LMFDB - Embedded newform 1859.2.a.e.1.1

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:	$3$
Coefficient field:	3.3.756.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 6x - 2 $ x^3 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.26180$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.26180 q^{3} -1.00000 q^{4} -2.11575 q^{5} +2.26180 q^{6} -3.37755 q^{7} +3.00000 q^{8} +2.11575 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.26180 q^{3} -1.00000 q^{4} -2.11575 q^{5} +2.26180 q^{6} -3.37755 q^{7} +3.00000 q^{8} +2.11575 q^{9} +2.11575 q^{10} -1.00000 q^{11} +2.26180 q^{12} +3.37755 q^{14} +4.78541 q^{15} -1.00000 q^{16} -2.14605 q^{17} -2.11575 q^{18} -3.14605 q^{19} +2.11575 q^{20} +7.63935 q^{21} +1.00000 q^{22} +4.52360 q^{23} -6.78541 q^{24} -0.523604 q^{25} +2.00000 q^{27} +3.37755 q^{28} +3.49330 q^{29} -4.78541 q^{30} +9.27871 q^{31} -5.00000 q^{32} +2.26180 q^{33} +2.14605 q^{34} +7.14605 q^{35} -2.11575 q^{36} +9.16296 q^{37} +3.14605 q^{38} -6.34725 q^{40} -10.0169 q^{41} -7.63935 q^{42} +2.52360 q^{43} +1.00000 q^{44} -4.47640 q^{45} -4.52360 q^{46} +1.96970 q^{47} +2.26180 q^{48} +4.40786 q^{49} +0.523604 q^{50} +4.85395 q^{51} +7.75510 q^{53} -2.00000 q^{54} +2.11575 q^{55} -10.1327 q^{56} +7.11575 q^{57} -3.49330 q^{58} +6.03030 q^{59} -4.78541 q^{60} +9.78541 q^{61} -9.27871 q^{62} -7.14605 q^{63} +7.00000 q^{64} -2.26180 q^{66} -4.03030 q^{67} +2.14605 q^{68} -10.2315 q^{69} -7.14605 q^{70} -6.00000 q^{71} +6.34725 q^{72} -10.8405 q^{73} -9.16296 q^{74} +1.18429 q^{75} +3.14605 q^{76} +3.37755 q^{77} +1.66966 q^{79} +2.11575 q^{80} -10.8709 q^{81} +10.0169 q^{82} -5.66966 q^{83} -7.63935 q^{84} +4.54051 q^{85} -2.52360 q^{86} -7.90116 q^{87} -3.00000 q^{88} -9.34725 q^{89} +4.47640 q^{90} -4.52360 q^{92} -20.9866 q^{93} -1.96970 q^{94} +6.65626 q^{95} +11.3090 q^{96} -11.6394 q^{97} -4.40786 q^{98} -2.11575 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{4} - 3 q^{5} + 9 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^4 - 3 * q^5 + 9 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} - 3 q^{4} - 3 q^{5} + 9 q^{8} + 3 q^{9} + 3 q^{10} - 3 q^{11} - 6 q^{15} - 3 q^{16} - 3 q^{17} - 3 q^{18} - 6 q^{19} + 3 q^{20} + 6 q^{21} + 3 q^{22} + 12 q^{25} + 6 q^{27} - 3 q^{29} + 6 q^{30} - 6 q^{31} - 15 q^{32} + 3 q^{34} + 18 q^{35} - 3 q^{36} - 3 q^{37} + 6 q^{38} - 9 q^{40} - 3 q^{41} - 6 q^{42} - 6 q^{43} + 3 q^{44} - 27 q^{45} + 6 q^{47} + 3 q^{49} - 12 q^{50} + 18 q^{51} + 3 q^{53} - 6 q^{54} + 3 q^{55} + 18 q^{57} + 3 q^{58} + 18 q^{59} + 6 q^{60} + 9 q^{61} + 6 q^{62} - 18 q^{63} + 21 q^{64} - 12 q^{67} + 3 q^{68} - 24 q^{69} - 18 q^{70} - 18 q^{71} + 9 q^{72} - 9 q^{73} + 3 q^{74} + 24 q^{75} + 6 q^{76} - 12 q^{79} + 3 q^{80} - 9 q^{81} + 3 q^{82} - 6 q^{84} - 27 q^{85} + 6 q^{86} - 9 q^{88} - 18 q^{89} + 27 q^{90} - 36 q^{93} - 6 q^{94} - 24 q^{95} - 18 q^{97} - 3 q^{98} - 3 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 3 * q^4 - 3 * q^5 + 9 * q^8 + 3 * q^9 + 3 * q^10 - 3 * q^11 - 6 * q^15 - 3 * q^16 - 3 * q^17 - 3 * q^18 - 6 * q^19 + 3 * q^20 + 6 * q^21 + 3 * q^22 + 12 * q^25 + 6 * q^27 - 3 * q^29 + 6 * q^30 - 6 * q^31 - 15 * q^32 + 3 * q^34 + 18 * q^35 - 3 * q^36 - 3 * q^37 + 6 * q^38 - 9 * q^40 - 3 * q^41 - 6 * q^42 - 6 * q^43 + 3 * q^44 - 27 * q^45 + 6 * q^47 + 3 * q^49 - 12 * q^50 + 18 * q^51 + 3 * q^53 - 6 * q^54 + 3 * q^55 + 18 * q^57 + 3 * q^58 + 18 * q^59 + 6 * q^60 + 9 * q^61 + 6 * q^62 - 18 * q^63 + 21 * q^64 - 12 * q^67 + 3 * q^68 - 24 * q^69 - 18 * q^70 - 18 * q^71 + 9 * q^72 - 9 * q^73 + 3 * q^74 + 24 * q^75 + 6 * q^76 - 12 * q^79 + 3 * q^80 - 9 * q^81 + 3 * q^82 - 6 * q^84 - 27 * q^85 + 6 * q^86 - 9 * q^88 - 18 * q^89 + 27 * q^90 - 36 * q^93 - 6 * q^94 - 24 * q^95 - 18 * q^97 - 3 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	−2.26180	−1.30585	−0.652926	−	0.757422i	$-0.726459\pi$
$3$	−2.26180	−1.30585	−0.652926	+	0.757422i	$0.726459\pi$
$4$	−1.00000	−0.500000
$5$	−2.11575	−0.946192	−0.473096	−	0.881011i	$-0.656864\pi$
$5$	−2.11575	−0.946192	−0.473096	+	0.881011i	$0.656864\pi$
$6$	2.26180	0.923377
$7$	−3.37755	−1.27659	−0.638297	−	0.769790i	$-0.720361\pi$
$7$	−3.37755	−1.27659	−0.638297	+	0.769790i	$0.720361\pi$
$8$	3.00000	1.06066
$9$	2.11575	0.705250
$10$	2.11575	0.669059
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.26180	0.652926
$13$	0	0
$13$	0	0
$14$	3.37755	0.902689
$15$	4.78541	1.23559
$16$	−1.00000	−0.250000
$17$	−2.14605	−0.520494	−0.260247	−	0.965542i	$-0.583804\pi$
$17$	−2.14605	−0.520494	−0.260247	+	0.965542i	$0.583804\pi$
$18$	−2.11575	−0.498687
$19$	−3.14605	−0.721754	−0.360877	−	0.932613i	$-0.617523\pi$
$19$	−3.14605	−0.721754	−0.360877	+	0.932613i	$0.617523\pi$
$20$	2.11575	0.473096
$21$	7.63935	1.66704
$22$	1.00000	0.213201
$23$	4.52360	0.943237	0.471618	−	0.881803i	$-0.343670\pi$
$23$	4.52360	0.943237	0.471618	+	0.881803i	$0.343670\pi$
$24$	−6.78541	−1.38507
$25$	−0.523604	−0.104721
$26$	0	0
$27$	2.00000	0.384900
$28$	3.37755	0.638297
$29$	3.49330	0.648690	0.324345	−	0.945939i	$-0.394856\pi$
$29$	3.49330	0.648690	0.324345	+	0.945939i	$0.394856\pi$
$30$	−4.78541	−0.873692
$31$	9.27871	1.66651	0.833253	−	0.552893i	$-0.186476\pi$
$31$	9.27871	1.66651	0.833253	+	0.552893i	$0.186476\pi$
$32$	−5.00000	−0.883883
$33$	2.26180	0.393729
$34$	2.14605	0.368045
$35$	7.14605	1.20790
$36$	−2.11575	−0.352625
$37$	9.16296	1.50638	0.753191	−	0.657802i	$-0.228514\pi$
$37$	9.16296	1.50638	0.753191	+	0.657802i	$0.228514\pi$
$38$	3.14605	0.510357
$39$	0	0
$40$	−6.34725	−1.00359
$41$	−10.0169	−1.56438	−0.782189	−	0.623041i	$-0.785897\pi$
$41$	−10.0169	−1.56438	−0.782189	+	0.623041i	$0.785897\pi$
$42$	−7.63935	−1.17878
$43$	2.52360	0.384846	0.192423	−	0.981312i	$-0.438365\pi$
$43$	2.52360	0.384846	0.192423	+	0.981312i	$0.438365\pi$
$44$	1.00000	0.150756
