LMFDB - Embedded newform 3549.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.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:	$28.3389076774$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.473.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 5x - 1 $ x^3 - 5*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.33006$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.33006 q^{2} -1.00000 q^{3} +3.42917 q^{4} +0.900885 q^{5} +2.33006 q^{6} +1.00000 q^{7} -3.33006 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.33006 q^{2} -1.00000 q^{3} +3.42917 q^{4} +0.900885 q^{5} +2.33006 q^{6} +1.00000 q^{7} -3.33006 q^{8} +1.00000 q^{9} -2.09911 q^{10} +2.90089 q^{11} -3.42917 q^{12} -2.33006 q^{14} -0.900885 q^{15} +0.900885 q^{16} +1.66994 q^{17} -2.33006 q^{18} -3.66012 q^{19} +3.08929 q^{20} -1.00000 q^{21} -6.75923 q^{22} -4.42917 q^{23} +3.33006 q^{24} -4.18841 q^{25} -1.00000 q^{27} +3.42917 q^{28} +5.33006 q^{29} +2.09911 q^{30} +6.56100 q^{31} +4.56100 q^{32} -2.90089 q^{33} -3.89106 q^{34} +0.900885 q^{35} +3.42917 q^{36} +8.61758 q^{37} +8.52829 q^{38} -3.00000 q^{40} -7.32023 q^{41} +2.33006 q^{42} -4.42917 q^{43} +9.94764 q^{44} +0.900885 q^{45} +10.3202 q^{46} +6.95746 q^{47} -0.900885 q^{48} +1.00000 q^{49} +9.75923 q^{50} -1.66994 q^{51} -0.141653 q^{53} +2.33006 q^{54} +2.61336 q^{55} -3.33006 q^{56} +3.66012 q^{57} -12.4193 q^{58} +9.48575 q^{59} -3.08929 q^{60} -2.51846 q^{61} -15.2875 q^{62} +1.00000 q^{63} -12.4292 q^{64} +6.75923 q^{66} +0.00982378 q^{67} +5.72652 q^{68} +4.42917 q^{69} -2.09911 q^{70} +14.0893 q^{71} -3.33006 q^{72} -2.57083 q^{73} -20.0795 q^{74} +4.18841 q^{75} -12.5512 q^{76} +2.90089 q^{77} -9.41935 q^{79} +0.811594 q^{80} +1.00000 q^{81} +17.0566 q^{82} +1.58065 q^{83} -3.42917 q^{84} +1.50443 q^{85} +10.3202 q^{86} -5.33006 q^{87} -9.66012 q^{88} +8.32023 q^{89} -2.09911 q^{90} -15.1884 q^{92} -6.56100 q^{93} -16.2113 q^{94} -3.29734 q^{95} -4.56100 q^{96} -7.70266 q^{97} -2.33006 q^{98} +2.90089 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} + 4 q^{4} + 2 q^{5} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^3 + 4 * q^4 + 2 * q^5 + 3 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{3} + 4 q^{4} + 2 q^{5} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 7 q^{10} + 8 q^{11} - 4 q^{12} - 2 q^{15} + 2 q^{16} + 12 q^{17} + 3 q^{19} - 11 q^{20} - 3 q^{21} - 7 q^{22} - 7 q^{23} + 3 q^{24} + 7 q^{25} - 3 q^{27} + 4 q^{28} + 9 q^{29} + 7 q^{30} + 5 q^{31} - q^{32} - 8 q^{33} + 10 q^{34} + 2 q^{35} + 4 q^{36} + 20 q^{38} - 9 q^{40} + 6 q^{41} - 7 q^{43} - 3 q^{44} + 2 q^{45} + 3 q^{46} + 9 q^{47} - 2 q^{48} + 3 q^{49} + 16 q^{50} - 12 q^{51} - 13 q^{53} + 26 q^{55} - 3 q^{56} - 3 q^{57} - 10 q^{58} + 11 q^{59} + 11 q^{60} + 19 q^{61} - 27 q^{62} + 3 q^{63} - 31 q^{64} + 7 q^{66} + 21 q^{67} + 13 q^{68} + 7 q^{69} - 7 q^{70} + 22 q^{71} - 3 q^{72} - 14 q^{73} - 19 q^{74} - 7 q^{75} - 2 q^{76} + 8 q^{77} - q^{79} + 22 q^{80} + 3 q^{81} + 40 q^{82} + 32 q^{83} - 4 q^{84} + q^{85} + 3 q^{86} - 9 q^{87} - 15 q^{88} - 3 q^{89} - 7 q^{90} - 26 q^{92} - 5 q^{93} + q^{94} - 12 q^{95} + q^{96} - 21 q^{97} + 8 q^{99}+O(q^{100}) $ 3 * q - 3 * q^3 + 4 * q^4 + 2 * q^5 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 7 * q^10 + 8 * q^11 - 4 * q^12 - 2 * q^15 + 2 * q^16 + 12 * q^17 + 3 * q^19 - 11 * q^20 - 3 * q^21 - 7 * q^22 - 7 * q^23 + 3 * q^24 + 7 * q^25 - 3 * q^27 + 4 * q^28 + 9 * q^29 + 7 * q^30 + 5 * q^31 - q^32 - 8 * q^33 + 10 * q^34 + 2 * q^35 + 4 * q^36 + 20 * q^38 - 9 * q^40 + 6 * q^41 - 7 * q^43 - 3 * q^44 + 2 * q^45 + 3 * q^46 + 9 * q^47 - 2 * q^48 + 3 * q^49 + 16 * q^50 - 12 * q^51 - 13 * q^53 + 26 * q^55 - 3 * q^56 - 3 * q^57 - 10 * q^58 + 11 * q^59 + 11 * q^60 + 19 * q^61 - 27 * q^62 + 3 * q^63 - 31 * q^64 + 7 * q^66 + 21 * q^67 + 13 * q^68 + 7 * q^69 - 7 * q^70 + 22 * q^71 - 3 * q^72 - 14 * q^73 - 19 * q^74 - 7 * q^75 - 2 * q^76 + 8 * q^77 - q^79 + 22 * q^80 + 3 * q^81 + 40 * q^82 + 32 * q^83 - 4 * q^84 + q^85 + 3 * q^86 - 9 * q^87 - 15 * q^88 - 3 * q^89 - 7 * q^90 - 26 * q^92 - 5 * q^93 + q^94 - 12 * q^95 + q^96 - 21 * q^97 + 8 * 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 $

$2$	−2.33006	−1.64760	−0.823800	−	0.566880i	$-0.808150\pi$
$2$	−2.33006	−1.64760	−0.823800	+	0.566880i	$0.808150\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.42917	1.71459
$5$	0.900885	0.402888	0.201444	−	0.979500i	$-0.435437\pi$
$5$	0.900885	0.402888	0.201444	+	0.979500i	$0.435437\pi$
$6$	2.33006	0.951242
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.33006	−1.17735
$9$	1.00000	0.333333
$10$	−2.09911	−0.663798
$11$	2.90089	0.874650	0.437325	−	0.899304i	$-0.355926\pi$
$11$	2.90089	0.874650	0.437325	+	0.899304i	$0.355926\pi$
$12$	−3.42917	−0.989917
$13$	0	0
$13$	0	0
$14$	−2.33006	−0.622734
$15$	−0.900885	−0.232608
$16$	0.900885	0.225221
$17$	1.66994	0.405020	0.202510	−	0.979280i	$-0.435090\pi$
$17$	1.66994	0.405020	0.202510	+	0.979280i	$0.435090\pi$
$18$	−2.33006	−0.549200
$19$	−3.66012	−0.839689	−0.419844	−	0.907596i	$-0.637915\pi$
$19$	−3.66012	−0.839689	−0.419844	+	0.907596i	$0.637915\pi$
$20$	3.08929	0.690787
$21$	−1.00000	−0.218218
$22$	−6.75923	−1.44107
$23$	−4.42917	−0.923547	−0.461773	−	0.886998i	$-0.652787\pi$
$23$	−4.42917	−0.923547	−0.461773	+	0.886998i	$0.652787\pi$
$24$	3.33006	0.679745
$25$	−4.18841	−0.837681
$26$	0	0
$27$	−1.00000	−0.192450
$28$	3.42917	0.648053
$29$	5.33006	0.989767	0.494884	−	0.868959i	$-0.335211\pi$
$29$	5.33006	0.989767	0.494884	+	0.868959i	$0.335211\pi$
$30$	2.09911	0.383244
$31$	6.56100	1.17839	0.589195	−	0.807991i	$-0.299445\pi$
$31$	6.56100	1.17839	0.589195	+	0.807991i	$0.299445\pi$
$32$	4.56100	0.806279
$33$	−2.90089	−0.504979
$34$	−3.89106	−0.667311
$35$	0.900885	0.152277
$36$	3.42917	0.571529
$37$	8.61758	1.41672	0.708361	−	0.705851i	$-0.249435\pi$
$37$	8.61758	1.41672	0.708361	+	0.705851i	$0.249435\pi$
$38$	8.52829	1.38347
$39$	0	0
$40$	−3.00000	−0.474342
