681	+	0.491848i	$0.163679\pi$
$60$	7.63752	0.986000
$61$	6.73084	0.861796	0.430898	−	0.902401i	$-0.358197\pi$
$61$	6.73084	0.861796	0.430898	+	0.902401i	$0.358197\pi$
$62$	20.2628	2.57338
$63$	0.193937	0.0244337
$64$	18.1187	2.26484
$65$	9.11871	1.13104
$66$	0.418190	0.0514757
$67$	1.00000	0.122169
$67$	1.00000	0.122169
$68$	19.4314	2.35640
$69$	−3.09332	−0.372392
$70$	−0.768452	−0.0918476
$71$	−1.11871	−0.132767	−0.0663834	−	0.997794i	$-0.521146\pi$
$71$	−1.11871	−0.132767	−0.0663834	+	0.997794i	$0.521146\pi$
$72$	8.44358	0.995086
$73$	−13.3127	−1.55813	−0.779064	−	0.626944i	$-0.784305\pi$
$73$	−13.3127	−1.55813	−0.779064	+	0.626944i	$0.784305\pi$
$74$	11.0181	1.28083
$75$	2.80606	0.324016
$76$	−38.7064	−4.43993
$77$	−0.0303172	−0.00345496
$78$	16.4690	1.86474
$79$	12.9624	1.45838	0.729191	−	0.684310i	$-0.239896\pi$
$79$	12.9624	1.45838	0.729191	+	0.684310i	$0.239896\pi$
$80$	−18.1817	−2.03278
$81$	1.00000	0.111111
$82$	24.0435	2.65516
$83$	−0.936996	−0.102849	−0.0514243	−	0.998677i	$-0.516376\pi$
$83$	−0.936996	−0.102849	−0.0514243	+	0.998677i	$0.516376\pi$
$84$	−1.00000	−0.109109
$85$	−5.58181	−0.605432
$86$	−2.67513	−0.288467
$87$	5.92478	0.635203
$88$	−1.31994	−0.140707
$89$	−15.8192	−1.67684	−0.838418	−	0.545028i	$-0.816519\pi$
$89$	−15.8192	−1.67684	−0.838418	+	0.545028i	$0.816519\pi$
$90$	−3.96239	−0.417672
$91$	−1.19394	−0.125159
$92$	15.9502	1.66292
$93$	−7.57452	−0.785441
$94$	14.9321	1.54013
$95$	11.1187	1.14076
$96$	−15.9502	−1.62791
$97$	−3.64244	−0.369834	−0.184917	−	0.982754i	$-0.559202\pi$
$97$	−3.64244	−0.369834	−0.184917	+	0.982754i	$0.559202\pi$
$98$	−18.6253	−1.88144
$99$	−0.156325	−0.0157113
$100$	−14.4690	−1.44690
$101$	16.9175	1.68335	0.841676	−	0.539983i	$-0.181569\pi$
$101$	16.9175	1.68335	0.841676	+	0.539983i	$0.181569\pi$
$102$	−10.0811	−0.998178
$103$	2.03032	0.200053	0.100027	−	0.994985i	$-0.468107\pi$
$103$	2.03032	0.200053	0.100027	+	0.994985i	$0.468107\pi$
$104$	−51.9814	−5.09720
$105$	0.287258	0.0280335
$106$	−6.45580	−0.627043
$107$	−4.15633	−0.401807	−0.200904	−	0.979611i	$-0.564388\pi$
$107$	−4.15633	−0.401807	−0.200904	+	0.979611i	$0.564388\pi$
$108$	−5.15633	−0.496168
$109$	−5.89446	−0.564587	−0.282293	−	0.959328i	$-0.591095\pi$
$109$	−5.89446	−0.564587	−0.282293	+	0.959328i	$0.591095\pi$
$110$	0.619421	0.0590595
$111$	−4.11871	−0.390931
$112$	2.38058	0.224944
$113$	−2.03032	−0.190996	−0.0954981	−	0.995430i	$-0.530444\pi$
$113$	−2.03032	−0.190996	−0.0954981	+	0.995430i	$0.530444\pi$
$114$	20.0811	1.88077
$115$	−4.58181	−0.427256
$116$	−30.5501	−2.83650
$117$	−6.15633	−0.569152
$118$	35.7816	3.29397
$119$	0.730841	0.0669961
$120$	12.5066	1.14169
$121$	−10.9756	−0.997778
$122$	18.0059	1.63018
$123$	−8.98778	−0.810401
$124$	39.0567	3.50739
$125$	11.5623	1.03416
$126$	0.518806	0.0462189
$127$	−2.34297	−0.207905	−0.103952	−	0.994582i	$-0.533149\pi$
$127$	−2.34297	−0.207905	−0.103952	+	0.994582i	$0.533149\pi$
$128$	16.5696	1.46456
$129$	1.00000	0.0880451
$130$	24.3938	2.13947
$131$	1.21933	0.106533	0.0532666	−	0.998580i	$-0.483037\pi$
$131$	1.21933	0.106533	0.0532666	+	0.998580i	$0.483037\pi$
$132$	0.806063	0.0701588
$133$	−1.45580	−0.126234
$134$	2.67513	0.231096
$135$	1.48119	0.127481
$136$	31.8192	2.72848
$137$	−16.9126	−1.44494	−0.722469	−	0.691404i	$-0.756993\pi$
$137$	−16.9126	−1.44494	−0.722469	+	0.691404i	$0.756993\pi$
$138$	−8.27504	−0.704418
$139$	18.1695	1.54112	0.770558	−	0.637369i	$-0.219977\pi$
$139$	18.1695	1.54112	0.770558	+	0.637369i	$0.219977\pi$
$140$	−1.48119	−0.125184
$141$	−5.58181	−0.470073
$142$	−2.99271	−0.251142
$143$	0.962389	0.0804790
$144$	12.2750	1.02292
$145$	8.77575	0.728786
$146$	−35.6131	−2.94736
$147$	6.96239	0.574248
$148$	21.2374	1.74571
$149$	13.0884	1.07224	0.536122	−	0.844141i	$-0.319889\pi$
$149$	13.0884	1.07224	0.536122	+	0.844141i	$0.319889\pi$
$150$	7.50659	0.612910
$151$	5.70782	0.464496	0.232248	−	0.972657i	$-0.425392\pi$
$151$	5.70782	0.464496	0.232248	+	0.972657i	$0.425392\pi$
$152$	−63.3825	−5.14100
$153$	3.76845	0.304661
$154$	−0.0811024	−0.00653542
$155$	−11.2193	−0.901158
$156$	31.7440	2.54156
$157$	−19.5745	−1.56222	−0.781108	−	0.624396i	$-0.785345\pi$
$157$	−19.5745	−1.56222	−0.781108	+	0.624396i	$0.785345\pi$
$158$	34.6761	2.75868
$159$	2.41327	0.191384
$160$	−23.6253	−1.86774
$161$	0.599908	0.0472794
$162$	2.67513	0.210178
$163$	−11.0376	−0.864532	−0.432266	−	0.901746i	$-0.642286\pi$
$163$	−11.0376	−0.864532	−0.432266	+	0.901746i	$0.642286\pi$
$164$	46.3439	3.61885
$165$	−0.231548	−0.0180260
$166$	−2.50659	−0.194549
$167$	−13.6072	−1.05296	−0.526478	−	0.850188i	$-0.676488\pi$
$167$	−13.6072	−1.05296	−0.526478	+	0.850188i	$0.676488\pi$
$168$	−1.63752	−0.126337
$169$	24.9003	1.91541
$170$	−14.9321	−1.14524
$171$	−7.50659	−0.574043
$172$	−5.15633	−0.393166
$173$	6.46898	0.491827	0.245914	−	0.969292i	$-0.420912\pi$
$173$	6.46898	0.491827	0.245914	+	0.969292i	$0.420912\pi$
$174$	15.8496	1.20155
$175$	−0.544198	−0.0411375
$176$	−1.91890	−0.144642
$177$	−13.3757	−1.00538
$178$	−42.3185	−3.17191
$179$	−5.50659	−0.411582	−0.205791	−	0.978596i	$-0.565977\pi$
$179$	−5.50659	−0.411582	−0.205791	+	0.978596i	$0.565977\pi$
$180$	−7.63752	−0.569267
$181$	−14.6932	−1.09214	−0.546070	−	0.837740i	$-0.683877\pi$