$45$	−4.47640	−0.667302
$46$	−4.52360	−0.666969
$47$	1.96970	0.287310	0.143655	−	0.989628i	$-0.454114\pi$
$47$	1.96970	0.287310	0.143655	+	0.989628i	$0.454114\pi$
$48$	2.26180	0.326463
$49$	4.40786	0.629694
$50$	0.523604	0.0740489
$51$	4.85395	0.679689
$52$	0	0
$53$	7.75510	1.06525	0.532623	−	0.846353i	$-0.321206\pi$
$53$	7.75510	1.06525	0.532623	+	0.846353i	$0.321206\pi$
$54$	−2.00000	−0.272166
$55$	2.11575	0.285288
$56$	−10.1327	−1.35403
$57$	7.11575	0.942504
$58$	−3.49330	−0.458693
$59$	6.03030	0.785079	0.392539	−	0.919735i	$-0.371597\pi$
$59$	6.03030	0.785079	0.392539	+	0.919735i	$0.371597\pi$
$60$	−4.78541	−0.617793
$61$	9.78541	1.25289	0.626446	−	0.779464i	$-0.284509\pi$
$61$	9.78541	1.25289	0.626446	+	0.779464i	$0.284509\pi$
$62$	−9.27871	−1.17840
$63$	−7.14605	−0.900318
$64$	7.00000	0.875000
$65$	0	0
$66$	−2.26180	−0.278409
$67$	−4.03030	−0.492380	−0.246190	−	0.969222i	$-0.579179\pi$
$67$	−4.03030	−0.492380	−0.246190	+	0.969222i	$0.579179\pi$
$68$	2.14605	0.260247
$69$	−10.2315	−1.23173
$70$	−7.14605	−0.854117
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	6.34725	0.748030
$73$	−10.8405	−1.26879	−0.634395	−	0.773009i	$-0.718751\pi$
$73$	−10.8405	−1.26879	−0.634395	+	0.773009i	$0.718751\pi$
$74$	−9.16296	−1.06517
$75$	1.18429	0.136750
$76$	3.14605	0.360877
$77$	3.37755	0.384908
$78$	0	0
$79$	1.66966	0.187851	0.0939256	−	0.995579i	$-0.470058\pi$
$79$	1.66966	0.187851	0.0939256	+	0.995579i	$0.470058\pi$
$80$	2.11575	0.236548
$81$	−10.8709	−1.20787
$82$	10.0169	1.10618
$83$	−5.66966	−0.622326	−0.311163	−	0.950357i	$-0.600718\pi$
$83$	−5.66966	−0.622326	−0.311163	+	0.950357i	$0.600718\pi$
$84$	−7.63935	−0.833522
$85$	4.54051	0.492487
$86$	−2.52360	−0.272127
$87$	−7.90116	−0.847093
$88$	−3.00000	−0.319801
$89$	−9.34725	−0.990806	−0.495403	−	0.868663i	$-0.664980\pi$
$89$	−9.34725	−0.990806	−0.495403	+	0.868663i	$0.664980\pi$
$90$	4.47640	0.471854
$91$	0	0
$92$	−4.52360	−0.471618
$93$	−20.9866	−2.17621
$94$	−1.96970	−0.203159
$95$	6.65626	0.682918
$96$	11.3090	1.15422
$97$	−11.6394	−1.18180	−0.590899	−	0.806746i	$-0.701227\pi$
$97$	−11.6394	−1.18180	−0.590899	+	0.806746i	$0.701227\pi$
$98$	−4.40786	−0.445261
$99$	−2.11575	−0.212641
$100$	0.523604	0.0523604
$101$	0.901156	0.0896684	0.0448342	−	0.998994i	$-0.485724\pi$
$101$	0.901156	0.0896684	0.0448342	+	0.998994i	$0.485724\pi$
$102$	−4.85395	−0.480612
$103$	13.0472	1.28558	0.642790	−	0.766043i	$-0.277777\pi$
$103$	13.0472	1.28558	0.642790	+	0.766043i	$0.277777\pi$
$104$	0	0
$105$	−16.1630	−1.57734
$106$	−7.75510	−0.753242
$107$	−13.6091	−1.31564	−0.657818	−	0.753177i	$-0.728521\pi$
$107$	−13.6091	−1.31564	−0.657818	+	0.753177i	$0.728521\pi$
$108$	−2.00000	−0.192450
$109$	−18.6866	−1.78985	−0.894924	−	0.446218i	$-0.852770\pi$
$109$	−18.6866	−1.78985	−0.894924	+	0.446218i	$0.852770\pi$
$110$	−2.11575	−0.201729
$111$	−20.7248	−1.96711
$112$	3.37755	0.319149
$113$	12.6394	1.18901	0.594505	−	0.804092i	$-0.297348\pi$
$113$	12.6394	1.18901	0.594505	+	0.804092i	$0.297348\pi$
$114$	−7.11575	−0.666451
$115$	−9.57081	−0.892483
$116$	−3.49330	−0.324345
$117$	0	0
$118$	−6.03030	−0.555134
$119$	7.24840	0.664460
$120$	14.3562	1.31054
$121$	1.00000	0.0909091
$122$	−9.78541	−0.885929
$123$	22.6563	2.04285
$124$	−9.27871	−0.833253
$125$	11.6866	1.04528
$126$	7.14605	0.636621
$127$	11.5102	1.02137	0.510683	−	0.859769i	$-0.329393\pi$
$127$	11.5102	1.02137	0.510683	+	0.859769i	$0.329393\pi$
$128$	3.00000	0.265165
$129$	−5.70789	−0.502552
$130$	0	0
$131$	13.6091	1.18903	0.594514	−	0.804085i	$-0.297344\pi$
$131$	13.6091	1.18903	0.594514	+	0.804085i	$0.297344\pi$
$132$	−2.26180	−0.196865
$133$	10.6260	0.921387
$134$	4.03030	0.348165
$135$	−4.23150	−0.364189
$136$	−6.43816	−0.552068
$137$	15.1024	1.29028	0.645140	−	0.764064i	$-0.276799\pi$
$137$	15.1024	1.29028	0.645140	+	0.764064i	$0.276799\pi$
$138$	10.2315	0.870963
$139$	−15.2787	−1.29592	−0.647962	−	0.761673i	$-0.724378\pi$
$139$	−15.2787	−1.29592	−0.647962	+	0.761673i	$0.724378\pi$
$140$	−7.14605	−0.603952
$141$	−4.45506	−0.375184
$142$	6.00000	0.503509
$143$	0	0
$144$	−2.11575	−0.176312
$145$	−7.39095	−0.613785
$146$	10.8405	0.897170
$147$	−9.96970	−0.822287
$148$	−9.16296	−0.753191
$149$	−4.37755	−0.358623	−0.179312	−	0.983792i	$-0.557387\pi$
$149$	−4.37755	−0.358623	−0.179312	+	0.983792i	$0.557387\pi$
$150$	−1.18429	−0.0966969
$151$	−2.29211	−0.186529	−0.0932645	−	0.995641i	$-0.529730\pi$
$151$	−2.29211	−0.186529	−0.0932645	+	0.995641i	$0.529730\pi$
$152$	−9.43816	−0.765536
$153$	−4.54051	−0.367078
$154$	−3.37755	−0.272171
$155$	−19.6314	−1.57683
$156$	0	0
$157$	−24.0472	−1.91918	−0.959588	−	0.281408i	$-0.909198\pi$
$157$	−24.0472	−1.91918	−0.959588	+	0.281408i	$0.909198\pi$
$158$	−1.66966	−0.132831
$159$	−17.5405	−1.39105
$160$	10.5787	0.836323
$161$	−15.2787	−1.20413
$162$	10.8709	0.854095
$163$	6.55391	0.513342	0.256671	−	0.966499i	$-0.417374\pi$
$163$	6.55391	0.513342	0.256671	+	0.966499i	$0.417374\pi$
$164$	10.0169	0.782189
$165$	−4.78541	−0.372543
$166$	5.66966	0.440051
$167$	18.3259	1.41810	0.709051	−	0.705157i	$-0.249124\pi$
$167$	18.3259	1.41810	0.709051	+	0.705157i	$0.249124\pi$
$168$	22.9181	1.76817
$169$	0	0
$170$	−4.54051	−0.348241
$171$	−6.65626	−0.509017
$172$	−2.52360	−0.192423
$173$	14.6866	1.11660	0.558299	−	0.829640i	$-0.311454\pi$
$173$	14.6866	1.11660	0.558299	+	0.829640i	$0.311454\pi$
$174$	7.90116	0.598985
$175$	1.76850	0.133686
$176$	1.00000	0.0753778
$177$	−13.6394	−1.02520
$178$	9.34725	0.700606
$179$	−6.49330	−0.485332	−0.242666	−	0.970110i	$-0.578022\pi$
$179$	−6.49330	−0.485332	−0.242666	+	0.970110i	$0.578022\pi$
$180$	4.47640	0.333651
$181$	−17.1630	−1.27571	−0.637856	−	0.770155i	$-0.720179\pi$
$181$	−17.1630	−1.27571	−0.637856	+	0.770155i	$0.720179\pi$
$182$	0	0
$183$	−22.1327	−1.63609
$184$	13.5708	1.00045
$185$	−19.3865	−1.42533
