LMFDB - Embedded newform 1859.2.a.r.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, 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("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1859.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:	$14.8441897358$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 10x^{7} - x^{6} + 31x^{5} + 9x^{4} - 31x^{3} - 15x^{2} + 2x + 1 $ x^9 - 10x^7 - x^6 + 31x^5 + 9x^4 - 31x^3 - 15x^2 + 2x + 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			1.9
Root			$-2.31116$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.31116 q^{2} +0.0765450 q^{3} +3.34148 q^{4} -2.51567 q^{5} +0.176908 q^{6} -0.902363 q^{7} +3.10039 q^{8} -2.99414 q^{9} +O(q^{10})$	\(q+2.31116 q^{2} +0.0765450 q^{3} +3.34148 q^{4} -2.51567 q^{5} +0.176908 q^{6} -0.902363 q^{7} +3.10039 q^{8} -2.99414 q^{9} -5.81412 q^{10} -1.00000 q^{11} +0.255774 q^{12} -2.08551 q^{14} -0.192562 q^{15} +0.482546 q^{16} +0.496094 q^{17} -6.91995 q^{18} +0.163057 q^{19} -8.40605 q^{20} -0.0690714 q^{21} -2.31116 q^{22} -6.14586 q^{23} +0.237319 q^{24} +1.32857 q^{25} -0.458822 q^{27} -3.01523 q^{28} -7.90688 q^{29} -0.445042 q^{30} -0.681774 q^{31} -5.08554 q^{32} -0.0765450 q^{33} +1.14655 q^{34} +2.27004 q^{35} -10.0049 q^{36} +10.7755 q^{37} +0.376851 q^{38} -7.79954 q^{40} -3.96260 q^{41} -0.159635 q^{42} -6.61622 q^{43} -3.34148 q^{44} +7.53226 q^{45} -14.2041 q^{46} +12.4599 q^{47} +0.0369365 q^{48} -6.18574 q^{49} +3.07055 q^{50} +0.0379735 q^{51} +8.25234 q^{53} -1.06041 q^{54} +2.51567 q^{55} -2.79768 q^{56} +0.0124812 q^{57} -18.2741 q^{58} +4.55959 q^{59} -0.643442 q^{60} -9.48162 q^{61} -1.57569 q^{62} +2.70180 q^{63} -12.7186 q^{64} -0.176908 q^{66} -5.86499 q^{67} +1.65769 q^{68} -0.470435 q^{69} +5.24645 q^{70} +0.678278 q^{71} -9.28300 q^{72} -5.99712 q^{73} +24.9040 q^{74} +0.101696 q^{75} +0.544851 q^{76} +0.902363 q^{77} +2.76069 q^{79} -1.21392 q^{80} +8.94730 q^{81} -9.15823 q^{82} -6.65517 q^{83} -0.230801 q^{84} -1.24801 q^{85} -15.2912 q^{86} -0.605233 q^{87} -3.10039 q^{88} +5.27690 q^{89} +17.4083 q^{90} -20.5363 q^{92} -0.0521865 q^{93} +28.7968 q^{94} -0.410196 q^{95} -0.389273 q^{96} -11.8888 q^{97} -14.2963 q^{98} +2.99414 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 5 q^{3} + 2 q^{4} + 4 q^{5} + 11 q^{6} - q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) $ 9 * q - 5 * q^3 + 2 * q^4 + 4 * q^5 + 11 * q^6 - q^7 - 3 * q^8 + 2 * q^9	$ 9 q - 5 q^{3} + 2 q^{4} + 4 q^{5} + 11 q^{6} - q^{7} - 3 q^{8} + 2 q^{9} - 8 q^{10} - 9 q^{11} - 9 q^{12} - 3 q^{15} - 8 q^{16} - 8 q^{17} - 27 q^{18} + q^{19} - 12 q^{20} - 17 q^{21} + 6 q^{24} - 15 q^{25} - 23 q^{27} - 11 q^{28} - 22 q^{29} - 3 q^{30} + 6 q^{31} + 19 q^{32} + 5 q^{33} - 10 q^{34} - 15 q^{35} + 7 q^{36} + 15 q^{37} + q^{38} - 3 q^{40} - 10 q^{41} + 2 q^{42} - 19 q^{43} - 2 q^{44} + 2 q^{45} - 19 q^{46} + 2 q^{47} + 6 q^{48} - 20 q^{49} + 17 q^{50} - 2 q^{51} - 5 q^{53} + 27 q^{54} - 4 q^{55} - 16 q^{56} + 32 q^{57} + 11 q^{58} + 11 q^{59} + 6 q^{60} - 68 q^{61} - 21 q^{62} + 29 q^{63} - 23 q^{64} - 11 q^{66} - 5 q^{67} + 16 q^{68} - 34 q^{69} + 5 q^{70} + 34 q^{71} - 13 q^{72} - 26 q^{73} + q^{74} + 10 q^{75} + 11 q^{76} + q^{77} - 32 q^{79} - 8 q^{80} + 13 q^{81} - 42 q^{82} - 8 q^{83} + 13 q^{84} - 23 q^{85} - 30 q^{86} + 10 q^{87} + 3 q^{88} + 37 q^{89} + 21 q^{90} - 12 q^{92} - 20 q^{93} - 12 q^{94} - 4 q^{95} - 60 q^{96} - 3 q^{97} + 9 q^{98} - 2 q^{99}+O(q^{100}) $ 9 * q - 5 * q^3 + 2 * q^4 + 4 * q^5 + 11 * q^6 - q^7 - 3 * q^8 + 2 * q^9 - 8 * q^10 - 9 * q^11 - 9 * q^12 - 3 * q^15 - 8 * q^16 - 8 * q^17 - 27 * q^18 + q^19 - 12 * q^20 - 17 * q^21 + 6 * q^24 - 15 * q^25 - 23 * q^27 - 11 * q^28 - 22 * q^29 - 3 * q^30 + 6 * q^31 + 19 * q^32 + 5 * q^33 - 10 * q^34 - 15 * q^35 + 7 * q^36 + 15 * q^37 + q^38 - 3 * q^40 - 10 * q^41 + 2 * q^42 - 19 * q^43 - 2 * q^44 + 2 * q^45 - 19 * q^46 + 2 * q^47 + 6 * q^48 - 20 * q^49 + 17 * q^50 - 2 * q^51 - 5 * q^53 + 27 * q^54 - 4 * q^55 - 16 * q^56 + 32 * q^57 + 11 * q^58 + 11 * q^59 + 6 * q^60 - 68 * q^61 - 21 * q^62 + 29 * q^63 - 23 * q^64 - 11 * q^66 - 5 * q^67 + 16 * q^68 - 34 * q^69 + 5 * q^70 + 34 * q^71 - 13 * q^72 - 26 * q^73 + q^74 + 10 * q^75 + 11 * q^76 + q^77 - 32 * q^79 - 8 * q^80 + 13 * q^81 - 42 * q^82 - 8 * q^83 + 13 * q^84 - 23 * q^85 - 30 * q^86 + 10 * q^87 + 3 * q^88 + 37 * q^89 + 21 * q^90 - 12 * q^92 - 20 * q^93 - 12 * q^94 - 4 * q^95 - 60 * q^96 - 3 * q^97 + 9 * q^98 - 2 * 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 $

$2$	2.31116	1.63424	0.817120	−	0.576467i	$-0.195569\pi$
$2$	2.31116	1.63424	0.817120	+	0.576467i	$0.195569\pi$
$3$	0.0765450	0.0441933	0.0220966	−	0.999756i	$-0.492966\pi$
$3$	0.0765450	0.0441933	0.0220966	+	0.999756i	$0.492966\pi$
$4$	3.34148	1.67074
$5$	−2.51567	−1.12504	−0.562520	−	0.826784i	$-0.690168\pi$
$5$	−2.51567	−1.12504	−0.562520	+	0.826784i	$0.690168\pi$
$6$	0.176908	0.0722225
$7$	−0.902363	−0.341061	−0.170531	−	0.985352i	$-0.554548\pi$
$7$	−0.902363	−0.341061	−0.170531	+	0.985352i	$0.554548\pi$
$8$	3.10039	1.09615
$9$	−2.99414	−0.998047
$10$	−5.81412	−1.83859
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.255774	0.0738356
$13$	0	0
$13$	0	0
$14$	−2.08551	−0.557376
$15$	−0.192562	−0.0497192
$16$	0.482546	0.120636
$17$	0.496094	0.120320	0.0601602	−	0.998189i	$-0.480839\pi$
$17$	0.496094	0.120320	0.0601602	+	0.998189i	$0.480839\pi$
$18$	−6.91995	−1.63105
$19$	0.163057	0.0374077	0.0187039	−	0.999825i	$-0.494046\pi$
$19$	0.163057	0.0374077	0.0187039	+	0.999825i	$0.494046\pi$
$20$	−8.40605	−1.87965
$21$	−0.0690714	−0.0150726
$22$	−2.31116	−0.492742
$23$	−6.14586	−1.28150	−0.640750	−	0.767750i	$-0.721376\pi$
$23$	−6.14586	−1.28150	−0.640750	+	0.767750i	$0.721376\pi$
$24$	0.237319	0.0484426
$25$	1.32857	0.265714
$26$	0	0
$27$	−0.458822	−0.0883003
$28$	−3.01523	−0.569825
$29$	−7.90688	−1.46827	−0.734136	−	0.679003i	$-0.762412\pi$
$29$	−7.90688	−1.46827	−0.734136	+	0.679003i	$0.762412\pi$
$30$	−0.445042	−0.0812532
$31$	−0.681774	−0.122450	−0.0612252	−	0.998124i	$-0.519501\pi$