$41$	−7.32023	−1.14323	−0.571614	−	0.820522i	$-0.693683\pi$
$41$	−7.32023	−1.14323	−0.571614	+	0.820522i	$0.693683\pi$
$42$	2.33006	0.359536
$43$	−4.42917	−0.675443	−0.337721	−	0.941246i	$-0.609656\pi$
$43$	−4.42917	−0.675443	−0.337721	+	0.941246i	$0.609656\pi$
$44$	9.94764	1.49966
$45$	0.900885	0.134296
$46$	10.3202	1.52164
$47$	6.95746	1.01485	0.507425	−	0.861696i	$-0.330597\pi$
$47$	6.95746	1.01485	0.507425	+	0.861696i	$0.330597\pi$
$48$	−0.900885	−0.130032
$49$	1.00000	0.142857
$50$	9.75923	1.38016
$51$	−1.66994	−0.233839
$52$	0	0
$53$	−0.141653	−0.0194575	−0.00972874	−	0.999953i	$-0.503097\pi$
$53$	−0.141653	−0.0194575	−0.00972874	+	0.999953i	$0.503097\pi$
$54$	2.33006	0.317081
$55$	2.61336	0.352386
$56$	−3.33006	−0.444998
$57$	3.66012	0.484794
$58$	−12.4193	−1.63074
$59$	9.48575	1.23494	0.617470	−	0.786595i	$-0.288158\pi$
$59$	9.48575	1.23494	0.617470	+	0.786595i	$0.288158\pi$
$60$	−3.08929	−0.398826
$61$	−2.51846	−0.322456	−0.161228	−	0.986917i	$-0.551546\pi$
$61$	−2.51846	−0.322456	−0.161228	+	0.986917i	$0.551546\pi$
$62$	−15.2875	−1.94152
$63$	1.00000	0.125988
$64$	−12.4292	−1.55365
$65$	0	0
$66$	6.75923	0.832004
$67$	0.00982378	0.00120017	0.000600083	−	1.00000i	$-0.499809\pi$
$67$	0.00982378	0.00120017	0.000600083		1.00000i	$0.499809\pi$
$68$	5.72652	0.694442
$69$	4.42917	0.533210
$70$	−2.09911	−0.250892
$71$	14.0893	1.67209	0.836046	−	0.548660i	$-0.184862\pi$
$71$	14.0893	1.67209	0.836046	+	0.548660i	$0.184862\pi$
$72$	−3.33006	−0.392451
$73$	−2.57083	−0.300892	−0.150446	−	0.988618i	$-0.548071\pi$
$73$	−2.57083	−0.300892	−0.150446	+	0.988618i	$0.548071\pi$
$74$	−20.0795	−2.33419
$75$	4.18841	0.483635
$76$	−12.5512	−1.43972
$77$	2.90089	0.330587
$78$	0	0
$79$	−9.41935	−1.05976	−0.529880	−	0.848073i	$-0.677763\pi$
$79$	−9.41935	−1.05976	−0.529880	+	0.848073i	$0.677763\pi$
$80$	0.811594	0.0907389
$81$	1.00000	0.111111
$82$	17.0566	1.88358
$83$	1.58065	0.173499	0.0867494	−	0.996230i	$-0.472352\pi$
$83$	1.58065	0.173499	0.0867494	+	0.996230i	$0.472352\pi$
$84$	−3.42917	−0.374154
$85$	1.50443	0.163178
$86$	10.3202	1.11286
$87$	−5.33006	−0.571442
$88$	−9.66012	−1.02977
$89$	8.32023	0.881943	0.440972	−	0.897521i	$-0.354634\pi$
$89$	8.32023	0.881943	0.440972	+	0.897521i	$0.354634\pi$
$90$	−2.09911	−0.221266
$91$	0	0
$92$	−15.1884	−1.58350
$93$	−6.56100	−0.680344
$94$	−16.2113	−1.67207
$95$	−3.29734	−0.338300
$96$	−4.56100	−0.465505
$97$	−7.70266	−0.782086	−0.391043	−	0.920372i	$-0.627886\pi$
$97$	−7.70266	−0.782086	−0.391043	+	0.920372i	$0.627886\pi$
$98$	−2.33006	−0.235371
$99$	2.90089	0.291550
$100$	−14.3628	−1.43628
$101$	18.4095	1.83182	0.915908	−	0.401388i	$-0.131472\pi$
$101$	18.4095	1.83182	0.915908	+	0.401388i	$0.131472\pi$
$102$	3.89106	0.385272
$103$	8.05658	0.793838	0.396919	−	0.917854i	$-0.370079\pi$
$103$	8.05658	0.793838	0.396919	+	0.917854i	$0.370079\pi$
$104$	0	0
$105$	−0.900885	−0.0879174
$106$	0.330059	0.0320581
$107$	3.62740	0.350674	0.175337	−	0.984508i	$-0.443898\pi$
$107$	3.62740	0.350674	0.175337	+	0.984508i	$0.443898\pi$
$108$	−3.42917	−0.329972
$109$	−8.84852	−0.847535	−0.423767	−	0.905771i	$-0.639293\pi$
$109$	−8.84852	−0.847535	−0.423767	+	0.905771i	$0.639293\pi$
$110$	−6.08929	−0.580591
$111$	−8.61758	−0.817944
$112$	0.900885	0.0851256
$113$	−6.36277	−0.598559	−0.299280	−	0.954165i	$-0.596746\pi$
$113$	−6.36277	−0.598559	−0.299280	+	0.954165i	$0.596746\pi$
$114$	−8.52829	−0.798747
$115$	−3.99018	−0.372086
$116$	18.2777	1.69704
$117$	0	0
$118$	−22.1024	−2.03469
$119$	1.66994	0.153083
$120$	3.00000	0.273861
$121$	−2.58487	−0.234988
$122$	5.86817	0.531279
$123$	7.32023	0.660043
$124$	22.4988	2.02045
$125$	−8.27770	−0.740380
$126$	−2.33006	−0.207578
$127$	11.0795	0.983144	0.491572	−	0.870837i	$-0.336423\pi$
$127$	11.0795	0.983144	0.491572	+	0.870837i	$0.336423\pi$
$128$	19.8387	1.75351
$129$	4.42917	0.389967
$130$	0	0
$131$	−6.90089	−0.602933	−0.301467	−	0.953477i	$-0.597476\pi$
$131$	−6.90089	−0.602933	−0.301467	+	0.953477i	$0.597476\pi$
$132$	−9.94764	−0.865831
$133$	−3.66012	−0.317372
$134$	−0.0228900	−0.00197739
$135$	−0.900885	−0.0775358
$136$	−5.56100	−0.476852
$137$	12.5185	1.06952	0.534762	−	0.845003i	$-0.320401\pi$
$137$	12.5185	1.06952	0.534762	+	0.845003i	$0.320401\pi$
$138$	−10.3202	−0.878517
$139$	3.33006	0.282452	0.141226	−	0.989977i	$-0.454896\pi$
$139$	3.33006	0.282452	0.141226	+	0.989977i	$0.454896\pi$
$140$	3.08929	0.261093
$141$	−6.95746	−0.585924
$142$	−32.8289	−2.75494
$143$	0	0
$144$	0.900885	0.0750738
$145$	4.80177	0.398765
$146$	5.99018	0.495751
$147$	−1.00000	−0.0824786
$148$	29.5512	2.42909
$149$	15.6742	1.28408	0.642039	−	0.766672i	$-0.278089\pi$
$149$	15.6742	1.28408	0.642039	+	0.766672i	$0.278089\pi$
$150$	−9.75923	−0.796838
$151$	8.46189	0.688619	0.344309	−	0.938856i	$-0.388113\pi$
$151$	8.46189	0.688619	0.344309	+	0.938856i	$0.388113\pi$
$152$	12.1884	0.988610
$153$	1.66994	0.135007
$154$	−6.75923	−0.544674
$155$	5.91071	0.474760
$156$	0	0
$157$	−24.7396	−1.97443	−0.987217	−	0.159382i	$-0.949050\pi$
$157$	−24.7396	−1.97443	−0.987217	+	0.159382i	$0.949050\pi$
$158$	21.9476	1.74606
$159$	0.141653	0.0112338
$160$	4.10894	0.324840
$161$	−4.42917	−0.349068
$162$	−2.33006	−0.183067
$163$	−24.7167	−1.93596	−0.967980	−	0.251025i	$-0.919232\pi$
$163$	−24.7167	−1.93596	−0.967980	+	0.251025i	$0.919232\pi$
$164$	−25.1024	−1.96016
$165$	−2.61336	−0.203450
$166$	−3.68301	−0.285857
$167$	−10.7167	−0.829283	−0.414641	−	0.909985i	$-0.636093\pi$
$167$	−10.7167	−0.829283	−0.414641	+	0.909985i	$0.636093\pi$
$168$	3.33006	0.256920
$169$	0	0
$170$	−3.50540	−0.268852
$171$	−3.66012	−0.279896
$172$	−15.1884	−1.15811
$173$	−7.28752	−0.554060	−0.277030	−	0.960861i	$-0.589350\pi$
$173$	−7.28752	−0.554060	−0.277030	+	0.960861i	$0.589350\pi$
$174$	12.4193	0.941508
$175$	−4.18841	−0.316614
$176$	2.61336	0.196990
$177$	−9.48575	−0.712993
$178$	−19.3866	−1.45309
$179$	−17.1122	−1.27902	−0.639512	−	0.768781i	$-0.720864\pi$
$179$	−17.1122	−1.27902	−0.639512	+	0.768781i	$0.720864\pi$