$186$	20.9866	1.53881
$187$	2.14605	0.156935
$188$	−1.96970	−0.143655
$189$	−6.75510	−0.491361
$190$	−6.65626	−0.482896
$191$	17.9697	1.30024	0.650121	−	0.759831i	$-0.274718\pi$
$191$	17.9697	1.30024	0.650121	+	0.759831i	$0.274718\pi$
$192$	−15.8326	−1.14262
$193$	2.96970	0.213763	0.106882	−	0.994272i	$-0.465913\pi$
$193$	2.96970	0.213763	0.106882	+	0.994272i	$0.465913\pi$
$194$	11.6394	0.835657
$195$	0	0
$196$	−4.40786	−0.314847
$197$	−12.2315	−0.871458	−0.435729	−	0.900078i	$-0.643509\pi$
$197$	−12.2315	−0.871458	−0.435729	+	0.900078i	$0.643509\pi$
$198$	2.11575	0.150360
$199$	−0.201195	−0.0142624	−0.00713118	−	0.999975i	$-0.502270\pi$
$199$	−0.201195	−0.0142624	−0.00713118	+	0.999975i	$0.502270\pi$
$200$	−1.57081	−0.111073
$201$	9.11575	0.642975
$202$	−0.901156	−0.0634051
$203$	−11.7988	−0.828114
$204$	−4.85395	−0.339844
$205$	21.1933	1.48020
$206$	−13.0472	−0.909042
$207$	9.57081	0.665218
$208$	0	0
$209$	3.14605	0.217617
$210$	16.1630	1.11535
$211$	11.6697	0.803372	0.401686	−	0.915777i	$-0.368424\pi$
$211$	11.6697	0.803372	0.401686	+	0.915777i	$0.368424\pi$
$212$	−7.75510	−0.532623
$213$	13.5708	0.929857
$214$	13.6091	0.930296
$215$	−5.33931	−0.364138
$216$	6.00000	0.408248
$217$	−31.3393	−2.12745
$218$	18.6866	1.26561
$219$	24.5192	1.65685
$220$	−2.11575	−0.142644
$221$	0	0
$222$	20.7248	1.39096
$223$	7.50670	0.502686	0.251343	−	0.967898i	$-0.419128\pi$
$223$	7.50670	0.502686	0.251343	+	0.967898i	$0.419128\pi$
$224$	16.8878	1.12836
$225$	−1.10782	−0.0738544
$226$	−12.6394	−0.840757
$227$	3.47640	0.230736	0.115368	−	0.993323i	$-0.463195\pi$
$227$	3.47640	0.230736	0.115368	+	0.993323i	$0.463195\pi$
$228$	−7.11575	−0.471252
$229$	−13.4079	−0.886016	−0.443008	−	0.896518i	$-0.646089\pi$
$229$	−13.4079	−0.886016	−0.443008	+	0.896518i	$0.646089\pi$
$230$	9.57081	0.631081
$231$	−7.63935	−0.502633
$232$	10.4799	0.688039
$233$	0.292106	0.0191365	0.00956824	−	0.999954i	$-0.496954\pi$
$233$	0.292106	0.0191365	0.00956824	+	0.999954i	$0.496954\pi$
$234$	0	0
$235$	−4.16738	−0.271850
$236$	−6.03030	−0.392539
$237$	−3.77643	−0.245306
$238$	−7.24840	−0.469844
$239$	21.8023	1.41027	0.705137	−	0.709071i	$-0.250885\pi$
$239$	21.8023	1.41027	0.705137	+	0.709071i	$0.250885\pi$
$240$	−4.78541	−0.308897
$241$	2.54844	0.164160	0.0820798	−	0.996626i	$-0.473844\pi$
$241$	2.54844	0.164160	0.0820798	+	0.996626i	$0.473844\pi$
$242$	−1.00000	−0.0642824
$243$	18.5877	1.19240
$244$	−9.78541	−0.626446
$245$	−9.32592	−0.595811
$246$	−22.6563	−1.44451
$247$	0	0
$248$	27.8361	1.76760
$249$	12.8236	0.812665
$250$	−11.6866	−0.739123
$251$	−26.8192	−1.69281	−0.846407	−	0.532537i	$-0.821239\pi$
$251$	−26.8192	−1.69281	−0.846407	+	0.532537i	$0.821239\pi$
$252$	7.14605	0.450159
$253$	−4.52360	−0.284397
$254$	−11.5102	−0.722215
$255$	−10.2697	−0.643116
$256$	−17.0000	−1.06250
$257$	3.06854	0.191410	0.0957051	−	0.995410i	$-0.469489\pi$
$257$	3.06854	0.191410	0.0957051	+	0.995410i	$0.469489\pi$
$258$	5.70789	0.355358
$259$	−30.9484	−1.92304
$260$	0	0
$261$	7.39095	0.457488
$262$	−13.6091	−0.840770
$263$	2.29211	0.141337	0.0706686	−	0.997500i	$-0.477487\pi$
$263$	2.29211	0.141337	0.0706686	+	0.997500i	$0.477487\pi$
$264$	6.78541	0.417613
$265$	−16.4079	−1.00793
$266$	−10.6260	−0.651519
$267$	21.1416	1.29385
$268$	4.03030	0.246190
$269$	11.2449	0.685613	0.342807	−	0.939406i	$-0.388622\pi$
$269$	11.2449	0.685613	0.342807	+	0.939406i	$0.388622\pi$
$270$	4.23150	0.257521
$271$	4.29211	0.260727	0.130363	−	0.991466i	$-0.458386\pi$
$271$	4.29211	0.260727	0.130363	+	0.991466i	$0.458386\pi$
$272$	2.14605	0.130124
$273$	0	0
$274$	−15.1024	−0.912366
$275$	0.523604	0.0315745
$276$	10.2315	0.615864
$277$	−4.83262	−0.290364	−0.145182	−	0.989405i	$-0.546377\pi$
$277$	−4.83262	−0.290364	−0.145182	+	0.989405i	$0.546377\pi$
$278$	15.2787	0.916356
$279$	19.6314	1.17530
$280$	21.4382	1.28118
$281$	−3.78541	−0.225818	−0.112909	−	0.993605i	$-0.536017\pi$
$281$	−3.78541	−0.225818	−0.112909	+	0.993605i	$0.536017\pi$
$282$	4.45506	0.265295
$283$	−12.4248	−0.738575	−0.369288	−	0.929315i	$-0.620398\pi$
$283$	−12.4248	−0.738575	−0.369288	+	0.929315i	$0.620398\pi$
$284$	6.00000	0.356034
$285$	−15.0551	−0.891790
$286$	0	0
$287$	33.8326	1.99708
$288$	−10.5787	−0.623359
$289$	−12.3945	−0.729086
$290$	7.39095	0.434012
$291$	26.3259	1.54325
$292$	10.8405	0.634395
$293$	−16.9012	−0.987376	−0.493688	−	0.869639i	$-0.664352\pi$
$293$	−16.9012	−0.987376	−0.493688	+	0.869639i	$0.664352\pi$
$294$	9.96970	0.581445
$295$	−12.7586	−0.742835
$296$	27.4889	1.59776
$297$	−2.00000	−0.116052
$298$	4.37755	0.253585
$299$	0	0
$300$	−1.18429	−0.0683750
$301$	−8.52360	−0.491292
$302$	2.29211	0.131896
$303$	−2.03824	−0.117094
$304$	3.14605	0.180439
$305$	−20.7035	−1.18548
$306$	4.54051	0.259564
$307$	8.42476	0.480826	0.240413	−	0.970671i	$-0.422717\pi$
$307$	8.42476	0.480826	0.240413	+	0.970671i	$0.422717\pi$
$308$	−3.37755	−0.192454
$309$	−29.5102	−1.67878
$310$	19.6314	1.11499
$311$	−28.5877	−1.62106	−0.810530	−	0.585697i	$-0.800821\pi$
$311$	−28.5877	−1.62106	−0.810530	+	0.585697i	$0.800821\pi$
$312$	0	0
$313$	22.3945	1.26581	0.632905	−	0.774230i	$-0.281862\pi$
$313$	22.3945	1.26581	0.632905	+	0.774230i	$0.281862\pi$
$314$	24.0472	1.35706
$315$	15.1193	0.851874
$316$	−1.66966	−0.0939256
$317$	26.2708	1.47551	0.737757	−	0.675067i	$-0.235885\pi$
$317$	26.2708	1.47551	0.737757	+	0.675067i	$0.235885\pi$
$318$	17.5405	0.983623
$319$	−3.49330	−0.195587
$320$	−14.8102	−0.827918
$321$	30.7810	1.71803
$322$	15.2787	0.851449
$323$	6.75160	0.375669
$324$	10.8709	0.603936
$325$	0	0
$326$	−6.55391	−0.362987
$327$	42.2653	2.33728
$328$	−30.0507	−1.65927
$329$	−6.65275	−0.366778
$330$	4.78541	0.263428
$331$	8.29211	0.455775	0.227888	−	0.973687i	$-0.426818\pi$
$331$	8.29211	0.455775	0.227888	+	0.973687i	$0.426818\pi$
$332$	5.66966	0.311163
$333$	19.3865	1.06237