$31$	−0.681774	−0.122450	−0.0612252	+	0.998124i	$0.519501\pi$
$32$	−5.08554	−0.899005
$33$	−0.0765450	−0.0133248
$34$	1.14655	0.196632
$35$	2.27004	0.383708
$36$	−10.0049	−1.66748
$37$	10.7755	1.77149	0.885743	−	0.464177i	$-0.153650\pi$
$37$	10.7755	1.77149	0.885743	+	0.464177i	$0.153650\pi$
$38$	0.376851	0.0611332
$39$	0	0
$40$	−7.79954	−1.23322
$41$	−3.96260	−0.618855	−0.309427	−	0.950923i	$-0.600137\pi$
$41$	−3.96260	−0.618855	−0.309427	+	0.950923i	$0.600137\pi$
$42$	−0.159635	−0.0246323
$43$	−6.61622	−1.00896	−0.504482	−	0.863422i	$-0.668316\pi$
$43$	−6.61622	−1.00896	−0.504482	+	0.863422i	$0.668316\pi$
$44$	−3.34148	−0.503748
$45$	7.53226	1.12284
$46$	−14.2041	−2.09428
$47$	12.4599	1.81746	0.908728	−	0.417388i	$-0.137054\pi$
$47$	12.4599	1.81746	0.908728	+	0.417388i	$0.137054\pi$
$48$	0.0369365	0.00533132
$49$	−6.18574	−0.883677
$50$	3.07055	0.434241
$51$	0.0379735	0.00531735
$52$	0	0
$53$	8.25234	1.13355	0.566773	−	0.823874i	$-0.308192\pi$
$53$	8.25234	1.13355	0.566773	+	0.823874i	$0.308192\pi$
$54$	−1.06041	−0.144304
$55$	2.51567	0.339212
$56$	−2.79768	−0.373856
$57$	0.0124812	0.00165317
$58$	−18.2741	−2.39951
$59$	4.55959	0.593607	0.296804	−	0.954939i	$-0.404079\pi$
$59$	4.55959	0.593607	0.296804	+	0.954939i	$0.404079\pi$
$60$	−0.643442	−0.0830680
$61$	−9.48162	−1.21400	−0.606999	−	0.794703i	$-0.707627\pi$
$61$	−9.48162	−1.21400	−0.606999	+	0.794703i	$0.707627\pi$
$62$	−1.57569	−0.200113
$63$	2.70180	0.340395
$64$	−12.7186	−1.58983
$65$	0	0
$66$	−0.176908	−0.0217759
$67$	−5.86499	−0.716523	−0.358261	−	0.933621i	$-0.616630\pi$
$67$	−5.86499	−0.716523	−0.358261	+	0.933621i	$0.616630\pi$
$68$	1.65769	0.201024
$69$	−0.470435	−0.0566337
$70$	5.24645	0.627070
$71$	0.678278	0.0804968	0.0402484	−	0.999190i	$-0.487185\pi$
$71$	0.678278	0.0804968	0.0402484	+	0.999190i	$0.487185\pi$
$72$	−9.28300	−1.09401
$73$	−5.99712	−0.701909	−0.350955	−	0.936392i	$-0.614143\pi$
$73$	−5.99712	−0.701909	−0.350955	+	0.936392i	$0.614143\pi$
$74$	24.9040	2.89503
$75$	0.101696	0.0117428
$76$	0.544851	0.0624987
$77$	0.902363	0.102834
$78$	0	0
$79$	2.76069	0.310602	0.155301	−	0.987867i	$-0.450365\pi$
$79$	2.76069	0.310602	0.155301	+	0.987867i	$0.450365\pi$
$80$	−1.21392	−0.135721
$81$	8.94730	0.994145
$82$	−9.15823	−1.01136
$83$	−6.65517	−0.730499	−0.365250	−	0.930910i	$-0.619016\pi$
$83$	−6.65517	−0.730499	−0.365250	+	0.930910i	$0.619016\pi$
$84$	−0.230801	−0.0251825
$85$	−1.24801	−0.135365
$86$	−15.2912	−1.64889
$87$	−0.605233	−0.0648877
$88$	−3.10039	−0.330503
$89$	5.27690	0.559351	0.279675	−	0.960095i	$-0.409773\pi$
$89$	5.27690	0.559351	0.279675	+	0.960095i	$0.409773\pi$
$90$	17.4083	1.83499
$91$	0	0
$92$	−20.5363	−2.14105
$93$	−0.0521865	−0.00541148
$94$	28.7968	2.97016
$95$	−0.410196	−0.0420852
$96$	−0.389273	−0.0397300
$97$	−11.8888	−1.20712	−0.603561	−	0.797317i	$-0.706252\pi$
$97$	−11.8888	−1.20712	−0.603561	+	0.797317i	$0.706252\pi$
$98$	−14.2963	−1.44414
$99$	2.99414	0.300922
$100$	4.43940	0.443940
$101$	17.6439	1.75564	0.877818	−	0.478994i	$-0.158998\pi$
$101$	17.6439	1.75564	0.877818	+	0.478994i	$0.158998\pi$
$102$	0.0877630	0.00868983
$103$	−17.6110	−1.73527	−0.867633	−	0.497205i	$-0.834360\pi$
$103$	−17.6110	−1.73527	−0.867633	+	0.497205i	$0.834360\pi$
$104$	0	0
$105$	0.173761	0.0169573
$106$	19.0725	1.85249
$107$	3.88673	0.375744	0.187872	−	0.982193i	$-0.439841\pi$
$107$	3.88673	0.375744	0.187872	+	0.982193i	$0.439841\pi$
$108$	−1.53315	−0.147527
$109$	5.23165	0.501101	0.250550	−	0.968104i	$-0.419388\pi$
$109$	5.23165	0.501101	0.250550	+	0.968104i	$0.419388\pi$
$110$	5.81412	0.554354
$111$	0.824813	0.0782878
$112$	−0.435432	−0.0411444
$113$	4.30894	0.405351	0.202675	−	0.979246i	$-0.435036\pi$
$113$	4.30894	0.405351	0.202675	+	0.979246i	$0.435036\pi$
$114$	0.0288460	0.00270168
$115$	15.4609	1.44174
$116$	−26.4207	−2.45310
$117$	0	0
$118$	10.5380	0.970097
$119$	−0.447657	−0.0410366
$120$	−0.597016	−0.0544999
$121$	1.00000	0.0909091
$122$	−21.9136	−1.98396
$123$	−0.303318	−0.0273492
$124$	−2.27814	−0.204583
$125$	9.23608	0.826100
$126$	6.24431	0.556288
$127$	16.9577	1.50475	0.752375	−	0.658736i	$-0.228908\pi$
$127$	16.9577	1.50475	0.752375	+	0.658736i	$0.228908\pi$
$128$	−19.2237	−1.69915
$129$	−0.506439	−0.0445894
$130$	0	0
$131$	17.3712	1.51773	0.758864	−	0.651249i	$-0.225755\pi$
$131$	17.3712	1.51773	0.758864	+	0.651249i	$0.225755\pi$
$132$	−0.255774	−0.0222623
$133$	−0.147136	−0.0127583
$134$	−13.5550	−1.17097
$135$	1.15424	0.0993413
$136$	1.53808	0.131890
$137$	1.33177	0.113781	0.0568905	−	0.998380i	$-0.481881\pi$
$137$	1.33177	0.113781	0.0568905	+	0.998380i	$0.481881\pi$
$138$	−1.08725	−0.0925531
$139$	−12.3883	−1.05077	−0.525383	−	0.850866i	$-0.676078\pi$
$139$	−12.3883	−1.05077	−0.525383	+	0.850866i	$0.676078\pi$
$140$	7.58532	0.641076
$141$	0.953740	0.0803194
$142$	1.56761	0.131551
$143$	0	0
$144$	−1.44481	−0.120401
$145$	19.8911	1.65186
$146$	−13.8603	−1.14709
$147$	−0.473488	−0.0390526
$148$	36.0062	2.95969
$149$	12.6198	1.03386	0.516928	−	0.856029i	$-0.327075\pi$
$149$	12.6198	1.03386	0.516928	+	0.856029i	$0.327075\pi$
$150$	0.235035	0.0191906
$151$	20.9160	1.70212	0.851059	−	0.525069i	$-0.175961\pi$
$151$	20.9160	1.70212	0.851059	+	0.525069i	$0.175961\pi$
$152$	0.505539	0.0410046
$153$	−1.48537	−0.120085
$154$	2.08551	0.168055
$155$	1.71512	0.137761
$156$	0	0
$157$	−21.6030	−1.72411	−0.862055	−	0.506815i	$-0.830823\pi$
$157$	−21.6030	−1.72411	−0.862055	+	0.506815i	$0.830823\pi$
$158$	6.38041	0.507598
$159$	0.631676	0.0500951
$160$	12.7935	1.01142
$161$	5.54579	0.437070
$162$	20.6787	1.62467
$163$	−6.49395	−0.508645	−0.254323	−	0.967119i	$-0.581853\pi$
$163$	−6.49395	−0.508645	−0.254323	+	0.967119i	$0.581853\pi$
$164$	−13.2410	−1.03395
$165$	0.192562	0.0149909
$166$	−15.3812	−1.19381
$167$	−23.9165	−1.85072	−0.925358	−	0.379095i	$-0.876235\pi$
$167$	−23.9165	−1.85072	−0.925358	+	0.379095i	$0.876235\pi$
$168$	−0.214148	−0.0165219
$169$	0	0
$170$	−2.88435	−0.221219
$171$	−0.488214	−0.0373347
$172$	−22.1080	−1.68572