$180$	3.08929	0.230262
$181$	15.3529	1.14118	0.570588	−	0.821237i	$-0.306715\pi$
$181$	15.3529	1.14118	0.570588	+	0.821237i	$0.306715\pi$
$182$	0	0
$183$	2.51846	0.186170
$184$	14.7494	1.08734
$185$	7.76345	0.570780
$186$	15.2875	1.12094
$187$	4.84431	0.354251
$188$	23.8583	1.74005
$189$	−1.00000	−0.0727393
$190$	7.68301	0.557384
$191$	23.5512	1.70410	0.852052	−	0.523458i	$-0.175358\pi$
$191$	23.5512	1.70410	0.852052	+	0.523458i	$0.175358\pi$
$192$	12.4292	0.896998
$193$	−11.6840	−0.841031	−0.420516	−	0.907285i	$-0.638151\pi$
$193$	−11.6840	−0.841031	−0.420516	+	0.907285i	$0.638151\pi$
$194$	17.9476	1.28857
$195$	0	0
$196$	3.42917	0.244941
$197$	−22.9476	−1.63495	−0.817476	−	0.575963i	$-0.804627\pi$
$197$	−22.9476	−1.63495	−0.817476	+	0.575963i	$0.804627\pi$
$198$	−6.75923	−0.480358
$199$	27.8714	1.97575	0.987876	−	0.155245i	$-0.0496166\pi$
$199$	27.8714	1.97575	0.987876	+	0.155245i	$0.0496166\pi$
$200$	13.9476	0.986247
$201$	−0.00982378	−0.000692916 0
$202$	−42.8953	−3.01810
$203$	5.33006	0.374097
$204$	−5.72652	−0.400937
$205$	−6.59469	−0.460593
$206$	−18.7723	−1.30793
$207$	−4.42917	−0.307849
$208$	0	0
$209$	−10.6176	−0.734433
$210$	2.09911	0.144853
$211$	−6.80599	−0.468543	−0.234272	−	0.972171i	$-0.575271\pi$
$211$	−6.80599	−0.468543	−0.234272	+	0.972171i	$0.575271\pi$
$212$	−0.485751	−0.0333615
$213$	−14.0893	−0.965382
$214$	−8.45206	−0.577771
$215$	−3.99018	−0.272128
$216$	3.33006	0.226582
$217$	6.56100	0.445390
$218$	20.6176	1.39640
$219$	2.57083	0.173720
$220$	8.96168	0.604196
$221$	0	0
$222$	20.0795	1.34765
$223$	−20.5185	−1.37402	−0.687009	−	0.726649i	$-0.741077\pi$
$223$	−20.5185	−1.37402	−0.687009	+	0.726649i	$0.741077\pi$
$224$	4.56100	0.304745
$225$	−4.18841	−0.279227
$226$	14.8256	0.986186
$227$	1.50443	0.0998522	0.0499261	−	0.998753i	$-0.484101\pi$
$227$	1.50443	0.0998522	0.0499261	+	0.998753i	$0.484101\pi$
$228$	12.5512	0.831222
$229$	25.8148	1.70589	0.852946	−	0.521999i	$-0.174813\pi$
$229$	25.8148	1.70589	0.852946	+	0.521999i	$0.174813\pi$
$230$	9.29734	0.613049
$231$	−2.90089	−0.190864
$232$	−17.7494	−1.16531
$233$	−24.0369	−1.57471	−0.787356	−	0.616499i	$-0.788551\pi$
$233$	−24.0369	−1.57471	−0.787356	+	0.616499i	$0.788551\pi$
$234$	0	0
$235$	6.26787	0.408871
$236$	32.5283	2.11741
$237$	9.41935	0.611853
$238$	−3.89106	−0.252220
$239$	24.6601	1.59513	0.797565	−	0.603233i	$-0.206121\pi$
$239$	24.6601	1.59513	0.797565	+	0.603233i	$0.206121\pi$
$240$	−0.811594	−0.0523882
$241$	−3.96631	−0.255493	−0.127746	−	0.991807i	$-0.540774\pi$
$241$	−3.96631	−0.255493	−0.127746	+	0.991807i	$0.540774\pi$
$242$	6.02289	0.387166
$243$	−1.00000	−0.0641500
$244$	−8.63625	−0.552879
$245$	0.900885	0.0575554
$246$	−17.0566	−1.08749
$247$	0	0
$248$	−21.8485	−1.38738
$249$	−1.58065	−0.100170
$250$	19.2875	1.21985
$251$	−18.9575	−1.19658	−0.598292	−	0.801278i	$-0.704154\pi$
$251$	−18.9575	−1.19658	−0.598292	+	0.801278i	$0.704154\pi$
$252$	3.42917	0.216018
$253$	−12.8485	−0.807780
$254$	−25.8158	−1.61983
$255$	−1.50443	−0.0942108
$256$	−21.3670	−1.33544
$257$	15.1459	0.944773	0.472387	−	0.881391i	$-0.343393\pi$
$257$	15.1459	0.944773	0.472387	+	0.881391i	$0.343393\pi$
$258$	−10.3202	−0.642510
$259$	8.61758	0.535470
$260$	0	0
$261$	5.33006	0.329922
$262$	16.0795	0.993393
$263$	7.49460	0.462137	0.231068	−	0.972937i	$-0.425778\pi$
$263$	7.49460	0.462137	0.231068	+	0.972937i	$0.425778\pi$
$264$	9.66012	0.594539
$265$	−0.127613	−0.00783918
$266$	8.52829	0.522903
$267$	−8.32023	−0.509190
$268$	0.0336875	0.00205779
$269$	8.47593	0.516786	0.258393	−	0.966040i	$-0.416807\pi$
$269$	8.47593	0.516786	0.258393	+	0.966040i	$0.416807\pi$
$270$	2.09911	0.127748
$271$	1.65029	0.100248	0.0501241	−	0.998743i	$-0.484038\pi$
$271$	1.65029	0.100248	0.0501241	+	0.998743i	$0.484038\pi$
$272$	1.50443	0.0912192
$273$	0	0
$274$	−29.1688	−1.76215
$275$	−12.1501	−0.732678
$276$	15.1884	0.914235
$277$	32.5357	1.95488	0.977442	−	0.211205i	$-0.0677388\pi$
$277$	32.5357	1.95488	0.977442	+	0.211205i	$0.0677388\pi$
$278$	−7.75923	−0.465368
$279$	6.56100	0.392797
$280$	−3.00000	−0.179284
$281$	16.2777	0.971046	0.485523	−	0.874224i	$-0.338629\pi$
$281$	16.2777	0.971046	0.485523	+	0.874224i	$0.338629\pi$
$282$	16.2113	0.965369
$283$	25.5086	1.51633	0.758166	−	0.652062i	$-0.226096\pi$
$283$	25.5086	1.51633	0.758166	+	0.652062i	$0.226096\pi$
$284$	48.3146	2.86695
$285$	3.29734	0.195318
$286$	0	0
$287$	−7.32023	−0.432100
$288$	4.56100	0.268760
$289$	−14.2113	−0.835959
$290$	−11.1884	−0.657006
$291$	7.70266	0.451538
$292$	−8.81581	−0.515906
$293$	−10.3997	−0.607557	−0.303779	−	0.952743i	$-0.598248\pi$
$293$	−10.3997	−0.607557	−0.303779	+	0.952743i	$0.598248\pi$
$294$	2.33006	0.135892
$295$	8.54557	0.497542
$296$	−28.6970	−1.66798
$297$	−2.90089	−0.168326
$298$	−36.5217	−2.11565
$299$	0	0
$300$	14.3628	0.829235
$301$	−4.42917	−0.255293
$302$	−19.7167	−1.13457
$303$	−18.4095	−1.05760
$304$	−3.29734	−0.189116
$305$	−2.26885	−0.129914
$306$	−3.89106	−0.222437
$307$	30.3670	1.73314	0.866568	−	0.499059i	$-0.166321\pi$
$307$	30.3670	1.73314	0.866568	+	0.499059i	$0.166321\pi$
$308$	9.94764	0.566819
$309$	−8.05658	−0.458323
$310$	−13.7723	−0.782214
$311$	15.8485	0.898687	0.449344	−	0.893359i	$-0.351658\pi$
$311$	15.8485	0.898687	0.449344	+	0.893359i	$0.351658\pi$
$312$	0	0
$313$	20.7027	1.17018	0.585092	−	0.810967i	$-0.301059\pi$
$313$	20.7027	1.17018	0.585092	+	0.810967i	$0.301059\pi$
$314$	57.6447	3.25308
$315$	0.900885	0.0507591
$316$	−32.3006	−1.81705
$317$	−12.9705	−0.728497	−0.364249	−	0.931302i	$-0.618674\pi$
$317$	−12.9705	−0.728497	−0.364249	+	0.931302i	$0.618674\pi$
$318$	−0.330059	−0.0185088
$319$	15.4619	0.865700
$320$	−11.1973	−0.625946
$321$	−3.62740	−0.202462
$322$	10.3202	0.575124
$323$	−6.11218	−0.340091
$324$	3.42917	0.190510
$325$	0	0
$326$	57.5914	3.18969
$327$	8.84852	0.489324
$328$	24.3768	1.34598
$329$	6.95746	0.383577
$330$	6.08929	0.335204
$331$	26.4717	1.45502	0.727508	−	0.686099i	$-0.240678\pi$
