LMFDB - Embedded newform 2667.2.a.k.1.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2667,2,Mod(1,2667)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2667, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2667.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2667 = 3 \cdot 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2667.a (trivial)

Newform invariants

comment:select newform

sage:traces = [11,-2,11,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$21.2961022191$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 15 x^{9} + 25 x^{8} + 88 x^{7} - 112 x^{6} - 247 x^{5} + 215 x^{4} + 313 x^{3} + \cdots + 57 $ x^11 - 2x^10 - 15x^9 + 25x^8 + 88x^7 - 112x^6 - 247x^5 + 215x^4 + 313x^3 - 170x^2 - 121x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-1.81808$ of defining polynomial
Character	$\chi$	$=$	2667.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.81808 q^{2} +1.00000 q^{3} +1.30541 q^{4} -1.39765 q^{5} +1.81808 q^{6} -1.00000 q^{7} -1.26282 q^{8} +1.00000 q^{9} -2.54104 q^{10} +0.0844564 q^{11} +1.30541 q^{12} -3.52450 q^{13} -1.81808 q^{14} -1.39765 q^{15} -4.90673 q^{16} +4.93727 q^{17} +1.81808 q^{18} -3.17772 q^{19} -1.82451 q^{20} -1.00000 q^{21} +0.153548 q^{22} -3.91903 q^{23} -1.26282 q^{24} -3.04657 q^{25} -6.40782 q^{26} +1.00000 q^{27} -1.30541 q^{28} -7.80555 q^{29} -2.54104 q^{30} -6.27152 q^{31} -6.39517 q^{32} +0.0844564 q^{33} +8.97635 q^{34} +1.39765 q^{35} +1.30541 q^{36} +3.42797 q^{37} -5.77734 q^{38} -3.52450 q^{39} +1.76499 q^{40} -9.78445 q^{41} -1.81808 q^{42} +10.6350 q^{43} +0.110250 q^{44} -1.39765 q^{45} -7.12509 q^{46} +4.50967 q^{47} -4.90673 q^{48} +1.00000 q^{49} -5.53890 q^{50} +4.93727 q^{51} -4.60091 q^{52} -0.234825 q^{53} +1.81808 q^{54} -0.118041 q^{55} +1.26282 q^{56} -3.17772 q^{57} -14.1911 q^{58} -2.23465 q^{59} -1.82451 q^{60} +8.26515 q^{61} -11.4021 q^{62} -1.00000 q^{63} -1.81346 q^{64} +4.92602 q^{65} +0.153548 q^{66} -3.74734 q^{67} +6.44515 q^{68} -3.91903 q^{69} +2.54104 q^{70} -5.09148 q^{71} -1.26282 q^{72} +15.8865 q^{73} +6.23232 q^{74} -3.04657 q^{75} -4.14822 q^{76} -0.0844564 q^{77} -6.40782 q^{78} -10.3600 q^{79} +6.85789 q^{80} +1.00000 q^{81} -17.7889 q^{82} -5.52767 q^{83} -1.30541 q^{84} -6.90059 q^{85} +19.3353 q^{86} -7.80555 q^{87} -0.106653 q^{88} -15.0241 q^{89} -2.54104 q^{90} +3.52450 q^{91} -5.11593 q^{92} -6.27152 q^{93} +8.19894 q^{94} +4.44134 q^{95} -6.39517 q^{96} -9.13128 q^{97} +1.81808 q^{98} +0.0844564 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 2 q^{2} + 11 q^{3} + 12 q^{4} + q^{5} - 2 q^{6} - 11 q^{7} - 15 q^{8} + 11 q^{9} - 12 q^{10} - 7 q^{11} + 12 q^{12} - 24 q^{13} + 2 q^{14} + q^{15} - 6 q^{16} - 15 q^{17} - 2 q^{18} - 19 q^{19}+ \cdots - 7 q^{99}+O(q^{100}) $ 11 * q - 2 * q^2 + 11 * q^3 + 12 * q^4 + q^5 - 2 * q^6 - 11 * q^7 - 15 * q^8 + 11 * q^9 - 12 * q^10 - 7 * q^11 + 12 * q^12 - 24 * q^13 + 2 * q^14 + q^15 - 6 * q^16 - 15 * q^17 - 2 * q^18 - 19 * q^19 + 3 * q^20 - 11 * q^21 - 3 * q^22 - 11 * q^23 - 15 * q^24 + 10 * q^25 + 10 * q^26 + 11 * q^27 - 12 * q^28 - 10 * q^29 - 12 * q^30 - 20 * q^31 - 27 * q^32 - 7 * q^33 - 9 * q^34 - q^35 + 12 * q^36 - 22 * q^37 + 8 * q^38 - 24 * q^39 - 29 * q^40 + 9 * q^41 + 2 * q^42 - 17 * q^43 - 9 * q^44 + q^45 - 18 * q^46 - 7 * q^47 - 6 * q^48 + 11 * q^49 - 47 * q^50 - 15 * q^51 - 66 * q^52 - 28 * q^53 - 2 * q^54 - 24 * q^55 + 15 * q^56 - 19 * q^57 - 39 * q^58 + 35 * q^59 + 3 * q^60 - 6 * q^61 + 18 * q^62 - 11 * q^63 + 11 * q^64 - 43 * q^65 - 3 * q^66 - 22 * q^67 - 12 * q^68 - 11 * q^69 + 12 * q^70 - 22 * q^71 - 15 * q^72 - 29 * q^73 + 14 * q^74 + 10 * q^75 + 10 * q^76 + 7 * q^77 + 10 * q^78 - 20 * q^79 + 66 * q^80 + 11 * q^81 - 24 * q^82 + 17 * q^83 - 12 * q^84 - 50 * q^85 - 12 * q^86 - 10 * q^87 + 2 * q^88 - q^89 - 12 * q^90 + 24 * q^91 - 22 * q^92 - 20 * q^93 + q^94 + 10 * q^95 - 27 * q^96 - 45 * q^97 - 2 * q^98 - 7 * q^99