$181$	−14.6932	−1.09214	−0.546070	+	0.837740i	$0.683877\pi$
$182$	−3.19394	−0.236750
$183$	−6.73084	−0.497558
$184$	26.1187	1.92550
$185$	−6.10062	−0.448526
$186$	−20.2628	−1.48574
$187$	−0.589104	−0.0430795
$188$	28.7816	2.09912
$189$	−0.193937	−0.0141068
$190$	29.7440	2.15786
$191$	−7.53690	−0.545351	−0.272676	−	0.962106i	$-0.587909\pi$
$191$	−7.53690	−0.545351	−0.272676	+	0.962106i	$0.587909\pi$
$192$	−18.1187	−1.30761
$193$	−4.27504	−0.307724	−0.153862	−	0.988092i	$-0.549171\pi$
$193$	−4.27504	−0.307724	−0.153862	+	0.988092i	$0.549171\pi$
$194$	−9.74401	−0.699579
$195$	−9.11871	−0.653005
$196$	−35.9003	−2.56431
$197$	−3.32487	−0.236887	−0.118444	−	0.992961i	$-0.537790\pi$
$197$	−3.32487	−0.236887	−0.118444	+	0.992961i	$0.537790\pi$
$198$	−0.418190	−0.0297195
$199$	−11.3503	−0.804599	−0.402299	−	0.915508i	$-0.631789\pi$
$199$	−11.3503	−0.804599	−0.402299	+	0.915508i	$0.631789\pi$
$200$	−23.6932	−1.67536
$201$	−1.00000	−0.0705346
$202$	45.2565	3.18423
$203$	−1.14903	−0.0806462
$204$	−19.4314	−1.36047
$205$	−13.3127	−0.929796
$206$	5.43136	0.378421
$207$	3.09332	0.215001
$208$	−75.5691	−5.23978
$209$	1.17347	0.0811705
$210$	0.768452	0.0530282
$211$	26.7513	1.84164	0.920818	−	0.389993i	$-0.127522\pi$
$211$	26.7513	1.84164	0.920818	+	0.389993i	$0.127522\pi$
$212$	−12.4436	−0.854629
$213$	1.11871	0.0766530
$214$	−11.1187	−0.760060
$215$	1.48119	0.101017
$216$	−8.44358	−0.574513
$217$	1.46898	0.0997206
$218$	−15.7685	−1.06797
$219$	13.3127	0.899586
$220$	1.19394	0.0804952
$221$	−23.1998	−1.56059
$222$	−11.0181	−0.739486
$223$	−0.850969	−0.0569851	−0.0284926	−	0.999594i	$-0.509071\pi$
$223$	−0.850969	−0.0569851	−0.0284926	+	0.999594i	$0.509071\pi$
$224$	3.09332	0.206681
$225$	−2.80606	−0.187071
$226$	−5.43136	−0.361289
$227$	−5.13823	−0.341036	−0.170518	−	0.985355i	$-0.554544\pi$
$227$	−5.13823	−0.341036	−0.170518	+	0.985355i	$0.554544\pi$
$228$	38.7064	2.56339
$229$	−8.57452	−0.566620	−0.283310	−	0.959028i	$-0.591433\pi$
$229$	−8.57452	−0.566620	−0.283310	+	0.959028i	$0.591433\pi$
$230$	−12.2569	−0.808199
$231$	0.0303172	0.00199472
$232$	−50.0263	−3.28439
$233$	18.2569	1.19605	0.598026	−	0.801477i	$-0.295952\pi$
$233$	18.2569	1.19605	0.598026	+	0.801477i	$0.295952\pi$
$234$	−16.4690	−1.07661
$235$	−8.26774	−0.539328
$236$	68.9692	4.48951
$237$	−12.9624	−0.841998
$238$	1.95509	0.126730
$239$	9.87399	0.638695	0.319348	−	0.947638i	$-0.396536\pi$
$239$	9.87399	0.638695	0.319348	+	0.947638i	$0.396536\pi$
$240$	18.1817	1.17362
$241$	−18.9452	−1.22037	−0.610185	−	0.792259i	$-0.708905\pi$
$241$	−18.9452	−1.22037	−0.610185	+	0.792259i	$0.708905\pi$
$242$	−29.3611	−1.88740
$243$	−1.00000	−0.0641500
$244$	34.7064	2.22185
$245$	10.3127	0.658851
$246$	−24.0435	−1.53296
$247$	46.2130	2.94046
$248$	63.9560	4.06121
$249$	0.936996	0.0593797
$250$	30.9307	1.95623
$251$	−0.775746	−0.0489647	−0.0244823	−	0.999700i	$-0.507794\pi$
$251$	−0.775746	−0.0489647	−0.0244823	+	0.999700i	$0.507794\pi$
$252$	1.00000	0.0629941
$253$	−0.483564	−0.0304014
$254$	−6.26774	−0.393273
$255$	5.58181	0.349546
$256$	8.08840	0.505525
$257$	−3.84955	−0.240129	−0.120064	−	0.992766i	$-0.538310\pi$
$257$	−3.84955	−0.240129	−0.120064	+	0.992766i	$0.538310\pi$
$258$	2.67513	0.166546
$259$	0.798769	0.0496331
$260$	47.0191	2.91600
$261$	−5.92478	−0.366735
$262$	3.26187	0.201519
$263$	−25.4264	−1.56786	−0.783931	−	0.620848i	$-0.786788\pi$
$263$	−25.4264	−1.56786	−0.783931	+	0.620848i	$0.786788\pi$
$264$	1.31994	0.0812370
$265$	3.57452	0.219581
$266$	−3.89446	−0.238785
$267$	15.8192	0.968122
$268$	5.15633	0.314973
$269$	−15.1793	−0.925501	−0.462751	−	0.886489i	$-0.653137\pi$
$269$	−15.1793	−0.925501	−0.462751	+	0.886489i	$0.653137\pi$
$270$	3.96239	0.241143
$271$	4.33709	0.263459	0.131730	−	0.991286i	$-0.457947\pi$
$271$	4.33709	0.263459	0.131730	+	0.991286i	$0.457947\pi$
$272$	46.2579	2.80480
$273$	1.19394	0.0722603
$274$	−45.2433	−2.73325
$275$	0.438658	0.0264521
$276$	−15.9502	−0.960087
$277$	18.0640	1.08536	0.542679	−	0.839940i	$-0.317410\pi$
$277$	18.0640	1.08536	0.542679	+	0.839940i	$0.317410\pi$
$278$	48.6058	2.91518
$279$	7.57452	0.453474
$280$	−2.42548	−0.144950
$281$	−1.84367	−0.109984	−0.0549922	−	0.998487i	$-0.517513\pi$
$281$	−1.84367	−0.109984	−0.0549922	+	0.998487i	$0.517513\pi$
$282$	−14.9321	−0.889192
$283$	−5.43136	−0.322861	−0.161431	−	0.986884i	$-0.551611\pi$
$283$	−5.43136	−0.322861	−0.161431	+	0.986884i	$0.551611\pi$
$284$	−5.76845	−0.342295
$285$	−11.1187	−0.658616
$286$	2.57452	0.152234
$287$	1.74306	0.102890
$288$	15.9502	0.939873
$289$	−2.79877	−0.164633
$290$	23.4763	1.37857
$291$	3.64244	0.213524
$292$	−68.6444	−4.01711
$293$	20.5139	1.19843	0.599217	−	0.800587i	$-0.295479\pi$
$293$	20.5139	1.19843	0.599217	+	0.800587i	$0.295479\pi$
$294$	18.6253	1.08625
$295$	−19.8119	−1.15350
$296$	34.7767	2.02135
$297$	0.156325	0.00907091
$298$	35.0132	2.02826
$299$	−19.0435	−1.10131
$300$	14.4690	0.835367
$301$	−0.193937	−0.0111783
$302$	15.2692	0.878641
$303$	−16.9175	−0.971884
$304$	−92.1436	−5.28480
$305$	−9.96968	−0.570862
$306$	10.0811	0.576298
$307$	−5.67276	−0.323762	−0.161881	−	0.986810i	$-0.551756\pi$
$307$	−5.67276	−0.323762	−0.161881	+	0.986810i	$0.551756\pi$
$308$	−0.156325	−0.00890745
$309$	−2.03032	−0.115501
$310$	−30.0132	−1.70463