$331$	26.4717	1.45502	0.727508	+	0.686099i	$0.240678\pi$
$332$	5.42032	0.297479
$333$	8.61758	0.472240
$334$	24.9705	1.36633
$335$	0.00885010	0.000483532 0
$336$	−0.900885	−0.0491473
$337$	7.02289	0.382561	0.191281	−	0.981535i	$-0.438736\pi$
$337$	7.02289	0.382561	0.191281	+	0.981535i	$0.438736\pi$
$338$	0	0
$339$	6.36277	0.345578
$340$	5.15893	0.279783
$341$	19.0327	1.03068
$342$	8.52829	0.461157
$343$	1.00000	0.0539949
$344$	14.7494	0.795235
$345$	3.99018	0.214824
$346$	16.9804	0.912869
$347$	−13.4432	−0.721670	−0.360835	−	0.932630i	$-0.617508\pi$
$347$	−13.4432	−0.721670	−0.360835	+	0.932630i	$0.617508\pi$
$348$	−18.2777	−0.979787
$349$	1.26463	0.0676942	0.0338471	−	0.999427i	$-0.489224\pi$
$349$	1.26463	0.0676942	0.0338471	+	0.999427i	$0.489224\pi$
$350$	9.75923	0.521653
$351$	0	0
$352$	13.2309	0.705212
$353$	17.9944	0.957745	0.478872	−	0.877884i	$-0.341046\pi$
$353$	17.9944	0.957745	0.478872	+	0.877884i	$0.341046\pi$
$354$	22.1024	1.17473
$355$	12.6928	0.673666
$356$	28.5315	1.51217
$357$	−1.66994	−0.0883827
$358$	39.8724	2.10732
$359$	23.7167	1.25172	0.625860	−	0.779936i	$-0.284748\pi$
$359$	23.7167	1.25172	0.625860	+	0.779936i	$0.284748\pi$
$360$	−3.00000	−0.158114
$361$	−5.60354	−0.294923
$362$	−35.7733	−1.88020
$363$	2.58487	0.135670
$364$	0	0
$365$	−2.31602	−0.121226
$366$	−5.86817	−0.306734
$367$	23.0042	1.20081	0.600405	−	0.799696i	$-0.295006\pi$
$367$	23.0042	1.20081	0.600405	+	0.799696i	$0.295006\pi$
$368$	−3.99018	−0.208002
$369$	−7.32023	−0.381076
$370$	−18.0893	−0.940417
$371$	−0.141653	−0.00735423
$372$	−22.4988	−1.16651
$373$	6.54233	0.338749	0.169374	−	0.985552i	$-0.445825\pi$
$373$	6.54233	0.338749	0.169374	+	0.985552i	$0.445825\pi$
$374$	−11.2875	−0.583664
$375$	8.27770	0.427458
$376$	−23.1688	−1.19484
$377$	0	0
$378$	2.33006	0.119845
$379$	−9.86720	−0.506844	−0.253422	−	0.967356i	$-0.581556\pi$
$379$	−9.86720	−0.506844	−0.253422	+	0.967356i	$0.581556\pi$
$380$	−11.3072	−0.580046
$381$	−11.0795	−0.567618
$382$	−54.8756	−2.80768
$383$	19.4334	0.993000	0.496500	−	0.868037i	$-0.334618\pi$
$383$	19.4334	0.993000	0.496500	+	0.868037i	$0.334618\pi$
$384$	−19.8387	−1.01239
$385$	2.61336	0.133189
$386$	27.2244	1.38568
$387$	−4.42917	−0.225148
$388$	−26.4137	−1.34095
$389$	23.9804	1.21585	0.607926	−	0.793994i	$-0.292002\pi$
$389$	23.9804	1.21585	0.607926	+	0.793994i	$0.292002\pi$
$390$	0	0
$391$	−7.39646	−0.374055
$392$	−3.33006	−0.168193
$393$	6.90089	0.348104
$394$	53.4693	2.69375
$395$	−8.48575	−0.426964
$396$	9.94764	0.499888
$397$	38.3146	1.92296	0.961478	−	0.274882i	$-0.0886387\pi$
$397$	38.3146	1.92296	0.961478	+	0.274882i	$0.0886387\pi$
$398$	−64.9420	−3.25525
$399$	3.66012	0.183235
$400$	−3.77327	−0.188664
$401$	8.93360	0.446123	0.223061	−	0.974804i	$-0.428395\pi$
$401$	8.93360	0.446123	0.223061	+	0.974804i	$0.428395\pi$
$402$	0.0228900	0.00114165
$403$	0	0
$404$	63.1295	3.14081
$405$	0.900885	0.0447653
$406$	−12.4193	−0.616362
$407$	24.9986	1.23914
$408$	5.56100	0.275311
$409$	1.92475	0.0951727	0.0475863	−	0.998867i	$-0.484847\pi$
$409$	1.92475	0.0951727	0.0475863	+	0.998867i	$0.484847\pi$
$410$	15.3660	0.758873
$411$	−12.5185	−0.617490
$412$	27.6274	1.36110
$413$	9.48575	0.466763
$414$	10.3202	0.507212
$415$	1.42398	0.0699006
$416$	0	0
$417$	−3.33006	−0.163074
$418$	24.7396	1.21005
$419$	−21.4759	−1.04917	−0.524584	−	0.851359i	$-0.675779\pi$
$419$	−21.4759	−1.04917	−0.524584	+	0.851359i	$0.675779\pi$
$420$	−3.08929	−0.150742
$421$	−34.8050	−1.69629	−0.848146	−	0.529762i	$-0.822281\pi$
$421$	−34.8050	−1.69629	−0.848146	+	0.529762i	$0.822281\pi$
$422$	15.8583	0.771972
$423$	6.95746	0.338283
$424$	0.471711	0.0229083
$425$	−6.99439	−0.339278
$426$	32.8289	1.59056
$427$	−2.51846	−0.121877
$428$	12.4390	0.601262
$429$	0	0
$430$	9.29734	0.448358
$431$	24.0795	1.15987	0.579934	−	0.814664i	$-0.303078\pi$
$431$	24.0795	1.15987	0.579934	+	0.814664i	$0.303078\pi$
$432$	−0.900885	−0.0433439
$433$	1.87800	0.0902507	0.0451253	−	0.998981i	$-0.485631\pi$
$433$	1.87800	0.0902507	0.0451253	+	0.998981i	$0.485631\pi$
$434$	−15.2875	−0.733824
$435$	−4.80177	−0.230227
$436$	−30.3431	−1.45317
$437$	16.2113	0.775491
$438$	−5.99018	−0.286222
$439$	−22.4998	−1.07386	−0.536928	−	0.843628i	$-0.680415\pi$
$439$	−22.4998	−1.07386	−0.536928	+	0.843628i	$0.680415\pi$
$440$	−8.70266	−0.414883
$441$	1.00000	0.0476190
$442$	0	0
$443$	16.4988	0.783882	0.391941	−	0.919990i	$-0.371804\pi$
$443$	16.4988	0.783882	0.391941	+	0.919990i	$0.371804\pi$
$444$	−29.5512	−1.40244
$445$	7.49557	0.355324
$446$	47.8092	2.26383
$447$	−15.6742	−0.741362
$448$	−12.4292	−0.587223
$449$	−33.9182	−1.60070	−0.800349	−	0.599535i	$-0.795352\pi$
$449$	−33.9182	−1.60070	−0.800349	+	0.599535i	$0.795352\pi$
$450$	9.75923	0.460055
$451$	−21.2352	−0.999925
$452$	−21.8191	−1.02628
$453$	−8.46189	−0.397574
$454$	−3.50540	−0.164517
$455$	0	0
$456$	−12.1884	−0.570774
$457$	−4.56198	−0.213400	−0.106700	−	0.994291i	$-0.534028\pi$
$457$	−4.56198	−0.213400	−0.106700	+	0.994291i	$0.534028\pi$
$458$	−60.1501	−2.81063
$459$	−1.66994	−0.0779462
$460$	−13.6830	−0.637974
$461$	−5.75038	−0.267822	−0.133911	−	0.990993i	$-0.542754\pi$
$461$	−5.75038	−0.267822	−0.133911	+	0.990993i	$0.542754\pi$
$462$	6.75923	0.314468
$463$	−19.3726	−0.900321	−0.450160	−	0.892948i	$-0.648633\pi$
$463$	−19.3726	−0.900321	−0.450160	+	0.892948i	$0.648633\pi$
$464$	4.80177	0.222917
$465$	−5.91071	−0.274103
$466$	56.0075	2.59450
$467$	−27.7723	−1.28515	−0.642574	−	0.766223i	$-0.722134\pi$
$467$	−27.7723	−1.28515	−0.642574	+	0.766223i	$0.722134\pi$
$468$	0	0
$469$	0.00982378	0.000453620 0
$470$	−14.6045	−0.673656
$471$	24.7396	1.13994
$472$	−31.5881	−1.45396
$473$	−12.8485	−0.590776
$474$	−21.9476	−1.00809
$475$	15.3301	0.703391
$476$	5.72652	0.262475
$477$	−0.141653	−0.00648582
$478$	−57.4595	−2.62814
$479$	−11.8911	−0.543316	−0.271658	−	0.962394i	$-0.587572\pi$
$479$	−11.8911	−0.543316	−0.271658	+	0.962394i	$0.587572\pi$
$480$	−4.10894	−0.187547
