LMFDB - Embedded newform 3381.2.a.z.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, 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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.3176240.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 9x^{3} + 7x^{2} + 19x - 9 $ x^5 - x^4 - 9x^3 + 7x^2 + 19*x - 9
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.34113$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34113 q^{2} +1.00000 q^{3} +3.48089 q^{4} -1.12582 q^{5} -2.34113 q^{6} -3.46695 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.34113 q^{2} +1.00000 q^{3} +3.48089 q^{4} -1.12582 q^{5} -2.34113 q^{6} -3.46695 q^{8} +1.00000 q^{9} +2.63569 q^{10} +3.82202 q^{11} +3.48089 q^{12} -4.94784 q^{13} -1.12582 q^{15} +1.15480 q^{16} +0.110775 q^{17} -2.34113 q^{18} +2.32608 q^{19} -3.91885 q^{20} -8.94784 q^{22} +1.00000 q^{23} -3.46695 q^{24} -3.73253 q^{25} +11.5835 q^{26} +1.00000 q^{27} -2.85100 q^{29} +2.63569 q^{30} +5.60671 q^{31} +4.23035 q^{32} +3.82202 q^{33} -0.259338 q^{34} +3.48089 q^{36} -8.34693 q^{37} -5.44566 q^{38} -4.94784 q^{39} +3.90316 q^{40} +3.39140 q^{41} +0.947838 q^{43} +13.3040 q^{44} -1.12582 q^{45} -2.34113 q^{46} +12.9339 q^{47} +1.15480 q^{48} +8.73833 q^{50} +0.110775 q^{51} -17.2229 q^{52} +4.09060 q^{53} -2.34113 q^{54} -4.30290 q^{55} +2.32608 q^{57} +6.67456 q^{58} -3.27392 q^{59} -3.91885 q^{60} +12.8836 q^{61} -13.1260 q^{62} -12.2134 q^{64} +5.57038 q^{65} -8.94784 q^{66} -9.37122 q^{67} +0.385595 q^{68} +1.00000 q^{69} -1.97682 q^{71} -3.46695 q^{72} +4.84800 q^{73} +19.5413 q^{74} -3.73253 q^{75} +8.09684 q^{76} +11.5835 q^{78} -11.7239 q^{79} -1.30010 q^{80} +1.00000 q^{81} -7.93970 q^{82} -2.79303 q^{83} -0.124713 q^{85} -2.21901 q^{86} -2.85100 q^{87} -13.2507 q^{88} +8.96869 q^{89} +2.63569 q^{90} +3.48089 q^{92} +5.60671 q^{93} -30.2799 q^{94} -2.61875 q^{95} +4.23035 q^{96} +4.88733 q^{97} +3.82202 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 5 q^{3} + 9 q^{4} + 2 q^{5} + q^{6} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + q^2 + 5 * q^3 + 9 * q^4 + 2 * q^5 + q^6 + 3 * q^8 + 5 * q^9	$ 5 q + q^{2} + 5 q^{3} + 9 q^{4} + 2 q^{5} + q^{6} + 3 q^{8} + 5 q^{9} - 2 q^{11} + 9 q^{12} + 4 q^{13} + 2 q^{15} + q^{16} + 2 q^{17} + q^{18} + 8 q^{19} + 12 q^{20} - 16 q^{22} + 5 q^{23} + 3 q^{24} + 5 q^{25} + 16 q^{26} + 5 q^{27} + 4 q^{29} + 12 q^{31} + 7 q^{32} - 2 q^{33} + 10 q^{34} + 9 q^{36} - 6 q^{37} - 8 q^{38} + 4 q^{39} + 30 q^{40} + 6 q^{41} - 24 q^{43} + 16 q^{44} + 2 q^{45} + q^{46} + 24 q^{47} + q^{48} - 3 q^{50} + 2 q^{51} - 4 q^{52} + 2 q^{53} + q^{54} + 8 q^{55} + 8 q^{57} + 4 q^{58} + 16 q^{59} + 12 q^{60} + 22 q^{61} + 6 q^{62} - 29 q^{64} + 22 q^{65} - 16 q^{66} - 16 q^{67} + 14 q^{68} + 5 q^{69} + 16 q^{71} + 3 q^{72} + 8 q^{74} + 5 q^{75} + 30 q^{76} + 16 q^{78} + 12 q^{79} - 6 q^{80} + 5 q^{81} + 24 q^{82} + 10 q^{83} - 14 q^{85} - 20 q^{86} + 4 q^{87} - 8 q^{88} - 16 q^{89} + 9 q^{92} + 12 q^{93} - 32 q^{94} + 18 q^{95} + 7 q^{96} - 4 q^{97} - 2 q^{99}+O(q^{100}) $ 5 * q + q^2 + 5 * q^3 + 9 * q^4 + 2 * q^5 + q^6 + 3 * q^8 + 5 * q^9 - 2 * q^11 + 9 * q^12 + 4 * q^13 + 2 * q^15 + q^16 + 2 * q^17 + q^18 + 8 * q^19 + 12 * q^20 - 16 * q^22 + 5 * q^23 + 3 * q^24 + 5 * q^25 + 16 * q^26 + 5 * q^27 + 4 * q^29 + 12 * q^31 + 7 * q^32 - 2 * q^33 + 10 * q^34 + 9 * q^36 - 6 * q^37 - 8 * q^38 + 4 * q^39 + 30 * q^40 + 6 * q^41 - 24 * q^43 + 16 * q^44 + 2 * q^45 + q^46 + 24 * q^47 + q^48 - 3 * q^50 + 2 * q^51 - 4 * q^52 + 2 * q^53 + q^54 + 8 * q^55 + 8 * q^57 + 4 * q^58 + 16 * q^59 + 12 * q^60 + 22 * q^61 + 6 * q^62 - 29 * q^64 + 22 * q^65 - 16 * q^66 - 16 * q^67 + 14 * q^68 + 5 * q^69 + 16 * q^71 + 3 * q^72 + 8 * q^74 + 5 * q^75 + 30 * q^76 + 16 * q^78 + 12 * q^79 - 6 * q^80 + 5 * q^81 + 24 * q^82 + 10 * q^83 - 14 * q^85 - 20 * q^86 + 4 * q^87 - 8 * q^88 - 16 * q^89 + 9 * q^92 + 12 * q^93 - 32 * q^94 + 18 * q^95 + 7 * q^96 - 4 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.34113	−1.65543	−0.827714	−	0.561150i	$-0.810359\pi$
$2$	−2.34113	−1.65543	−0.827714	+	0.561150i	$0.810359\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.48089	1.74044
$5$	−1.12582	−0.503482	−0.251741	−	0.967795i	$-0.581003\pi$
$5$	−1.12582	−0.503482	−0.251741	+	0.967795i	$0.581003\pi$
$6$	−2.34113	−0.955762
$7$	0	0
$7$	0	0
$8$	−3.46695	−1.22575
$9$	1.00000	0.333333
$10$	2.63569	0.833479
$11$	3.82202	1.15238	0.576191	−	0.817315i	$-0.304539\pi$
$11$	3.82202	1.15238	0.576191	+	0.817315i	$0.304539\pi$
$12$	3.48089	1.00485
$13$	−4.94784	−1.37228	−0.686142	−	0.727468i	$-0.740697\pi$
$13$	−4.94784	−1.37228	−0.686142	+	0.727468i	$0.740697\pi$
$14$	0	0
$15$	−1.12582	−0.290686
$16$	1.15480	0.288701
$17$	0.110775	0.0268668	0.0134334	−	0.999910i	$-0.495724\pi$
$17$	0.110775	0.0268668	0.0134334	+	0.999910i	$0.495724\pi$
$18$	−2.34113	−0.551810
$19$	2.32608	0.533640	0.266820	−	0.963746i	$-0.414027\pi$
$19$	2.32608	0.533640	0.266820	+	0.963746i	$0.414027\pi$
$20$	−3.91885	−0.876282
$21$	0	0
$22$	−8.94784	−1.90769
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−3.46695	−0.707688
$25$	−3.73253	−0.746506
$26$	11.5835	2.27172
$27$	1.00000	0.192450
$28$	0	0
$29$	−2.85100	−0.529418	−0.264709	−	0.964328i	$-0.585276\pi$
$29$	−2.85100	−0.529418	−0.264709	+	0.964328i	$0.585276\pi$
$30$	2.63569	0.481209
$31$	5.60671	1.00699	0.503497	−	0.863997i	$-0.332046\pi$
$31$	5.60671	1.00699	0.503497	+	0.863997i	$0.332046\pi$
$32$	4.23035	0.747828
$33$	3.82202	0.665328
$34$	−0.259338	−0.0444761
$35$	0	0
$36$	3.48089	0.580148
$37$	−8.34693	−1.37223	−0.686114	−	0.727494i	$-0.740685\pi$
$37$	−8.34693	−1.37223	−0.686114	+	0.727494i	$0.740685\pi$
$38$	−5.44566	−0.883403
$39$	−4.94784	−0.792288
$40$	3.90316	0.617144