$311$	−3.45580	−0.195961	−0.0979803	−	0.995188i	$-0.531238\pi$
$311$	−3.45580	−0.195961	−0.0979803	+	0.995188i	$0.531238\pi$
$312$	51.9814	2.94287
$313$	0.493413	0.0278894	0.0139447	−	0.999903i	$-0.495561\pi$
$313$	0.493413	0.0278894	0.0139447	+	0.999903i	$0.495561\pi$
$314$	−52.3644	−2.95509
$315$	−0.287258	−0.0161851
$316$	66.8383	3.75995
$317$	17.6932	0.993751	0.496875	−	0.867822i	$-0.334481\pi$
$317$	17.6932	0.993751	0.496875	+	0.867822i	$0.334481\pi$
$318$	6.45580	0.362023
$319$	0.926192	0.0518568
$320$	−26.8373	−1.50025
$321$	4.15633	0.231983
$322$	1.60483	0.0894338
$323$	−28.2882	−1.57400
$324$	5.15633	0.286463
$325$	17.2750	0.958247
$326$	−29.5271	−1.63535
$327$	5.89446	0.325964
$328$	75.8891	4.19027
$329$	1.08252	0.0596811
$330$	−0.619421	−0.0340980
$331$	−1.26187	−0.0693584	−0.0346792	−	0.999398i	$-0.511041\pi$
$331$	−1.26187	−0.0693584	−0.0346792	+	0.999398i	$0.511041\pi$
$332$	−4.83146	−0.265161
$333$	4.11871	0.225704
$334$	−36.4010	−1.99178
$335$	−1.48119	−0.0809263
$336$	−2.38058	−0.129871
$337$	26.5804	1.44793	0.723963	−	0.689839i	$-0.242319\pi$
$337$	26.5804	1.44793	0.723963	+	0.689839i	$0.242319\pi$
$338$	66.6117	3.62320
$339$	2.03032	0.110272
$340$	−28.7816	−1.56090
$341$	−1.18409	−0.0641219
$342$	−20.0811	−1.08586
$343$	−2.70782	−0.146208
$344$	−8.44358	−0.455247
$345$	4.58181	0.246676
$346$	17.3054	0.930342
$347$	−2.63989	−0.141717	−0.0708583	−	0.997486i	$-0.522574\pi$
$347$	−2.63989	−0.141717	−0.0708583	+	0.997486i	$0.522574\pi$
$348$	30.5501	1.63766
$349$	28.7948	1.54135	0.770675	−	0.637228i	$-0.219919\pi$
$349$	28.7948	1.54135	0.770675	+	0.637228i	$0.219919\pi$
$350$	−1.45580	−0.0778159
$351$	6.15633	0.328600
$352$	−2.49341	−0.132899
$353$	−12.5188	−0.666309	−0.333154	−	0.942872i	$-0.608113\pi$
$353$	−12.5188	−0.666309	−0.333154	+	0.942872i	$0.608113\pi$
$354$	−35.7816	−1.90177
$355$	1.65703	0.0879462
$356$	−81.5691	−4.32316
$357$	−0.730841	−0.0386802
$358$	−14.7308	−0.778549
$359$	21.5828	1.13909	0.569547	−	0.821959i	$-0.307119\pi$
$359$	21.5828	1.13909	0.569547	+	0.821959i	$0.307119\pi$
$360$	−12.5066	−0.659155
$361$	37.3488	1.96573
$362$	−39.3063	−2.06589
$363$	10.9756	0.576068
$364$	−6.15633	−0.322679
$365$	19.7186	1.03212
$366$	−18.0059	−0.941182
$367$	2.97698	0.155397	0.0776985	−	0.996977i	$-0.475243\pi$
$367$	2.97698	0.155397	0.0776985	+	0.996977i	$0.475243\pi$
$368$	37.9706	1.97936
$369$	8.98778	0.467885
$370$	−16.3199	−0.848434
$371$	−0.468020	−0.0242984
$372$	−39.0567	−2.02499
$373$	−12.2823	−0.635955	−0.317978	−	0.948098i	$-0.603004\pi$
$373$	−12.2823	−0.635955	−0.317978	+	0.948098i	$0.603004\pi$
$374$	−1.57593	−0.0814894
$375$	−11.5623	−0.597074
$376$	47.1305	2.43057
$377$	36.4749	1.87855
$378$	−0.518806	−0.0266845
$379$	3.55405	0.182559	0.0912796	−	0.995825i	$-0.470904\pi$
$379$	3.55405	0.182559	0.0912796	+	0.995825i	$0.470904\pi$
$380$	57.3317	2.94105
$381$	2.34297	0.120034
$382$	−20.1622	−1.03159
$383$	29.5877	1.51186	0.755930	−	0.654652i	$-0.227185\pi$
$383$	29.5877	1.51186	0.755930	+	0.654652i	$0.227185\pi$
$384$	−16.5696	−0.845563
$385$	0.0449056	0.00228860
$386$	−11.4363	−0.582092
$387$	−1.00000	−0.0508329
$388$	−18.7816	−0.953493
$389$	−25.7196	−1.30403	−0.652017	−	0.758204i	$-0.726077\pi$
$389$	−25.7196	−1.30403	−0.652017	+	0.758204i	$0.726077\pi$
$390$	−24.3938	−1.23523
$391$	11.6570	0.589521
$392$	−58.7875	−2.96922
$393$	−1.21933	−0.0615070
$394$	−8.89446	−0.448096
$395$	−19.1998	−0.966048
$396$	−0.806063	−0.0405062
$397$	10.9380	0.548960	0.274480	−	0.961593i	$-0.411494\pi$
$397$	10.9380	0.548960	0.274480	+	0.961593i	$0.411494\pi$
$398$	−30.3634	−1.52198
$399$	1.45580	0.0728812
$400$	−34.4445	−1.72223
$401$	27.9502	1.39576	0.697882	−	0.716212i	$-0.254126\pi$
$401$	27.9502	1.39576	0.697882	+	0.716212i	$0.254126\pi$
$402$	−2.67513	−0.133423
$403$	−46.6312	−2.32286
$404$	87.2320	4.33996
$405$	−1.48119	−0.0736011
$406$	−3.07381	−0.152551
$407$	−0.643859	−0.0319149
$408$	−31.8192	−1.57529
$409$	29.5633	1.46181	0.730904	−	0.682480i	$-0.239099\pi$
$409$	29.5633	1.46181	0.730904	+	0.682480i	$0.239099\pi$
$410$	−35.6131	−1.75880
$411$	16.9126	0.834235
$412$	10.4690	0.515769
$413$	2.59403	0.127644
$414$	8.27504	0.406696
$415$	1.38787	0.0681280
$416$	−98.1944	−4.81438
$417$	−18.1695	−0.889764
$418$	3.13918	0.153542
$419$	32.7826	1.60153	0.800767	−	0.598976i	$-0.204426\pi$
$419$	32.7826	1.60153	0.800767	+	0.598976i	$0.204426\pi$
$420$	1.48119	0.0722749
$421$	−2.98541	−0.145500	−0.0727500	−	0.997350i	$-0.523178\pi$
$421$	−2.98541	−0.145500	−0.0727500	+	0.997350i	$0.523178\pi$
$422$	71.5633	3.48364
$423$	5.58181	0.271397
$424$	−20.3766	−0.989576
$425$	−10.5745	−0.512939
$426$	2.99271	0.144997
$427$	1.30536	0.0631706
$428$	−21.4314	−1.03592
$429$	−0.962389	−0.0464646
$430$	3.96239	0.191083
$431$	5.40009	0.260113	0.130057	−	0.991507i	$-0.458484\pi$
$431$	5.40009	0.260113	0.130057	+	0.991507i	$0.458484\pi$
$432$	−12.2750	−0.590583
$433$	−15.8496	−0.761681	−0.380840	−	0.924641i	$-0.624365\pi$
$433$	−15.8496	−0.761681	−0.380840	+	0.924641i	$0.624365\pi$
$434$	3.92970	0.188632
$435$	−8.77575	−0.420765
$436$	−30.3938	−1.45560
$437$	−23.2203	−1.11078
$438$	35.6131	1.70166
$439$	15.5125	0.740370	0.370185	−	0.928958i	$-0.379294\pi$
$439$	15.5125	0.740370	0.370185	+	0.928958i	$0.379294\pi$