Coefficient data

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

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

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

$2$	1.81808	1.28558	0.642788	−	0.766044i	$-0.277778\pi$
$2$	1.81808	1.28558	0.642788	+	0.766044i	$0.277778\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.30541	0.652704
$5$	−1.39765	−0.625049	−0.312524	−	0.949910i	$-0.601175\pi$
$5$	−1.39765	−0.625049	−0.312524	+	0.949910i	$0.601175\pi$
$6$	1.81808	0.742227
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.26282	−0.446475
$9$	1.00000	0.333333
$10$	−2.54104	−0.803547
$11$	0.0844564	0.0254646	0.0127323	−	0.999919i	$-0.495947\pi$
$11$	0.0844564	0.0254646	0.0127323	+	0.999919i	$0.495947\pi$
$12$	1.30541	0.376839
$13$	−3.52450	−0.977520	−0.488760	−	0.872418i	$-0.662551\pi$
$13$	−3.52450	−0.977520	−0.488760	+	0.872418i	$0.662551\pi$
$14$	−1.81808	−0.485902
$15$	−1.39765	−0.360872
$16$	−4.90673	−1.22668
$17$	4.93727	1.19746	0.598732	−	0.800949i	$-0.295671\pi$
$17$	4.93727	1.19746	0.598732	+	0.800949i	$0.295671\pi$
$18$	1.81808	0.428525
$19$	−3.17772	−0.729018	−0.364509	−	0.931200i	$-0.618763\pi$
$19$	−3.17772	−0.729018	−0.364509	+	0.931200i	$0.618763\pi$
$20$	−1.82451	−0.407972
$21$	−1.00000	−0.218218
$22$	0.153548	0.0327366
$23$	−3.91903	−0.817173	−0.408587	−	0.912720i	$-0.633978\pi$
$23$	−3.91903	−0.817173	−0.408587	+	0.912720i	$0.633978\pi$
$24$	−1.26282	−0.257773
$25$	−3.04657	−0.609314
$26$	−6.40782	−1.25668
$27$	1.00000	0.192450
$28$	−1.30541	−0.246699
$29$	−7.80555	−1.44945	−0.724727	−	0.689036i	$-0.758034\pi$
$29$	−7.80555	−1.44945	−0.724727	+	0.689036i	$0.758034\pi$
$30$	−2.54104	−0.463928
$31$	−6.27152	−1.12640	−0.563199	−	0.826321i	$-0.690430\pi$
$31$	−6.27152	−1.12640	−0.563199	+	0.826321i	$0.690430\pi$
$32$	−6.39517	−1.13052
$33$	0.0844564	0.0147020
$34$	8.97635	1.53943
$35$	1.39765	0.236246
$36$	1.30541	0.217568
$37$	3.42797	0.563555	0.281778	−	0.959480i	$-0.409076\pi$
$37$	3.42797	0.563555	0.281778	+	0.959480i	$0.409076\pi$
$38$	−5.77734	−0.937208
$39$	−3.52450	−0.564372
$40$	1.76499	0.279069
$41$	−9.78445	−1.52807	−0.764037	−	0.645172i	$-0.776786\pi$