$41$	3.39140	0.529648	0.264824	−	0.964297i	$-0.414686\pi$
$41$	3.39140	0.529648	0.264824	+	0.964297i	$0.414686\pi$
$42$	0	0
$43$	0.947838	0.144544	0.0722719	−	0.997385i	$-0.476975\pi$
$43$	0.947838	0.144544	0.0722719	+	0.997385i	$0.476975\pi$
$44$	13.3040	2.00566
$45$	−1.12582	−0.167827
$46$	−2.34113	−0.345181
$47$	12.9339	1.88660	0.943302	−	0.331937i	$-0.107702\pi$
$47$	12.9339	1.88660	0.943302	+	0.331937i	$0.107702\pi$
$48$	1.15480	0.166682
$49$	0	0
$50$	8.73833	1.23579
$51$	0.110775	0.0155116
$52$	−17.2229	−2.38838
$53$	4.09060	0.561887	0.280943	−	0.959724i	$-0.409353\pi$
$53$	4.09060	0.561887	0.280943	+	0.959724i	$0.409353\pi$
$54$	−2.34113	−0.318587
$55$	−4.30290	−0.580204
$56$	0	0
$57$	2.32608	0.308097
$58$	6.67456	0.876413
$59$	−3.27392	−0.426228	−0.213114	−	0.977027i	$-0.568361\pi$
$59$	−3.27392	−0.426228	−0.213114	+	0.977027i	$0.568361\pi$
$60$	−3.91885	−0.505922
$61$	12.8836	1.64958	0.824790	−	0.565439i	$-0.191293\pi$
$61$	12.8836	1.64958	0.824790	+	0.565439i	$0.191293\pi$
$62$	−13.1260	−1.66701
$63$	0	0
$64$	−12.2134	−1.52668
$65$	5.57038	0.690920
$66$	−8.94784	−1.10140
$67$	−9.37122	−1.14488	−0.572438	−	0.819948i	$-0.694002\pi$
$67$	−9.37122	−1.14488	−0.572438	+	0.819948i	$0.694002\pi$
$68$	0.385595	0.0467602
$69$	1.00000	0.120386
$70$	0	0
$71$	−1.97682	−0.234605	−0.117303	−	0.993096i	$-0.537425\pi$
$71$	−1.97682	−0.234605	−0.117303	+	0.993096i	$0.537425\pi$
$72$	−3.46695	−0.408584
$73$	4.84800	0.567415	0.283708	−	0.958911i	$-0.408435\pi$
$73$	4.84800	0.567415	0.283708	+	0.958911i	$0.408435\pi$
$74$	19.5413	2.27162
$75$	−3.73253	−0.430995
$76$	8.09684	0.928771
$77$	0	0
$78$	11.5835	1.31158
$79$	−11.7239	−1.31905	−0.659523	−	0.751685i	$-0.729242\pi$
$79$	−11.7239	−1.31905	−0.659523	+	0.751685i	$0.729242\pi$
$80$	−1.30010	−0.145356
$81$	1.00000	0.111111
$82$	−7.93970	−0.876794
$83$	−2.79303	−0.306575	−0.153288	−	0.988182i	$-0.548986\pi$
$83$	−2.79303	−0.306575	−0.153288	+	0.988182i	$0.548986\pi$
$84$	0	0
$85$	−0.124713	−0.0135270
$86$	−2.21901	−0.239282
$87$	−2.85100	−0.305659
$88$	−13.2507	−1.41253
$89$	8.96869	0.950679	0.475339	−	0.879802i	$-0.342325\pi$
$89$	8.96869	0.950679	0.475339	+	0.879802i	$0.342325\pi$
$90$	2.63569	0.277826
$91$	0	0
$92$	3.48089	0.362908
$93$	5.60671	0.581389
$94$	−30.2799	−3.12314
$95$	−2.61875	−0.268678
$96$	4.23035	0.431759
$97$	4.88733	0.496233	0.248117	−	0.968730i	$-0.420188\pi$
$97$	4.88733	0.496233	0.248117	+	0.968730i	$0.420188\pi$
$98$	0	0
$99$	3.82202	0.384127
$100$	−12.9925	−1.29925
$101$	3.71794	0.369949	0.184975	−	0.982743i	$-0.440780\pi$
$101$	3.71794	0.369949	0.184975	+	0.982743i	$0.440780\pi$
$102$	−0.259338	−0.0256783
$103$	−2.27952	−0.224607	−0.112304	−	0.993674i	$-0.535823\pi$
$103$	−2.27952	−0.224607	−0.112304	+	0.993674i	$0.535823\pi$
$104$	17.1539	1.68208
$105$	0	0
$106$	−9.57662	−0.930163
$107$	1.20026	0.116034	0.0580169	−	0.998316i	$-0.481522\pi$
$107$	1.20026	0.116034	0.0580169	+	0.998316i	$0.481522\pi$
$108$	3.48089	0.334949
$109$	13.8259	1.32428	0.662142	−	0.749378i	$-0.269648\pi$
$109$	13.8259	1.32428	0.662142	+	0.749378i	$0.269648\pi$
$110$	10.0737	0.960486
$111$	−8.34693	−0.792256
$112$	0	0
$113$	5.93949	0.558741	0.279370	−	0.960183i	$-0.409874\pi$
$113$	5.93949	0.558741	0.279370	+	0.960183i	$0.409874\pi$
$114$	−5.44566	−0.510033
$115$	−1.12582	−0.104983
$116$	−9.92401	−0.921421
$117$	−4.94784	−0.457428
$118$	7.66467	0.705591
$119$	0	0
$120$	3.90316	0.356308
$121$	3.60782	0.327983
$122$	−30.1622	−2.73076
$123$	3.39140	0.305792
$124$	19.5163	1.75262
$125$	9.83126	0.879334
$126$	0	0
$127$	−12.0039	−1.06517	−0.532587	−	0.846375i	$-0.678780\pi$
$127$	−12.0039	−1.06517	−0.532587	+	0.846375i	$0.678780\pi$
$128$	20.1325	1.77948
$129$	0.947838	0.0834525
$130$	−13.0410	−1.14377
$131$	12.0157	1.04982	0.524908	−	0.851159i	$-0.324100\pi$
$131$	12.0157	1.04982	0.524908	+	0.851159i	$0.324100\pi$
$132$	13.3040	1.15797
$133$	0	0
$134$	21.9392	1.89526
$135$	−1.12582	−0.0968952
$136$	−0.384051	−0.0329321
$137$	12.5043	1.06831	0.534156	−	0.845386i	$-0.320629\pi$
$137$	12.5043	1.06831	0.534156	+	0.845386i	$0.320629\pi$
$138$	−2.34113	−0.199290
$139$	1.75506	0.148862	0.0744312	−	0.997226i	$-0.476286\pi$
$139$	1.75506	0.148862	0.0744312	+	0.997226i	$0.476286\pi$
$140$	0	0
$141$	12.9339	1.08923
$142$	4.62799	0.388373
$143$	−18.9107	−1.58139
$144$	1.15480	0.0962336
$145$	3.20971	0.266552
$146$	−11.3498	−0.939316
$147$	0	0
$148$	−29.0547	−2.38828
$149$	16.9785	1.39093	0.695465	−	0.718560i	$-0.255198\pi$
$149$	16.9785	1.39093	0.695465	+	0.718560i	$0.255198\pi$
$150$	8.73833	0.713482
$151$	5.46506	0.444740	0.222370	−	0.974962i	$-0.428621\pi$
$151$	5.46506	0.444740	0.222370	+	0.974962i	$0.428621\pi$
$152$	−8.06442	−0.654111
$153$	0.110775	0.00895561
$154$	0	0
$155$	−6.31215	−0.507004
$156$	−17.2229	−1.37893
$157$	1.36452	0.108900	0.0544502	−	0.998516i	$-0.482659\pi$
$157$	1.36452	0.108900	0.0544502	+	0.998516i	$0.482659\pi$
$158$	27.4472	2.18359
$159$	4.09060	0.324405
$160$	−4.76262	−0.376518
$161$	0	0
$162$	−2.34113	−0.183937
$163$	−7.43126	−0.582062	−0.291031	−	0.956714i	$-0.593998\pi$
$163$	−7.43126	−0.582062	−0.291031	+	0.956714i	$0.593998\pi$
$164$	11.8051	0.921822
$165$	−4.30290	−0.334981
$166$	6.53885	0.507514
$167$	−12.2063	−0.944550	−0.472275	−	0.881451i	$-0.656567\pi$
$167$	−12.2063	−0.944550	−0.472275	+	0.881451i	$0.656567\pi$
$168$	0	0
$169$	11.4811	0.883161
$170$	0.291968	0.0223929
$171$	2.32608	0.177880
$172$	3.29932	0.251571
$173$	−14.2767	−1.08544	−0.542720	−	0.839914i	$-0.682605\pi$
$173$	−14.2767	−1.08544	−0.542720	+	0.839914i	$0.682605\pi$
$174$	6.67456	0.505997
$175$	0	0
$176$	4.41368	0.332694
$177$	−3.27392	−0.246083
$178$	−20.9969	−1.57378
$179$	−3.52635	−0.263572	−0.131786	−	0.991278i	$-0.542071\pi$