$440$	1.95509	0.0932055
$441$	−6.96239	−0.331542
$442$	−62.0625	−2.95201
$443$	−7.79289	−0.370251	−0.185126	−	0.982715i	$-0.559269\pi$
$443$	−7.79289	−0.370251	−0.185126	+	0.982715i	$0.559269\pi$
$444$	−21.2374	−1.00788
$445$	23.4314	1.11075
$446$	−2.27645	−0.107793
$447$	−13.0884	−0.619060
$448$	3.51388	0.166015
$449$	−1.91890	−0.0905584	−0.0452792	−	0.998974i	$-0.514418\pi$
$449$	−1.91890	−0.0905584	−0.0452792	+	0.998974i	$0.514418\pi$
$450$	−7.50659	−0.353864
$451$	−1.40502	−0.0661596
$452$	−10.4690	−0.492419
$453$	−5.70782	−0.268177
$454$	−13.7454	−0.645105
$455$	1.76845	0.0829063
$456$	63.3825	2.96816
$457$	0.972238	0.0454794	0.0227397	−	0.999741i	$-0.492761\pi$
$457$	0.972238	0.0454794	0.0227397	+	0.999741i	$0.492761\pi$
$458$	−22.9380	−1.07182
$459$	−3.76845	−0.175896
$460$	−23.6253	−1.10154
$461$	2.20123	0.102522	0.0512608	−	0.998685i	$-0.483676\pi$
$461$	2.20123	0.102522	0.0512608	+	0.998685i	$0.483676\pi$
$462$	0.0811024	0.00377322
$463$	6.06793	0.282001	0.141000	−	0.990010i	$-0.454968\pi$
$463$	6.06793	0.282001	0.141000	+	0.990010i	$0.454968\pi$
$464$	−72.7269	−3.37626
$465$	11.2193	0.520284
$466$	48.8397	2.26246
$467$	−16.3430	−0.756262	−0.378131	−	0.925752i	$-0.623433\pi$
$467$	−16.3430	−0.756262	−0.378131	+	0.925752i	$0.623433\pi$
$468$	−31.7440	−1.46737
$469$	0.193937	0.00895516
$470$	−22.1173	−1.02019
$471$	19.5745	0.901946
$472$	112.938	5.19841
$473$	0.156325	0.00718784
$474$	−34.6761	−1.59273
$475$	21.0640	0.966481
$476$	3.76845	0.172727
$477$	−2.41327	−0.110496
$478$	26.4142	1.20816
$479$	16.9878	0.776192	0.388096	−	0.921619i	$-0.373133\pi$
$479$	16.9878	0.776192	0.388096	+	0.921619i	$0.373133\pi$
$480$	23.6253	1.07834
$481$	−25.3561	−1.15614
$482$	−50.6810	−2.30846
$483$	−0.599908	−0.0272968
$484$	−56.5936	−2.57243
$485$	5.39517	0.244982
$486$	−2.67513	−0.121346
$487$	5.21108	0.236137	0.118068	−	0.993005i	$-0.462330\pi$
$487$	5.21108	0.236137	0.118068	+	0.993005i	$0.462330\pi$
$488$	56.8324	2.57268
$489$	11.0376	0.499138
$490$	27.5877	1.24628
$491$	−23.3249	−1.05264	−0.526318	−	0.850288i	$-0.676428\pi$
$491$	−23.3249	−1.05264	−0.526318	+	0.850288i	$0.676428\pi$
$492$	−46.3439	−2.08935
$493$	−22.3272	−1.00557
$494$	123.626	5.56219
$495$	0.231548	0.0104073
$496$	92.9775	4.17481
$497$	−0.216960	−0.00973196
$498$	2.50659	0.112323
$499$	−9.02302	−0.403926	−0.201963	−	0.979393i	$-0.564732\pi$
$499$	−9.02302	−0.403926	−0.201963	+	0.979393i	$0.564732\pi$
$500$	59.6190	2.66624
$501$	13.6072	0.607925
$502$	−2.07522	−0.0926217
$503$	−42.2433	−1.88354	−0.941768	−	0.336263i	$-0.890837\pi$
$503$	−42.2433	−1.88354	−0.941768	+	0.336263i	$0.890837\pi$
$504$	1.63752	0.0729409
$505$	−25.0581	−1.11507
$506$	−1.29360	−0.0575074
$507$	−24.9003	−1.10586
$508$	−12.0811	−0.536012
$509$	13.8799	0.615214	0.307607	−	0.951513i	$-0.400472\pi$
$509$	13.8799	0.615214	0.307607	+	0.951513i	$0.400472\pi$
$510$	14.9321	0.661203
$511$	−2.58181	−0.114213
$512$	−11.5017	−0.508306
$513$	7.50659	0.331424
$514$	−10.2981	−0.454228
$515$	−3.00729	−0.132517
$516$	5.15633	0.226995
$517$	−0.872577	−0.0383759
$518$	2.13681	0.0938861
$519$	−6.46898	−0.283957
$520$	76.9946	3.37644
$521$	−10.2170	−0.447613	−0.223807	−	0.974634i	$-0.571848\pi$
$521$	−10.2170	−0.447613	−0.223807	+	0.974634i	$0.571848\pi$
$522$	−15.8496	−0.693716
$523$	41.2057	1.80180	0.900900	−	0.434027i	$-0.142908\pi$
$523$	41.2057	1.80180	0.900900	+	0.434027i	$0.142908\pi$
$524$	6.28726	0.274660
$525$	0.544198	0.0237508
$526$	−68.0191	−2.96577
$527$	28.5442	1.24340
$528$	1.91890	0.0835093
$529$	−13.4314	−0.583972
$530$	9.56230	0.415360
$531$	13.3757	0.580454
$532$	−7.50659	−0.325452
$533$	−55.3317	−2.39668
$534$	42.3185	1.83130
$535$	6.15633	0.266161
$536$	8.44358	0.364707
$537$	5.50659	0.237627
$538$	−40.6067	−1.75068
$539$	1.08840	0.0468806
$540$	7.63752	0.328667
$541$	−4.42407	−0.190206	−0.0951028	−	0.995467i	$-0.530318\pi$
$541$	−4.42407	−0.190206	−0.0951028	+	0.995467i	$0.530318\pi$
$542$	11.6023	0.498361
$543$	14.6932	0.630547
$544$	60.1075	2.57709
$545$	8.73084	0.373988
$546$	3.19394	0.136688
$547$	15.2315	0.651254	0.325627	−	0.945498i	$-0.394425\pi$
$547$	15.2315	0.651254	0.325627	+	0.945498i	$0.394425\pi$
$548$	−87.2067	−3.72528
$549$	6.73084	0.287265
$550$	1.17347	0.0500369
$551$	44.4749	1.89469
$552$	−26.1187	−1.11169
$553$	2.51388	0.106901
$554$	48.3235	2.05307
$555$	6.10062	0.258957
$556$	93.6878	3.97325
$557$	32.8930	1.39372	0.696862	−	0.717206i	$-0.254579\pi$
$557$	32.8930	1.39372	0.696862	+	0.717206i	$0.254579\pi$
$558$	20.2628	0.857794
$559$	6.15633	0.260385
$560$	−3.52610	−0.149005
$561$	0.589104	0.0248720
$562$	−4.93207	−0.208047
$563$	−12.7454	−0.537156	−0.268578	−	0.963258i	$-0.586554\pi$
$563$	−12.7454	−0.537156	−0.268578	+	0.963258i	$0.586554\pi$
$564$	−28.7816	−1.21193
$565$	3.00729	0.126518
$566$	−14.5296	−0.610725
$567$	0.193937	0.00814457
$568$	−9.44595	−0.396343
$569$	−25.8094	−1.08199	−0.540993	−	0.841027i	$-0.681951\pi$
$569$	−25.8094	−1.08199	−0.540993	+	0.841027i	$0.681951\pi$
$570$	−29.7440	−1.24584
$571$	−34.6820	−1.45140	−0.725698	−	0.688014i	$-0.758483\pi$
$571$	−34.6820	−1.45140	−0.725698	+	0.688014i	$0.758483\pi$
$572$	4.96239	0.207488
$573$	7.53690	0.314859
$574$	4.66291	0.194626
$575$	−8.68006	−0.361983