$173$	−19.7354	−1.50045	−0.750226	−	0.661181i	$-0.770055\pi$
$173$	−19.7354	−1.50045	−0.750226	+	0.661181i	$0.770055\pi$
$174$	−1.39879	−0.106042
$175$	−1.19885	−0.0906249
$176$	−0.482546	−0.0363732
$177$	0.349014	0.0262335
$178$	12.1958	0.914113
$179$	16.2319	1.21323	0.606616	−	0.794995i	$-0.292526\pi$
$179$	16.2319	1.21323	0.606616	+	0.794995i	$0.292526\pi$
$180$	25.1689	1.87598
$181$	−3.78208	−0.281120	−0.140560	−	0.990072i	$-0.544890\pi$
$181$	−3.78208	−0.281120	−0.140560	+	0.990072i	$0.544890\pi$
$182$	0	0
$183$	−0.725771	−0.0536505
$184$	−19.0545	−1.40472
$185$	−27.1076	−1.99299
$186$	−0.120612	−0.00884366
$187$	−0.496094	−0.0362780
$188$	41.6344	3.03650
$189$	0.414024	0.0301158
$190$	−0.948030	−0.0687773
$191$	−17.7589	−1.28499	−0.642494	−	0.766291i	$-0.722100\pi$
$191$	−17.7589	−1.28499	−0.642494	+	0.766291i	$0.722100\pi$
$192$	−0.973546	−0.0702597
$193$	9.28279	0.668190	0.334095	−	0.942539i	$-0.391569\pi$
$193$	9.28279	0.668190	0.334095	+	0.942539i	$0.391569\pi$
$194$	−27.4769	−1.97273
$195$	0	0
$196$	−20.6696	−1.47640
$197$	1.81753	0.129494	0.0647469	−	0.997902i	$-0.479376\pi$
$197$	1.81753	0.129494	0.0647469	+	0.997902i	$0.479376\pi$
$198$	6.91995	0.491780
$199$	−7.23953	−0.513196	−0.256598	−	0.966518i	$-0.582602\pi$
$199$	−7.23953	−0.513196	−0.256598	+	0.966518i	$0.582602\pi$
$200$	4.11909	0.291264
$201$	−0.448936	−0.0316655
$202$	40.7780	2.86913
$203$	7.13488	0.500770
$204$	0.126888	0.00888392
$205$	9.96858	0.696236
$206$	−40.7020	−2.83584
$207$	18.4016	1.27900
$208$	0	0
$209$	−0.163057	−0.0112789
$210$	0.401589	0.0277123
$211$	−18.4159	−1.26780	−0.633900	−	0.773415i	$-0.718547\pi$
$211$	−18.4159	−1.26780	−0.633900	+	0.773415i	$0.718547\pi$
$212$	27.5751	1.89386
$213$	0.0519188	0.00355742
$214$	8.98287	0.614057
$215$	16.6442	1.13512
$216$	−1.42253	−0.0967907
$217$	0.615208	0.0417631
$218$	12.0912	0.818919
$219$	−0.459049	−0.0310197
$220$	8.40605	0.566736
$221$	0	0
$222$	1.90628	0.127941
$223$	6.81746	0.456531	0.228265	−	0.973599i	$-0.426695\pi$
$223$	6.81746	0.456531	0.228265	+	0.973599i	$0.426695\pi$
$224$	4.58900	0.306616
$225$	−3.97793	−0.265195
$226$	9.95866	0.662441
$227$	−20.3563	−1.35109	−0.675547	−	0.737317i	$-0.736093\pi$
$227$	−20.3563	−1.35109	−0.675547	+	0.737317i	$0.736093\pi$
$228$	0.0417056	0.00276202
$229$	−11.7048	−0.773474	−0.386737	−	0.922190i	$-0.626398\pi$
$229$	−11.7048	−0.773474	−0.386737	+	0.922190i	$0.626398\pi$
$230$	35.7327	2.35615
$231$	0.0690714	0.00454457
$232$	−24.5144	−1.60945
$233$	22.1904	1.45374	0.726872	−	0.686773i	$-0.240973\pi$
$233$	22.1904	1.45374	0.726872	+	0.686773i	$0.240973\pi$
$234$	0	0
$235$	−31.3448	−2.04471
$236$	15.2358	0.991765
$237$	0.211317	0.0137265
$238$	−1.03461	−0.0670637
$239$	−8.55458	−0.553350	−0.276675	−	0.960964i	$-0.589233\pi$
$239$	−8.55458	−0.553350	−0.276675	+	0.960964i	$0.589233\pi$
$240$	−0.0929198	−0.00599795
$241$	−1.36272	−0.0877804	−0.0438902	−	0.999036i	$-0.513975\pi$
$241$	−1.36272	−0.0877804	−0.0438902	+	0.999036i	$0.513975\pi$
$242$	2.31116	0.148567
$243$	2.06134	0.132235
$244$	−31.6827	−2.02828
$245$	15.5613	0.994172
$246$	−0.701017	−0.0446952
$247$	0	0
$248$	−2.11377	−0.134224
$249$	−0.509420	−0.0322832
$250$	21.3461	1.35005
$251$	7.11720	0.449233	0.224617	−	0.974447i	$-0.427887\pi$
$251$	7.11720	0.449233	0.224617	+	0.974447i	$0.427887\pi$
$252$	9.02803	0.568712
$253$	6.14586	0.386387
$254$	39.1920	2.45912
$255$	−0.0955286	−0.00598223
$256$	−18.9920	−1.18700
$257$	−7.55108	−0.471023	−0.235512	−	0.971872i	$-0.575677\pi$
$257$	−7.55108	−0.471023	−0.235512	+	0.971872i	$0.575677\pi$
$258$	−1.17046	−0.0728699
$259$	−9.72344	−0.604185
$260$	0	0
$261$	23.6743	1.46540
$262$	40.1477	2.48033
$263$	−18.9964	−1.17137	−0.585683	−	0.810540i	$-0.699174\pi$
$263$	−18.9964	−1.17137	−0.585683	+	0.810540i	$0.699174\pi$
$264$	−0.237319	−0.0146060
$265$	−20.7601	−1.27528
$266$	−0.340056	−0.0208502
$267$	0.403921	0.0247195
$268$	−19.5978	−1.19712
$269$	0.0900059	0.00548776	0.00274388	−	0.999996i	$-0.499127\pi$
$269$	0.0900059	0.00548776	0.00274388	+	0.999996i	$0.499127\pi$
$270$	2.66764	0.162348
$271$	−16.9993	−1.03264	−0.516318	−	0.856397i	$-0.672698\pi$
$271$	−16.9993	−1.03264	−0.516318	+	0.856397i	$0.672698\pi$
$272$	0.239388	0.0145150
$273$	0	0
$274$	3.07794	0.185945
$275$	−1.32857	−0.0801159
$276$	−1.57195	−0.0946203
$277$	−21.3786	−1.28452	−0.642258	−	0.766489i	$-0.722002\pi$
$277$	−21.3786	−1.28452	−0.642258	+	0.766489i	$0.722002\pi$
$278$	−28.6315	−1.71720
$279$	2.04133	0.122211
$280$	7.03802	0.420602
$281$	17.4109	1.03865	0.519325	−	0.854577i	$-0.326184\pi$
$281$	17.4109	1.03865	0.519325	+	0.854577i	$0.326184\pi$
$282$	2.20425	0.131261
$283$	0.529976	0.0315038	0.0157519	−	0.999876i	$-0.494986\pi$
$283$	0.529976	0.0315038	0.0157519	+	0.999876i	$0.494986\pi$
$284$	2.26646	0.134489
$285$	−0.0313985	−0.00185988
$286$	0	0
$287$	3.57571	0.211067
$288$	15.2268	0.897249
$289$	−16.7539	−0.985523
$290$	45.9715	2.69954
$291$	−0.910027	−0.0533467
$292$	−20.0393	−1.17271
$293$	−3.12202	−0.182390	−0.0911951	−	0.995833i	$-0.529069\pi$
$293$	−3.12202	−0.182390	−0.0911951	+	0.995833i	$0.529069\pi$
$294$	−1.09431	−0.0638214
$295$	−11.4704	−0.667832
$296$	33.4083	1.94182
$297$	0.458822	0.0266235
$298$	29.1665	1.68957
$299$	0	0
$300$	0.339814	0.0196192
$301$	5.97023	0.344118
$302$	48.3403	2.78167
$303$	1.35056	0.0775874
$304$	0.0786822	0.00451274
$305$	23.8526	1.36580
$306$	−3.43294	−0.196248
$307$	8.03358	0.458501	0.229250	−	0.973368i	$-0.426373\pi$
$307$	8.03358	0.458501	0.229250	+	0.973368i	$0.426373\pi$
$308$	3.01523	0.171809
$309$	−1.34804	−0.0766871
$310$	3.96392	0.225135
$311$	−24.6158	−1.39584	−0.697918	−	0.716178i	$-0.745890\pi$
$311$	−24.6158	−1.39584	−0.697918	+	0.716178i	$0.745890\pi$
$312$	0	0
$313$	17.8895	1.01117	0.505587	−	0.862776i	$-0.331276\pi$
$313$	17.8895	1.01117	0.505587	+	0.862776i	$0.331276\pi$
$314$	−49.9282	−2.81761
$315$	−6.79683	−0.382958
$316$	9.22480	0.518935
$317$	12.0177	0.674983	0.337492	−	0.941329i	$-0.390422\pi$
$317$	12.0177	0.674983	0.337492	+	0.941329i	$0.390422\pi$