$481$	0	0
$482$	9.24174	0.420950
$483$	4.42917	0.201534
$484$	−8.86396	−0.402907
$485$	−6.93921	−0.315093
$486$	2.33006	0.105694
$487$	−22.2735	−1.00931	−0.504654	−	0.863322i	$-0.668380\pi$
$487$	−22.2735	−1.00931	−0.504654	+	0.863322i	$0.668380\pi$
$488$	8.38664	0.379645
$489$	24.7167	1.11773
$490$	−2.09911	−0.0948283
$491$	6.18841	0.279279	0.139639	−	0.990202i	$-0.455406\pi$
$491$	6.18841	0.279279	0.139639	+	0.990202i	$0.455406\pi$
$492$	25.1024	1.13170
$493$	8.90089	0.400876
$494$	0	0
$495$	2.61336	0.117462
$496$	5.91071	0.265399
$497$	14.0893	0.631991
$498$	3.68301	0.165040
$499$	18.4236	0.824752	0.412376	−	0.911014i	$-0.364699\pi$
$499$	18.4236	0.824752	0.412376	+	0.911014i	$0.364699\pi$
$500$	−28.3857	−1.26945
$501$	10.7167	0.478787
$502$	44.1720	1.97149
$503$	23.5273	1.04903	0.524516	−	0.851401i	$-0.324246\pi$
$503$	23.5273	1.04903	0.524516	+	0.851401i	$0.324246\pi$
$504$	−3.33006	−0.148333
$505$	16.5849	0.738017
$506$	29.9378	1.33090
$507$	0	0
$508$	37.9934	1.68569
$509$	4.59469	0.203656	0.101828	−	0.994802i	$-0.467531\pi$
$509$	4.59469	0.203656	0.101828	+	0.994802i	$0.467531\pi$
$510$	3.50540	0.155222
$511$	−2.57083	−0.113727
$512$	10.1089	0.446756
$513$	3.66012	0.161598
$514$	−35.2908	−1.55661
$515$	7.25805	0.319828
$516$	15.1884	0.668632
$517$	20.1828	0.887638
$518$	−20.0795	−0.882241
$519$	7.28752	0.319887
$520$	0	0
$521$	−2.95325	−0.129384	−0.0646920	−	0.997905i	$-0.520607\pi$
$521$	−2.95325	−0.129384	−0.0646920	+	0.997905i	$0.520607\pi$
$522$	−12.4193	−0.543580
$523$	22.3431	0.976997	0.488498	−	0.872565i	$-0.337545\pi$
$523$	22.3431	0.976997	0.488498	+	0.872565i	$0.337545\pi$
$524$	−23.6643	−1.03378
$525$	4.18841	0.182797
$526$	−17.4629	−0.761417
$527$	10.9565	0.477272
$528$	−2.61336	−0.113732
$529$	−3.38242	−0.147062
$530$	0.297345	0.0129158
$531$	9.48575	0.411647
$532$	−12.5512	−0.544163
$533$	0	0
$534$	19.3866	0.838942
$535$	3.26787	0.141282
$536$	−0.0327138	−0.00141302
$537$	17.1122	0.738445
$538$	−19.7494	−0.851457
$539$	2.90089	0.124950
$540$	−3.08929	−0.132942
$541$	−2.66994	−0.114790	−0.0573949	−	0.998352i	$-0.518279\pi$
$541$	−2.66994	−0.114790	−0.0573949	+	0.998352i	$0.518279\pi$
$542$	−3.84528	−0.165169
$543$	−15.3529	−0.658858
$544$	7.61661	0.326559
$545$	−7.97150	−0.341462
$546$	0	0
$547$	−12.1973	−0.521517	−0.260759	−	0.965404i	$-0.583973\pi$
$547$	−12.1973	−0.521517	−0.260759	+	0.965404i	$0.583973\pi$
$548$	42.9280	1.83379
$549$	−2.51846	−0.107485
$550$	28.3104	1.20716
$551$	−19.5086	−0.831096
$552$	−14.7494	−0.627777
$553$	−9.41935	−0.400552
$554$	−75.8102	−3.22087
$555$	−7.76345	−0.329540
$556$	11.4193	0.484288
$557$	21.9902	0.931754	0.465877	−	0.884850i	$-0.345739\pi$
$557$	21.9902	0.931754	0.465877	+	0.884850i	$0.345739\pi$
$558$	−15.2875	−0.647172
$559$	0	0
$560$	0.811594	0.0342961
$561$	−4.84431	−0.204527
$562$	−37.9280	−1.59990
$563$	−22.2908	−0.939444	−0.469722	−	0.882814i	$-0.655646\pi$
$563$	−22.2908	−0.939444	−0.469722	+	0.882814i	$0.655646\pi$
$564$	−23.8583	−1.00462
$565$	−5.73213	−0.241152
$566$	−59.4366	−2.49831
$567$	1.00000	0.0419961
$568$	−46.9182	−1.96864
$569$	28.7863	1.20679	0.603393	−	0.797444i	$-0.293815\pi$
$569$	28.7863	1.20679	0.603393	+	0.797444i	$0.293815\pi$
$570$	−7.68301	−0.321806
$571$	18.4432	0.771824	0.385912	−	0.922535i	$-0.373887\pi$
$571$	18.4432	0.771824	0.385912	+	0.922535i	$0.373887\pi$
$572$	0	0
$573$	−23.5512	−0.983865
$574$	17.0566	0.711928
$575$	18.5512	0.773638
$576$	−12.4292	−0.517882
$577$	−1.10894	−0.0461657	−0.0230829	−	0.999734i	$-0.507348\pi$
$577$	−1.10894	−0.0461657	−0.0230829	+	0.999734i	$0.507348\pi$
$578$	33.1132	1.37733
$579$	11.6840	0.485570
$580$	16.4661	0.683718
$581$	1.58065	0.0655764
$582$	−17.9476	−0.743954
$583$	−0.410918	−0.0170185
$584$	8.56100	0.354257
$585$	0	0
$586$	24.2319	1.00101
$587$	24.7789	1.02273	0.511367	−	0.859362i	$-0.329139\pi$
$587$	24.7789	1.02273	0.511367	+	0.859362i	$0.329139\pi$
$588$	−3.42917	−0.141417
$589$	−24.0140	−0.989481
$590$	−19.9117	−0.819751
$591$	22.9476	0.943940
$592$	7.76345	0.319076
$593$	14.7157	0.604302	0.302151	−	0.953260i	$-0.402295\pi$
$593$	14.7157	0.604302	0.302151	+	0.953260i	$0.402295\pi$
$594$	6.75923	0.277335
$595$	1.50443	0.0616754
$596$	53.7494	2.20166
$597$	−27.8714	−1.14070
$598$	0	0
$599$	−10.8018	−0.441348	−0.220674	−	0.975348i	$-0.570826\pi$
$599$	−10.8018	−0.441348	−0.220674	+	0.975348i	$0.570826\pi$
$600$	−13.9476	−0.569410
$601$	−0.900885	−0.0367479	−0.0183739	−	0.999831i	$-0.505849\pi$
$601$	−0.900885	−0.0367479	−0.0183739	+	0.999831i	$0.505849\pi$
$602$	10.3202	0.420621
$603$	0.00982378	0.000400055 0
$604$	29.0173	1.18070
$605$	−2.32867	−0.0946738
$606$	42.8953	1.74250
$607$	−11.4324	−0.464027	−0.232014	−	0.972713i	$-0.574531\pi$
$607$	−11.4324	−0.464027	−0.232014	+	0.972713i	$0.574531\pi$
$608$	−16.6938	−0.677023
$609$	−5.33006	−0.215985
$610$	5.28655	0.214046
$611$	0	0
$612$	5.72652	0.231481
$613$	3.34312	0.135028	0.0675138	−	0.997718i	$-0.478493\pi$
$613$	3.34312	0.135028	0.0675138	+	0.997718i	$0.478493\pi$
$614$	−70.7569	−2.85551
$615$	6.59469	0.265924
$616$	−9.66012	−0.389217
$617$	−8.22112	−0.330970	−0.165485	−	0.986212i	$-0.552919\pi$
$617$	−8.22112	−0.330970	−0.165485	+	0.986212i	$0.552919\pi$
$618$	18.7723	0.755133
$619$	−1.98035	−0.0795971	−0.0397985	−	0.999208i	$-0.512672\pi$
$619$	−1.98035	−0.0795971	−0.0397985	+	0.999208i	$0.512672\pi$
$620$	20.2688	0.814016
$621$	4.42917	0.177737
$622$	−36.9280	−1.48068
$623$	8.32023	0.333343
$624$	0	0
$625$	13.4848	0.539391
$626$	−48.2384	−1.92799
$627$	10.6176	0.424025
$628$	−84.8363	−3.38534
$629$	14.3909	0.573801
$630$	−2.09911	−0.0836307
$631$	12.4151	0.494239	0.247119	−	0.968985i	$-0.420516\pi$
$631$	12.4151	0.494239	0.247119	+	0.968985i	$0.420516\pi$
$632$	31.3670	1.24771
$633$	6.80599	0.270514
$634$	30.2221	1.20027
$635$	9.98133	0.396097
$636$	0.485751	0.0192613
$637$	0	0
$638$	−36.0271	−1.42633
$639$	14.0893	0.557364
$640$	17.8724	0.706468
$641$	−11.5708	−0.457020	−0.228510	−	0.973542i	$-0.573385\pi$