$334$	−18.3259	−1.00275
$335$	8.52711	0.465886
$336$	−7.63935	−0.416761
$337$	−0.0516349	−0.00281273	−0.00140637	−	0.999999i	$-0.500448\pi$
$337$	−0.0516349	−0.00281273	−0.00140637	+	0.999999i	$0.500448\pi$
$338$	0	0
$339$	−28.5877	−1.55267
$340$	−4.54051	−0.246244
$341$	−9.27871	−0.502470
$342$	6.65626	0.359929
$343$	8.75510	0.472731
$344$	7.57081	0.408191
$345$	21.6473	1.16545
$346$	−14.6866	−0.789555
$347$	−8.62245	−0.462877	−0.231439	−	0.972850i	$-0.574343\pi$
$347$	−8.62245	−0.462877	−0.231439	+	0.972850i	$0.574343\pi$
$348$	7.90116	0.423546
$349$	−30.0000	−1.60586	−0.802932	−	0.596071i	$-0.796728\pi$
$349$	−30.0000	−1.60586	−0.802932	+	0.596071i	$0.796728\pi$
$350$	−1.76850	−0.0945304
$351$	0	0
$352$	5.00000	0.266501
$353$	0.476396	0.0253560	0.0126780	−	0.999920i	$-0.495964\pi$
$353$	0.476396	0.0253560	0.0126780	+	0.999920i	$0.495964\pi$
$354$	13.6394	0.724923
$355$	12.6945	0.673754
$356$	9.34725	0.495403
$357$	−16.3945	−0.867687
$358$	6.49330	0.343182
$359$	10.2315	0.539998	0.269999	−	0.962861i	$-0.412977\pi$
$359$	10.2315	0.539998	0.269999	+	0.962861i	$0.412977\pi$
$360$	−13.4292	−0.707780
$361$	−9.10235	−0.479071
$362$	17.1630	0.902065
$363$	−2.26180	−0.118714
$364$	0	0
$365$	22.9359	1.20052
$366$	22.1327	1.15689
$367$	21.3393	1.11390	0.556952	−	0.830545i	$-0.311971\pi$
$367$	21.3393	1.11390	0.556952	+	0.830545i	$0.311971\pi$
$368$	−4.52360	−0.235809
$369$	−21.1933	−1.10328
$370$	19.3865	1.00786
$371$	−26.1933	−1.35989
$372$	20.9866	1.08810
$373$	21.2271	1.09910	0.549548	−	0.835462i	$-0.314800\pi$
$373$	21.2271	1.09910	0.549548	+	0.835462i	$0.314800\pi$
$374$	−2.14605	−0.110970
$375$	−26.4327	−1.36498
$376$	5.90909	0.304738
$377$	0	0
$378$	6.75510	0.347445
$379$	1.04721	0.0537915	0.0268958	−	0.999638i	$-0.491438\pi$
$379$	1.04721	0.0537915	0.0268958	+	0.999638i	$0.491438\pi$
$380$	−6.65626	−0.341459
$381$	−26.0338	−1.33375
$382$	−17.9697	−0.919410
$383$	28.9866	1.48115	0.740573	−	0.671976i	$-0.234554\pi$
$383$	28.9866	1.48115	0.740573	+	0.671976i	$0.234554\pi$
$384$	−6.78541	−0.346266
$385$	−7.14605	−0.364197
$386$	−2.96970	−0.151154
$387$	5.33931	0.271413
$388$	11.6394	0.590899
$389$	15.5653	0.789195	0.394597	−	0.918854i	$-0.370884\pi$
$389$	15.5653	0.789195	0.394597	+	0.918854i	$0.370884\pi$
$390$	0	0
$391$	−9.70789	−0.490949
$392$	13.2236	0.667891
$393$	−30.7810	−1.55270
$394$	12.2315	0.616214
$395$	−3.53258	−0.177743
$396$	2.11575	0.106320
$397$	−18.9787	−0.952512	−0.476256	−	0.879307i	$-0.658006\pi$
$397$	−18.9787	−0.952512	−0.476256	+	0.879307i	$0.658006\pi$
$398$	0.201195	0.0100850
$399$	−24.0338	−1.20320
$400$	0.523604	0.0261802
$401$	9.52360	0.475586	0.237793	−	0.971316i	$-0.423576\pi$
$401$	9.52360	0.475586	0.237793	+	0.971316i	$0.423576\pi$
$402$	−9.11575	−0.454652
$403$	0	0
$404$	−0.901156	−0.0448342
$405$	23.0000	1.14288
$406$	11.7988	0.585565
$407$	−9.16296	−0.454191
$408$	14.5618	0.720919
$409$	−9.91455	−0.490243	−0.245122	−	0.969492i	$-0.578828\pi$
$409$	−9.91455	−0.490243	−0.245122	+	0.969492i	$0.578828\pi$
$410$	−21.1933	−1.04666
$411$	−34.1585	−1.68492
$412$	−13.0472	−0.642790
$413$	−20.3677	−1.00223
$414$	−9.57081	−0.470380
$415$	11.9956	0.588840
$416$	0	0
$417$	34.5574	1.69228
$418$	−3.14605	−0.153878
$419$	7.01340	0.342627	0.171313	−	0.985217i	$-0.445199\pi$
$419$	7.01340	0.342627	0.171313	+	0.985217i	$0.445199\pi$
$420$	16.1630	0.788672
$421$	−33.9787	−1.65602	−0.828009	−	0.560714i	$-0.810527\pi$
$421$	−33.9787	−1.65602	−0.828009	+	0.560714i	$0.810527\pi$
$422$	−11.6697	−0.568070
$423$	4.16738	0.202625
$424$	23.2653	1.12986
$425$	1.12368	0.0545066
$426$	−13.5708	−0.657508
$427$	−33.0507	−1.59944
$428$	13.6091	0.657818
$429$	0	0
$430$	5.33931	0.257485
$431$	−7.86735	−0.378957	−0.189478	−	0.981885i	$-0.560680\pi$
$431$	−7.86735	−0.378957	−0.189478	+	0.981885i	$0.560680\pi$
$432$	−2.00000	−0.0962250
$433$	−13.6528	−0.656109	−0.328055	−	0.944659i	$-0.606393\pi$
$433$	−13.6528	−0.656109	−0.328055	+	0.944659i	$0.606393\pi$
$434$	31.3393	1.50434
$435$	16.7169	0.801512
$436$	18.6866	0.894924
$437$	−14.2315	−0.680785
$438$	−24.5192	−1.17157
$439$	−8.33034	−0.397586	−0.198793	−	0.980042i	$-0.563702\pi$
$439$	−8.33034	−0.397586	−0.198793	+	0.980042i	$0.563702\pi$
$440$	6.34725	0.302593
$441$	9.32592	0.444091
$442$	0	0
$443$	−25.2484	−1.19959	−0.599794	−	0.800154i	$-0.704751\pi$
$443$	−25.2484	−1.19959	−0.599794	+	0.800154i	$0.704751\pi$
$444$	20.7248	0.983555
$445$	19.7764	0.937493
$446$	−7.50670	−0.355452
$447$	9.90116	0.468309
$448$	−23.6429	−1.11702
$449$	37.2708	1.75892	0.879458	−	0.475976i	$-0.157905\pi$
$449$	37.2708	1.75892	0.879458	+	0.475976i	$0.157905\pi$
$450$	1.10782	0.0522229
$451$	10.0169	0.471678
$452$	−12.6394	−0.594505
$453$	5.18429	0.243579
$454$	−3.47640	−0.163155
$455$	0	0
$456$	21.3472	0.999676
$457$	3.09091	0.144587	0.0722933	−	0.997383i	$-0.476968\pi$
$457$	3.09091	0.144587	0.0722933	+	0.997383i	$0.476968\pi$
$458$	13.4079	0.626508
$459$	−4.29211	−0.200338
$460$	9.57081	0.446241
$461$	22.4799	1.04699	0.523497	−	0.852028i	$-0.324627\pi$
$461$	22.4799	1.04699	0.523497	+	0.852028i	$0.324627\pi$
$462$	7.63935	0.355415
$463$	29.0507	1.35010	0.675051	−	0.737771i	$-0.264122\pi$
$463$	29.0507	1.35010	0.675051	+	0.737771i	$0.264122\pi$
$464$	−3.49330	−0.162172
$465$	44.4024	2.05911
$466$	−0.292106	−0.0135315
$467$	−7.47990	−0.346129	−0.173064	−	0.984911i	$-0.555367\pi$
$467$	−7.47990	−0.346129	−0.173064	+	0.984911i	$0.555367\pi$
$468$	0	0
$469$	13.6126	0.628570
$470$	4.16738	0.192227
$471$	54.3900	2.50616
$472$	18.0909	0.832702
$473$	−2.52360	−0.116035
$474$	3.77643	0.173457
$475$	1.64729	0.0755827
$476$	−7.24840	−0.332230
$477$	16.4079	0.751264
$478$	−21.8023	−0.997215
$479$	−8.62245	−0.393970	−0.196985	−	0.980407i	$-0.563115\pi$
$479$	−8.62245	−0.393970	−0.196985	+	0.980407i	$0.563115\pi$
$480$	−23.9270	−1.09211