$318$	1.45991	0.0818675
$319$	7.90688	0.442700
$320$	31.9958	1.78862
$321$	0.297510	0.0166054
$322$	12.8172	0.714277
$323$	0.0808913	0.00450091
$324$	29.8973	1.66096
$325$	0	0
$326$	−15.0086	−0.831249
$327$	0.400457	0.0221453
$328$	−12.2856	−0.678360
$329$	−11.2433	−0.619864
$330$	0.445042	0.0244987
$331$	14.5067	0.797363	0.398681	−	0.917089i	$-0.369468\pi$
$331$	14.5067	0.797363	0.398681	+	0.917089i	$0.369468\pi$
$332$	−22.2381	−1.22048
$333$	−32.2634	−1.76803
$334$	−55.2750	−3.02451
$335$	14.7544	0.806116
$336$	−0.0333301	−0.00181831
$337$	12.3169	0.670942	0.335471	−	0.942051i	$-0.391105\pi$
$337$	12.3169	0.670942	0.335471	+	0.942051i	$0.391105\pi$
$338$	0	0
$339$	0.329828	0.0179138
$340$	−4.17019	−0.226160
$341$	0.681774	0.0369202
$342$	−1.12834	−0.0610139
$343$	11.8983	0.642449
$344$	−20.5129	−1.10598
$345$	1.18346	0.0637151
$346$	−45.6117	−2.45210
$347$	10.6707	0.572831	0.286416	−	0.958105i	$-0.407536\pi$
$347$	10.6707	0.572831	0.286416	+	0.958105i	$0.407536\pi$
$348$	−2.02237	−0.108411
$349$	−6.20697	−0.332252	−0.166126	−	0.986105i	$-0.553126\pi$
$349$	−6.20697	−0.332252	−0.166126	+	0.986105i	$0.553126\pi$
$350$	−2.77075	−0.148103
$351$	0	0
$352$	5.08554	0.271060
$353$	−32.0425	−1.70545	−0.852725	−	0.522360i	$-0.825052\pi$
$353$	−32.0425	−1.70545	−0.852725	+	0.522360i	$0.825052\pi$
$354$	0.806628	0.0428718
$355$	−1.70632	−0.0905621
$356$	17.6327	0.934530
$357$	−0.0342659	−0.00181354
$358$	37.5147	1.98271
$359$	−9.52942	−0.502943	−0.251472	−	0.967865i	$-0.580915\pi$
$359$	−9.52942	−0.502943	−0.251472	+	0.967865i	$0.580915\pi$
$360$	23.3529	1.23081
$361$	−18.9734	−0.998601
$362$	−8.74101	−0.459418
$363$	0.0765450	0.00401757
$364$	0	0
$365$	15.0867	0.789676
$366$	−1.67738	−0.0876779
$367$	14.5524	0.759626	0.379813	−	0.925063i	$-0.375988\pi$
$367$	14.5524	0.759626	0.379813	+	0.925063i	$0.375988\pi$
$368$	−2.96566	−0.154595
$369$	11.8646	0.617646
$370$	−62.6502	−3.25703
$371$	−7.44661	−0.386609
$372$	−0.174380	−0.00904119
$373$	−25.3257	−1.31131	−0.655657	−	0.755059i	$-0.727608\pi$
$373$	−25.3257	−1.31131	−0.655657	+	0.755059i	$0.727608\pi$
$374$	−1.14655	−0.0592869
$375$	0.706976	0.0365081
$376$	38.6304	1.99221
$377$	0	0
$378$	0.956878	0.0492165
$379$	−11.9802	−0.615381	−0.307690	−	0.951487i	$-0.599556\pi$
$379$	−11.9802	−0.615381	−0.307690	+	0.951487i	$0.599556\pi$
$380$	−1.37066	−0.0703135
$381$	1.29802	0.0664998
$382$	−41.0437	−2.09998
$383$	−30.3287	−1.54972	−0.774861	−	0.632131i	$-0.782180\pi$
$383$	−30.3287	−1.54972	−0.774861	+	0.632131i	$0.782180\pi$
$384$	−1.47148	−0.0750912
$385$	−2.27004	−0.115692
$386$	21.4541	1.09198
$387$	19.8099	1.00699
$388$	−39.7261	−2.01679
$389$	−26.1686	−1.32680	−0.663400	−	0.748265i	$-0.730887\pi$
$389$	−26.1686	−1.32680	−0.663400	+	0.748265i	$0.730887\pi$
$390$	0	0
$391$	−3.04892	−0.154190
$392$	−19.1782	−0.968646
$393$	1.32968	0.0670734
$394$	4.20062	0.211624
$395$	−6.94497	−0.349439
$396$	10.0049	0.502764
$397$	−34.0153	−1.70718	−0.853589	−	0.520947i	$-0.825579\pi$
$397$	−34.0153	−1.70718	−0.853589	+	0.520947i	$0.825579\pi$
$398$	−16.7317	−0.838686
$399$	−0.0112626	−0.000563833 0
$400$	0.641097	0.0320548
$401$	26.4654	1.32162	0.660809	−	0.750554i	$-0.270213\pi$
$401$	26.4654	1.32162	0.660809	+	0.750554i	$0.270213\pi$
$402$	−1.03757	−0.0517490
$403$	0	0
$404$	58.9569	2.93322
$405$	−22.5084	−1.11845
$406$	16.4899	0.818379
$407$	−10.7755	−0.534123
$408$	0.117733	0.00582863
$409$	27.2503	1.34744	0.673721	−	0.738986i	$-0.264695\pi$
$409$	27.2503	1.34744	0.673721	+	0.738986i	$0.264695\pi$
$410$	23.0390	1.13782
$411$	0.101941	0.00502836
$412$	−58.8470	−2.89918
$413$	−4.11440	−0.202457
$414$	42.5290	2.09019
$415$	16.7422	0.821841
$416$	0	0
$417$	−0.948267	−0.0464368
$418$	−0.376851	−0.0184324
$419$	26.8939	1.31385	0.656926	−	0.753955i	$-0.271857\pi$
$419$	26.8939	1.31385	0.656926	+	0.753955i	$0.271857\pi$
$420$	0.580618	0.0283313
$421$	26.9888	1.31535	0.657676	−	0.753301i	$-0.271540\pi$
$421$	26.9888	1.31535	0.657676	+	0.753301i	$0.271540\pi$
$422$	−42.5621	−2.07189
$423$	−37.3066	−1.81391
$424$	25.5855	1.24254
$425$	0.659096	0.0319708
$426$	0.119993	0.00581368
$427$	8.55587	0.414047
$428$	12.9874	0.627772
$429$	0	0
$430$	38.4675	1.85507
$431$	−30.6577	−1.47673	−0.738365	−	0.674401i	$-0.764402\pi$
$431$	−30.6577	−1.47673	−0.738365	+	0.674401i	$0.764402\pi$
$432$	−0.221402	−0.0106522
$433$	−14.0931	−0.677272	−0.338636	−	0.940917i	$-0.609966\pi$
$433$	−14.0931	−0.677272	−0.338636	+	0.940917i	$0.609966\pi$
$434$	1.42185	0.0682509
$435$	1.52256	0.0730013
$436$	17.4815	0.837210
$437$	−1.00212	−0.0479380
$438$	−1.06094	−0.0506936
$439$	−11.0105	−0.525505	−0.262752	−	0.964863i	$-0.584630\pi$
$439$	−11.0105	−0.525505	−0.262752	+	0.964863i	$0.584630\pi$
$440$	7.79954	0.371829
$441$	18.5210	0.881951
$442$	0	0
$443$	14.5980	0.693572	0.346786	−	0.937944i	$-0.387273\pi$
$443$	14.5980	0.693572	0.346786	+	0.937944i	$0.387273\pi$
$444$	2.75610	0.130799
$445$	−13.2749	−0.629292
$446$	15.7563	0.746081
$447$	0.965985	0.0456895
$448$	11.4768	0.542228
$449$	30.5582	1.44213	0.721065	−	0.692868i	$-0.243653\pi$
$449$	30.5582	1.44213	0.721065	+	0.692868i	$0.243653\pi$
$450$	−9.19366	−0.433393
$451$	3.96260	0.186592
$452$	14.3982	0.677236
$453$	1.60101	0.0752222
$454$	−47.0467	−2.20801
$455$	0	0
$456$	0.0386965	0.00181213
$457$	7.74021	0.362072	0.181036	−	0.983477i	$-0.442055\pi$
$457$	7.74021	0.362072	0.181036	+	0.983477i	$0.442055\pi$
$458$	−27.0517	−1.26404
$459$	−0.227618	−0.0106243
$460$	51.6624	2.40877
$461$	−35.3789	−1.64776	−0.823879	−	0.566766i	$-0.808194\pi$
$461$	−35.3789	−1.64776	−0.823879	+	0.566766i	$0.808194\pi$
$462$	0.159635	0.00742692
$463$	15.4651	0.718722	0.359361	−	0.933199i	$-0.382995\pi$
$463$	15.4651	0.718722	0.359361	+	0.933199i	$0.382995\pi$
$464$	−3.81543	−0.177127
$465$	0.131284	0.00608813
$466$	51.2858	2.37577
$467$	24.8780	1.15122	0.575608	−	0.817726i	$-0.304766\pi$
$467$	24.8780	1.15122	0.575608	+	0.817726i	$0.304766\pi$
$468$	0	0
$469$	5.29235	0.244378
$470$	−72.4431	−3.34155
$471$	−1.65361	−0.0761941