$179$	−3.52635	−0.263572	−0.131786	+	0.991278i	$0.542071\pi$
$180$	−3.91885	−0.292094
$181$	8.48459	0.630655	0.315327	−	0.948983i	$-0.397886\pi$
$181$	8.48459	0.630655	0.315327	+	0.948983i	$0.397886\pi$
$182$	0	0
$183$	12.8836	0.952385
$184$	−3.46695	−0.255587
$185$	9.39715	0.690892
$186$	−13.1260	−0.962447
$187$	0.423383	0.0309608
$188$	45.0215	3.28353
$189$	0	0
$190$	6.13084	0.444778
$191$	−4.72483	−0.341877	−0.170938	−	0.985282i	$-0.554680\pi$
$191$	−4.72483	−0.341877	−0.170938	+	0.985282i	$0.554680\pi$
$192$	−12.2134	−0.881427
$193$	−8.70074	−0.626293	−0.313147	−	0.949705i	$-0.601383\pi$
$193$	−8.70074	−0.626293	−0.313147	+	0.949705i	$0.601383\pi$
$194$	−11.4419	−0.821479
$195$	5.57038	0.398903
$196$	0	0
$197$	11.5462	0.822633	0.411316	−	0.911493i	$-0.365069\pi$
$197$	11.5462	0.822633	0.411316	+	0.911493i	$0.365069\pi$
$198$	−8.94784	−0.635895
$199$	14.6302	1.03711	0.518554	−	0.855045i	$-0.326471\pi$
$199$	14.6302	1.03711	0.518554	+	0.855045i	$0.326471\pi$
$200$	12.9405	0.915031
$201$	−9.37122	−0.660995
$202$	−8.70419	−0.612425
$203$	0	0
$204$	0.385595	0.0269970
$205$	−3.81811	−0.266668
$206$	5.33664	0.371822
$207$	1.00000	0.0695048
$208$	−5.71378	−0.396179
$209$	8.89033	0.614957
$210$	0	0
$211$	17.1691	1.18197	0.590984	−	0.806684i	$-0.298740\pi$
$211$	17.1691	1.18197	0.590984	+	0.806684i	$0.298740\pi$
$212$	14.2389	0.977932
$213$	−1.97682	−0.135450
$214$	−2.80997	−0.192086
$215$	−1.06709	−0.0727753
$216$	−3.46695	−0.235896
$217$	0	0
$218$	−32.3683	−2.19226
$219$	4.84800	0.327597
$220$	−14.9779	−1.00981
$221$	−0.548096	−0.0368689
$222$	19.5413	1.31152
$223$	−27.1325	−1.81693	−0.908463	−	0.417966i	$-0.862743\pi$
$223$	−27.1325	−1.81693	−0.908463	+	0.417966i	$0.862743\pi$
$224$	0	0
$225$	−3.73253	−0.248835
$226$	−13.9051	−0.924955
$227$	15.1425	1.00504	0.502522	−	0.864565i	$-0.332406\pi$
$227$	15.1425	1.00504	0.502522	+	0.864565i	$0.332406\pi$
$228$	8.09684	0.536226
$229$	−25.1054	−1.65901	−0.829505	−	0.558499i	$-0.811378\pi$
$229$	−25.1054	−1.65901	−0.829505	+	0.558499i	$0.811378\pi$
$230$	2.63569	0.173792
$231$	0	0
$232$	9.88428	0.648935
$233$	13.7617	0.901560	0.450780	−	0.892635i	$-0.351146\pi$
$233$	13.7617	0.901560	0.450780	+	0.892635i	$0.351146\pi$
$234$	11.5835	0.757239
$235$	−14.5612	−0.949871
$236$	−11.3962	−0.741826
$237$	−11.7239	−0.761551
$238$	0	0
$239$	−4.25718	−0.275374	−0.137687	−	0.990476i	$-0.543967\pi$
$239$	−4.25718	−0.275374	−0.137687	+	0.990476i	$0.543967\pi$
$240$	−1.30010	−0.0839212
$241$	17.4390	1.12334	0.561671	−	0.827361i	$-0.310159\pi$
$241$	17.4390	1.12334	0.561671	+	0.827361i	$0.310159\pi$
$242$	−8.44636	−0.542953
$243$	1.00000	0.0641500
$244$	44.8465	2.87100
$245$	0	0
$246$	−7.93970	−0.506217
$247$	−11.5091	−0.732306
$248$	−19.4382	−1.23433
$249$	−2.79303	−0.177001
$250$	−23.0163	−1.45568
$251$	6.93168	0.437524	0.218762	−	0.975778i	$-0.429798\pi$
$251$	6.93168	0.437524	0.218762	+	0.975778i	$0.429798\pi$
$252$	0	0
$253$	3.82202	0.240288
$254$	28.1027	1.76332
$255$	−0.124713	−0.00780980
$256$	−22.7059	−1.41912
$257$	−28.4106	−1.77220	−0.886101	−	0.463492i	$-0.846596\pi$
$257$	−28.4106	−1.77220	−0.886101	+	0.463492i	$0.846596\pi$
$258$	−2.21901	−0.138150
$259$	0	0
$260$	19.3899	1.20251
$261$	−2.85100	−0.176473
$262$	−28.1303	−1.73790
$263$	−10.9144	−0.673012	−0.336506	−	0.941681i	$-0.609245\pi$
$263$	−10.9144	−0.673012	−0.336506	+	0.941681i	$0.609245\pi$
$264$	−13.2507	−0.815527
$265$	−4.60528	−0.282900
$266$	0	0
$267$	8.96869	0.548875
$268$	−32.6202	−1.99259
$269$	19.1561	1.16797	0.583985	−	0.811765i	$-0.301493\pi$
$269$	19.1561	1.16797	0.583985	+	0.811765i	$0.301493\pi$
$270$	2.63569	0.160403
$271$	7.56414	0.459489	0.229744	−	0.973251i	$-0.426211\pi$
$271$	7.56414	0.459489	0.229744	+	0.973251i	$0.426211\pi$
$272$	0.127923	0.00775648
$273$	0	0
$274$	−29.2741	−1.76851
$275$	−14.2658	−0.860259
$276$	3.48089	0.209525
$277$	21.2099	1.27438	0.637190	−	0.770706i	$-0.280096\pi$
$277$	21.2099	1.27438	0.637190	+	0.770706i	$0.280096\pi$
$278$	−4.10883	−0.246431
$279$	5.60671	0.335665
$280$	0	0
$281$	−32.5617	−1.94247	−0.971233	−	0.238131i	$-0.923465\pi$
$281$	−32.5617	−1.94247	−0.971233	+	0.238131i	$0.923465\pi$
$282$	−30.2799	−1.80314
$283$	3.00157	0.178425	0.0892124	−	0.996013i	$-0.471565\pi$
$283$	3.00157	0.178425	0.0892124	+	0.996013i	$0.471565\pi$
$284$	−6.88109	−0.408318
$285$	−2.61875	−0.155122
$286$	44.2724	2.61788
$287$	0	0
$288$	4.23035	0.249276
$289$	−16.9877	−0.999278
$290$	−7.51436	−0.441258
$291$	4.88733	0.286500
$292$	16.8753	0.987555
$293$	−16.9154	−0.988209	−0.494105	−	0.869402i	$-0.664504\pi$
$293$	−16.9154	−0.988209	−0.494105	+	0.869402i	$0.664504\pi$
$294$	0	0
$295$	3.68585	0.214598
$296$	28.9384	1.68201
$297$	3.82202	0.221776
$298$	−39.7488	−2.30258
$299$	−4.94784	−0.286141
$300$	−12.9925	−0.750123
$301$	0	0
$302$	−12.7944	−0.736235
$303$	3.71794	0.213590
$304$	2.68617	0.154062
$305$	−14.5047	−0.830534
$306$	−0.259338	−0.0148254
$307$	32.3431	1.84592	0.922960	−	0.384895i	$-0.125762\pi$
$307$	32.3431	1.84592	0.922960	+	0.384895i	$0.125762\pi$
$308$	0	0
$309$	−2.27952	−0.129677
$310$	14.7776	0.839309
$311$	23.7481	1.34663	0.673316	−	0.739355i	$-0.264869\pi$
$311$	23.7481	1.34663	0.673316	+	0.739355i	$0.264869\pi$
$312$	17.1539	0.971149
$313$	29.0070	1.63957	0.819786	−	0.572670i	$-0.194092\pi$
$313$	29.0070	1.63957	0.819786	+	0.572670i	$0.194092\pi$
$314$	−3.19451	−0.180277
$315$	0	0
$316$	−40.8097	−2.29572
$317$	8.64663	0.485643	0.242822	−	0.970071i	$-0.421927\pi$
$317$	8.64663	0.485643	0.242822	+	0.970071i	$0.421927\pi$
$318$	−9.57662	−0.537030
$319$	−10.8966	−0.610091
$320$	13.7501	0.768655
$321$	1.20026	0.0669922
$322$	0	0
$323$	0.257671	0.0143372
$324$	3.48089	0.193383
$325$	18.4679	1.02442
$326$	17.3976	0.963561
$327$	13.8259	0.764576