$481$	0	0
$482$	−2.54844	−0.116078
$483$	34.5574	1.57242
$484$	−1.00000	−0.0454545
$485$	24.6260	1.11821
$486$	−18.5877	−0.843156
$487$	−8.09091	−0.366634	−0.183317	−	0.983054i	$-0.558683\pi$
$487$	−8.09091	−0.366634	−0.183317	+	0.983054i	$0.558683\pi$
$488$	29.3562	1.32889
$489$	−14.8236	−0.670348
$490$	9.32592	0.421302
$491$	4.62245	0.208608	0.104304	−	0.994545i	$-0.466738\pi$
$491$	4.62245	0.208608	0.104304	+	0.994545i	$0.466738\pi$
$492$	−22.6563	−1.02142
$493$	−7.49681	−0.337639
$494$	0	0
$495$	4.47640	0.201199
$496$	−9.27871	−0.416626
$497$	20.2653	0.909023
$498$	−12.8236	−0.574641
$499$	−39.5137	−1.76888	−0.884438	−	0.466657i	$-0.845458\pi$
$499$	−39.5137	−1.76888	−0.884438	+	0.466657i	$0.845458\pi$
$500$	−11.6866	−0.522639
$501$	−41.4496	−1.85183
$502$	26.8192	1.19700
$503$	−37.7035	−1.68111	−0.840557	−	0.541723i	$-0.817772\pi$
$503$	−37.7035	−1.68111	−0.840557	+	0.541723i	$0.817772\pi$
$504$	−21.4382	−0.954931
$505$	−1.90662	−0.0848435
$506$	4.52360	0.201099
$507$	0	0
$508$	−11.5102	−0.510683
$509$	7.72129	0.342240	0.171120	−	0.985250i	$-0.445261\pi$
$509$	7.72129	0.342240	0.171120	+	0.985250i	$0.445261\pi$
$510$	10.2697	0.454752
$511$	36.6145	1.61973
$512$	11.0000	0.486136
$513$	−6.29211	−0.277803
$514$	−3.06854	−0.135348
$515$	−27.6046	−1.21641
$516$	5.70789	0.251276
$517$	−1.96970	−0.0866272
$518$	30.9484	1.35979
$519$	−33.2181	−1.45811
$520$	0	0
$521$	5.48979	0.240512	0.120256	−	0.992743i	$-0.461628\pi$
$521$	5.48979	0.240512	0.120256	+	0.992743i	$0.461628\pi$
$522$	−7.39095	−0.323493
$523$	41.2137	1.80215	0.901074	−	0.433665i	$-0.142780\pi$
$523$	41.2137	1.80215	0.901074	+	0.433665i	$0.142780\pi$
$524$	−13.6091	−0.594514
$525$	−4.00000	−0.174574
$526$	−2.29211	−0.0999406
$527$	−19.9126	−0.867406
$528$	−2.26180	−0.0984323
$529$	−2.53700	−0.110304
$530$	16.4079	0.712712
$531$	12.7586	0.553677
$532$	−10.6260	−0.460694
$533$	0	0
$534$	−21.1416	−0.914888
$535$	28.7933	1.24484
$536$	−12.0909	−0.522248
$537$	14.6866	0.633772
$538$	−11.2449	−0.484802
$539$	−4.40786	−0.189860
$540$	4.23150	0.182095
$541$	−31.2539	−1.34371	−0.671854	−	0.740683i	$-0.734502\pi$
$541$	−31.2539	−1.34371	−0.671854	+	0.740683i	$0.734502\pi$
$542$	−4.29211	−0.184362
$543$	38.8192	1.66589
$544$	10.7303	0.460056
$545$	39.5361	1.69354
$546$	0	0
$547$	2.40239	0.102719	0.0513594	−	0.998680i	$-0.483645\pi$
$547$	2.40239	0.102719	0.0513594	+	0.998680i	$0.483645\pi$
$548$	−15.1024	−0.645140
$549$	20.7035	0.883602
$550$	−0.523604	−0.0223266
$551$	−10.9901	−0.468194
$552$	−30.6945	−1.30644
$553$	−5.63935	−0.239810
$554$	4.83262	0.205318
$555$	43.8485	1.86126
$556$	15.2787	0.647962
$557$	−2.44609	−0.103644	−0.0518221	−	0.998656i	$-0.516503\pi$
$557$	−2.44609	−0.103644	−0.0518221	+	0.998656i	$0.516503\pi$
$558$	−19.6314	−0.831064
$559$	0	0
$560$	−7.14605	−0.301976
$561$	−4.85395	−0.204934
$562$	3.78541	0.159678
$563$	38.4586	1.62084	0.810418	−	0.585852i	$-0.199240\pi$
$563$	38.4586	1.62084	0.810418	+	0.585852i	$0.199240\pi$
$564$	4.45506	0.187592
$565$	−26.7417	−1.12503
$566$	12.4248	0.522252
$567$	36.7169	1.54196
$568$	−18.0000	−0.755263
$569$	39.2519	1.64553	0.822763	−	0.568385i	$-0.192431\pi$
$569$	39.2519	1.64553	0.822763	+	0.568385i	$0.192431\pi$
$570$	15.0551	0.630591
$571$	−39.3349	−1.64611	−0.823057	−	0.567959i	$-0.807733\pi$
$571$	−39.3349	−1.64611	−0.823057	+	0.567959i	$0.807733\pi$
$572$	0	0
$573$	−40.6439	−1.69792
$574$	−33.8326	−1.41215
$575$	−2.36858	−0.0987766
$576$	14.8102	0.617094
$577$	24.0890	1.00284	0.501418	−	0.865205i	$-0.332812\pi$
$577$	24.0890	1.00284	0.501418	+	0.865205i	$0.332812\pi$
$578$	12.3945	0.515541
$579$	−6.71687	−0.279143
$580$	7.39095	0.306892
$581$	19.1496	0.794458
$582$	−26.3259	−1.09124
$583$	−7.75510	−0.321184
$584$	−32.5216	−1.34576
$585$	0	0
$586$	16.9012	0.698180
$587$	−24.4665	−1.00984	−0.504920	−	0.863166i	$-0.668478\pi$
$587$	−24.4665	−1.00984	−0.504920	+	0.863166i	$0.668478\pi$
$588$	9.96970	0.411143
$589$	−29.1913	−1.20281
$590$	12.7586	0.525264
$591$	27.6652	1.13800
$592$	−9.16296	−0.376595
$593$	−33.6215	−1.38067	−0.690335	−	0.723490i	$-0.742537\pi$
$593$	−33.6215	−1.38067	−0.690335	+	0.723490i	$0.742537\pi$
$594$	2.00000	0.0820610
$595$	−15.3358	−0.628707
$596$	4.37755	0.179312
$597$	0.455064	0.0186245
$598$	0	0
$599$	3.01340	0.123124	0.0615621	−	0.998103i	$-0.480392\pi$
$599$	3.01340	0.123124	0.0615621	+	0.998103i	$0.480392\pi$
$600$	3.55287	0.145045
$601$	−18.5743	−0.757662	−0.378831	−	0.925466i	$-0.623674\pi$
$601$	−18.5743	−0.757662	−0.378831	+	0.925466i	$0.623674\pi$
$602$	8.52360	0.347396
$603$	−8.52711	−0.347251
$604$	2.29211	0.0932645
$605$	−2.11575	−0.0860174
$606$	2.03824	0.0827977
$607$	−19.2137	−0.779859	−0.389930	−	0.920845i	$-0.627501\pi$
$607$	−19.2137	−0.779859	−0.389930	+	0.920845i	$0.627501\pi$
$608$	15.7303	0.637946
$609$	26.6866	1.08139
$610$	20.7035	0.838259
$611$	0	0
$612$	4.54051	0.183539
$613$	−18.9350	−0.764776	−0.382388	−	0.924002i	$-0.624898\pi$
$613$	−18.9350	−0.764776	−0.382388	+	0.924002i	$0.624898\pi$
$614$	−8.42476	−0.339996
$615$	−47.9350	−1.93292
$616$	10.1327	0.408256
$617$	1.72129	0.0692966	0.0346483	−	0.999400i	$-0.488969\pi$
$617$	1.72129	0.0692966	0.0346483	+	0.999400i	$0.488969\pi$
$618$	29.5102	1.18707
$619$	−16.3562	−0.657412	−0.328706	−	0.944432i	$-0.606613\pi$
$619$	−16.3562	−0.657412	−0.328706	+	0.944432i	$0.606613\pi$
$620$	19.6314	0.788417
$621$	9.04721	0.363052
$622$	28.5877	1.14626
$623$	31.5708	1.26486
$624$	0	0
$625$	−22.1078	−0.884313
$626$	−22.3945	−0.895063
$627$	−7.11575	−0.284176
$628$	24.0472	0.959588
$629$	−19.6642	−0.784063
$630$	−15.1193	−0.602366
$631$	21.0775	0.839083	0.419541	−	0.907736i	$-0.362191\pi$
$631$	21.0775	0.839083	0.419541	+	0.907736i	$0.362191\pi$
$632$	5.00897	0.199246
$633$	−26.3945	−1.04909
$634$	−26.2708	−1.04335
$635$	−24.3527	−0.966408
$636$	17.5405	0.695526