$472$	14.1365	0.650685
$473$	6.61622	0.304214
$474$	0.488388	0.0224324
$475$	0.216632	0.00993978
$476$	−1.49584	−0.0685616
$477$	−24.7087	−1.13133
$478$	−19.7710	−0.904307
$479$	32.6677	1.49262	0.746312	−	0.665597i	$-0.231823\pi$
$479$	32.6677	1.49262	0.746312	+	0.665597i	$0.231823\pi$
$480$	0.979280	0.0446978
$481$	0	0
$482$	−3.14947	−0.143454
$483$	0.424503	0.0193156
$484$	3.34148	0.151886
$485$	29.9082	1.35806
$486$	4.76409	0.216103
$487$	−3.54643	−0.160704	−0.0803519	−	0.996767i	$-0.525604\pi$
$487$	−3.54643	−0.160704	−0.0803519	+	0.996767i	$0.525604\pi$
$488$	−29.3967	−1.33073
$489$	−0.497080	−0.0224787
$490$	35.9646	1.62472
$491$	−16.7844	−0.757471	−0.378736	−	0.925505i	$-0.623641\pi$
$491$	−16.7844	−0.757471	−0.378736	+	0.925505i	$0.623641\pi$
$492$	−1.01353	−0.0456935
$493$	−3.92255	−0.176663
$494$	0	0
$495$	−7.53226	−0.338550
$496$	−0.328987	−0.0147720
$497$	−0.612054	−0.0274544
$498$	−1.17735	−0.0527585
$499$	−0.189404	−0.00847887	−0.00423944	−	0.999991i	$-0.501349\pi$
$499$	−0.189404	−0.00847887	−0.00423944	+	0.999991i	$0.501349\pi$
$500$	30.8622	1.38020
$501$	−1.83069	−0.0817892
$502$	16.4490	0.734156
$503$	35.9635	1.60353	0.801767	−	0.597637i	$-0.203894\pi$
$503$	35.9635	1.60353	0.801767	+	0.597637i	$0.203894\pi$
$504$	8.37664	0.373125
$505$	−44.3862	−1.97516
$506$	14.2041	0.631449
$507$	0	0
$508$	56.6638	2.51405
$509$	1.39309	0.0617476	0.0308738	−	0.999523i	$-0.490171\pi$
$509$	1.39309	0.0617476	0.0308738	+	0.999523i	$0.490171\pi$
$510$	−0.220782	−0.00977641
$511$	5.41158	0.239394
$512$	−5.44616	−0.240689
$513$	−0.0748139	−0.00330311
$514$	−17.4518	−0.769765
$515$	44.3035	1.95224
$516$	−1.69226	−0.0744974
$517$	−12.4599	−0.547984
$518$	−22.4725	−0.987384
$519$	−1.51064	−0.0663099
$520$	0	0
$521$	−5.17184	−0.226582	−0.113291	−	0.993562i	$-0.536139\pi$
$521$	−5.17184	−0.226582	−0.113291	+	0.993562i	$0.536139\pi$
$522$	54.7153	2.39482
$523$	−5.08523	−0.222361	−0.111181	−	0.993800i	$-0.535463\pi$
$523$	−5.08523	−0.222361	−0.111181	+	0.993800i	$0.535463\pi$
$524$	58.0456	2.53573
$525$	−0.0917664	−0.00400501
$526$	−43.9037	−1.91429
$527$	−0.338224	−0.0147333
$528$	−0.0369365	−0.00160745
$529$	14.7715	0.642241
$530$	−47.9801	−2.08412
$531$	−13.6520	−0.592448
$532$	−0.491653	−0.0213159
$533$	0	0
$534$	0.933528	0.0403977
$535$	−9.77771	−0.422727
$536$	−18.1838	−0.785419
$537$	1.24248	0.0536168
$538$	0.208019	0.00896832
$539$	6.18574	0.266439
$540$	3.85688	0.165974
$541$	−38.1992	−1.64231	−0.821155	−	0.570705i	$-0.806670\pi$
$541$	−38.1992	−1.64231	−0.821155	+	0.570705i	$0.806670\pi$
$542$	−39.2883	−1.68758
$543$	−0.289500	−0.0124236
$544$	−2.52290	−0.108169
$545$	−13.1611	−0.563759
$546$	0	0
$547$	5.98933	0.256085	0.128043	−	0.991769i	$-0.459131\pi$
$547$	5.98933	0.256085	0.128043	+	0.991769i	$0.459131\pi$
$548$	4.45009	0.190099
$549$	28.3893	1.21163
$550$	−3.07055	−0.130929
$551$	−1.28927	−0.0549247
$552$	−1.45853	−0.0620792
$553$	−2.49114	−0.105934
$554$	−49.4095	−2.09921
$555$	−2.07495	−0.0880769
$556$	−41.3955	−1.75556
$557$	6.23907	0.264358	0.132179	−	0.991226i	$-0.457803\pi$
$557$	6.23907	0.264358	0.132179	+	0.991226i	$0.457803\pi$
$558$	4.71785	0.199722
$559$	0	0
$560$	1.09540	0.0462891
$561$	−0.0379735	−0.00160324
$562$	40.2395	1.69740
$563$	17.0033	0.716604	0.358302	−	0.933606i	$-0.383356\pi$
$563$	17.0033	0.716604	0.358302	+	0.933606i	$0.383356\pi$
$564$	3.18691	0.134193
$565$	−10.8398	−0.456036
$566$	1.22486	0.0514848
$567$	−8.07372	−0.339064
$568$	2.10293	0.0882369
$569$	−14.7381	−0.617853	−0.308927	−	0.951086i	$-0.599970\pi$
$569$	−14.7381	−0.617853	−0.308927	+	0.951086i	$0.599970\pi$
$570$	−0.0725670	−0.00303950
$571$	15.9324	0.666748	0.333374	−	0.942795i	$-0.391813\pi$
$571$	15.9324	0.666748	0.333374	+	0.942795i	$0.391813\pi$
$572$	0	0
$573$	−1.35935	−0.0567878
$574$	8.26405	0.344935
$575$	−8.16521	−0.340513
$576$	38.0813	1.58672
$577$	−9.41121	−0.391794	−0.195897	−	0.980624i	$-0.562762\pi$
$577$	−9.41121	−0.391794	−0.195897	+	0.980624i	$0.562762\pi$
$578$	−38.7210	−1.61058
$579$	0.710552	0.0295295
$580$	66.4657	2.75984
$581$	6.00538	0.249145
$582$	−2.10322	−0.0871813
$583$	−8.25234	−0.341777
$584$	−18.5934	−0.769400
$585$	0	0
$586$	−7.21550	−0.298070
$587$	0.729436	0.0301070	0.0150535	−	0.999887i	$-0.495208\pi$
$587$	0.729436	0.0301070	0.0150535	+	0.999887i	$0.495208\pi$
$588$	−1.58215	−0.0652468
$589$	−0.111168	−0.00458059
$590$	−26.5100	−1.09140
$591$	0.139123	0.00572276
$592$	5.19968	0.213706
$593$	10.4491	0.429091	0.214546	−	0.976714i	$-0.431173\pi$
$593$	10.4491	0.429091	0.214546	+	0.976714i	$0.431173\pi$
$594$	1.06041	0.0435093
$595$	1.12615	0.0461678
$596$	42.1689	1.72731
$597$	−0.554150	−0.0226798
$598$	0	0
$599$	−31.0241	−1.26761	−0.633806	−	0.773492i	$-0.718508\pi$
$599$	−31.0241	−1.26761	−0.633806	+	0.773492i	$0.718508\pi$
$600$	0.315296	0.0128719
$601$	−16.0164	−0.653321	−0.326660	−	0.945142i	$-0.605923\pi$
$601$	−16.0164	−0.653321	−0.326660	+	0.945142i	$0.605923\pi$
$602$	13.7982	0.562372
$603$	17.5606	0.715123
$604$	69.8904	2.84380
$605$	−2.51567	−0.102276
$606$	3.12136	0.126796
$607$	−8.06204	−0.327228	−0.163614	−	0.986524i	$-0.552315\pi$
$607$	−8.06204	−0.327228	−0.163614	+	0.986524i	$0.552315\pi$
$608$	−0.829230	−0.0336297
$609$	0.546140	0.0221307
$610$	55.1273	2.23204
$611$	0	0
$612$	−4.96335	−0.200632
$613$	−20.7812	−0.839346	−0.419673	−	0.907675i	$-0.637855\pi$
$613$	−20.7812	−0.839346	−0.419673	+	0.907675i	$0.637855\pi$
$614$	18.5669	0.749300
$615$	0.763046	0.0307690
$616$	2.79768	0.112722
$617$	1.78239	0.0717562	0.0358781	−	0.999356i	$-0.488577\pi$
$617$	1.78239	0.0717562	0.0358781	+	0.999356i	$0.488577\pi$
$618$	−3.11554	−0.125325
$619$	−11.1527	−0.448265	−0.224133	−	0.974559i	$-0.571955\pi$
$619$	−11.1527	−0.448265	−0.224133	+	0.974559i	$0.571955\pi$
$620$	5.73103	0.230164
$621$	2.81985	0.113157
$622$	−56.8912	−2.28113
$623$	−4.76168	−0.190773
$624$	0	0
$625$	−29.8778	−1.19511
$626$	41.3456	1.65250
$627$	−0.0124812	−0.000498450 0
$628$	−72.1862	−2.88054
$629$	5.34567	0.213146
$630$	−15.7086	−0.625846