$41$	−9.78445	−1.52807	−0.764037	+	0.645172i	$0.776786\pi$
$42$	−1.81808	−0.280536
$43$	10.6350	1.62183	0.810913	−	0.585167i	$-0.198971\pi$
$43$	10.6350	1.62183	0.810913	+	0.585167i	$0.198971\pi$
$44$	0.110250	0.0166208
$45$	−1.39765	−0.208350
$46$	−7.12509	−1.05054
$47$	4.50967	0.657803	0.328902	−	0.944364i	$-0.393322\pi$
$47$	4.50967	0.657803	0.328902	+	0.944364i	$0.393322\pi$
$48$	−4.90673	−0.708225
$49$	1.00000	0.142857
$50$	−5.53890	−0.783319
$51$	4.93727	0.691356
$52$	−4.60091	−0.638031
$53$	−0.234825	−0.0322557	−0.0161279	−	0.999870i	$-0.505134\pi$
$53$	−0.234825	−0.0322557	−0.0161279	+	0.999870i	$0.505134\pi$
$54$	1.81808	0.247409
$55$	−0.118041	−0.0159166
$56$	1.26282	0.168752
$57$	−3.17772	−0.420899
$58$	−14.1911	−1.86338
$59$	−2.23465	−0.290927	−0.145463	−	0.989364i	$-0.546467\pi$
$59$	−2.23465	−0.290927	−0.145463	+	0.989364i	$0.546467\pi$
$60$	−1.82451	−0.235543
$61$	8.26515	1.05824	0.529122	−	0.848546i	$-0.322521\pi$
$61$	8.26515	1.05824	0.529122	+	0.848546i	$0.322521\pi$
$62$	−11.4021	−1.44807
$63$	−1.00000	−0.125988
$64$	−1.81346	−0.226682
$65$	4.92602	0.610998
$66$	0.153548	0.0189005
$67$	−3.74734	−0.457810	−0.228905	−	0.973449i	$-0.573515\pi$
$67$	−3.74734	−0.457810	−0.228905	+	0.973449i	$0.573515\pi$
$68$	6.44515	0.781590
$69$	−3.91903	−0.471795
$70$	2.54104	0.303712
$71$	−5.09148	−0.604248	−0.302124	−	0.953269i	$-0.597696\pi$
$71$	−5.09148	−0.604248	−0.302124	+	0.953269i	$0.597696\pi$
$72$	−1.26282	−0.148825
$73$	15.8865	1.85937	0.929686	−	0.368353i	$-0.120078\pi$
$73$	15.8865	1.85937	0.929686	+	0.368353i	$0.120078\pi$
$74$	6.23232	0.724493
$75$	−3.04657	−0.351788
$76$	−4.14822	−0.475833
$77$	−0.0844564	−0.00962470
$78$	−6.40782	−0.725542
$79$	−10.3600	−1.16560	−0.582798	−	0.812617i	$-0.698042\pi$
$79$	−10.3600	−1.16560	−0.582798	+	0.812617i	$0.698042\pi$
$80$	6.85789	0.766736
$81$	1.00000	0.111111
$82$	−17.7889	−1.96446
$83$	−5.52767	−0.606741	−0.303370	−	0.952873i	$-0.598112\pi$
$83$	−5.52767	−0.606741	−0.303370	+	0.952873i	$0.598112\pi$
$84$	−1.30541	−0.142432
$85$	−6.90059	−0.748474
$86$	19.3353	2.08498
$87$	−7.80555	−0.836842
$88$	−0.106653	−0.0113693
$89$	−15.0241	−1.59255	−0.796276	−	0.604934i	$-0.793199\pi$