$576$	18.1187	0.754946
$577$	−29.9149	−1.24537	−0.622687	−	0.782471i	$-0.713959\pi$
$577$	−29.9149	−1.24537	−0.622687	+	0.782471i	$0.713959\pi$
$578$	−7.48707	−0.311421
$579$	4.27504	0.177665
$580$	45.2506	1.87893
$581$	−0.181718	−0.00753892
$582$	9.74401	0.403902
$583$	0.377254	0.0156243
$584$	−112.406	−4.65141
$585$	9.11871	0.377012
$586$	54.8773	2.26696
$587$	−45.5026	−1.87809	−0.939047	−	0.343789i	$-0.888290\pi$
$587$	−45.5026	−1.87809	−0.939047	+	0.343789i	$0.888290\pi$
$588$	35.9003	1.48051
$589$	−56.8588	−2.34282
$590$	−52.9995	−2.18196
$591$	3.32487	0.136767
$592$	50.5574	2.07790
$593$	9.22521	0.378834	0.189417	−	0.981897i	$-0.439340\pi$
$593$	9.22521	0.378834	0.189417	+	0.981897i	$0.439340\pi$
$594$	0.418190	0.0171586
$595$	−1.08252	−0.0443789
$596$	67.4880	2.76442
$597$	11.3503	0.464535
$598$	−50.9438	−2.08325
$599$	2.98286	0.121876	0.0609381	−	0.998142i	$-0.480591\pi$
$599$	2.98286	0.121876	0.0609381	+	0.998142i	$0.480591\pi$
$600$	23.6932	0.967272
$601$	1.50071	0.0612151	0.0306076	−	0.999531i	$-0.490256\pi$
$601$	1.50071	0.0612151	0.0306076	+	0.999531i	$0.490256\pi$
$602$	−0.518806	−0.0211449
$603$	1.00000	0.0407231
$604$	29.4314	1.19755
$605$	16.2569	0.660939
$606$	−45.2565	−1.83842
$607$	−4.59498	−0.186505	−0.0932523	−	0.995643i	$-0.529726\pi$
$607$	−4.59498	−0.186505	−0.0932523	+	0.995643i	$0.529726\pi$
$608$	−119.731	−4.85575
$609$	1.14903	0.0465611
$610$	−26.6702	−1.07985
$611$	−34.3634	−1.39020
$612$	19.4314	0.785466
$613$	−13.7250	−0.554346	−0.277173	−	0.960820i	$-0.589398\pi$
$613$	−13.7250	−0.554346	−0.277173	+	0.960820i	$0.589398\pi$
$614$	−15.1754	−0.612428
$615$	13.3127	0.536818
$616$	−0.255986	−0.0103140
$617$	−43.6834	−1.75863	−0.879313	−	0.476244i	$-0.841998\pi$
$617$	−43.6834	−1.75863	−0.879313	+	0.476244i	$0.841998\pi$
$618$	−5.43136	−0.218482
$619$	−25.1089	−1.00921	−0.504605	−	0.863350i	$-0.668362\pi$
$619$	−25.1089	−1.00921	−0.504605	+	0.863350i	$0.668362\pi$
$620$	−57.8505	−2.32333
$621$	−3.09332	−0.124131
$622$	−9.24472	−0.370680
$623$	−3.06793	−0.122914
$624$	75.5691	3.02519
$625$	−3.09569	−0.123828
$626$	1.31994	0.0527556
$627$	−1.17347	−0.0468638
$628$	−100.933	−4.02765
$629$	15.5212	0.618870
$630$	−0.768452	−0.0306159
$631$	−21.6121	−0.860365	−0.430183	−	0.902742i	$-0.641551\pi$
$631$	−21.6121	−0.860365	−0.430183	+	0.902742i	$0.641551\pi$
$632$	109.449	4.35365
$633$	−26.7513	−1.06327
$634$	47.3317	1.87978
$635$	3.47039	0.137718
$636$	12.4436	0.493420
$637$	42.8627	1.69828
$638$	2.47768	0.0980925
$639$	−1.11871	−0.0442556
$640$	−24.5428	−0.970139
$641$	0.681010	0.0268983	0.0134491	−	0.999910i	$-0.495719\pi$
$641$	0.681010	0.0268983	0.0134491	+	0.999910i	$0.495719\pi$
$642$	11.1187	0.438821
$643$	−31.0336	−1.22385	−0.611924	−	0.790917i	$-0.709604\pi$
$643$	−31.0336	−1.22385	−0.611924	+	0.790917i	$0.709604\pi$
$644$	3.09332	0.121894
$645$	−1.48119	−0.0583220
$646$	−75.6747	−2.97738
$647$	−47.3112	−1.86000	−0.929998	−	0.367564i	$-0.880192\pi$
$647$	−47.3112	−1.86000	−0.929998	+	0.367564i	$0.880192\pi$
$648$	8.44358	0.331695
$649$	−2.09095	−0.0820770
$650$	46.2130	1.81262
$651$	−1.46898	−0.0575737
$652$	−56.9135	−2.22891
$653$	32.3439	1.26572	0.632858	−	0.774268i	$-0.281882\pi$
$653$	32.3439	1.26572	0.632858	+	0.774268i	$0.281882\pi$
$654$	15.7685	0.616595
$655$	−1.80606	−0.0705687
$656$	110.325	4.30748
$657$	−13.3127	−0.519376
$658$	2.89587	0.112893
$659$	32.4553	1.26428	0.632140	−	0.774854i	$-0.282177\pi$
$659$	32.4553	1.26428	0.632140	+	0.774854i	$0.282177\pi$
$660$	−1.19394	−0.0464739
$661$	12.7367	0.495401	0.247701	−	0.968837i	$-0.420325\pi$
$661$	12.7367	0.495401	0.247701	+	0.968837i	$0.420325\pi$
$662$	−3.37565	−0.131199
$663$	23.1998	0.901006
$664$	−7.91160	−0.307030
$665$	2.15633	0.0836187
$666$	11.0181	0.426943
$667$	−18.3272	−0.709634
$668$	−70.1632	−2.71469
$669$	0.850969	0.0329004
$670$	−3.96239	−0.153080
$671$	−1.05220	−0.0406197
$672$	−3.09332	−0.119327
$673$	−12.4544	−0.480081	−0.240041	−	0.970763i	$-0.577161\pi$
$673$	−12.4544	−0.480081	−0.240041	+	0.970763i	$0.577161\pi$
$674$	71.1060	2.73890
$675$	2.80606	0.108005
$676$	128.394	4.93824
$677$	15.3698	0.590708	0.295354	−	0.955388i	$-0.404562\pi$
$677$	15.3698	0.590708	0.295354	+	0.955388i	$0.404562\pi$
$678$	5.43136	0.208590
$679$	−0.706403	−0.0271093
$680$	−47.1305	−1.80737
$681$	5.13823	0.196897
$682$	−3.16759	−0.121293
$683$	17.3317	0.663179	0.331590	−	0.943424i	$-0.392415\pi$
$683$	17.3317	0.663179	0.331590	+	0.943424i	$0.392415\pi$
$684$	−38.7064	−1.47998
$685$	25.0508	0.957141
$686$	−7.24377	−0.276568
$687$	8.57452	0.327138
$688$	−12.2750	−0.467981
$689$	14.8568	0.566001
$690$	12.2569	0.466614
$691$	14.8364	0.564403	0.282201	−	0.959355i	$-0.408935\pi$
$691$	14.8364	0.564403	0.282201	+	0.959355i	$0.408935\pi$
$692$	33.3561	1.26801
$693$	−0.0303172	−0.00115165
$694$	−7.06205	−0.268072
$695$	−26.9126	−1.02085
$696$	50.0263	1.89624
$697$	33.8700	1.28292
$698$	77.0299	2.91562
$699$	−18.2569	−0.690541
$700$	−2.80606	−0.106059
$701$	30.2325	1.14187	0.570933	−	0.820997i	$-0.306582\pi$
$701$	30.2325	1.14187	0.570933	+	0.820997i	$0.306582\pi$
$702$	16.4690	0.621581
$703$	−30.9175	−1.16607
$704$	−2.83241	−0.106751
$705$	8.26774	0.311381
$706$	−33.4894	−1.26039
$707$	3.28092	0.123392
$708$	−68.9692	−2.59202