$631$	−29.9931	−1.19400	−0.597002	−	0.802240i	$-0.703642\pi$
$631$	−29.9931	−1.19400	−0.597002	+	0.802240i	$0.703642\pi$
$632$	8.55921	0.340467
$633$	−1.40964	−0.0560283
$634$	27.7750	1.10308
$635$	−42.6598	−1.69290
$636$	2.11073	0.0836960
$637$	0	0
$638$	18.2741	0.723479
$639$	−2.03086	−0.0803396
$640$	48.3605	1.91161
$641$	5.96381	0.235556	0.117778	−	0.993040i	$-0.462423\pi$
$641$	5.96381	0.235556	0.117778	+	0.993040i	$0.462423\pi$
$642$	0.687594	0.0271372
$643$	3.98156	0.157017	0.0785087	−	0.996913i	$-0.474984\pi$
$643$	3.98156	0.157017	0.0785087	+	0.996913i	$0.474984\pi$
$644$	18.5312	0.730231
$645$	1.27403	0.0501649
$646$	0.186953	0.00735557
$647$	27.1081	1.06573	0.532864	−	0.846201i	$-0.321116\pi$
$647$	27.1081	1.06573	0.532864	+	0.846201i	$0.321116\pi$
$648$	27.7401	1.08974
$649$	−4.55959	−0.178979
$650$	0	0
$651$	0.0470911	0.00184565
$652$	−21.6994	−0.849815
$653$	−22.7887	−0.891793	−0.445896	−	0.895085i	$-0.647115\pi$
$653$	−22.7887	−0.891793	−0.445896	+	0.895085i	$0.647115\pi$
$654$	0.925521	0.0361908
$655$	−43.7001	−1.70750
$656$	−1.91214	−0.0746564
$657$	17.9562	0.700538
$658$	−25.9852	−1.01301
$659$	−40.6595	−1.58387	−0.791934	−	0.610606i	$-0.790926\pi$
$659$	−40.6595	−1.58387	−0.791934	+	0.610606i	$0.790926\pi$
$660$	0.643442	0.0250459
$661$	−15.3841	−0.598371	−0.299185	−	0.954195i	$-0.596715\pi$
$661$	−15.3841	−0.598371	−0.299185	+	0.954195i	$0.596715\pi$
$662$	33.5275	1.30308
$663$	0	0
$664$	−20.6336	−0.800739
$665$	0.370146	0.0143536
$666$	−74.5661	−2.88938
$667$	48.5946	1.88159
$668$	−79.9166	−3.09207
$669$	0.521843	0.0201756
$670$	34.0997	1.31739
$671$	9.48162	0.366034
$672$	0.351265	0.0135504
$673$	−18.9586	−0.730800	−0.365400	−	0.930851i	$-0.619068\pi$
$673$	−18.9586	−0.730800	−0.365400	+	0.930851i	$0.619068\pi$
$674$	28.4663	1.09648
$675$	−0.609578	−0.0234627
$676$	0	0
$677$	−29.6328	−1.13888	−0.569441	−	0.822032i	$-0.692840\pi$
$677$	−29.6328	−1.13888	−0.569441	+	0.822032i	$0.692840\pi$
$678$	0.762286	0.0292754
$679$	10.7280	0.411703
$680$	−3.86930	−0.148381
$681$	−1.55817	−0.0597093
$682$	1.57569	0.0603364
$683$	−31.7824	−1.21612	−0.608060	−	0.793891i	$-0.708052\pi$
$683$	−31.7824	−1.21612	−0.608060	+	0.793891i	$0.708052\pi$
$684$	−1.63136	−0.0623766
$685$	−3.35029	−0.128008
$686$	27.4990	1.04992
$687$	−0.895944	−0.0341824
$688$	−3.19263	−0.121718
$689$	0	0
$690$	2.73516	0.104126
$691$	27.1740	1.03375	0.516874	−	0.856061i	$-0.327095\pi$
$691$	27.1740	1.03375	0.516874	+	0.856061i	$0.327095\pi$
$692$	−65.9454	−2.50687
$693$	−2.70180	−0.102633
$694$	24.6617	0.936144
$695$	31.1649	1.18215
$696$	−1.87646	−0.0711269
$697$	−1.96582	−0.0744608
$698$	−14.3453	−0.542979
$699$	1.69857	0.0642458
$700$	−4.00595	−0.151411
$701$	−7.54325	−0.284905	−0.142452	−	0.989802i	$-0.545499\pi$
$701$	−7.54325	−0.284905	−0.142452	+	0.989802i	$0.545499\pi$
$702$	0	0
$703$	1.75702	0.0662673
$704$	12.7186	0.479351
$705$	−2.39929	−0.0903625
$706$	−74.0555	−2.78712
$707$	−15.9212	−0.598780
$708$	1.16622	0.0438294
$709$	14.6121	0.548770	0.274385	−	0.961620i	$-0.411526\pi$
$709$	14.6121	0.548770	0.274385	+	0.961620i	$0.411526\pi$
$710$	−3.94359	−0.148000
$711$	−8.26589	−0.309995
$712$	16.3605	0.613134
$713$	4.19009	0.156920
$714$	−0.0791941	−0.00296377
$715$	0	0
$716$	54.2388	2.02700
$717$	−0.654811	−0.0244544
$718$	−22.0241	−0.821930
$719$	−23.8674	−0.890105	−0.445052	−	0.895505i	$-0.646815\pi$
$719$	−23.8674	−0.890105	−0.445052	+	0.895505i	$0.646815\pi$
$720$	3.63466	0.135456
$721$	15.8915	0.591832
$722$	−43.8507	−1.63195
$723$	−0.104309	−0.00387931
$724$	−12.6378	−0.469679
$725$	−10.5049	−0.390141
$726$	0.176908	0.00656568
$727$	30.2851	1.12321	0.561606	−	0.827405i	$-0.310184\pi$
$727$	30.2851	1.12321	0.561606	+	0.827405i	$0.310184\pi$
$728$	0	0
$729$	−26.6841	−0.988301
$730$	34.8679	1.29052
$731$	−3.28226	−0.121399
$732$	−2.42515	−0.0896362
$733$	8.56655	0.316413	0.158206	−	0.987406i	$-0.449429\pi$
$733$	8.56655	0.316413	0.158206	+	0.987406i	$0.449429\pi$
$734$	33.6329	1.24141
$735$	1.19114	0.0439357
$736$	31.2550	1.15207
$737$	5.86499	0.216040
$738$	27.4210	1.00938
$739$	13.4555	0.494967	0.247484	−	0.968892i	$-0.420396\pi$
$739$	13.4555	0.494967	0.247484	+	0.968892i	$0.420396\pi$
$740$	−90.5797	−3.32977
$741$	0	0
$742$	−17.2103	−0.631811
$743$	2.01519	0.0739300	0.0369650	−	0.999317i	$-0.488231\pi$
$743$	2.01519	0.0739300	0.0369650	+	0.999317i	$0.488231\pi$
$744$	−0.161798	−0.00593182
$745$	−31.7473	−1.16313
$746$	−58.5319	−2.14300
$747$	19.9265	0.729073
$748$	−1.65769	−0.0606111
$749$	−3.50724	−0.128152
$750$	1.63394	0.0596630
$751$	33.0737	1.20688	0.603438	−	0.797410i	$-0.293797\pi$
$751$	33.0737	1.20688	0.603438	+	0.797410i	$0.293797\pi$
$752$	6.01245	0.219251
$753$	0.544786	0.0198531
$754$	0	0
$755$	−52.6176	−1.91495
$756$	1.38345	0.0503157
$757$	36.6026	1.33034	0.665172	−	0.746690i	$-0.268358\pi$
$757$	36.6026	1.33034	0.665172	+	0.746690i	$0.268358\pi$
$758$	−27.6882	−1.00568
$759$	0.470435	0.0170757
$760$	−1.27177	−0.0461318
$761$	33.0656	1.19863	0.599314	−	0.800514i	$-0.295440\pi$
$761$	33.0656	1.19863	0.599314	+	0.800514i	$0.295440\pi$
$762$	2.99995	0.108677
$763$	−4.72085	−0.170906
$764$	−59.3410	−2.14688
$765$	3.73670	0.135101
$766$	−70.0945	−2.53262
$767$	0	0
$768$	−1.45374	−0.0524574
$769$	−40.2683	−1.45211	−0.726056	−	0.687636i	$-0.758648\pi$
$769$	−40.2683	−1.45211	−0.726056	+	0.687636i	$0.758648\pi$
$770$	−5.24645	−0.189069
$771$	−0.577998	−0.0208161
$772$	31.0183	1.11637
$773$	7.62982	0.274426	0.137213	−	0.990542i	$-0.456186\pi$
$773$	7.62982	0.274426	0.137213	+	0.990542i	$0.456186\pi$
$774$	45.7839	1.64567
$775$	−0.905786	−0.0325368
$776$	−36.8598	−1.32319
$777$	−0.744281	−0.0267009
$778$	−60.4800	−2.16831
$779$	−0.646128	−0.0231500
$780$	0	0
$781$	−0.678278	−0.0242707
$782$	−7.04655	−0.251984
$783$	3.62785	0.129649
$784$	−2.98490	−0.106604
$785$	54.3460	1.93969
$786$	3.07311	0.109614
$787$	−37.2688	−1.32849	−0.664245	−	0.747515i	$-0.731247\pi$
$787$	−37.2688	−1.32849	−0.664245	+	0.747515i	$0.731247\pi$
$788$	6.07325	0.216351
$789$	−1.45408	−0.0517665