$641$	−11.5708	−0.457020	−0.228510	+	0.973542i	$0.573385\pi$
$642$	8.45206	0.333576
$643$	2.35953	0.0930508	0.0465254	−	0.998917i	$-0.485185\pi$
$643$	2.35953	0.0930508	0.0465254	+	0.998917i	$0.485185\pi$
$644$	−15.1884	−0.598507
$645$	3.99018	0.157113
$646$	14.2417	0.560334
$647$	9.52829	0.374596	0.187298	−	0.982303i	$-0.440027\pi$
$647$	9.52829	0.374596	0.187298	+	0.982303i	$0.440027\pi$
$648$	−3.33006	−0.130817
$649$	27.5171	1.08014
$650$	0	0
$651$	−6.56100	−0.257146
$652$	−84.7578	−3.31937
$653$	−15.3487	−0.600642	−0.300321	−	0.953838i	$-0.597094\pi$
$653$	−15.3487	−0.600642	−0.300321	+	0.953838i	$0.597094\pi$
$654$	−20.6176	−0.806211
$655$	−6.21690	−0.242915
$656$	−6.59469	−0.257479
$657$	−2.57083	−0.100297
$658$	−16.2113	−0.631982
$659$	24.4956	0.954212	0.477106	−	0.878846i	$-0.341686\pi$
$659$	24.4956	0.954212	0.477106	+	0.878846i	$0.341686\pi$
$660$	−8.96168	−0.348833
$661$	0.646078	0.0251295	0.0125648	−	0.999921i	$-0.496000\pi$
$661$	0.646078	0.0251295	0.0125648	+	0.999921i	$0.496000\pi$
$662$	−61.6806	−2.39729
$663$	0	0
$664$	−5.26366	−0.204270
$665$	−3.29734	−0.127866
$666$	−20.0795	−0.778064
$667$	−23.6078	−0.914096
$668$	−36.7494	−1.42188
$669$	20.5185	0.793290
$670$	−0.0206212	−0.000796668 0
$671$	−7.30578	−0.282036
$672$	−4.56100	−0.175944
$673$	−42.3702	−1.63325	−0.816626	−	0.577167i	$-0.804158\pi$
$673$	−42.3702	−1.63325	−0.816626	+	0.577167i	$0.804158\pi$
$674$	−16.3637	−0.630308
$675$	4.18841	0.161212
$676$	0	0
$677$	25.7723	0.990510	0.495255	−	0.868748i	$-0.335075\pi$
$677$	25.7723	0.990510	0.495255	+	0.868748i	$0.335075\pi$
$678$	−14.8256	−0.569375
$679$	−7.70266	−0.295601
$680$	−5.00982	−0.192118
$681$	−1.50443	−0.0576497
$682$	−44.3473	−1.69815
$683$	11.3726	0.435160	0.217580	−	0.976042i	$-0.430184\pi$
$683$	11.3726	0.435160	0.217580	+	0.976042i	$0.430184\pi$
$684$	−12.5512	−0.479906
$685$	11.2777	0.430899
$686$	−2.33006	−0.0889621
$687$	−25.8148	−0.984897
$688$	−3.99018	−0.152124
$689$	0	0
$690$	−9.29734	−0.353944
$691$	14.5423	0.553216	0.276608	−	0.960983i	$-0.410790\pi$
$691$	14.5423	0.553216	0.276608	+	0.960983i	$0.410790\pi$
$692$	−24.9902	−0.949984
$693$	2.90089	0.110196
$694$	31.3235	1.18902
$695$	3.00000	0.113796
$696$	17.7494	0.672790
$697$	−12.2244	−0.463031
$698$	−2.94666	−0.111533
$699$	24.0369	0.909160
$700$	−14.3628	−0.542862
$701$	−5.69844	−0.215227	−0.107614	−	0.994193i	$-0.534321\pi$
$701$	−5.69844	−0.215227	−0.107614	+	0.994193i	$0.534321\pi$
$702$	0	0
$703$	−31.5414	−1.18960
$704$	−36.0556	−1.35890
$705$	−6.26787	−0.236062
$706$	−41.9280	−1.57798
$707$	18.4095	0.692361
$708$	−32.5283	−1.22249
$709$	40.8626	1.53463	0.767313	−	0.641273i	$-0.221593\pi$
$709$	40.8626	1.53463	0.767313	+	0.641273i	$0.221593\pi$
$710$	−29.5750	−1.10993
$711$	−9.41935	−0.353253
$712$	−27.7069	−1.03836
$713$	−29.0598	−1.08830
$714$	3.89106	0.145619
$715$	0	0
$716$	−58.6806	−2.19300
$717$	−24.6601	−0.920949
$718$	−55.2613	−2.06233
$719$	27.5685	1.02813	0.514065	−	0.857751i	$-0.328139\pi$
$719$	27.5685	1.02813	0.514065	+	0.857751i	$0.328139\pi$
$720$	0.811594	0.0302463
$721$	8.05658	0.300043
$722$	13.0566	0.485915
$723$	3.96631	0.147509
$724$	52.6479	1.95664
$725$	−22.3245	−0.829109
$726$	−6.02289	−0.223530
$727$	9.72652	0.360737	0.180368	−	0.983599i	$-0.442271\pi$
$727$	9.72652	0.360737	0.180368	+	0.983599i	$0.442271\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	5.39646	0.199732
$731$	−7.39646	−0.273568
$732$	8.63625	0.319205
$733$	52.3843	1.93486	0.967429	−	0.253144i	$-0.0814647\pi$
$733$	52.3843	1.93486	0.967429	+	0.253144i	$0.0814647\pi$
$734$	−53.6012	−1.97846
$735$	−0.900885	−0.0332296
$736$	−20.2015	−0.744636
$737$	0.0284977	0.00104972
$738$	17.0566	0.627861
$739$	52.8321	1.94346	0.971730	−	0.236093i	$-0.0758670\pi$
$739$	52.8321	1.94346	0.971730	+	0.236093i	$0.0758670\pi$
$740$	26.6222	0.978652
$741$	0	0
$742$	0.330059	0.0121168
$743$	−18.4717	−0.677661	−0.338831	−	0.940847i	$-0.610031\pi$
$743$	−18.4717	−0.677661	−0.338831	+	0.940847i	$0.610031\pi$
$744$	21.8485	0.801006
$745$	14.1206	0.517339
$746$	−15.2440	−0.558123
$747$	1.58065	0.0578330
$748$	16.6120	0.607394
$749$	3.62740	0.132542
$750$	−19.2875	−0.704281
$751$	18.0837	0.659883	0.329941	−	0.944001i	$-0.392971\pi$
$751$	18.0837	0.659883	0.329941	+	0.944001i	$0.392971\pi$
$752$	6.26787	0.228566
$753$	18.9575	0.690848
$754$	0	0
$755$	7.62319	0.277436
$756$	−3.42917	−0.124718
$757$	40.7863	1.48240	0.741202	−	0.671282i	$-0.234256\pi$
$757$	40.7863	1.48240	0.741202	+	0.671282i	$0.234256\pi$
$758$	22.9911	0.835076
$759$	12.8485	0.466372
$760$	10.9804	0.398299
$761$	−18.4956	−0.670464	−0.335232	−	0.942136i	$-0.608815\pi$
$761$	−18.4956	−0.670464	−0.335232	+	0.942136i	$0.608815\pi$
$762$	25.8158	0.935208
$763$	−8.84852	−0.320338
$764$	80.7611	2.92183
$765$	1.50443	0.0543926
$766$	−45.2809	−1.63607
$767$	0	0
$768$	21.3670	0.771015
$769$	−50.5161	−1.82166	−0.910829	−	0.412785i	$-0.864556\pi$
$769$	−50.5161	−1.82166	−0.910829	+	0.412785i	$0.864556\pi$
$770$	−6.08929	−0.219443
$771$	−15.1459	−0.545465
$772$	−40.0664	−1.44202
$773$	2.57407	0.0925828	0.0462914	−	0.998928i	$-0.485260\pi$
$773$	2.57407	0.0925828	0.0462914	+	0.998928i	$0.485260\pi$
$774$	10.3202	0.370953
$775$	−27.4801	−0.987116
$776$	25.6503	0.920792
$777$	−8.61758	−0.309154
$778$	−55.8756	−2.00324
$779$	26.7929	0.959956
$780$	0	0
$781$	40.8714	1.46249
$782$	17.2342	0.616293
$783$	−5.33006	−0.190481
$784$	0.900885	0.0321745
$785$	−22.2875	−0.795476
$786$	−16.0795	−0.573536
$787$	−20.4998	−0.730739	−0.365369	−	0.930863i	$-0.619057\pi$
$787$	−20.4998	−0.730739	−0.365369	+	0.930863i	$0.619057\pi$
$788$	−78.6914	−2.80327
$789$	−7.49460	−0.266815
$790$	19.7723	0.703467
$791$	−6.36277	−0.226234
$792$	−9.66012	−0.343257
$793$	0	0
$794$	−89.2753	−3.16826
$795$	0.127613	0.00452595
$796$	95.5759	3.38760
$797$	−55.4834	−1.96532	−0.982661	−	0.185410i	$-0.940639\pi$
$797$	−55.4834	−1.96532	−0.982661	+	0.185410i	$0.940639\pi$