$637$	0	0
$638$	3.49330	0.138301
$639$	−12.6945	−0.502187
$640$	−6.34725	−0.250897
$641$	−4.53700	−0.179201	−0.0896004	−	0.995978i	$-0.528559\pi$
$641$	−4.53700	−0.179201	−0.0896004	+	0.995978i	$0.528559\pi$
$642$	−30.7810	−1.21483
$643$	0.983094	0.0387695	0.0193847	−	0.999812i	$-0.493829\pi$
$643$	0.983094	0.0387695	0.0193847	+	0.999812i	$0.493829\pi$
$644$	15.2787	0.602065
$645$	12.0765	0.475511
$646$	−6.75160	−0.265638
$647$	−46.6856	−1.83540	−0.917701	−	0.397272i	$-0.869957\pi$
$647$	−46.6856	−1.83540	−0.917701	+	0.397272i	$0.869957\pi$
$648$	−32.6126	−1.28114
$649$	−6.03030	−0.236710
$650$	0	0
$651$	70.8833	2.77814
$652$	−6.55391	−0.256671
$653$	−25.8709	−1.01240	−0.506202	−	0.862415i	$-0.668951\pi$
$653$	−25.8709	−1.01240	−0.506202	+	0.862415i	$0.668951\pi$
$654$	−42.2653	−1.65270
$655$	−28.7933	−1.12505
$656$	10.0169	0.391094
$657$	−22.9359	−0.894814
$658$	6.65275	0.259351
$659$	17.4988	0.681655	0.340828	−	0.940126i	$-0.389293\pi$
$659$	17.4988	0.681655	0.340828	+	0.940126i	$0.389293\pi$
$660$	4.78541	0.186272
$661$	−21.6528	−0.842194	−0.421097	−	0.907016i	$-0.638355\pi$
$661$	−21.6528	−0.842194	−0.421097	+	0.907016i	$0.638355\pi$
$662$	−8.29211	−0.322282
$663$	0	0
$664$	−17.0090	−0.660076
$665$	−22.4819	−0.871809
$666$	−19.3865	−0.751213
$667$	15.8023	0.611868
$668$	−18.3259	−0.709051
$669$	−16.9787	−0.656433
$670$	−8.52711	−0.329431
$671$	−9.78541	−0.377761
$672$	−38.1968	−1.47347
$673$	−23.8798	−0.920500	−0.460250	−	0.887789i	$-0.652240\pi$
$673$	−23.8798	−0.920500	−0.460250	+	0.887789i	$0.652240\pi$
$674$	0.0516349	0.00198890
$675$	−1.04721	−0.0403071
$676$	0	0
$677$	−12.6945	−0.487889	−0.243945	−	0.969789i	$-0.578441\pi$
$677$	−12.6945	−0.487889	−0.243945	+	0.969789i	$0.578441\pi$
$678$	28.5877	1.09790
$679$	39.3125	1.50868
$680$	13.6215	0.522362
$681$	−7.86292	−0.301308
$682$	9.27871	0.355300
$683$	37.8699	1.44905	0.724526	−	0.689247i	$-0.242059\pi$
$683$	37.8699	1.44905	0.724526	+	0.689247i	$0.242059\pi$
$684$	6.65626	0.254508
$685$	−31.9528	−1.22085
$686$	−8.75510	−0.334271
$687$	30.3259	1.15701
$688$	−2.52360	−0.0962115
$689$	0	0
$690$	−21.6473	−0.824098
$691$	−25.7417	−0.979261	−0.489630	−	0.871930i	$-0.662868\pi$
$691$	−25.7417	−0.979261	−0.489630	+	0.871930i	$0.662868\pi$
$692$	−14.6866	−0.558299
$693$	7.14605	0.271456
$694$	8.62245	0.327304
$695$	32.3259	1.22619
$696$	−23.7035	−0.898478
$697$	21.4968	0.814250
$698$	30.0000	1.13552
$699$	−0.660685	−0.0249894
$700$	−1.76850	−0.0668431
$701$	−33.5023	−1.26536	−0.632682	−	0.774412i	$-0.718046\pi$
$701$	−33.5023	−1.26536	−0.632682	+	0.774412i	$0.718046\pi$
$702$	0	0
$703$	−28.8272	−1.08724
$704$	−7.00000	−0.263822
$705$	9.42580	0.354996
$706$	−0.476396	−0.0179294
$707$	−3.04370	−0.114470
$708$	13.6394	0.512598
$709$	30.9235	1.16136	0.580679	−	0.814133i	$-0.302787\pi$
$709$	30.9235	1.16136	0.580679	+	0.814133i	$0.302787\pi$
$710$	−12.6945	−0.476416
$711$	3.53258	0.132482
$712$	−28.0417	−1.05091
$713$	41.9732	1.57191
$714$	16.3945	0.613547
$715$	0	0
$716$	6.49330	0.242666
$717$	−49.3125	−1.84161
$718$	−10.2315	−0.381836
$719$	9.21810	0.343777	0.171889	−	0.985116i	$-0.445013\pi$
$719$	9.21810	0.343777	0.171889	+	0.985116i	$0.445013\pi$
$720$	4.47640	0.166825
$721$	−44.0676	−1.64116
$722$	9.10235	0.338754
$723$	−5.76408	−0.214368
$724$	17.1630	0.637856
$725$	−1.82911	−0.0679314
$726$	2.26180	0.0839434
$727$	33.5102	1.24282	0.621412	−	0.783484i	$-0.286559\pi$
$727$	33.5102	1.24282	0.621412	+	0.783484i	$0.286559\pi$
$728$	0	0
$729$	−9.42919	−0.349229
$730$	−22.9359	−0.848895
$731$	−5.41579	−0.200310
$732$	22.1327	0.818046
$733$	1.29561	0.0478546	0.0239273	−	0.999714i	$-0.492383\pi$
$733$	1.29561	0.0478546	0.0239273	+	0.999714i	$0.492383\pi$
$734$	−21.3393	−0.787648
$735$	21.0934	0.778041
$736$	−22.6180	−0.833711
$737$	4.03030	0.148458
$738$	21.1933	0.780135
$739$	−28.8495	−1.06125	−0.530623	−	0.847608i	$-0.678042\pi$
$739$	−28.8495	−1.06125	−0.530623	+	0.847608i	$0.678042\pi$
$740$	19.3865	0.712663
$741$	0	0
$742$	26.1933	0.961585
$743$	31.7373	1.16433	0.582164	−	0.813071i	$-0.302206\pi$
$743$	31.7373	1.16433	0.582164	+	0.813071i	$0.302206\pi$
$744$	−62.9598	−2.30822
$745$	9.26180	0.339326
$746$	−21.2271	−0.777178
$747$	−11.9956	−0.438895
$748$	−2.14605	−0.0784675
$749$	45.9653	1.67953
$750$	26.4327	0.965186
$751$	−36.1282	−1.31834	−0.659169	−	0.751995i	$-0.729092\pi$
$751$	−36.1282	−1.31834	−0.659169	+	0.751995i	$0.729092\pi$
$752$	−1.96970	−0.0718274
$753$	60.6598	2.21056
$754$	0	0
$755$	4.84952	0.176492
$756$	6.75510	0.245681
$757$	−22.0527	−0.801518	−0.400759	−	0.916183i	$-0.631254\pi$
$757$	−22.0527	−0.801518	−0.400759	+	0.916183i	$0.631254\pi$
$758$	−1.04721	−0.0380363
$759$	10.2315	0.371380
$760$	19.9688	0.724344
$761$	−40.1620	−1.45587	−0.727936	−	0.685645i	$-0.759520\pi$
$761$	−40.1620	−1.45587	−0.727936	+	0.685645i	$0.759520\pi$
$762$	26.0338	0.943105
$763$	63.1148	2.28491
$764$	−17.9697	−0.650121
$765$	9.60658	0.347327
$766$	−28.9866	−1.04733
$767$	0	0
$768$	38.4506	1.38747
$769$	24.9598	0.900074	0.450037	−	0.893010i	$-0.351411\pi$
$769$	24.9598	0.900074	0.450037	+	0.893010i	$0.351411\pi$
$770$	7.14605	0.257526
$771$	−6.94043	−0.249954
$772$	−2.96970	−0.106882
$773$	−5.46846	−0.196687	−0.0983435	−	0.995153i	$-0.531354\pi$
$773$	−5.46846	−0.196687	−0.0983435	+	0.995153i	$0.531354\pi$
$774$	−5.33931	−0.191918
$775$	−4.85837	−0.174518
$776$	−34.9181	−1.25349
$777$	69.9991	2.51120
$778$	−15.5653	−0.558045
$779$	31.5137	1.12910
$780$	0	0
$781$	6.00000	0.214697
$782$	9.70789	0.347154
$783$	6.98660	0.249681
$784$	−4.40786	−0.157423
$785$	50.8779	1.81591
$786$	30.7810	1.09792
$787$	−37.5484	−1.33846	−0.669229	−	0.743056i	$-0.733375\pi$
$787$	−37.5484	−1.33846	−0.669229	+	0.743056i	$0.733375\pi$
$788$	12.2315	0.435729
$789$	−5.18429	−0.184566
$790$	3.53258	0.125683
$791$	−42.6901	−1.51788