$709$	−3.56467	−0.133874	−0.0669369	−	0.997757i	$-0.521323\pi$
$709$	−3.56467	−0.133874	−0.0669369	+	0.997757i	$0.521323\pi$
$710$	4.43278	0.166359
$711$	12.9624	0.486128
$712$	−133.571	−5.00579
$713$	23.4304	0.877476
$714$	−1.95509	−0.0731676
$715$	−1.42548	−0.0533101
$716$	−28.3938	−1.06112
$717$	−9.87399	−0.368751
$718$	57.7367	2.15472
$719$	12.5393	0.467636	0.233818	−	0.972280i	$-0.424878\pi$
$719$	12.5393	0.467636	0.233818	+	0.972280i	$0.424878\pi$
$720$	−18.1817	−0.677593
$721$	0.393753	0.0146641
$722$	99.9131	3.71838
$723$	18.9452	0.704581
$724$	−75.7631	−2.81571
$725$	16.6253	0.617448
$726$	29.3611	1.08969
$727$	27.1524	1.00703	0.503513	−	0.863988i	$-0.332041\pi$
$727$	27.1524	1.00703	0.503513	+	0.863988i	$0.332041\pi$
$728$	−10.0811	−0.373631
$729$	1.00000	0.0370370
$730$	52.7499	1.95236
$731$	−3.76845	−0.139381
$732$	−34.7064	−1.28279
$733$	−33.4763	−1.23647	−0.618237	−	0.785992i	$-0.712153\pi$
$733$	−33.4763	−1.23647	−0.618237	+	0.785992i	$0.712153\pi$
$734$	7.96380	0.293949
$735$	−10.3127	−0.380388
$736$	49.3390	1.81866
$737$	−0.156325	−0.00575831
$738$	24.0435	0.885053
$739$	−24.6483	−0.906703	−0.453352	−	0.891332i	$-0.649772\pi$
$739$	−24.6483	−0.906703	−0.453352	+	0.891332i	$0.649772\pi$
$740$	−31.4568	−1.15637
$741$	−46.2130	−1.69768
$742$	−1.25202	−0.0459630
$743$	−46.6321	−1.71077	−0.855384	−	0.517995i	$-0.826679\pi$
$743$	−46.6321	−1.71077	−0.855384	+	0.517995i	$0.826679\pi$
$744$	−63.9560	−2.34474
$745$	−19.3865	−0.710265
$746$	−32.8568	−1.20297
$747$	−0.936996	−0.0342829
$748$	−3.03761	−0.111066
$749$	−0.806063	−0.0294529
$750$	−30.9307	−1.12943
$751$	−21.4109	−0.781295	−0.390647	−	0.920540i	$-0.627749\pi$
$751$	−21.4109	−0.781295	−0.390647	+	0.920540i	$0.627749\pi$
$752$	68.5169	2.49856
$753$	0.775746	0.0282698
$754$	97.5750	3.55347
$755$	−8.45439	−0.307687
$756$	−1.00000	−0.0363696
$757$	−3.08840	−0.112250	−0.0561248	−	0.998424i	$-0.517874\pi$
$757$	−3.08840	−0.112250	−0.0561248	+	0.998424i	$0.517874\pi$
$758$	9.50754	0.345329
$759$	0.483564	0.0175523
$760$	93.8818	3.40545
$761$	37.3014	1.35217	0.676087	−	0.736822i	$-0.263674\pi$
$761$	37.3014	1.35217	0.676087	+	0.736822i	$0.263674\pi$
$762$	6.26774	0.227056
$763$	−1.14315	−0.0413849
$764$	−38.8627	−1.40600
$765$	−5.58181	−0.201811
$766$	79.1509	2.85984
$767$	−82.3449	−2.97330
$768$	−8.08840	−0.291865
$769$	9.12856	0.329184	0.164592	−	0.986362i	$-0.447369\pi$
$769$	9.12856	0.329184	0.164592	+	0.986362i	$0.447369\pi$
$770$	0.120128	0.00432913
$771$	3.84955	0.138638
$772$	−22.0435	−0.793363
$773$	32.2638	1.16045	0.580224	−	0.814457i	$-0.302965\pi$
$773$	32.2638	1.16045	0.580224	+	0.814457i	$0.302965\pi$
$774$	−2.67513	−0.0961556
$775$	−21.2546	−0.763487
$776$	−30.7553	−1.10405
$777$	−0.798769	−0.0286557
$778$	−68.8032	−2.46672
$779$	−67.4676	−2.41728
$780$	−47.0191	−1.68355
$781$	0.174883	0.00625781
$782$	31.1841	1.11514
$783$	5.92478	0.211734
$784$	−85.4636	−3.05227
$785$	28.9937	1.03483
$786$	−3.26187	−0.116347
$787$	−52.3620	−1.86650	−0.933252	−	0.359222i	$-0.883042\pi$
$787$	−52.3620	−1.86650	−0.933252	+	0.359222i	$0.883042\pi$
$788$	−17.1441	−0.610734
$789$	25.4264	0.905205
$790$	−51.3620	−1.82738
$791$	−0.393753	−0.0140002
$792$	−1.31994	−0.0469022
$793$	−41.4372	−1.47148
$794$	29.2605	1.03841
$795$	−3.57452	−0.126775
$796$	−58.5256	−2.07439
$797$	13.7929	0.488569	0.244285	−	0.969704i	$-0.421447\pi$
$797$	13.7929	0.488569	0.244285	+	0.969704i	$0.421447\pi$
$798$	3.89446	0.137862
$799$	21.0348	0.744157
$800$	−44.7572	−1.58241
$801$	−15.8192	−0.558945
$802$	74.7704	2.64023
$803$	2.08110	0.0734405
$804$	−5.15633	−0.181850
$805$	−0.888580	−0.0313183
$806$	−124.745	−4.39394
$807$	15.1793	0.534338
$808$	142.844	5.02524
$809$	32.8881	1.15628	0.578142	−	0.815936i	$-0.303778\pi$
$809$	32.8881	1.15628	0.578142	+	0.815936i	$0.303778\pi$
$810$	−3.96239	−0.139224
$811$	44.2262	1.55299	0.776495	−	0.630123i	$-0.216996\pi$
$811$	44.2262	1.55299	0.776495	+	0.630123i	$0.216996\pi$
$812$	−5.92478	−0.207919
$813$	−4.33709	−0.152108
$814$	−1.72241	−0.0603703
$815$	16.3488	0.572675
$816$	−46.2579	−1.61935
$817$	7.50659	0.262622
$818$	79.0856	2.76516
$819$	−1.19394	−0.0417195
$820$	−68.6444	−2.39716
$821$	10.5091	0.366772	0.183386	−	0.983041i	$-0.441294\pi$
$821$	10.5091	0.366772	0.183386	+	0.983041i	$0.441294\pi$
$822$	45.2433	1.57804
$823$	34.8686	1.21544	0.607722	−	0.794150i	$-0.292084\pi$
$823$	34.8686	1.21544	0.607722	+	0.794150i	$0.292084\pi$
$824$	17.1432	0.597210
$825$	−0.438658	−0.0152721
$826$	6.93937	0.241451
$827$	45.8653	1.59489	0.797446	−	0.603390i	$-0.206184\pi$
$827$	45.8653	1.59489	0.797446	+	0.603390i	$0.206184\pi$
$828$	15.9502	0.554307
$829$	5.19982	0.180597	0.0902985	−	0.995915i	$-0.471218\pi$
$829$	5.19982	0.180597	0.0902985	+	0.995915i	$0.471218\pi$
$830$	3.71274	0.128871
$831$	−18.0640	−0.626632
$832$	−111.545	−3.86712
$833$	−26.2374	−0.909073
$834$	−48.6058	−1.68308
$835$	20.1549	0.697489
$836$	6.05079	0.209271
$837$	−7.57452	−0.261814
$838$	87.6977	3.02947
$839$	42.8324	1.47874	0.739370	−	0.673300i	$-0.235124\pi$
$839$	42.8324	1.47874	0.739370	+	0.673300i	$0.235124\pi$
$840$	2.42548	0.0836872
$841$	6.10299	0.210448
$842$	−7.98637	−0.275228
$843$	1.84367	0.0634995
$844$	137.938	4.74804
$845$	−36.8822	−1.26879