$798$	−8.52829	−0.301898
$799$	11.6186	0.411035
$800$	−19.1033	−0.675405
$801$	8.32023	0.293981
$802$	−20.8158	−0.735032
$803$	−7.45767	−0.263176
$804$	−0.0336875	−0.00118806
$805$	−3.99018	−0.140635
$806$	0	0
$807$	−8.47593	−0.298367
$808$	−61.3048	−2.15670
$809$	−5.22770	−0.183796	−0.0918981	−	0.995768i	$-0.529293\pi$
$809$	−5.22770	−0.183796	−0.0918981	+	0.995768i	$0.529293\pi$
$810$	−2.09911	−0.0737554
$811$	−14.5989	−0.512637	−0.256318	−	0.966592i	$-0.582510\pi$
$811$	−14.5989	−0.512637	−0.256318	+	0.966592i	$0.582510\pi$
$812$	18.2777	0.641421
$813$	−1.65029	−0.0578783
$814$	−58.2482	−2.04160
$815$	−22.2669	−0.779975
$816$	−1.50443	−0.0526654
$817$	16.2113	0.567161
$818$	−4.48478	−0.156807
$819$	0	0
$820$	−22.6143	−0.789727
$821$	−52.1589	−1.82036	−0.910180	−	0.414214i	$-0.864057\pi$
$821$	−52.1589	−1.82036	−0.910180	+	0.414214i	$0.864057\pi$
$822$	29.1688	1.01738
$823$	−2.33988	−0.0815632	−0.0407816	−	0.999168i	$-0.512985\pi$
$823$	−2.33988	−0.0815632	−0.0407816	+	0.999168i	$0.512985\pi$
$824$	−26.8289	−0.934628
$825$	12.1501	0.423012
$826$	−22.1024	−0.769039
$827$	10.3581	0.360188	0.180094	−	0.983649i	$-0.442360\pi$
$827$	10.3581	0.360188	0.180094	+	0.983649i	$0.442360\pi$
$828$	−15.1884	−0.527834
$829$	18.2440	0.633641	0.316820	−	0.948486i	$-0.397385\pi$
$829$	18.2440	0.633641	0.316820	+	0.948486i	$0.397385\pi$
$830$	−3.31797	−0.115168
$831$	−32.5357	−1.12865
$832$	0	0
$833$	1.66994	0.0578600
$834$	7.75923	0.268680
$835$	−9.65451	−0.334108
$836$	−36.4095	−1.25925
$837$	−6.56100	−0.226781
$838$	50.0402	1.72861
$839$	47.7807	1.64957	0.824787	−	0.565444i	$-0.191295\pi$
$839$	47.7807	1.64957	0.824787	+	0.565444i	$0.191295\pi$
$840$	3.00000	0.103510
$841$	−0.590474	−0.0203612
$842$	81.0977	2.79481
$843$	−16.2777	−0.560634
$844$	−23.3389	−0.803358
$845$	0	0
$846$	−16.2113	−0.557356
$847$	−2.58487	−0.0888171
$848$	−0.127613	−0.00438224
$849$	−25.5086	−0.875454
$850$	16.2973	0.558994
$851$	−38.1688	−1.30841
$852$	−48.3146	−1.65523
$853$	3.27867	0.112260	0.0561298	−	0.998423i	$-0.482124\pi$
$853$	3.27867	0.112260	0.0561298	+	0.998423i	$0.482124\pi$
$854$	5.86817	0.200805
$855$	−3.29734	−0.112767
$856$	−12.0795	−0.412868
$857$	−26.3016	−0.898444	−0.449222	−	0.893420i	$-0.648299\pi$
$857$	−26.3016	−0.898444	−0.449222	+	0.893420i	$0.648299\pi$
$858$	0	0
$859$	−47.0313	−1.60469	−0.802344	−	0.596862i	$-0.796414\pi$
$859$	−47.0313	−1.60469	−0.802344	+	0.596862i	$0.796414\pi$
$860$	−13.6830	−0.466587
$861$	7.32023	0.249473
$862$	−56.1066	−1.91100
$863$	−42.9649	−1.46254	−0.731271	−	0.682087i	$-0.761073\pi$
$863$	−42.9649	−1.46254	−0.731271	+	0.682087i	$0.761073\pi$
$864$	−4.56100	−0.155168
$865$	−6.56522	−0.223224
$866$	−4.37584	−0.148697
$867$	14.2113	0.482641
$868$	22.4988	0.763660
$869$	−27.3245	−0.926919
$870$	11.1884	0.379322
$871$	0	0
$872$	29.4661	0.997848
$873$	−7.70266	−0.260695
$874$	−37.7733	−1.27770
$875$	−8.27770	−0.279837
$876$	8.81581	0.297859
$877$	−52.8766	−1.78552	−0.892758	−	0.450536i	$-0.851233\pi$
$877$	−52.8766	−1.78552	−0.892758	+	0.450536i	$0.851233\pi$
$878$	52.4258	1.76929
$879$	10.3997	0.350773
$880$	2.35434	0.0793648
$881$	4.16033	0.140165	0.0700825	−	0.997541i	$-0.477674\pi$
$881$	4.16033	0.140165	0.0700825	+	0.997541i	$0.477674\pi$
$882$	−2.33006	−0.0784572
$883$	23.1164	0.777929	0.388964	−	0.921253i	$-0.372833\pi$
$883$	23.1164	0.777929	0.388964	+	0.921253i	$0.372833\pi$
$884$	0	0
$885$	−8.54557	−0.287256
$886$	−38.4432	−1.29153
$887$	−13.6035	−0.456762	−0.228381	−	0.973572i	$-0.573343\pi$
$887$	−13.6035	−0.456762	−0.228381	+	0.973572i	$0.573343\pi$
$888$	28.6970	0.963010
$889$	11.0795	0.371593
$890$	−17.4651	−0.585432
$891$	2.90089	0.0971833
$892$	−70.3614	−2.35587
$893$	−25.4651	−0.852158
$894$	36.5217	1.22147
$895$	−15.4161	−0.515304
$896$	19.8387	0.662764
$897$	0	0
$898$	79.0313	2.63731
$899$	34.9705	1.16633
$900$	−14.3628	−0.478759
$901$	−0.236551	−0.00788067
$902$	49.4792	1.64748
$903$	4.42917	0.147394
$904$	21.1884	0.704716
$905$	13.8312	0.459766
$906$	19.7167	0.655043
$907$	−8.35392	−0.277387	−0.138694	−	0.990335i	$-0.544290\pi$
$907$	−8.35392	−0.277387	−0.138694	+	0.990335i	$0.544290\pi$
$908$	5.15893	0.171205
$909$	18.4095	0.610605
$910$	0	0
$911$	−43.8471	−1.45272	−0.726360	−	0.687314i	$-0.758790\pi$
$911$	−43.8471	−1.45272	−0.726360	+	0.687314i	$0.758790\pi$
$912$	3.29734	0.109186
$913$	4.58528	0.151751
$914$	10.6297	0.351598
$915$	2.26885	0.0750058
$916$	88.5236	2.92490
$917$	−6.90089	−0.227887
$918$	3.89106	0.128424
$919$	−5.70266	−0.188113	−0.0940566	−	0.995567i	$-0.529983\pi$
$919$	−5.70266	−0.188113	−0.0940566	+	0.995567i	$0.529983\pi$
$920$	13.2875	0.438077
$921$	−30.3670	−1.00063
$922$	13.3987	0.441264
$923$	0	0
$924$	−9.94764	−0.327253
$925$	−36.0939	−1.18676
$926$	45.1393	1.48337
$927$	8.05658	0.264613
$928$	24.3104	0.798028
$929$	1.55354	0.0509701	0.0254851	−	0.999675i	$-0.491887\pi$
$929$	1.55354	0.0509701	0.0254851	+	0.999675i	$0.491887\pi$
$930$	13.7723	0.451611
$931$	−3.66012	−0.119956
$932$	−82.4268	−2.69998
$933$	−15.8485	−0.518857
$934$	64.7111	2.11741
$935$	4.36416	0.142723
$936$	0	0
$937$	21.2267	0.693447	0.346723	−	0.937967i	$-0.387294\pi$
$937$	21.2267	0.693447	0.346723	+	0.937967i	$0.387294\pi$
$938$	−0.0228900	−0.000747385 0
$939$	−20.7027	−0.675606
$940$	21.4936	0.701045
$941$	54.2950	1.76997	0.884983	−	0.465624i	$-0.154170\pi$
$941$	54.2950	1.76997	0.884983	+	0.465624i	$0.154170\pi$
$942$	−57.6447	−1.87817
$943$	32.4226	1.05582
$944$	8.54557	0.278135
$945$	−0.900885	−0.0293058
$946$	29.9378	0.973362
$947$	−2.43663	−0.0791799	−0.0395900	−	0.999216i	$-0.512605\pi$
$947$	−2.43663	−0.0791799	−0.0395900	+	0.999216i	$0.512605\pi$
$948$	32.3006	1.04907
$949$	0	0
$950$	−35.7199	−1.15891
$951$	12.9705	0.420598
$952$	−5.56100	−0.180233
$953$	−31.0837	−1.00690	−0.503450	−	0.864025i	$-0.667936\pi$
$953$	−31.0837	−1.00690	−0.503450	+	0.864025i	$0.667936\pi$
$954$	0.330059	0.0106860
$955$	21.2169	0.686563
$956$	84.5638	2.73499