$790$	−16.0510	−0.571068
$791$	−3.88823	−0.138249
$792$	9.28300	0.329857
$793$	0	0
$794$	−78.6149	−2.78994
$795$	−1.58908	−0.0563590
$796$	−24.1908	−0.857419
$797$	26.4280	0.936129	0.468064	−	0.883694i	$-0.344951\pi$
$797$	26.4280	0.936129	0.468064	+	0.883694i	$0.344951\pi$
$798$	−0.0260296	−0.000921438 0
$799$	6.18125	0.218677
$800$	−6.75650	−0.238878
$801$	−15.7998	−0.558258
$802$	61.1659	2.15984
$803$	5.99712	0.211634
$804$	−1.50011	−0.0529049
$805$	−13.9514	−0.491721
$806$	0	0
$807$	0.00688951	0.000242522 0
$808$	54.7031	1.92445
$809$	−21.1450	−0.743419	−0.371710	−	0.928349i	$-0.621228\pi$
$809$	−21.1450	−0.743419	−0.371710	+	0.928349i	$0.621228\pi$
$810$	−52.0207	−1.82782
$811$	17.6938	0.621315	0.310657	−	0.950522i	$-0.399451\pi$
$811$	17.6938	0.621315	0.310657	+	0.950522i	$0.399451\pi$
$812$	23.8411	0.836658
$813$	−1.30122	−0.0456356
$814$	−24.9040	−0.872885
$815$	16.3366	0.572246
$816$	0.0183239	0.000641466 0
$817$	−1.07882	−0.0377431
$818$	62.9800	2.20204
$819$	0	0
$820$	33.3099	1.16323
$821$	−19.5009	−0.680586	−0.340293	−	0.940319i	$-0.610526\pi$
$821$	−19.5009	−0.680586	−0.340293	+	0.940319i	$0.610526\pi$
$822$	0.235601	0.00821754
$823$	12.4720	0.434745	0.217372	−	0.976089i	$-0.430251\pi$
$823$	12.4720	0.434745	0.217372	+	0.976089i	$0.430251\pi$
$824$	−54.6011	−1.90212
$825$	−0.101696	−0.00354059
$826$	−9.50906	−0.330863
$827$	8.85501	0.307919	0.153959	−	0.988077i	$-0.450797\pi$
$827$	8.85501	0.307919	0.153959	+	0.988077i	$0.450797\pi$
$828$	61.4885	2.13687
$829$	−31.6903	−1.10065	−0.550326	−	0.834950i	$-0.685496\pi$
$829$	−31.6903	−1.10065	−0.550326	+	0.834950i	$0.685496\pi$
$830$	38.6939	1.34309
$831$	−1.63643	−0.0567670
$832$	0	0
$833$	−3.06871	−0.106324
$834$	−2.19160	−0.0758889
$835$	60.1659	2.08213
$836$	−0.544851	−0.0188441
$837$	0.312813	0.0108124
$838$	62.1562	2.14715
$839$	33.1834	1.14562	0.572809	−	0.819689i	$-0.305854\pi$
$839$	33.1834	1.14562	0.572809	+	0.819689i	$0.305854\pi$
$840$	0.538726	0.0185878
$841$	33.5188	1.15582
$842$	62.3755	2.14960
$843$	1.33272	0.0459013
$844$	−61.5363	−2.11817
$845$	0	0
$846$	−86.2216	−2.96436
$847$	−0.902363	−0.0310056
$848$	3.98213	0.136747
$849$	0.0405670	0.00139226
$850$	1.52328	0.0522481
$851$	−66.2248	−2.27016
$852$	0.173486	0.00594353
$853$	−32.0263	−1.09656	−0.548279	−	0.836295i	$-0.684717\pi$
$853$	−32.0263	−1.09656	−0.548279	+	0.836295i	$0.684717\pi$
$854$	19.7740	0.676653
$855$	1.22818	0.0420030
$856$	12.0504	0.411873
$857$	−14.7172	−0.502729	−0.251364	−	0.967893i	$-0.580879\pi$
$857$	−14.7172	−0.502729	−0.251364	+	0.967893i	$0.580879\pi$
$858$	0	0
$859$	−15.7605	−0.537742	−0.268871	−	0.963176i	$-0.586651\pi$
$859$	−15.7605	−0.537742	−0.268871	+	0.963176i	$0.586651\pi$
$860$	55.6163	1.89650
$861$	0.273703	0.00932776
$862$	−70.8551	−2.41333
$863$	10.8406	0.369019	0.184510	−	0.982831i	$-0.440930\pi$
$863$	10.8406	0.369019	0.184510	+	0.982831i	$0.440930\pi$
$864$	2.33336	0.0793824
$865$	49.6476	1.68807
$866$	−32.5715	−1.10683
$867$	−1.28243	−0.0435535
$868$	2.05571	0.0697753
$869$	−2.76069	−0.0936499
$870$	3.51889	0.119302
$871$	0	0
$872$	16.2201	0.549284
$873$	35.5967	1.20476
$874$	−2.31607	−0.0783422
$875$	−8.33430	−0.281751
$876$	−1.53391	−0.0518259
$877$	6.70212	0.226315	0.113157	−	0.993577i	$-0.463904\pi$
$877$	6.70212	0.226315	0.113157	+	0.993577i	$0.463904\pi$
$878$	−25.4472	−0.858801
$879$	−0.238975	−0.00806043
$880$	1.21392	0.0409213
$881$	3.84089	0.129403	0.0647014	−	0.997905i	$-0.479391\pi$
$881$	3.84089	0.129403	0.0647014	+	0.997905i	$0.479391\pi$
$882$	42.8050	1.44132
$883$	31.2986	1.05328	0.526641	−	0.850088i	$-0.323451\pi$
$883$	31.2986	1.05328	0.526641	+	0.850088i	$0.323451\pi$
$884$	0	0
$885$	−0.878002	−0.0295137
$886$	33.7384	1.13346
$887$	50.9535	1.71085	0.855426	−	0.517925i	$-0.173295\pi$
$887$	50.9535	1.71085	0.855426	+	0.517925i	$0.173295\pi$
$888$	2.55724	0.0858154
$889$	−15.3020	−0.513212
$890$	−30.6805	−1.02841
$891$	−8.94730	−0.299746
$892$	22.7804	0.762745
$893$	2.03166	0.0679870
$894$	2.23255	0.0746677
$895$	−40.8341	−1.36493
$896$	17.3468	0.579515
$897$	0	0
$898$	70.6250	2.35679
$899$	5.39071	0.179790
$900$	−13.2922	−0.443073
$901$	4.09393	0.136389
$902$	9.15823	0.304936
$903$	0.456992	0.0152077
$904$	13.3594	0.444327
$905$	9.51445	0.316271
$906$	3.70021	0.122931
$907$	30.9398	1.02734	0.513670	−	0.857988i	$-0.328286\pi$
$907$	30.9398	1.02734	0.513670	+	0.857988i	$0.328286\pi$
$908$	−68.0202	−2.25733
$909$	−52.8284	−1.75221
$910$	0	0
$911$	−25.7570	−0.853368	−0.426684	−	0.904401i	$-0.640318\pi$
$911$	−25.7570	−0.853368	−0.426684	+	0.904401i	$0.640318\pi$
$912$	0.00602273	0.000199433 0
$913$	6.65517	0.220254
$914$	17.8889	0.591712
$915$	1.82580	0.0603590
$916$	−39.1114	−1.29228
$917$	−15.6751	−0.517638
$918$	−0.526064	−0.0173627
$919$	23.2202	0.765965	0.382982	−	0.923756i	$-0.374897\pi$
$919$	23.2202	0.765965	0.382982	+	0.923756i	$0.374897\pi$
$920$	47.9349	1.58037
$921$	0.614931	0.0202627
$922$	−81.7664	−2.69283
$923$	0	0
$924$	0.230801	0.00759280
$925$	14.3161	0.470709
$926$	35.7423	1.17457
$927$	52.7299	1.73188
$928$	40.2107	1.31998
$929$	15.6703	0.514126	0.257063	−	0.966395i	$-0.417245\pi$
$929$	15.6703	0.514126	0.257063	+	0.966395i	$0.417245\pi$
$930$	0.303418	0.00994947
$931$	−1.00863	−0.0330564
$932$	74.1490	2.42883
$933$	−1.88422	−0.0616866
$934$	57.4971	1.88136
$935$	1.24801	0.0408141
$936$	0	0
$937$	−4.52095	−0.147693	−0.0738465	−	0.997270i	$-0.523527\pi$
$937$	−4.52095	−0.147693	−0.0738465	+	0.997270i	$0.523527\pi$
$938$	12.2315	0.399373
$939$	1.36935	0.0446871
$940$	−104.738	−3.41618
$941$	−37.5825	−1.22516	−0.612578	−	0.790410i	$-0.709867\pi$
$941$	−37.5825	−1.22516	−0.612578	+	0.790410i	$0.709867\pi$
$942$	−3.82175	−0.124519
$943$	24.3536	0.793062
$944$	2.20021	0.0716107
$945$	−1.04155	−0.0338815
$946$	15.2912	0.497159
$947$	28.8823	0.938550	0.469275	−	0.883052i	$-0.344515\pi$
$947$	28.8823	0.938550	0.469275	+	0.883052i	$0.344515\pi$
$948$	0.706112	0.0229335
$949$	0	0
$950$	0.500673	0.0162440
$951$	0.919898	0.0298297
$952$	−1.38791	−0.0449824