$328$	−11.7578	−0.649216
$329$	0	0
$330$	10.0737	0.554537
$331$	21.2765	1.16946	0.584730	−	0.811228i	$-0.301200\pi$
$331$	21.2765	1.16946	0.584730	+	0.811228i	$0.301200\pi$
$332$	−9.72224	−0.533577
$333$	−8.34693	−0.457409
$334$	28.5765	1.56364
$335$	10.5503	0.576425
$336$	0	0
$337$	24.9908	1.36134	0.680669	−	0.732591i	$-0.261689\pi$
$337$	24.9908	1.36134	0.680669	+	0.732591i	$0.261689\pi$
$338$	−26.8787	−1.46201
$339$	5.93949	0.322589
$340$	−0.434110	−0.0235429
$341$	21.4289	1.16044
$342$	−5.44566	−0.294468
$343$	0	0
$344$	−3.28611	−0.177175
$345$	−1.12582	−0.0606121
$346$	33.4237	1.79687
$347$	10.5840	0.568177	0.284089	−	0.958798i	$-0.408309\pi$
$347$	10.5840	0.568177	0.284089	+	0.958798i	$0.408309\pi$
$348$	−9.92401	−0.531983
$349$	36.2307	1.93938	0.969691	−	0.244333i	$-0.0785690\pi$
$349$	36.2307	1.93938	0.969691	+	0.244333i	$0.0785690\pi$
$350$	0	0
$351$	−4.94784	−0.264096
$352$	16.1685	0.861783
$353$	27.5686	1.46733	0.733664	−	0.679513i	$-0.237809\pi$
$353$	27.5686	1.46733	0.733664	+	0.679513i	$0.237809\pi$
$354$	7.66467	0.407373
$355$	2.22555	0.118120
$356$	31.2190	1.65460
$357$	0	0
$358$	8.25564	0.436324
$359$	−18.1592	−0.958408	−0.479204	−	0.877703i	$-0.659075\pi$
$359$	−18.1592	−0.958408	−0.479204	+	0.877703i	$0.659075\pi$
$360$	3.90316	0.205715
$361$	−13.5893	−0.715228
$362$	−19.8635	−1.04400
$363$	3.60782	0.189361
$364$	0	0
$365$	−5.45798	−0.285684
$366$	−30.1622	−1.57661
$367$	22.7608	1.18811	0.594053	−	0.804426i	$-0.297527\pi$
$367$	22.7608	1.18811	0.594053	+	0.804426i	$0.297527\pi$
$368$	1.15480	0.0601983
$369$	3.39140	0.176549
$370$	−21.9999	−1.14372
$371$	0	0
$372$	19.5163	1.01187
$373$	26.3079	1.36217	0.681085	−	0.732204i	$-0.261508\pi$
$373$	26.3079	1.36217	0.681085	+	0.732204i	$0.261508\pi$
$374$	−0.991195	−0.0512535
$375$	9.83126	0.507684
$376$	−44.8412	−2.31251
$377$	14.1063	0.726511
$378$	0	0
$379$	9.28585	0.476982	0.238491	−	0.971145i	$-0.423347\pi$
$379$	9.28585	0.476982	0.238491	+	0.971145i	$0.423347\pi$
$380$	−9.11558	−0.467620
$381$	−12.0039	−0.614979
$382$	11.0614	0.565953
$383$	26.7935	1.36908	0.684541	−	0.728975i	$-0.260003\pi$
$383$	26.7935	1.36908	0.684541	+	0.728975i	$0.260003\pi$
$384$	20.1325	1.02738
$385$	0	0
$386$	20.3696	1.03678
$387$	0.947838	0.0481813
$388$	17.0123	0.863666
$389$	29.7757	1.50969	0.754843	−	0.655906i	$-0.227713\pi$
$389$	29.7757	1.50969	0.754843	+	0.655906i	$0.227713\pi$
$390$	−13.0410	−0.660355
$391$	0.110775	0.00560212
$392$	0	0
$393$	12.0157	0.606111
$394$	−27.0312	−1.36181
$395$	13.1990	0.664116
$396$	13.3040	0.668552
$397$	−30.8171	−1.54667	−0.773333	−	0.634000i	$-0.781412\pi$
$397$	−30.8171	−1.54667	−0.773333	+	0.634000i	$0.781412\pi$
$398$	−34.2512	−1.71686
$399$	0	0
$400$	−4.31034	−0.215517
$401$	−7.81980	−0.390502	−0.195251	−	0.980753i	$-0.562552\pi$
$401$	−7.81980	−0.390502	−0.195251	+	0.980753i	$0.562552\pi$
$402$	21.9392	1.09423
$403$	−27.7411	−1.38188
$404$	12.9417	0.643876
$405$	−1.12582	−0.0559425
$406$	0	0
$407$	−31.9021	−1.58133
$408$	−0.384051	−0.0190133
$409$	27.2674	1.34829	0.674144	−	0.738600i	$-0.264513\pi$
$409$	27.2674	1.34829	0.674144	+	0.738600i	$0.264513\pi$
$410$	8.93868	0.441450
$411$	12.5043	0.616790
$412$	−7.93474	−0.390917
$413$	0	0
$414$	−2.34113	−0.115060
$415$	3.14445	0.154355
$416$	−20.9311	−1.02623
$417$	1.75506	0.0859457
$418$	−20.8134	−1.01802
$419$	15.6333	0.763737	0.381869	−	0.924217i	$-0.375281\pi$
$419$	15.6333	0.763737	0.381869	+	0.924217i	$0.375281\pi$
$420$	0	0
$421$	−17.6843	−0.861879	−0.430939	−	0.902381i	$-0.641818\pi$
$421$	−17.6843	−0.861879	−0.430939	+	0.902381i	$0.641818\pi$
$422$	−40.1950	−1.95666
$423$	12.9339	0.628868
$424$	−14.1819	−0.688734
$425$	−0.413470	−0.0200562
$426$	4.62799	0.224227
$427$	0	0
$428$	4.17798	0.201950
$429$	−18.9107	−0.913018
$430$	2.49821	0.120474
$431$	21.9204	1.05587	0.527935	−	0.849285i	$-0.322966\pi$
$431$	21.9204	1.05587	0.527935	+	0.849285i	$0.322966\pi$
$432$	1.15480	0.0555605
$433$	−24.8089	−1.19224	−0.596119	−	0.802896i	$-0.703291\pi$
$433$	−24.8089	−1.19224	−0.596119	+	0.802896i	$0.703291\pi$
$434$	0	0
$435$	3.20971	0.153894
$436$	48.1265	2.30484
$437$	2.32608	0.111272
$438$	−11.3498	−0.542314
$439$	27.0862	1.29276	0.646378	−	0.763018i	$-0.276283\pi$
$439$	27.0862	1.29276	0.646378	+	0.763018i	$0.276283\pi$
$440$	14.9180	0.711186
$441$	0	0
$442$	1.28316	0.0610338
$443$	34.4268	1.63567	0.817834	−	0.575454i	$-0.195175\pi$
$443$	34.4268	1.63567	0.817834	+	0.575454i	$0.195175\pi$
$444$	−29.0547	−1.37888
$445$	−10.0971	−0.478650
$446$	63.5207	3.00779
$447$	16.9785	0.803054
$448$	0	0
$449$	−12.4440	−0.587268	−0.293634	−	0.955918i	$-0.594865\pi$
$449$	−12.4440	−0.587268	−0.293634	+	0.955918i	$0.594865\pi$
$450$	8.73833	0.411929
$451$	12.9620	0.610356
$452$	20.6747	0.972457
$453$	5.46506	0.256771
$454$	−35.4506	−1.66378
$455$	0	0
$456$	−8.06442	−0.377651
$457$	15.4439	0.722434	0.361217	−	0.932482i	$-0.382361\pi$
$457$	15.4439	0.722434	0.361217	+	0.932482i	$0.382361\pi$
$458$	58.7750	2.74637
$459$	0.110775	0.00517052
$460$	−3.91885	−0.182718
$461$	−8.59766	−0.400433	−0.200217	−	0.979752i	$-0.564165\pi$
$461$	−8.59766	−0.400433	−0.200217	+	0.979752i	$0.564165\pi$
$462$	0	0
$463$	−7.64225	−0.355166	−0.177583	−	0.984106i	$-0.556828\pi$
$463$	−7.64225	−0.355166	−0.177583	+	0.984106i	$0.556828\pi$
$464$	−3.29235	−0.152843
$465$	−6.31215	−0.292719
$466$	−32.2180	−1.49247
$467$	31.8652	1.47454	0.737272	−	0.675596i	$-0.236114\pi$
$467$	31.8652	1.47454	0.737272	+	0.675596i	$0.236114\pi$
$468$	−17.2229	−0.796127
$469$	0	0
$470$	34.0898	1.57244
$471$	1.36452	0.0628737
$472$	11.3505	0.522450
$473$	3.62265	0.166570
$474$	27.4472	1.26069
$475$	−8.68217	−0.398365
$476$	0	0
$477$	4.09060	0.187296
$478$	9.96661	0.455862