$957$	−15.4619	−0.499812
$958$	27.7069	0.895168
$959$	12.5185	0.404242
$960$	11.1973	0.361390
$961$	12.0468	0.388605
$962$	0	0
$963$	3.62740	0.116891
$964$	−13.6012	−0.438064
$965$	−10.5259	−0.338841
$966$	−10.3202	−0.332048
$967$	3.01965	0.0971053	0.0485527	−	0.998821i	$-0.484539\pi$
$967$	3.01965	0.0971053	0.0485527	+	0.998821i	$0.484539\pi$
$968$	8.60776	0.276664
$969$	6.11218	0.196352
$970$	16.1688	0.519148
$971$	41.5750	1.33421	0.667103	−	0.744965i	$-0.267534\pi$
$971$	41.5750	1.33421	0.667103	+	0.744965i	$0.267534\pi$
$972$	−3.42917	−0.109991
$973$	3.33006	0.106757
$974$	51.8985	1.66294
$975$	0	0
$976$	−2.26885	−0.0726240
$977$	21.5512	0.689483	0.344742	−	0.938698i	$-0.387967\pi$
$977$	21.5512	0.689483	0.344742	+	0.938698i	$0.387967\pi$
$978$	−57.5914	−1.84157
$979$	24.1360	0.771391
$980$	3.08929	0.0986838
$981$	−8.84852	−0.282512
$982$	−14.4193	−0.460140
$983$	23.4619	0.748318	0.374159	−	0.927365i	$-0.377931\pi$
$983$	23.4619	0.748318	0.374159	+	0.927365i	$0.377931\pi$
$984$	−24.3768	−0.777104
$985$	−20.6732	−0.658702
$986$	−20.7396	−0.660483
$987$	−6.95746	−0.221458
$988$	0	0
$989$	19.6176	0.623803
$990$	−6.08929	−0.193530
$991$	−26.2538	−0.833981	−0.416990	−	0.908911i	$-0.636915\pi$
$991$	−26.2538	−0.833981	−0.416990	+	0.908911i	$0.636915\pi$
$992$	29.9247	0.950112
$993$	−26.4717	−0.840054
$994$	−32.8289	−1.04127
$995$	25.1089	0.796007
$996$	−5.42032	−0.171750
$997$	1.49039	0.0472010	0.0236005	−	0.999721i	$-0.492487\pi$
$997$	1.49039	0.0472010	0.0236005	+	0.999721i	$0.492487\pi$
$998$	−42.9280	−1.35886
$999$	−8.61758	−0.272648

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.m.1.1		3
13.3	even	3		273.2.k.b.22.3	✓	6
13.9	even	3		273.2.k.b.211.3	yes	6
13.12	even	2		3549.2.a.l.1.3		3
39.29	odd	6		819.2.o.f.568.1		6
39.35	odd	6		819.2.o.f.757.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.b.22.3	✓	6	13.3	even	3
273.2.k.b.211.3	yes	6	13.9	even	3
819.2.o.f.568.1		6	39.29	odd	6
819.2.o.f.757.1		6	39.35	odd	6
3549.2.a.l.1.3		3	13.12	even	2
3549.2.a.m.1.1		3	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:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q-2.33006 q^{2} -1.00000 q^{3} +3.42917 q^{4} +0.900885 q^{5} +2.33006 q^{6} +1.00000 q^{7} -3.33006 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.33006 q^{2} -1.00000 q^{3} +3.42917 q^{4} +0.900885 q^{5} +2.33006 q^{6} +1.00000 q^{7} -3.33006 q^{8} +1.00000 q^{9} -2.09911 q^{10} +2.90089 q^{11} -3.42917 q^{12} -2.33006 q^{14} -0.900885 q^{15} +0.900885 q^{16} +1.66994 q^{17} -2.33006 q^{18} -3.66012 q^{19} +3.08929 q^{20} -1.00000 q^{21} -6.75923 q^{22} -4.42917 q^{23} +3.33006 q^{24} -4.18841 q^{25} -1.00000 q^{27} +3.42917 q^{28} +5.33006 q^{29} +2.09911 q^{30} +6.56100 q^{31} +4.56100 q^{32} -2.90089 q^{33} -3.89106 q^{34} +0.900885 q^{35} +3.42917 q^{36} +8.61758 q^{37} +8.52829 q^{38} -3.00000 q^{40} -7.32023 q^{41} +2.33006 q^{42} -4.42917 q^{43} +9.94764 q^{44} +0.900885 q^{45} +10.3202 q^{46} +6.95746 q^{47} -0.900885 q^{48} +1.00000 q^{49} +9.75923 q^{50} -1.66994 q^{51} -0.141653 q^{53} +2.33006 q^{54} +2.61336 q^{55} -3.33006 q^{56} +3.66012 q^{57} -12.4193 q^{58} +9.48575 q^{59} -3.08929 q^{60} -2.51846 q^{61} -15.2875 q^{62} +1.00000 q^{63} -12.4292 q^{64} +6.75923 q^{66} +0.00982378 q^{67} +5.72652 q^{68} +4.42917 q^{69} -2.09911 q^{70} +14.0893 q^{71} -3.33006 q^{72} -2.57083 q^{73} -20.0795 q^{74} +4.18841 q^{75} -12.5512 q^{76} +2.90089 q^{77} -9.41935 q^{79} +0.811594 q^{80} +1.00000 q^{81} +17.0566 q^{82} +1.58065 q^{83} -3.42917 q^{84} +1.50443 q^{85} +10.3202 q^{86} -5.33006 q^{87} -9.66012 q^{88} +8.32023 q^{89} -2.09911 q^{90} -15.1884 q^{92} -6.56100 q^{93} -16.2113 q^{94} -3.29734 q^{95} -4.56100 q^{96} -7.70266 q^{97} -2.33006 q^{98} +2.90089 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} + 4 q^{4} + 2 q^{5} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^3 + 4 * q^4 + 2 * q^5 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{3} + 4 q^{4} + 2 q^{5} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 7 q^{10} + 8 q^{11} - 4 q^{12} - 2 q^{15} + 2 q^{16} + 12 q^{17} + 3 q^{19} - 11 q^{20} - 3 q^{21} - 7 q^{22} - 7 q^{23} + 3 q^{24} + 7 q^{25} - 3 q^{27} + 4 q^{28} + 9 q^{29} + 7 q^{30} + 5 q^{31} - q^{32} - 8 q^{33} + 10 q^{34} + 2 q^{35} + 4 q^{36} + 20 q^{38} - 9 q^{40} + 6 q^{41} - 7 q^{43} - 3 q^{44} + 2 q^{45} + 3 q^{46} + 9 q^{47} - 2 q^{48} + 3 q^{49} + 16 q^{50} - 12 q^{51} - 13 q^{53} + 26 q^{55} - 3 q^{56} - 3 q^{57} - 10 q^{58} + 11 q^{59} + 11 q^{60} + 19 q^{61} - 27 q^{62} + 3 q^{63} - 31 q^{64} + 7 q^{66} + 21 q^{67} + 13 q^{68} + 7 q^{69} - 7 q^{70} + 22 q^{71} - 3 q^{72} - 14 q^{73} - 19 q^{74} - 7 q^{75} - 2 q^{76} + 8 q^{77} - q^{79} + 22 q^{80} + 3 q^{81} + 40 q^{82} + 32 q^{83} - 4 q^{84} + q^{85} + 3 q^{86} - 9 q^{87} - 15 q^{88} - 3 q^{89} - 7 q^{90} - 26 q^{92} - 5 q^{93} + q^{94} - 12 q^{95} + q^{96} - 21 q^{97} + 8 q^{99}+O(q^{100}) \) 3 * q - 3 * q^3 + 4 * q^4 + 2 * q^5 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 7 * q^10 + 8 * q^11 - 4 * q^12 - 2 * q^15 + 2 * q^16 + 12 * q^17 + 3 * q^19 - 11 * q^20 - 3 * q^21 - 7 * q^22 - 7 * q^23 + 3 * q^24 + 7 * q^25 - 3 * q^27 + 4 * q^28 + 9 * q^29 + 7 * q^30 + 5 * q^31 - q^32 - 8 * q^33 + 10 * q^34 + 2 * q^35 + 4 * q^36 + 20 * q^38 - 9 * q^40 + 6 * q^41 - 7 * q^43 - 3 * q^44 + 2 * q^45 + 3 * q^46 + 9 * q^47 - 2 * q^48 + 3 * q^49 + 16 * q^50 - 12 * q^51 - 13 * q^53 + 26 * q^55 - 3 * q^56 - 3 * q^57 - 10 * q^58 + 11 * q^59 + 11 * q^60 + 19 * q^61 - 27 * q^62 + 3 * q^63 - 31 * q^64 + 7 * q^66 + 21 * q^67 + 13 * q^68 + 7 * q^69 - 7 * q^70 + 22 * q^71 - 3 * q^72 - 14 * q^73 - 19 * q^74 - 7 * q^75 - 2 * q^76 + 8 * q^77 - q^79 + 22 * q^80 + 3 * q^81 + 40 * q^82 + 32 * q^83 - 4 * q^84 + q^85 + 3 * q^86 - 9 * q^87 - 15 * q^88 - 3 * q^89 - 7 * q^90 - 26 * q^92 - 5 * q^93 + q^94 - 12 * q^95 + q^96 - 21 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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