$846$	14.9321	0.513375
$847$	−2.12856	−0.0731383
$848$	−29.6229	−1.01726
$849$	5.43136	0.186404
$850$	−28.2882	−0.970278
$851$	12.7405	0.436739
$852$	5.76845	0.197624
$853$	11.2506	0.385213	0.192607	−	0.981276i	$-0.438306\pi$
$853$	11.2506	0.385213	0.192607	+	0.981276i	$0.438306\pi$
$854$	3.49200	0.119494
$855$	11.1187	0.380252
$856$	−35.0943	−1.19950
$857$	4.61847	0.157764	0.0788819	−	0.996884i	$-0.474865\pi$
$857$	4.61847	0.157764	0.0788819	+	0.996884i	$0.474865\pi$
$858$	−2.57452	−0.0878925
$859$	−3.12856	−0.106745	−0.0533726	−	0.998575i	$-0.516997\pi$
$859$	−3.12856	−0.106745	−0.0533726	+	0.998575i	$0.516997\pi$
$860$	7.63752	0.260437
$861$	−1.74306	−0.0594033
$862$	14.4460	0.492031
$863$	35.0894	1.19446	0.597228	−	0.802072i	$-0.296269\pi$
$863$	35.0894	1.19446	0.597228	+	0.802072i	$0.296269\pi$
$864$	−15.9502	−0.542636
$865$	−9.58181	−0.325791
$866$	−42.3996	−1.44080
$867$	2.79877	0.0950512
$868$	7.57452	0.257096
$869$	−2.02635	−0.0687391
$870$	−23.4763	−0.795920
$871$	−6.15633	−0.208599
$872$	−49.7704	−1.68544
$873$	−3.64244	−0.123278
$874$	−62.1173	−2.10115
$875$	2.24235	0.0758053
$876$	68.6444	2.31928
$877$	−4.29806	−0.145135	−0.0725676	−	0.997363i	$-0.523119\pi$
$877$	−4.29806	−0.145135	−0.0725676	+	0.997363i	$0.523119\pi$
$878$	41.4979	1.40049
$879$	−20.5139	−0.691916
$880$	2.84226	0.0958126
$881$	−32.1260	−1.08235	−0.541176	−	0.840909i	$-0.682021\pi$
$881$	−32.1260	−1.08235	−0.541176	+	0.840909i	$0.682021\pi$
$882$	−18.6253	−0.627146
$883$	10.7137	0.360545	0.180272	−	0.983617i	$-0.442302\pi$
$883$	10.7137	0.360545	0.180272	+	0.983617i	$0.442302\pi$
$884$	−119.626	−4.02345
$885$	19.8119	0.665971
$886$	−20.8470	−0.700369
$887$	−36.8637	−1.23776	−0.618881	−	0.785485i	$-0.712414\pi$
$887$	−36.8637	−1.23776	−0.618881	+	0.785485i	$0.712414\pi$
$888$	−34.7767	−1.16703
$889$	−0.454387	−0.0152397
$890$	62.6820	2.10110
$891$	−0.156325	−0.00523709
$892$	−4.38787	−0.146917
$893$	−41.9003	−1.40214
$894$	−35.0132	−1.17102
$895$	8.15633	0.272636
$896$	3.21345	0.107354
$897$	19.0435	0.635844
$898$	−5.13330	−0.171301
$899$	−44.8773	−1.49674
$900$	−14.4690	−0.482299
$901$	−9.09428	−0.302974
$902$	−3.75860	−0.125148
$903$	0.193937	0.00645380
$904$	−17.1432	−0.570173
$905$	21.7635	0.723444
$906$	−15.2692	−0.507284
$907$	−34.3634	−1.14102	−0.570510	−	0.821291i	$-0.693254\pi$
$907$	−34.3634	−1.14102	−0.570510	+	0.821291i	$0.693254\pi$
$908$	−26.4944	−0.879246
$909$	16.9175	0.561117
$910$	4.73084	0.156826
$911$	−6.89305	−0.228377	−0.114188	−	0.993459i	$-0.536427\pi$
$911$	−6.89305	−0.228377	−0.114188	+	0.993459i	$0.536427\pi$
$912$	92.1436	3.05118
$913$	0.146476	0.00484765
$914$	2.60086	0.0860289
$915$	9.96968	0.329588
$916$	−44.2130	−1.46084
$917$	0.236473	0.00780901
$918$	−10.0811	−0.332726
$919$	−25.0968	−0.827868	−0.413934	−	0.910307i	$-0.635846\pi$
$919$	−25.0968	−0.827868	−0.413934	+	0.910307i	$0.635846\pi$
$920$	−38.6869	−1.27547
$921$	5.67276	0.186924
$922$	5.88858	0.193930
$923$	6.88717	0.226694
$924$	0.156325	0.00514272
$925$	−11.5574	−0.380004
$926$	16.2325	0.533433
$927$	2.03032	0.0666844
$928$	−94.5012	−3.10215
$929$	−29.2908	−0.960999	−0.480499	−	0.876995i	$-0.659545\pi$
$929$	−29.2908	−0.960999	−0.480499	+	0.876995i	$0.659545\pi$
$930$	30.0132	0.984171
$931$	52.2638	1.71288
$932$	94.1387	3.08362
$933$	3.45580	0.113138
$934$	−43.7196	−1.43055
$935$	0.872577	0.0285363
$936$	−51.9814	−1.69907
$937$	54.0811	1.76675	0.883376	−	0.468664i	$-0.155265\pi$
$937$	54.0811	1.76675	0.883376	+	0.468664i	$0.155265\pi$
$938$	0.518806	0.0169396
$939$	−0.493413	−0.0161019
$940$	−42.6312	−1.39048
$941$	−5.31994	−0.173425	−0.0867126	−	0.996233i	$-0.527636\pi$
$941$	−5.31994	−0.173425	−0.0867126	+	0.996233i	$0.527636\pi$
$942$	52.3644	1.70612
$943$	27.8021	0.905361
$944$	164.187	5.34382
$945$	0.287258	0.00934449
$946$	0.418190	0.0135965
$947$	−13.4666	−0.437606	−0.218803	−	0.975769i	$-0.570215\pi$
$947$	−13.4666	−0.437606	−0.218803	+	0.975769i	$0.570215\pi$
$948$	−66.8383	−2.17081
$949$	81.9570	2.66044
$950$	56.3488	1.82820
$951$	−17.6932	−0.573742
$952$	6.17091	0.200000
$953$	−32.9741	−1.06814	−0.534069	−	0.845441i	$-0.679338\pi$
$953$	−32.9741	−1.06814	−0.534069	+	0.845441i	$0.679338\pi$
$954$	−6.45580	−0.209014
$955$	11.1636	0.361246
$956$	50.9135	1.64666
$957$	−0.926192	−0.0299395
$958$	45.4445	1.46825
$959$	−3.27996	−0.105916
$960$	26.8373	0.866171
$961$	26.3733	0.850751
$962$	−67.8310	−2.18696
$963$	−4.15633	−0.133936
$964$	−97.6878	−3.14631
$965$	6.33216	0.203840
$966$	−1.60483	−0.0516346
$967$	39.9814	1.28572	0.642858	−	0.765985i	$-0.277748\pi$
$967$	39.9814	1.28572	0.642858	+	0.765985i	$0.277748\pi$
$968$	−92.6731	−2.97863
$969$	28.2882	0.908748
$970$	14.4328	0.463409
$971$	12.1808	0.390899	0.195450	−	0.980714i	$-0.437383\pi$
$971$	12.1808	0.390899	0.195450	+	0.980714i	$0.437383\pi$
$972$	−5.15633	−0.165389
$973$	3.52373	0.112966
$974$	13.9403	0.446677
$975$	−17.2750	−0.553244
$976$	82.6213	2.64464
$977$	−18.9380	−0.605879	−0.302939	−	0.953010i	$-0.597968\pi$
$977$	−18.9380	−0.605879	−0.302939	+	0.953010i	$0.597968\pi$
$978$	29.5271	0.944171
$979$	2.47295	0.0790357
$980$	53.1754	1.69863
$981$	−5.89446	−0.188196
$982$	−62.3971	−1.99117
$983$	−6.63989	−0.211780	−0.105890	−	0.994378i	$-0.533769\pi$