$953$	−35.6115	−1.15357	−0.576784	−	0.816897i	$-0.695693\pi$
$953$	−35.6115	−1.15357	−0.576784	+	0.816897i	$0.695693\pi$
$954$	−57.1058	−1.84887
$955$	44.6754	1.44566
$956$	−28.5850	−0.924505
$957$	0.605233	0.0195644
$958$	75.5003	2.43931
$959$	−1.20174	−0.0388063
$960$	2.44912	0.0790449
$961$	−30.5352	−0.985006
$962$	0	0
$963$	−11.6374	−0.375011
$964$	−4.55350	−0.146658
$965$	−23.3524	−0.751740
$966$	0.981097	0.0315663
$967$	33.1846	1.06715	0.533573	−	0.845754i	$-0.320849\pi$
$967$	33.1846	1.06715	0.533573	+	0.845754i	$0.320849\pi$
$968$	3.10039	0.0996503
$969$	0.00619183	0.000198910 0
$970$	69.1227	2.21940
$971$	45.5720	1.46247	0.731237	−	0.682124i	$-0.238943\pi$
$971$	45.5720	1.46247	0.731237	+	0.682124i	$0.238943\pi$
$972$	6.88792	0.220930
$973$	11.1788	0.358376
$974$	−8.19638	−0.262629
$975$	0	0
$976$	−4.57531	−0.146452
$977$	−17.8770	−0.571936	−0.285968	−	0.958239i	$-0.592315\pi$
$977$	−17.8770	−0.571936	−0.285968	+	0.958239i	$0.592315\pi$
$978$	−1.14883	−0.0367356
$979$	−5.27690	−0.168651
$980$	51.9977	1.66100
$981$	−15.6643	−0.500122
$982$	−38.7916	−1.23789
$983$	−18.0628	−0.576114	−0.288057	−	0.957613i	$-0.593009\pi$
$983$	−18.0628	−0.576114	−0.288057	+	0.957613i	$0.593009\pi$
$984$	−0.940403	−0.0299789
$985$	−4.57230	−0.145686
$986$	−9.06567	−0.288710
$987$	−0.860620	−0.0273938
$988$	0	0
$989$	40.6623	1.29299
$990$	−17.4083	−0.553272
$991$	−13.1386	−0.417361	−0.208681	−	0.977984i	$-0.566917\pi$
$991$	−13.1386	−0.417361	−0.208681	+	0.977984i	$0.566917\pi$
$992$	3.46719	0.110083
$993$	1.11042	0.0352381
$994$	−1.41456	−0.0448670
$995$	18.2122	0.577366
$996$	−1.70222	−0.0539369
$997$	−27.3507	−0.866205	−0.433103	−	0.901345i	$-0.642581\pi$
$997$	−27.3507	−0.866205	−0.433103	+	0.901345i	$0.642581\pi$
$998$	−0.437743	−0.0138565
$999$	−4.94405	−0.156423

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.r.1.9	yes	9
13.12	even	2		1859.2.a.q.1.1	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.q.1.1	✓	9	13.12	even	2
1859.2.a.r.1.9	yes	9	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+2.31116 q^{2} +0.0765450 q^{3} +3.34148 q^{4} -2.51567 q^{5} +0.176908 q^{6} -0.902363 q^{7} +3.10039 q^{8} -2.99414 q^{9} +O(q^{10})\)	\(q+2.31116 q^{2} +0.0765450 q^{3} +3.34148 q^{4} -2.51567 q^{5} +0.176908 q^{6} -0.902363 q^{7} +3.10039 q^{8} -2.99414 q^{9} -5.81412 q^{10} -1.00000 q^{11} +0.255774 q^{12} -2.08551 q^{14} -0.192562 q^{15} +0.482546 q^{16} +0.496094 q^{17} -6.91995 q^{18} +0.163057 q^{19} -8.40605 q^{20} -0.0690714 q^{21} -2.31116 q^{22} -6.14586 q^{23} +0.237319 q^{24} +1.32857 q^{25} -0.458822 q^{27} -3.01523 q^{28} -7.90688 q^{29} -0.445042 q^{30} -0.681774 q^{31} -5.08554 q^{32} -0.0765450 q^{33} +1.14655 q^{34} +2.27004 q^{35} -10.0049 q^{36} +10.7755 q^{37} +0.376851 q^{38} -7.79954 q^{40} -3.96260 q^{41} -0.159635 q^{42} -6.61622 q^{43} -3.34148 q^{44} +7.53226 q^{45} -14.2041 q^{46} +12.4599 q^{47} +0.0369365 q^{48} -6.18574 q^{49} +3.07055 q^{50} +0.0379735 q^{51} +8.25234 q^{53} -1.06041 q^{54} +2.51567 q^{55} -2.79768 q^{56} +0.0124812 q^{57} -18.2741 q^{58} +4.55959 q^{59} -0.643442 q^{60} -9.48162 q^{61} -1.57569 q^{62} +2.70180 q^{63} -12.7186 q^{64} -0.176908 q^{66} -5.86499 q^{67} +1.65769 q^{68} -0.470435 q^{69} +5.24645 q^{70} +0.678278 q^{71} -9.28300 q^{72} -5.99712 q^{73} +24.9040 q^{74} +0.101696 q^{75} +0.544851 q^{76} +0.902363 q^{77} +2.76069 q^{79} -1.21392 q^{80} +8.94730 q^{81} -9.15823 q^{82} -6.65517 q^{83} -0.230801 q^{84} -1.24801 q^{85} -15.2912 q^{86} -0.605233 q^{87} -3.10039 q^{88} +5.27690 q^{89} +17.4083 q^{90} -20.5363 q^{92} -0.0521865 q^{93} +28.7968 q^{94} -0.410196 q^{95} -0.389273 q^{96} -11.8888 q^{97} -14.2963 q^{98} +2.99414 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 5 q^{3} + 2 q^{4} + 4 q^{5} + 11 q^{6} - q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) \) 9 * q - 5 * q^3 + 2 * q^4 + 4 * q^5 + 11 * q^6 - q^7 - 3 * q^8 + 2 * q^9	\( 9 q - 5 q^{3} + 2 q^{4} + 4 q^{5} + 11 q^{6} - q^{7} - 3 q^{8} + 2 q^{9} - 8 q^{10} - 9 q^{11} - 9 q^{12} - 3 q^{15} - 8 q^{16} - 8 q^{17} - 27 q^{18} + q^{19} - 12 q^{20} - 17 q^{21} + 6 q^{24} - 15 q^{25} - 23 q^{27} - 11 q^{28} - 22 q^{29} - 3 q^{30} + 6 q^{31} + 19 q^{32} + 5 q^{33} - 10 q^{34} - 15 q^{35} + 7 q^{36} + 15 q^{37} + q^{38} - 3 q^{40} - 10 q^{41} + 2 q^{42} - 19 q^{43} - 2 q^{44} + 2 q^{45} - 19 q^{46} + 2 q^{47} + 6 q^{48} - 20 q^{49} + 17 q^{50} - 2 q^{51} - 5 q^{53} + 27 q^{54} - 4 q^{55} - 16 q^{56} + 32 q^{57} + 11 q^{58} + 11 q^{59} + 6 q^{60} - 68 q^{61} - 21 q^{62} + 29 q^{63} - 23 q^{64} - 11 q^{66} - 5 q^{67} + 16 q^{68} - 34 q^{69} + 5 q^{70} + 34 q^{71} - 13 q^{72} - 26 q^{73} + q^{74} + 10 q^{75} + 11 q^{76} + q^{77} - 32 q^{79} - 8 q^{80} + 13 q^{81} - 42 q^{82} - 8 q^{83} + 13 q^{84} - 23 q^{85} - 30 q^{86} + 10 q^{87} + 3 q^{88} + 37 q^{89} + 21 q^{90} - 12 q^{92} - 20 q^{93} - 12 q^{94} - 4 q^{95} - 60 q^{96} - 3 q^{97} + 9 q^{98} - 2 q^{99}+O(q^{100}) \) 9 * q - 5 * q^3 + 2 * q^4 + 4 * q^5 + 11 * q^6 - q^7 - 3 * q^8 + 2 * q^9 - 8 * q^10 - 9 * q^11 - 9 * q^12 - 3 * q^15 - 8 * q^16 - 8 * q^17 - 27 * q^18 + q^19 - 12 * q^20 - 17 * q^21 + 6 * q^24 - 15 * q^25 - 23 * q^27 - 11 * q^28 - 22 * q^29 - 3 * q^30 + 6 * q^31 + 19 * q^32 + 5 * q^33 - 10 * q^34 - 15 * q^35 + 7 * q^36 + 15 * q^37 + q^38 - 3 * q^40 - 10 * q^41 + 2 * q^42 - 19 * q^43 - 2 * q^44 + 2 * q^45 - 19 * q^46 + 2 * q^47 + 6 * q^48 - 20 * q^49 + 17 * q^50 - 2 * q^51 - 5 * q^53 + 27 * q^54 - 4 * q^55 - 16 * q^56 + 32 * q^57 + 11 * q^58 + 11 * q^59 + 6 * q^60 - 68 * q^61 - 21 * q^62 + 29 * q^63 - 23 * q^64 - 11 * q^66 - 5 * q^67 + 16 * q^68 - 34 * q^69 + 5 * q^70 + 34 * q^71 - 13 * q^72 - 26 * q^73 + q^74 + 10 * q^75 + 11 * q^76 + q^77 - 32 * q^79 - 8 * q^80 + 13 * q^81 - 42 * q^82 - 8 * q^83 + 13 * q^84 - 23 * q^85 - 30 * q^86 + 10 * q^87 + 3 * q^88 + 37 * q^89 + 21 * q^90 - 12 * q^92 - 20 * q^93 - 12 * q^94 - 4 * q^95 - 60 * q^96 - 3 * q^97 + 9 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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