$479$	−21.3298	−0.974583	−0.487292	−	0.873239i	$-0.662015\pi$
$479$	−21.3298	−0.974583	−0.487292	+	0.873239i	$0.662015\pi$
$480$	−4.76262	−0.217383
$481$	41.2993	1.88308
$482$	−40.8269	−1.85961
$483$	0	0
$484$	12.5584	0.570836
$485$	−5.50226	−0.249845
$486$	−2.34113	−0.106196
$487$	−2.16938	−0.0983038	−0.0491519	−	0.998791i	$-0.515652\pi$
$487$	−2.16938	−0.0983038	−0.0491519	+	0.998791i	$0.515652\pi$
$488$	−44.6669	−2.02198
$489$	−7.43126	−0.336053
$490$	0	0
$491$	−14.5960	−0.658710	−0.329355	−	0.944206i	$-0.606831\pi$
$491$	−14.5960	−0.658710	−0.329355	+	0.944206i	$0.606831\pi$
$492$	11.8051	0.532214
$493$	−0.315819	−0.0142238
$494$	26.9443	1.21228
$495$	−4.30290	−0.193401
$496$	6.47465	0.290720
$497$	0	0
$498$	6.53885	0.293013
$499$	20.9864	0.939479	0.469739	−	0.882805i	$-0.344348\pi$
$499$	20.9864	0.939479	0.469739	+	0.882805i	$0.344348\pi$
$500$	34.2215	1.53043
$501$	−12.2063	−0.545336
$502$	−16.2280	−0.724290
$503$	−27.0683	−1.20691	−0.603457	−	0.797395i	$-0.706211\pi$
$503$	−27.0683	−1.20691	−0.603457	+	0.797395i	$0.706211\pi$
$504$	0	0
$505$	−4.18574	−0.186263
$506$	−8.94784	−0.397780
$507$	11.4811	0.509893
$508$	−41.7843	−1.85388
$509$	−35.5977	−1.57784	−0.788920	−	0.614496i	$-0.789359\pi$
$509$	−35.5977	−1.57784	−0.788920	+	0.614496i	$0.789359\pi$
$510$	0.291968	0.0129286
$511$	0	0
$512$	12.8925	0.569774
$513$	2.32608	0.102699
$514$	66.5128	2.93375
$515$	2.56633	0.113086
$516$	3.29932	0.145244
$517$	49.4336	2.17409
$518$	0	0
$519$	−14.2767	−0.626679
$520$	−19.3122	−0.846897
$521$	−23.0790	−1.01111	−0.505555	−	0.862795i	$-0.668712\pi$
$521$	−23.0790	−1.01111	−0.505555	+	0.862795i	$0.668712\pi$
$522$	6.67456	0.292138
$523$	−16.7716	−0.733371	−0.366686	−	0.930345i	$-0.619508\pi$
$523$	−16.7716	−0.733371	−0.366686	+	0.930345i	$0.619508\pi$
$524$	41.8253	1.82715
$525$	0	0
$526$	25.5521	1.11412
$527$	0.621082	0.0270548
$528$	4.41368	0.192081
$529$	1.00000	0.0434783
$530$	10.7816	0.468321
$531$	−3.27392	−0.142076
$532$	0	0
$533$	−16.7801	−0.726826
$534$	−20.9969	−0.908623
$535$	−1.35128	−0.0584210
$536$	32.4896	1.40333
$537$	−3.52635	−0.152173
$538$	−44.8470	−1.93349
$539$	0	0
$540$	−3.91885	−0.168641
$541$	23.1100	0.993577	0.496789	−	0.867872i	$-0.334512\pi$
$541$	23.1100	0.993577	0.496789	+	0.867872i	$0.334512\pi$
$542$	−17.7086	−0.760650
$543$	8.48459	0.364109
$544$	0.468617	0.0200918
$545$	−15.5655	−0.666753
$546$	0	0
$547$	24.6768	1.05510	0.527551	−	0.849523i	$-0.323110\pi$
$547$	24.6768	1.05510	0.527551	+	0.849523i	$0.323110\pi$
$548$	43.5260	1.85934
$549$	12.8836	0.549860
$550$	33.3981	1.42410
$551$	−6.63167	−0.282519
$552$	−3.46695	−0.147563
$553$	0	0
$554$	−49.6552	−2.10965
$555$	9.39715	0.398887
$556$	6.10917	0.259087
$557$	−3.12157	−0.132265	−0.0661326	−	0.997811i	$-0.521066\pi$
$557$	−3.12157	−0.132265	−0.0661326	+	0.997811i	$0.521066\pi$
$558$	−13.1260	−0.555669
$559$	−4.68975	−0.198355
$560$	0	0
$561$	0.423383	0.0178752
$562$	76.2311	3.21561
$563$	39.9189	1.68238	0.841190	−	0.540740i	$-0.181856\pi$
$563$	39.9189	1.68238	0.841190	+	0.540740i	$0.181856\pi$
$564$	45.0215	1.89575
$565$	−6.68680	−0.281316
$566$	−7.02706	−0.295370
$567$	0	0
$568$	6.85354	0.287568
$569$	21.2881	0.892442	0.446221	−	0.894923i	$-0.352769\pi$
$569$	21.2881	0.892442	0.446221	+	0.894923i	$0.352769\pi$
$570$	6.13084	0.256793
$571$	−6.61683	−0.276906	−0.138453	−	0.990369i	$-0.544213\pi$
$571$	−6.61683	−0.276906	−0.138453	+	0.990369i	$0.544213\pi$
$572$	−65.8261	−2.75233
$573$	−4.72483	−0.197383
$574$	0	0
$575$	−3.73253	−0.155657
$576$	−12.2134	−0.508892
$577$	−22.6350	−0.942306	−0.471153	−	0.882051i	$-0.656162\pi$
$577$	−22.6350	−0.942306	−0.471153	+	0.882051i	$0.656162\pi$
$578$	39.7705	1.65423
$579$	−8.70074	−0.361590
$580$	11.1727	0.463919
$581$	0	0
$582$	−11.4419	−0.474281
$583$	15.6343	0.647508
$584$	−16.8078	−0.695511
$585$	5.57038	0.230307
$586$	39.6012	1.63591
$587$	5.40333	0.223019	0.111510	−	0.993763i	$-0.464431\pi$
$587$	5.40333	0.223019	0.111510	+	0.993763i	$0.464431\pi$
$588$	0	0
$589$	13.0417	0.537373
$590$	−8.62905	−0.355252
$591$	11.5462	0.474947
$592$	−9.63907	−0.396163
$593$	−13.1425	−0.539700	−0.269850	−	0.962902i	$-0.586974\pi$
$593$	−13.1425	−0.539700	−0.269850	+	0.962902i	$0.586974\pi$
$594$	−8.94784	−0.367134
$595$	0	0
$596$	59.1001	2.42084
$597$	14.6302	0.598775
$598$	11.5835	0.473686
$599$	−25.8290	−1.05534	−0.527672	−	0.849448i	$-0.676935\pi$
$599$	−25.8290	−1.05534	−0.527672	+	0.849448i	$0.676935\pi$
$600$	12.9405	0.528293
$601$	−3.87672	−0.158135	−0.0790673	−	0.996869i	$-0.525194\pi$
$601$	−3.87672	−0.158135	−0.0790673	+	0.996869i	$0.525194\pi$
$602$	0	0
$603$	−9.37122	−0.381626
$604$	19.0232	0.774045
$605$	−4.06175	−0.165134
$606$	−8.70419	−0.353584
$607$	−20.8366	−0.845733	−0.422867	−	0.906192i	$-0.638976\pi$
$607$	−20.8366	−0.845733	−0.422867	+	0.906192i	$0.638976\pi$
$608$	9.84016	0.399071
$609$	0	0
$610$	33.9573	1.37489
$611$	−63.9948	−2.58895
$612$	0.385595	0.0155867
$613$	−47.5937	−1.92229	−0.961146	−	0.276040i	$-0.910978\pi$
$613$	−47.5937	−1.92229	−0.961146	+	0.276040i	$0.910978\pi$
$614$	−75.7195	−3.05579
$615$	−3.81811	−0.153961
$616$	0	0
$617$	27.6353	1.11256	0.556278	−	0.830996i	$-0.312229\pi$
$617$	27.6353	1.11256	0.556278	+	0.830996i	$0.312229\pi$
$618$	5.33664	0.214671
$619$	16.3505	0.657181	0.328591	−	0.944472i	$-0.393426\pi$
$619$	16.3505	0.657181	0.328591	+	0.944472i	$0.393426\pi$
$620$	−21.9719	−0.882412
$621$	1.00000	0.0401286
$622$	−55.5974	−2.22925
$623$	0	0
$624$	−5.71378	−0.228734
$625$	7.59441	0.303776
$626$	−67.9091	−2.71419
$627$	8.89033	0.355046
$628$	4.74973	0.189535
$629$	−0.924630	−0.0368674
$630$	0	0
$631$	−30.0687	−1.19702	−0.598508	−	0.801117i	$-0.704240\pi$
$631$	−30.0687	−1.19702	−0.598508	+	0.801117i	$0.704240\pi$
$632$	40.6463	1.61682