$983$	−6.63989	−0.211780	−0.105890	+	0.994378i	$0.533769\pi$
$984$	−75.8891	−2.41926
$985$	4.92478	0.156916
$986$	−59.7283	−1.90214
$987$	−1.08252	−0.0344569
$988$	238.289	7.58099
$989$	−3.09332	−0.0983619
$990$	0.619421	0.0196865
$991$	−25.7962	−0.819444	−0.409722	−	0.912210i	$-0.634374\pi$
$991$	−25.7962	−0.819444	−0.409722	+	0.912210i	$0.634374\pi$
$992$	120.815	3.83587
$993$	1.26187	0.0400441
$994$	−0.580395	−0.0184090
$995$	16.8119	0.532974
$996$	4.83146	0.153091
$997$	18.6424	0.590412	0.295206	−	0.955434i	$-0.404612\pi$
$997$	18.6424	0.590412	0.295206	+	0.955434i	$0.404612\pi$
$998$	−24.1378	−0.764068
$999$	−4.11871	−0.130310

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.a.d.1.3	✓	3
3.2	odd	2		603.2.a.i.1.1		3
4.3	odd	2		3216.2.a.u.1.1		3
5.4	even	2		5025.2.a.m.1.1		3
7.6	odd	2		9849.2.a.ba.1.3		3
12.11	even	2		9648.2.a.bn.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.a.d.1.3	✓	3	1.1	even	1	trivial
603.2.a.i.1.1		3	3.2	odd	2
3216.2.a.u.1.1		3	4.3	odd	2
5025.2.a.m.1.1		3	5.4	even	2
9648.2.a.bn.1.3		3	12.11	even	2
9849.2.a.ba.1.3		3	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.a (trivial)

\(f(q)\)	\(=\)	\(q+2.67513 q^{2} -1.00000 q^{3} +5.15633 q^{4} -1.48119 q^{5} -2.67513 q^{6} +0.193937 q^{7} +8.44358 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.67513 q^{2} -1.00000 q^{3} +5.15633 q^{4} -1.48119 q^{5} -2.67513 q^{6} +0.193937 q^{7} +8.44358 q^{8} +1.00000 q^{9} -3.96239 q^{10} -0.156325 q^{11} -5.15633 q^{12} -6.15633 q^{13} +0.518806 q^{14} +1.48119 q^{15} +12.2750 q^{16} +3.76845 q^{17} +2.67513 q^{18} -7.50659 q^{19} -7.63752 q^{20} -0.193937 q^{21} -0.418190 q^{22} +3.09332 q^{23} -8.44358 q^{24} -2.80606 q^{25} -16.4690 q^{26} -1.00000 q^{27} +1.00000 q^{28} -5.92478 q^{29} +3.96239 q^{30} +7.57452 q^{31} +15.9502 q^{32} +0.156325 q^{33} +10.0811 q^{34} -0.287258 q^{35} +5.15633 q^{36} +4.11871 q^{37} -20.0811 q^{38} +6.15633 q^{39} -12.5066 q^{40} +8.98778 q^{41} -0.518806 q^{42} -1.00000 q^{43} -0.806063 q^{44} -1.48119 q^{45} +8.27504 q^{46} +5.58181 q^{47} -12.2750 q^{48} -6.96239 q^{49} -7.50659 q^{50} -3.76845 q^{51} -31.7440 q^{52} -2.41327 q^{53} -2.67513 q^{54} +0.231548 q^{55} +1.63752 q^{56} +7.50659 q^{57} -15.8496 q^{58} +13.3757 q^{59} +7.63752 q^{60} +6.73084 q^{61} +20.2628 q^{62} +0.193937 q^{63} +18.1187 q^{64} +9.11871 q^{65} +0.418190 q^{66} +1.00000 q^{67} +19.4314 q^{68} -3.09332 q^{69} -0.768452 q^{70} -1.11871 q^{71} +8.44358 q^{72} -13.3127 q^{73} +11.0181 q^{74} +2.80606 q^{75} -38.7064 q^{76} -0.0303172 q^{77} +16.4690 q^{78} +12.9624 q^{79} -18.1817 q^{80} +1.00000 q^{81} +24.0435 q^{82} -0.936996 q^{83} -1.00000 q^{84} -5.58181 q^{85} -2.67513 q^{86} +5.92478 q^{87} -1.31994 q^{88} -15.8192 q^{89} -3.96239 q^{90} -1.19394 q^{91} +15.9502 q^{92} -7.57452 q^{93} +14.9321 q^{94} +11.1187 q^{95} -15.9502 q^{96} -3.64244 q^{97} -18.6253 q^{98} -0.156325 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 5 q^{4} + q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 5 * q^4 + q^5 - 3 * q^6 + q^7 + 9 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 5 q^{4} + q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 3 q^{9} - q^{10} + 10 q^{11} - 5 q^{12} - 8 q^{13} + 7 q^{14} - q^{15} + 5 q^{16} + 3 q^{18} - 2 q^{19} - 7 q^{20} - q^{21} + 3 q^{23} - 9 q^{24} - 8 q^{25} - 18 q^{26} - 3 q^{27} + 3 q^{28} + 4 q^{29} + q^{30} + 11 q^{31} + 11 q^{32} - 10 q^{33} - 2 q^{34} + 5 q^{35} + 5 q^{36} - 9 q^{37} - 28 q^{38} + 8 q^{39} - 17 q^{40} + q^{41} - 7 q^{42} - 3 q^{43} - 2 q^{44} + q^{45} - 7 q^{46} + 18 q^{47} - 5 q^{48} - 10 q^{49} - 2 q^{50} - 32 q^{52} + 7 q^{53} - 3 q^{54} + 12 q^{55} - 11 q^{56} + 2 q^{57} - 4 q^{58} + 15 q^{59} + 7 q^{60} - 2 q^{61} + 3 q^{62} + q^{63} + 33 q^{64} + 6 q^{65} + 3 q^{67} + 16 q^{68} - 3 q^{69} + 9 q^{70} + 18 q^{71} + 9 q^{72} - 19 q^{73} + 5 q^{74} + 8 q^{75} - 42 q^{76} + 2 q^{77} + 18 q^{78} + 28 q^{79} - 29 q^{80} + 3 q^{81} + 29 q^{82} - 7 q^{83} - 3 q^{84} - 18 q^{85} - 3 q^{86} - 4 q^{87} + 4 q^{88} - 6 q^{89} - q^{90} - 4 q^{91} + 11 q^{92} - 11 q^{93} + 36 q^{94} + 12 q^{95} - 11 q^{96} - 8 q^{97} - 14 q^{98} + 10 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 5 * q^4 + q^5 - 3 * q^6 + q^7 + 9 * q^8 + 3 * q^9 - q^10 + 10 * q^11 - 5 * q^12 - 8 * q^13 + 7 * q^14 - q^15 + 5 * q^16 + 3 * q^18 - 2 * q^19 - 7 * q^20 - q^21 + 3 * q^23 - 9 * q^24 - 8 * q^25 - 18 * q^26 - 3 * q^27 + 3 * q^28 + 4 * q^29 + q^30 + 11 * q^31 + 11 * q^32 - 10 * q^33 - 2 * q^34 + 5 * q^35 + 5 * q^36 - 9 * q^37 - 28 * q^38 + 8 * q^39 - 17 * q^40 + q^41 - 7 * q^42 - 3 * q^43 - 2 * q^44 + q^45 - 7 * q^46 + 18 * q^47 - 5 * q^48 - 10 * q^49 - 2 * q^50 - 32 * q^52 + 7 * q^53 - 3 * q^54 + 12 * q^55 - 11 * q^56 + 2 * q^57 - 4 * q^58 + 15 * q^59 + 7 * q^60 - 2 * q^61 + 3 * q^62 + q^63 + 33 * q^64 + 6 * q^65 + 3 * q^67 + 16 * q^68 - 3 * q^69 + 9 * q^70 + 18 * q^71 + 9 * q^72 - 19 * q^73 + 5 * q^74 + 8 * q^75 - 42 * q^76 + 2 * q^77 + 18 * q^78 + 28 * q^79 - 29 * q^80 + 3 * q^81 + 29 * q^82 - 7 * q^83 - 3 * q^84 - 18 * q^85 - 3 * q^86 - 4 * q^87 + 4 * q^88 - 6 * q^89 - q^90 - 4 * q^91 + 11 * q^92 - 11 * q^93 + 36 * q^94 + 12 * q^95 - 11 * q^96 - 8 * q^97 - 14 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more