$792$	−6.34725	−0.225540
$793$	0	0
$794$	18.9787	0.673528
$795$	37.1113	1.31620
$796$	0.201195	0.00713118
$797$	7.76057	0.274893	0.137447	−	0.990509i	$-0.456110\pi$
$797$	7.76057	0.274893	0.137447	+	0.990509i	$0.456110\pi$
$798$	24.0338	0.850788
$799$	−4.22707	−0.149543
$800$	2.61802	0.0925611
$801$	−19.7764	−0.698766
$802$	−9.52360	−0.336290
$803$	10.8405	0.382555
$804$	−9.11575	−0.321488
$805$	32.3259	1.13934
$806$	0	0
$807$	−25.4337	−0.895310
$808$	2.70347	0.0951077
$809$	−6.80674	−0.239312	−0.119656	−	0.992815i	$-0.538179\pi$
$809$	−6.80674	−0.239312	−0.119656	+	0.992815i	$0.538179\pi$
$810$	−23.0000	−0.808138
$811$	37.0810	1.30209	0.651045	−	0.759039i	$-0.274331\pi$
$811$	37.0810	1.30209	0.651045	+	0.759039i	$0.274331\pi$
$812$	11.7988	0.414057
$813$	−9.70789	−0.340471
$814$	9.16296	0.321162
$815$	−13.8664	−0.485720
$816$	−4.85395	−0.169922
$817$	−7.93939	−0.277764
$818$	9.91455	0.346654
$819$	0	0
$820$	−21.1933	−0.740101
$821$	0.170892	0.00596417	0.00298208	−	0.999996i	$-0.499051\pi$
$821$	0.170892	0.00596417	0.00298208	+	0.999996i	$0.499051\pi$
$822$	34.1585	1.19142
$823$	14.9260	0.520287	0.260144	−	0.965570i	$-0.416230\pi$
$823$	14.9260	0.520287	0.260144	+	0.965570i	$0.416230\pi$
$824$	39.1416	1.36356
$825$	−1.18429	−0.0412317
$826$	20.3677	0.708682
$827$	−10.0114	−0.348132	−0.174066	−	0.984734i	$-0.555691\pi$
$827$	−10.0114	−0.348132	−0.174066	+	0.984734i	$0.555691\pi$
$828$	−9.57081	−0.332609
$829$	−3.59214	−0.124760	−0.0623802	−	0.998052i	$-0.519869\pi$
$829$	−3.59214	−0.124760	−0.0623802	+	0.998052i	$0.519869\pi$
$830$	−11.9956	−0.416372
$831$	10.9304	0.379172
$832$	0	0
$833$	−9.45949	−0.327752
$834$	−34.5574	−1.19663
$835$	−38.7730	−1.34180
$836$	−3.14605	−0.108809
$837$	18.5574	0.641438
$838$	−7.01340	−0.242274
$839$	27.2216	0.939794	0.469897	−	0.882721i	$-0.344291\pi$
$839$	27.2216	0.939794	0.469897	+	0.882721i	$0.344291\pi$
$840$	−48.4889	−1.67303
$841$	−16.7968	−0.579202
$842$	33.9787	1.17098
$843$	8.56184	0.294885
$844$	−11.6697	−0.401686
$845$	0	0
$846$	−4.16738	−0.143278
$847$	−3.37755	−0.116054
$848$	−7.75510	−0.266311
$849$	28.1024	0.964470
$850$	−1.12368	−0.0385420
$851$	41.4496	1.42087
$852$	−13.5708	−0.464928
$853$	−26.7114	−0.914581	−0.457290	−	0.889317i	$-0.651180\pi$
$853$	−26.7114	−0.914581	−0.457290	+	0.889317i	$0.651180\pi$
$854$	33.0507	1.13097
$855$	14.0830	0.481628
$856$	−40.8272	−1.39544
$857$	−26.6955	−0.911902	−0.455951	−	0.890005i	$-0.650701\pi$
$857$	−26.6955	−0.911902	−0.455951	+	0.890005i	$0.650701\pi$
$858$	0	0
$859$	−21.3855	−0.729663	−0.364832	−	0.931073i	$-0.618873\pi$
$859$	−21.3855	−0.729663	−0.364832	+	0.931073i	$0.618873\pi$
$860$	5.33931	0.182069
$861$	−76.5227	−2.60789
$862$	7.86735	0.267963
$863$	−0.694496	−0.0236409	−0.0118205	−	0.999930i	$-0.503763\pi$
$863$	−0.694496	−0.0236409	−0.0118205	+	0.999930i	$0.503763\pi$
$864$	−10.0000	−0.340207
$865$	−31.0731	−1.05652
$866$	13.6528	0.463939
$867$	28.0338	0.952078
$868$	31.3393	1.06373
$869$	−1.66966	−0.0566392
$870$	−16.7169	−0.566755
$871$	0	0
$872$	−56.0597	−1.89842
$873$	−24.6260	−0.833462
$874$	14.2315	0.481388
$875$	−39.4720	−1.33440
$876$	−24.5192	−0.828426
$877$	17.2609	0.582859	0.291429	−	0.956592i	$-0.405869\pi$
$877$	17.2609	0.582859	0.291429	+	0.956592i	$0.405869\pi$
$878$	8.33034	0.281135
$879$	38.2271	1.28937
$880$	−2.11575	−0.0713219
$881$	27.7889	0.936232	0.468116	−	0.883667i	$-0.344933\pi$
$881$	27.7889	0.936232	0.468116	+	0.883667i	$0.344933\pi$
$882$	−9.32592	−0.314020
$883$	13.1505	0.442549	0.221274	−	0.975212i	$-0.428978\pi$
$883$	13.1505	0.442549	0.221274	+	0.975212i	$0.428978\pi$
$884$	0	0
$885$	28.8575	0.970033
$886$	25.2484	0.848237
$887$	−53.0204	−1.78025	−0.890126	−	0.455715i	$-0.849384\pi$
$887$	−53.0204	−1.78025	−0.890126	+	0.455715i	$0.849384\pi$
$888$	−62.1744	−2.08644
$889$	−38.8763	−1.30387
$890$	−19.7764	−0.662908
$891$	10.8709	0.364187
$892$	−7.50670	−0.251343
$893$	−6.19677	−0.207367
$894$	−9.90116	−0.331144
$895$	13.7382	0.459217
$896$	−10.1327	−0.338508
$897$	0	0
$898$	−37.2708	−1.24374
$899$	32.4133	1.08104
$900$	1.10782	0.0369272
$901$	−16.6429	−0.554454
$902$	−10.0169	−0.333526
$903$	19.2787	0.641555
$904$	37.9181	1.26114
$905$	36.3125	1.20707
$906$	−5.18429	−0.172236
$907$	−54.8192	−1.82024	−0.910121	−	0.414342i	$-0.864012\pi$
$907$	−54.8192	−1.82024	−0.910121	+	0.414342i	$0.864012\pi$
$908$	−3.47640	−0.115368
$909$	1.90662	0.0632386
$910$	0	0
$911$	−25.4799	−0.844187	−0.422093	−	0.906552i	$-0.638705\pi$
$911$	−25.4799	−0.844187	−0.422093	+	0.906552i	$0.638705\pi$
$912$	−7.11575	−0.235626
$913$	5.66966	0.187638
$914$	−3.09091	−0.102238
$915$	46.8272	1.54806
$916$	13.4079	0.443008
$917$	−45.9653	−1.51791
$918$	4.29211	0.141661
$919$	−14.2156	−0.468930	−0.234465	−	0.972125i	$-0.575334\pi$
$919$	−14.2156	−0.468930	−0.234465	+	0.972125i	$0.575334\pi$
$920$	−28.7124	−0.946621
$921$	−19.0551	−0.627888
$922$	−22.4799	−0.740336
$923$	0	0
$924$	7.63935	0.251316
$925$	−4.79777	−0.157750
$926$	−29.0507	−0.954666
$927$	27.6046	0.906655
$928$	−17.4665	−0.573366
$929$	4.60462	0.151073	0.0755364	−	0.997143i	$-0.475933\pi$
$929$	4.60462	0.151073	0.0755364	+	0.997143i	$0.475933\pi$
$930$	−44.4024	−1.45601
$931$	−13.8673	−0.454484
$932$	−0.292106	−0.00956824
$933$	64.6598	2.11687
$934$	7.47990	0.244750
$935$	−4.54051	−0.148491
$936$	0	0
$937$	−54.9002	−1.79351	−0.896756	−	0.442525i	$-0.854083\pi$
$937$	−54.9002	−1.79351	−0.896756	+	0.442525i	$0.854083\pi$
$938$	−13.6126	−0.444466
$939$	−50.6518	−1.65296
$940$	4.16738	0.135925
$941$	0.292106	0.00952237	0.00476119	−	0.999989i	$-0.498484\pi$
$941$	0.292106	0.00952237	0.00476119	+	0.999989i	$0.498484\pi$
$942$	−54.3900	−1.77212
$943$	−45.3125	−1.47558
$944$	−6.03030	−0.196270
$945$	14.2921	0.464922
$946$	2.52360	0.0820495
$947$	4.46300	0.145028	0.0725140	−	0.997367i	$-0.476898\pi$