$633$	17.1691	0.682409
$634$	−20.2429	−0.803947
$635$	13.5142	0.536297
$636$	14.2389	0.564609
$637$	0	0
$638$	25.5103	1.00996
$639$	−1.97682	−0.0782018
$640$	−22.6656	−0.895935
$641$	32.6876	1.29108	0.645542	−	0.763725i	$-0.276632\pi$
$641$	32.6876	1.29108	0.645542	+	0.763725i	$0.276632\pi$
$642$	−2.80997	−0.110901
$643$	−16.6487	−0.656560	−0.328280	−	0.944581i	$-0.606469\pi$
$643$	−16.6487	−0.656560	−0.328280	+	0.944581i	$0.606469\pi$
$644$	0	0
$645$	−1.06709	−0.0420168
$646$	−0.603242	−0.0237342
$647$	34.5694	1.35906	0.679532	−	0.733646i	$-0.262183\pi$
$647$	34.5694	1.35906	0.679532	+	0.733646i	$0.262183\pi$
$648$	−3.46695	−0.136195
$649$	−12.5130	−0.491178
$650$	−43.2359	−1.69585
$651$	0	0
$652$	−25.8674	−1.01305
$653$	−49.0313	−1.91874	−0.959372	−	0.282145i	$-0.908954\pi$
$653$	−49.0313	−1.91874	−0.959372	+	0.282145i	$0.908954\pi$
$654$	−32.3683	−1.26570
$655$	−13.5275	−0.528564
$656$	3.91640	0.152910
$657$	4.84800	0.189138
$658$	0	0
$659$	−24.5613	−0.956773	−0.478387	−	0.878149i	$-0.658778\pi$
$659$	−24.5613	−0.956773	−0.478387	+	0.878149i	$0.658778\pi$
$660$	−14.9779	−0.583015
$661$	−37.5214	−1.45941	−0.729707	−	0.683760i	$-0.760344\pi$
$661$	−37.5214	−1.45941	−0.729707	+	0.683760i	$0.760344\pi$
$662$	−49.8110	−1.93596
$663$	−0.548096	−0.0212863
$664$	9.68331	0.375785
$665$	0	0
$666$	19.5413	0.757208
$667$	−2.85100	−0.110391
$668$	−42.4887	−1.64394
$669$	−27.1325	−1.04900
$670$	−24.6996	−0.954231
$671$	49.2415	1.90095
$672$	0	0
$673$	34.6229	1.33462	0.667308	−	0.744782i	$-0.267446\pi$
$673$	34.6229	1.33462	0.667308	+	0.744782i	$0.267446\pi$
$674$	−58.5068	−2.25360
$675$	−3.73253	−0.143665
$676$	39.9644	1.53709
$677$	31.3959	1.20664	0.603322	−	0.797498i	$-0.293843\pi$
$677$	31.3959	1.20664	0.603322	+	0.797498i	$0.293843\pi$
$678$	−13.9051	−0.534023
$679$	0	0
$680$	0.432372	0.0165807
$681$	15.1425	0.580262
$682$	−50.1679	−1.92103
$683$	32.4841	1.24297	0.621484	−	0.783427i	$-0.286530\pi$
$683$	32.4841	1.24297	0.621484	+	0.783427i	$0.286530\pi$
$684$	8.09684	0.309590
$685$	−14.0776	−0.537876
$686$	0	0
$687$	−25.1054	−0.957830
$688$	1.09457	0.0417300
$689$	−20.2396	−0.771068
$690$	2.63569	0.100339
$691$	−4.82590	−0.183586	−0.0917930	−	0.995778i	$-0.529260\pi$
$691$	−4.82590	−0.183586	−0.0917930	+	0.995778i	$0.529260\pi$
$692$	−49.6957	−1.88915
$693$	0	0
$694$	−24.7784	−0.940576
$695$	−1.97588	−0.0749496
$696$	9.88428	0.374663
$697$	0.375681	0.0142300
$698$	−84.8207	−3.21051
$699$	13.7617	0.520516
$700$	0	0
$701$	26.7653	1.01091	0.505455	−	0.862853i	$-0.331325\pi$
$701$	26.7653	1.01091	0.505455	+	0.862853i	$0.331325\pi$
$702$	11.5835	0.437192
$703$	−19.4157	−0.732276
$704$	−46.6799	−1.75931
$705$	−14.5612	−0.548408
$706$	−64.5416	−2.42906
$707$	0	0
$708$	−11.3962	−0.428294
$709$	−23.5069	−0.882819	−0.441410	−	0.897306i	$-0.645521\pi$
$709$	−23.5069	−0.882819	−0.441410	+	0.897306i	$0.645521\pi$
$710$	−5.21029	−0.195539
$711$	−11.7239	−0.439682
$712$	−31.0940	−1.16530
$713$	5.60671	0.209973
$714$	0	0
$715$	21.2901	0.796204
$716$	−12.2748	−0.458732
$717$	−4.25718	−0.158987
$718$	42.5132	1.58658
$719$	−28.8356	−1.07539	−0.537694	−	0.843140i	$-0.680704\pi$
$719$	−28.8356	−1.07539	−0.537694	+	0.843140i	$0.680704\pi$
$720$	−1.30010	−0.0484519
$721$	0	0
$722$	31.8144	1.18401
$723$	17.4390	0.648562
$724$	29.5339	1.09762
$725$	10.6414	0.395213
$726$	−8.44636	−0.313474
$727$	−48.1271	−1.78493	−0.892467	−	0.451113i	$-0.851027\pi$
$727$	−48.1271	−1.78493	−0.892467	+	0.451113i	$0.851027\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	12.7778	0.472929
$731$	0.104997	0.00388344
$732$	44.8465	1.65757
$733$	−17.8828	−0.660515	−0.330258	−	0.943891i	$-0.607136\pi$
$733$	−17.8828	−0.660515	−0.330258	+	0.943891i	$0.607136\pi$
$734$	−53.2860	−1.96682
$735$	0	0
$736$	4.23035	0.155933
$737$	−35.8170	−1.31933
$738$	−7.93970	−0.292265
$739$	21.1566	0.778258	0.389129	−	0.921183i	$-0.372776\pi$
$739$	21.1566	0.778258	0.389129	+	0.921183i	$0.372776\pi$
$740$	32.7104	1.20246
$741$	−11.5091	−0.422797
$742$	0	0
$743$	−41.2282	−1.51252	−0.756258	−	0.654273i	$-0.772975\pi$
$743$	−41.2282	−1.51252	−0.756258	+	0.654273i	$0.772975\pi$
$744$	−19.4382	−0.712638
$745$	−19.1147	−0.700308
$746$	−61.5901	−2.25497
$747$	−2.79303	−0.102192
$748$	1.47375	0.0538856
$749$	0	0
$750$	−23.0163	−0.840435
$751$	35.9360	1.31132	0.655661	−	0.755055i	$-0.272390\pi$
$751$	35.9360	1.31132	0.655661	+	0.755055i	$0.272390\pi$
$752$	14.9361	0.544664
$753$	6.93168	0.252605
$754$	−33.0246	−1.20269
$755$	−6.15267	−0.223919
$756$	0	0
$757$	−7.84208	−0.285025	−0.142513	−	0.989793i	$-0.545518\pi$
$757$	−7.84208	−0.285025	−0.142513	+	0.989793i	$0.545518\pi$
$758$	−21.7394	−0.789610
$759$	3.82202	0.138730
$760$	9.07908	0.329333
$761$	32.8895	1.19224	0.596122	−	0.802894i	$-0.296707\pi$
$761$	32.8895	1.19224	0.596122	+	0.802894i	$0.296707\pi$
$762$	28.1027	1.01805
$763$	0	0
$764$	−16.4466	−0.595017
$765$	−0.124713	−0.00450899
$766$	−62.7269	−2.26642
$767$	16.1988	0.584906
$768$	−22.7059	−0.819329
$769$	37.8957	1.36655	0.683277	−	0.730160i	$-0.260554\pi$
$769$	37.8957	1.36655	0.683277	+	0.730160i	$0.260554\pi$
$770$	0	0
$771$	−28.4106	−1.02318
$772$	−30.2863	−1.09003
$773$	−12.5249	−0.450489	−0.225245	−	0.974302i	$-0.572318\pi$
$773$	−12.5249	−0.450489	−0.225245	+	0.974302i	$0.572318\pi$
$774$	−2.21901	−0.0797607
$775$	−20.9272	−0.751727
$776$	−16.9441	−0.608259
$777$	0	0
$778$	−69.7087	−2.49918
$779$	7.88868	0.282641
$780$	19.3899	0.694268
$781$	−7.55544	−0.270355
$782$	−0.259338	−0.00927391
$783$	−2.85100	−0.101886
$784$	0	0
$785$	−1.53620	−0.0548294
$786$	−28.1303	−1.00337
$787$	−37.3104	−1.32997	−0.664987	−	0.746855i	$-0.731563\pi$
$787$	−37.3104	−1.32997	−0.664987	+	0.746855i	$0.731563\pi$
$788$	40.1910	1.43175
$789$	−10.9144	−0.388564
$790$	−30.9007	−1.09940
$791$	0	0
$792$	−13.2507	−0.470845
$793$	−63.7461	−2.26369
$794$	72.1468	2.56039
$795$	−4.60528	−0.163332
$796$	50.9261	1.80503
$797$	41.2923	1.46265	0.731324	−	0.682031i	$-0.238903\pi$
$797$	41.2923	1.46265	0.731324	+	0.682031i	$0.238903\pi$
$798$	0	0
$799$	1.43275	0.0506870
$800$	−15.7899	−0.558258
$801$	8.96869	0.316893
$802$	18.3072	0.646449
$803$	18.5291	0.653879
$804$	−32.6202	−1.15042
$805$	0	0
$806$	64.9455	2.28761
$807$	19.1561	0.674327
$808$	−12.8899	−0.453466
$809$	16.5449	0.581689	0.290845	−	0.956770i	$-0.406064\pi$
$809$	16.5449	0.581689	0.290845	+	0.956770i	$0.406064\pi$
$810$	2.63569	0.0926088
$811$	−9.71524	−0.341148	−0.170574	−	0.985345i	$-0.554562\pi$
$811$	−9.71524	−0.341148	−0.170574	+	0.985345i	$0.554562\pi$
$812$	0	0
$813$	7.56414	0.265286
$814$	74.6870	2.61778
$815$	8.36627	0.293058
$816$	0.127923	0.00447821
$817$	2.20475	0.0771344
$818$	−63.8366	−2.23199
$819$	0	0
$820$	−13.2904	−0.464121
$821$	9.17172	0.320095	0.160048	−	0.987109i	$-0.448835\pi$
$821$	9.17172	0.320095	0.160048	+	0.987109i	$0.448835\pi$
$822$	−29.2741	−1.02105
$823$	−39.6851	−1.38334	−0.691668	−	0.722215i	$-0.743124\pi$
$823$	−39.6851	−1.38334	−0.691668	+	0.722215i	$0.743124\pi$
$824$	7.90297	0.275313
$825$	−14.2658	−0.496671
$826$	0	0
$827$	−2.14944	−0.0747432	−0.0373716	−	0.999301i	$-0.511899\pi$
$827$	−2.14944	−0.0747432	−0.0373716	+	0.999301i	$0.511899\pi$
$828$	3.48089	0.120969
$829$	−28.2850	−0.982377	−0.491189	−	0.871053i	$-0.663437\pi$
$829$	−28.2850	−0.982377	−0.491189	+	0.871053i	$0.663437\pi$
$830$	−7.36158	−0.255524
$831$	21.2099	0.735764
$832$	60.4300	2.09503
$833$	0	0
$834$	−4.10883	−0.142277
$835$	13.7421	0.475564
$836$	30.9463	1.07030
$837$	5.60671	0.193796
$838$	−36.5996	−1.26431
$839$	3.53058	0.121889	0.0609446	−	0.998141i	$-0.480589\pi$
$839$	3.53058	0.121889	0.0609446	+	0.998141i	$0.480589\pi$
$840$	0	0
$841$	−20.8718	−0.719717
$842$	41.4012	1.42678
$843$	−32.5617	−1.12148
$844$	59.7636	2.05715
$845$	−12.9257	−0.444656
$846$	−30.2799	−1.04105
$847$	0	0
$848$	4.72384	0.162217
$849$	3.00157	0.103014
$850$	0.967987	0.0332017
$851$	−8.34693	−0.286129
$852$	−6.88109	−0.235742
$853$	4.22598	0.144695	0.0723474	−	0.997379i	$-0.476951\pi$
$853$	4.22598	0.144695	0.0723474	+	0.997379i	$0.476951\pi$
$854$	0	0
$855$	−2.61875	−0.0895595
$856$	−4.16125	−0.142229
$857$	13.1165	0.448051	0.224025	−	0.974583i	$-0.428080\pi$
$857$	13.1165	0.448051	0.224025	+	0.974583i	$0.428080\pi$
$858$	44.2724	1.51144
$859$	−23.8591	−0.814062	−0.407031	−	0.913414i	$-0.633436\pi$
$859$	−23.8591	−0.814062	−0.407031	+	0.913414i	$0.633436\pi$
$860$	−3.71444	−0.126661
$861$	0	0
$862$	−51.3186	−1.74792
$863$	−47.9736	−1.63304	−0.816520	−	0.577317i	$-0.804100\pi$
$863$	−47.9736	−1.63304	−0.816520	+	0.577317i	$0.804100\pi$
$864$	4.23035	0.143920
$865$	16.0730	0.546499
$866$	58.0808	1.97367
$867$	−16.9877	−0.576934
$868$	0	0
$869$	−44.8091	−1.52004
$870$	−7.51436	−0.254761
$871$	46.3673	1.57110
$872$	−47.9338	−1.62324
$873$	4.88733	0.165411
$874$	−5.44566	−0.184202
$875$	0	0
$876$	16.8753	0.570165
$877$	−54.4883	−1.83994	−0.919970	−	0.391990i	$-0.871787\pi$
$877$	−54.4883	−1.83994	−0.919970	+	0.391990i	$0.871787\pi$
$878$	−63.4124	−2.14006
$879$	−16.9154	−0.570543
$880$	−4.96901	−0.167505
$881$	7.13228	0.240293	0.120146	−	0.992756i	$-0.461664\pi$
$881$	7.13228	0.240293	0.120146	+	0.992756i	$0.461664\pi$
$882$	0	0
$883$	15.7545	0.530181	0.265090	−	0.964224i	$-0.414598\pi$
$883$	15.7545	0.530181	0.265090	+	0.964224i	$0.414598\pi$
$884$	−1.90786	−0.0641683
$885$	3.68585	0.123898
$886$	−80.5977	−2.70773
$887$	−44.0581	−1.47933	−0.739664	−	0.672977i	$-0.765015\pi$
$887$	−44.0581	−1.47933	−0.739664	+	0.672977i	$0.765015\pi$
$888$	28.9384	0.971109
$889$	0	0
$890$	23.6387	0.792371
$891$	3.82202	0.128042
$892$	−94.4451	−3.16226
$893$	30.0853	1.00677
$894$	−39.7488	−1.32940
$895$	3.97003	0.132704
$896$	0	0
$897$	−4.94784	−0.165203
$898$	29.1330	0.972180
$899$	−15.9847	−0.533121
$900$	−12.9925	−0.433084
$901$	0.453135	0.0150961
$902$	−30.3457	−1.01040
$903$	0	0
$904$	−20.5919	−0.684877
$905$	−9.55212	−0.317523
$906$	−12.7944	−0.425066
$907$	15.5292	0.515639	0.257820	−	0.966193i	$-0.416996\pi$
$907$	15.5292	0.515639	0.257820	+	0.966193i	$0.416996\pi$
$908$	52.7094	1.74922
$909$	3.71794	0.123316
$910$	0	0
$911$	13.1574	0.435925	0.217963	−	0.975957i	$-0.430059\pi$
$911$	13.1574	0.435925	0.217963	+	0.975957i	$0.430059\pi$
$912$	2.68617	0.0889480
$913$	−10.6750	−0.353292
$914$	−36.1561	−1.19594
$915$	−14.5047	−0.479509
$916$	−87.3890	−2.88742
$917$	0	0
$918$	−0.259338	−0.00855943
$919$	−32.5522	−1.07380	−0.536899	−	0.843646i	$-0.680404\pi$
$919$	−32.5522	−1.07380	−0.536899	+	0.843646i	$0.680404\pi$
$920$	3.90316	0.128683
$921$	32.3431	1.06574
$922$	20.1282	0.662888
$923$	9.78099	0.321945
$924$	0	0
$925$	31.1552	1.02438
$926$	17.8915	0.587951
$927$	−2.27952	−0.0748691
$928$	−12.0607	−0.395913
$929$	21.9919	0.721530	0.360765	−	0.932657i	$-0.382516\pi$
$929$	21.9919	0.721530	0.360765	+	0.932657i	$0.382516\pi$
$930$	14.7776	0.484575
$931$	0	0
$932$	47.9030	1.56912
$933$	23.7481	0.777478
$934$	−74.6005	−2.44100
$935$	−0.476653	−0.0155882
$936$	17.1539	0.560693
$937$	−11.0435	−0.360776	−0.180388	−	0.983596i	$-0.557735\pi$
$937$	−11.0435	−0.360776	−0.180388	+	0.983596i	$0.557735\pi$
$938$	0	0
$939$	29.0070	0.946607
$940$	−50.6861	−1.65320
$941$	−6.56324	−0.213955	−0.106978	−	0.994261i	$-0.534117\pi$
$941$	−6.56324	−0.213955	−0.106978	+	0.994261i	$0.534117\pi$
$942$	−3.19451	−0.104083
$943$	3.39140	0.110439
$944$	−3.78074	−0.123053
$945$	0	0
$946$	−8.48110	−0.275744
$947$	−29.1957	−0.948734	−0.474367	−	0.880327i	$-0.657323\pi$
$947$	−29.1957	−0.948734	−0.474367	+	0.880327i	$0.657323\pi$