$947$	4.46300	0.145028	0.0725140	+	0.997367i	$0.476898\pi$
$948$	3.77643	0.122653
$949$	0	0
$950$	−1.64729	−0.0534451
$951$	−59.4193	−1.92680
$952$	21.7452	0.704766
$953$	−40.4809	−1.31131	−0.655653	−	0.755062i	$-0.727607\pi$
$953$	−40.4809	−1.31131	−0.655653	+	0.755062i	$0.727607\pi$
$954$	−16.4079	−0.531224
$955$	−38.0194	−1.23028
$956$	−21.8023	−0.705137
$957$	7.90116	0.255408
$958$	8.62245	0.278579
$959$	−51.0090	−1.64717
$960$	33.4978	1.08114
$961$	55.0944	1.77724
$962$	0	0
$963$	−28.7933	−0.927852
$964$	−2.54844	−0.0820798
$965$	−6.28313	−0.202261
$966$	−34.5574	−1.11187
$967$	1.00897	0.0324464	0.0162232	−	0.999868i	$-0.494836\pi$
$967$	1.00897	0.0324464	0.0162232	+	0.999868i	$0.494836\pi$
$968$	3.00000	0.0964237
$969$	−15.2708	−0.490568
$970$	−24.6260	−0.790692
$971$	25.8664	0.830093	0.415047	−	0.909800i	$-0.363765\pi$
$971$	25.8664	0.830093	0.415047	+	0.909800i	$0.363765\pi$
$972$	−18.5877	−0.596201
$973$	51.6046	1.65437
$974$	8.09091	0.259249
$975$	0	0
$976$	−9.78541	−0.313223
$977$	43.3677	1.38745	0.693727	−	0.720238i	$-0.255967\pi$
$977$	43.3677	1.38745	0.693727	+	0.720238i	$0.255967\pi$
$978$	14.8236	0.474008
$979$	9.34725	0.298739
$980$	9.32592	0.297905
$981$	−39.5361	−1.26229
$982$	−4.62245	−0.147508
$983$	17.0472	0.543722	0.271861	−	0.962337i	$-0.412361\pi$
$983$	17.0472	0.543722	0.271861	+	0.962337i	$0.412361\pi$
$984$	67.9688	2.16677
$985$	25.8788	0.824567
$986$	7.49681	0.238747
$987$	15.0472	0.478958
$988$	0	0
$989$	11.4158	0.363001
$990$	−4.47640	−0.142269
$991$	−40.0979	−1.27375	−0.636876	−	0.770966i	$-0.719774\pi$
$991$	−40.0979	−1.27375	−0.636876	+	0.770966i	$0.719774\pi$
$992$	−46.3935	−1.47300
$993$	−18.7551	−0.595175
$994$	−20.2653	−0.642777
$995$	0.425679	0.0134949
$996$	−12.8236	−0.406333
$997$	−54.0428	−1.71155	−0.855776	−	0.517346i	$-0.826920\pi$
$997$	−54.0428	−1.71155	−0.855776	+	0.517346i	$0.826920\pi$
$998$	39.5137	1.25078
$999$	18.3259	0.579806

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.e.1.1		3
13.4	even	6		143.2.e.a.133.3	yes	6
13.10	even	6		143.2.e.a.100.3	✓	6
13.12	even	2		1859.2.a.h.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.e.a.100.3	✓	6	13.10	even	6
143.2.e.a.133.3	yes	6	13.4	even	6
1859.2.a.e.1.1		3	1.1	even	1	trivial
1859.2.a.h.1.1		3	13.12	even	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.26180 q^{3} -1.00000 q^{4} -2.11575 q^{5} +2.26180 q^{6} -3.37755 q^{7} +3.00000 q^{8} +2.11575 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.26180 q^{3} -1.00000 q^{4} -2.11575 q^{5} +2.26180 q^{6} -3.37755 q^{7} +3.00000 q^{8} +2.11575 q^{9} +2.11575 q^{10} -1.00000 q^{11} +2.26180 q^{12} +3.37755 q^{14} +4.78541 q^{15} -1.00000 q^{16} -2.14605 q^{17} -2.11575 q^{18} -3.14605 q^{19} +2.11575 q^{20} +7.63935 q^{21} +1.00000 q^{22} +4.52360 q^{23} -6.78541 q^{24} -0.523604 q^{25} +2.00000 q^{27} +3.37755 q^{28} +3.49330 q^{29} -4.78541 q^{30} +9.27871 q^{31} -5.00000 q^{32} +2.26180 q^{33} +2.14605 q^{34} +7.14605 q^{35} -2.11575 q^{36} +9.16296 q^{37} +3.14605 q^{38} -6.34725 q^{40} -10.0169 q^{41} -7.63935 q^{42} +2.52360 q^{43} +1.00000 q^{44} -4.47640 q^{45} -4.52360 q^{46} +1.96970 q^{47} +2.26180 q^{48} +4.40786 q^{49} +0.523604 q^{50} +4.85395 q^{51} +7.75510 q^{53} -2.00000 q^{54} +2.11575 q^{55} -10.1327 q^{56} +7.11575 q^{57} -3.49330 q^{58} +6.03030 q^{59} -4.78541 q^{60} +9.78541 q^{61} -9.27871 q^{62} -7.14605 q^{63} +7.00000 q^{64} -2.26180 q^{66} -4.03030 q^{67} +2.14605 q^{68} -10.2315 q^{69} -7.14605 q^{70} -6.00000 q^{71} +6.34725 q^{72} -10.8405 q^{73} -9.16296 q^{74} +1.18429 q^{75} +3.14605 q^{76} +3.37755 q^{77} +1.66966 q^{79} +2.11575 q^{80} -10.8709 q^{81} +10.0169 q^{82} -5.66966 q^{83} -7.63935 q^{84} +4.54051 q^{85} -2.52360 q^{86} -7.90116 q^{87} -3.00000 q^{88} -9.34725 q^{89} +4.47640 q^{90} -4.52360 q^{92} -20.9866 q^{93} -1.96970 q^{94} +6.65626 q^{95} +11.3090 q^{96} -11.6394 q^{97} -4.40786 q^{98} -2.11575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{4} - 3 q^{5} + 9 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^4 - 3 * q^5 + 9 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{4} - 3 q^{5} + 9 q^{8} + 3 q^{9} + 3 q^{10} - 3 q^{11} - 6 q^{15} - 3 q^{16} - 3 q^{17} - 3 q^{18} - 6 q^{19} + 3 q^{20} + 6 q^{21} + 3 q^{22} + 12 q^{25} + 6 q^{27} - 3 q^{29} + 6 q^{30} - 6 q^{31} - 15 q^{32} + 3 q^{34} + 18 q^{35} - 3 q^{36} - 3 q^{37} + 6 q^{38} - 9 q^{40} - 3 q^{41} - 6 q^{42} - 6 q^{43} + 3 q^{44} - 27 q^{45} + 6 q^{47} + 3 q^{49} - 12 q^{50} + 18 q^{51} + 3 q^{53} - 6 q^{54} + 3 q^{55} + 18 q^{57} + 3 q^{58} + 18 q^{59} + 6 q^{60} + 9 q^{61} + 6 q^{62} - 18 q^{63} + 21 q^{64} - 12 q^{67} + 3 q^{68} - 24 q^{69} - 18 q^{70} - 18 q^{71} + 9 q^{72} - 9 q^{73} + 3 q^{74} + 24 q^{75} + 6 q^{76} - 12 q^{79} + 3 q^{80} - 9 q^{81} + 3 q^{82} - 6 q^{84} - 27 q^{85} + 6 q^{86} - 9 q^{88} - 18 q^{89} + 27 q^{90} - 36 q^{93} - 6 q^{94} - 24 q^{95} - 18 q^{97} - 3 q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^4 - 3 * q^5 + 9 * q^8 + 3 * q^9 + 3 * q^10 - 3 * q^11 - 6 * q^15 - 3 * q^16 - 3 * q^17 - 3 * q^18 - 6 * q^19 + 3 * q^20 + 6 * q^21 + 3 * q^22 + 12 * q^25 + 6 * q^27 - 3 * q^29 + 6 * q^30 - 6 * q^31 - 15 * q^32 + 3 * q^34 + 18 * q^35 - 3 * q^36 - 3 * q^37 + 6 * q^38 - 9 * q^40 - 3 * q^41 - 6 * q^42 - 6 * q^43 + 3 * q^44 - 27 * q^45 + 6 * q^47 + 3 * q^49 - 12 * q^50 + 18 * q^51 + 3 * q^53 - 6 * q^54 + 3 * q^55 + 18 * q^57 + 3 * q^58 + 18 * q^59 + 6 * q^60 + 9 * q^61 + 6 * q^62 - 18 * q^63 + 21 * q^64 - 12 * q^67 + 3 * q^68 - 24 * q^69 - 18 * q^70 - 18 * q^71 + 9 * q^72 - 9 * q^73 + 3 * q^74 + 24 * q^75 + 6 * q^76 - 12 * q^79 + 3 * q^80 - 9 * q^81 + 3 * q^82 - 6 * q^84 - 27 * q^85 + 6 * q^86 - 9 * q^88 - 18 * q^89 + 27 * q^90 - 36 * q^93 - 6 * q^94 - 24 * q^95 - 18 * q^97 - 3 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more