$948$	−40.8097	−1.32544
$949$	−23.9871	−0.778655
$950$	20.3261	0.659466
$951$	8.64663	0.280386
$952$	0	0
$953$	19.8598	0.643323	0.321662	−	0.946855i	$-0.395759\pi$
$953$	19.8598	0.643323	0.321662	+	0.946855i	$0.395759\pi$
$954$	−9.57662	−0.310054
$955$	5.31931	0.172129
$956$	−14.8188	−0.479273
$957$	−10.8966	−0.352236
$958$	49.9358	1.61335
$959$	0	0
$960$	13.7501	0.443783
$961$	0.435175	0.0140379
$962$	−96.6870	−3.11731
$963$	1.20026	0.0386780
$964$	60.7031	1.95511
$965$	9.79547	0.315327
$966$	0	0
$967$	−21.2580	−0.683610	−0.341805	−	0.939771i	$-0.611038\pi$
$967$	−21.2580	−0.683610	−0.341805	+	0.939771i	$0.611038\pi$
$968$	−12.5081	−0.402026
$969$	0.257671	0.00827760
$970$	12.8815	0.413600
$971$	17.6444	0.566236	0.283118	−	0.959085i	$-0.408631\pi$
$971$	17.6444	0.566236	0.283118	+	0.959085i	$0.408631\pi$
$972$	3.48089	0.111650
$973$	0	0
$974$	5.07879	0.162735
$975$	18.4679	0.591448
$976$	14.8781	0.476235
$977$	52.7121	1.68641	0.843205	−	0.537593i	$-0.180666\pi$
$977$	52.7121	1.68641	0.843205	+	0.537593i	$0.180666\pi$
$978$	17.3976	0.556312
$979$	34.2785	1.09554
$980$	0	0
$981$	13.8259	0.441428
$982$	34.1712	1.09045
$983$	−35.6801	−1.13802	−0.569009	−	0.822331i	$-0.692673\pi$
$983$	−35.6801	−1.13802	−0.569009	+	0.822331i	$0.692673\pi$
$984$	−11.7578	−0.374825
$985$	−12.9990	−0.414181
$986$	0.739373	0.0235464
$987$	0	0
$988$	−40.0618	−1.27454
$989$	0.947838	0.0301395
$990$	10.0737	0.320162
$991$	56.3010	1.78846	0.894229	−	0.447609i	$-0.147724\pi$
$991$	56.3010	1.78846	0.894229	+	0.447609i	$0.147724\pi$
$992$	23.7184	0.753059
$993$	21.2765	0.675188
$994$	0	0
$995$	−16.4710	−0.522165
$996$	−9.72224	−0.308061
$997$	16.5014	0.522605	0.261303	−	0.965257i	$-0.415848\pi$
$997$	16.5014	0.522605	0.261303	+	0.965257i	$0.415848\pi$
$998$	−49.1318	−1.55524
$999$	−8.34693	−0.264085

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.z.1.1	yes	5
7.6	odd	2		3381.2.a.y.1.1	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3381.2.a.y.1.1	✓	5	7.6	odd	2
3381.2.a.z.1.1	yes	5	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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q-2.34113 q^{2} +1.00000 q^{3} +3.48089 q^{4} -1.12582 q^{5} -2.34113 q^{6} -3.46695 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.34113 q^{2} +1.00000 q^{3} +3.48089 q^{4} -1.12582 q^{5} -2.34113 q^{6} -3.46695 q^{8} +1.00000 q^{9} +2.63569 q^{10} +3.82202 q^{11} +3.48089 q^{12} -4.94784 q^{13} -1.12582 q^{15} +1.15480 q^{16} +0.110775 q^{17} -2.34113 q^{18} +2.32608 q^{19} -3.91885 q^{20} -8.94784 q^{22} +1.00000 q^{23} -3.46695 q^{24} -3.73253 q^{25} +11.5835 q^{26} +1.00000 q^{27} -2.85100 q^{29} +2.63569 q^{30} +5.60671 q^{31} +4.23035 q^{32} +3.82202 q^{33} -0.259338 q^{34} +3.48089 q^{36} -8.34693 q^{37} -5.44566 q^{38} -4.94784 q^{39} +3.90316 q^{40} +3.39140 q^{41} +0.947838 q^{43} +13.3040 q^{44} -1.12582 q^{45} -2.34113 q^{46} +12.9339 q^{47} +1.15480 q^{48} +8.73833 q^{50} +0.110775 q^{51} -17.2229 q^{52} +4.09060 q^{53} -2.34113 q^{54} -4.30290 q^{55} +2.32608 q^{57} +6.67456 q^{58} -3.27392 q^{59} -3.91885 q^{60} +12.8836 q^{61} -13.1260 q^{62} -12.2134 q^{64} +5.57038 q^{65} -8.94784 q^{66} -9.37122 q^{67} +0.385595 q^{68} +1.00000 q^{69} -1.97682 q^{71} -3.46695 q^{72} +4.84800 q^{73} +19.5413 q^{74} -3.73253 q^{75} +8.09684 q^{76} +11.5835 q^{78} -11.7239 q^{79} -1.30010 q^{80} +1.00000 q^{81} -7.93970 q^{82} -2.79303 q^{83} -0.124713 q^{85} -2.21901 q^{86} -2.85100 q^{87} -13.2507 q^{88} +8.96869 q^{89} +2.63569 q^{90} +3.48089 q^{92} +5.60671 q^{93} -30.2799 q^{94} -2.61875 q^{95} +4.23035 q^{96} +4.88733 q^{97} +3.82202 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 5 q^{3} + 9 q^{4} + 2 q^{5} + q^{6} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + q^2 + 5 * q^3 + 9 * q^4 + 2 * q^5 + q^6 + 3 * q^8 + 5 * q^9	\( 5 q + q^{2} + 5 q^{3} + 9 q^{4} + 2 q^{5} + q^{6} + 3 q^{8} + 5 q^{9} - 2 q^{11} + 9 q^{12} + 4 q^{13} + 2 q^{15} + q^{16} + 2 q^{17} + q^{18} + 8 q^{19} + 12 q^{20} - 16 q^{22} + 5 q^{23} + 3 q^{24} + 5 q^{25} + 16 q^{26} + 5 q^{27} + 4 q^{29} + 12 q^{31} + 7 q^{32} - 2 q^{33} + 10 q^{34} + 9 q^{36} - 6 q^{37} - 8 q^{38} + 4 q^{39} + 30 q^{40} + 6 q^{41} - 24 q^{43} + 16 q^{44} + 2 q^{45} + q^{46} + 24 q^{47} + q^{48} - 3 q^{50} + 2 q^{51} - 4 q^{52} + 2 q^{53} + q^{54} + 8 q^{55} + 8 q^{57} + 4 q^{58} + 16 q^{59} + 12 q^{60} + 22 q^{61} + 6 q^{62} - 29 q^{64} + 22 q^{65} - 16 q^{66} - 16 q^{67} + 14 q^{68} + 5 q^{69} + 16 q^{71} + 3 q^{72} + 8 q^{74} + 5 q^{75} + 30 q^{76} + 16 q^{78} + 12 q^{79} - 6 q^{80} + 5 q^{81} + 24 q^{82} + 10 q^{83} - 14 q^{85} - 20 q^{86} + 4 q^{87} - 8 q^{88} - 16 q^{89} + 9 q^{92} + 12 q^{93} - 32 q^{94} + 18 q^{95} + 7 q^{96} - 4 q^{97} - 2 q^{99}+O(q^{100}) \) 5 * q + q^2 + 5 * q^3 + 9 * q^4 + 2 * q^5 + q^6 + 3 * q^8 + 5 * q^9 - 2 * q^11 + 9 * q^12 + 4 * q^13 + 2 * q^15 + q^16 + 2 * q^17 + q^18 + 8 * q^19 + 12 * q^20 - 16 * q^22 + 5 * q^23 + 3 * q^24 + 5 * q^25 + 16 * q^26 + 5 * q^27 + 4 * q^29 + 12 * q^31 + 7 * q^32 - 2 * q^33 + 10 * q^34 + 9 * q^36 - 6 * q^37 - 8 * q^38 + 4 * q^39 + 30 * q^40 + 6 * q^41 - 24 * q^43 + 16 * q^44 + 2 * q^45 + q^46 + 24 * q^47 + q^48 - 3 * q^50 + 2 * q^51 - 4 * q^52 + 2 * q^53 + q^54 + 8 * q^55 + 8 * q^57 + 4 * q^58 + 16 * q^59 + 12 * q^60 + 22 * q^61 + 6 * q^62 - 29 * q^64 + 22 * q^65 - 16 * q^66 - 16 * q^67 + 14 * q^68 + 5 * q^69 + 16 * q^71 + 3 * q^72 + 8 * q^74 + 5 * q^75 + 30 * q^76 + 16 * q^78 + 12 * q^79 - 6 * q^80 + 5 * q^81 + 24 * q^82 + 10 * q^83 - 14 * q^85 - 20 * q^86 + 4 * q^87 - 8 * q^88 - 16 * q^89 + 9 * q^92 + 12 * q^93 - 32 * q^94 + 18 * q^95 + 7 * q^96 - 4 * q^97 - 2 * q^99

Introduction

L-functions

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