$89$	−15.0241	−1.59255	−0.796276	+	0.604934i	$0.793199\pi$
$90$	−2.54104	−0.267849
$91$	3.52450	0.369468
$92$	−5.11593	−0.533372
$93$	−6.27152	−0.650326
$94$	8.19894	0.845656
$95$	4.44134	0.455672
$96$	−6.39517	−0.652704
$97$	−9.13128	−0.927141	−0.463571	−	0.886060i	$-0.653432\pi$
$97$	−9.13128	−0.927141	−0.463571	+	0.886060i	$0.653432\pi$
$98$	1.81808	0.183654
$99$	0.0844564	0.00848819
$100$	−3.97702	−0.397702
$101$	12.1017	1.20417	0.602084	−	0.798433i	$-0.294337\pi$
$101$	12.1017	1.20417	0.602084	+	0.798433i	$0.294337\pi$
$102$	8.97635	0.888791
$103$	−5.80333	−0.571819	−0.285909	−	0.958257i	$-0.592296\pi$
$103$	−5.80333	−0.571819	−0.285909	+	0.958257i	$0.592296\pi$
$104$	4.45082	0.436439
$105$	1.39765	0.136397
$106$	−0.426931	−0.0414672
$107$	−0.365904	−0.0353732	−0.0176866	−	0.999844i	$-0.505630\pi$
$107$	−0.365904	−0.0353732	−0.0176866	+	0.999844i	$0.505630\pi$
$108$	1.30541	0.125613
$109$	−14.5385	−1.39253	−0.696266	−	0.717784i	$-0.745156\pi$
$109$	−14.5385	−1.39253	−0.696266	+	0.717784i	$0.745156\pi$
$110$	−0.214607	−0.0204620
$111$	3.42797	0.325369
$112$	4.90673	0.463642
$113$	−7.14306	−0.671963	−0.335981	−	0.941869i	$-0.609068\pi$
$113$	−7.14306	−0.671963	−0.335981	+	0.941869i	$0.609068\pi$
$114$	−5.77734	−0.541097
$115$	5.47743	0.510773
$116$	−10.1894	−0.946064
$117$	−3.52450	−0.325840
$118$	−4.06277	−0.374008
$119$	−4.93727	−0.452599
$120$	1.76499	0.161121
$121$	−10.9929	−0.999352
$122$	15.0267	1.36045
$123$	−9.78445	−0.882234
$124$	−8.18689	−0.735205
$125$	11.2463	1.00590
$126$	−1.81808	−0.161967
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	9.49332	0.839099
$129$	10.6350	0.936361
$130$	8.95590	0.785484
$131$	21.8579	1.90973	0.954866	−	0.297037i	$-0.0959983\pi$
$131$	21.8579	1.90973	0.954866	+	0.297037i	$0.0959983\pi$
$132$	0.110250	0.00959604
$133$	3.17772	0.275543
$134$	−6.81295	−0.588550
$135$	−1.39765	−0.120291
$136$	−6.23490	−0.534638
$137$	10.8301	0.925281	0.462641	−	0.886546i	$-0.346902\pi$
$137$	10.8301	0.925281	0.462641	+	0.886546i	$0.346902\pi$
$138$	−7.12509	−0.606528
$139$	−14.1968	−1.20416	−0.602078	−	0.798437i	$-0.705660\pi$
$139$	−14.1968	−1.20416	−0.602078	+	0.798437i	$0.705660\pi$
$140$	1.82451	0.154199
$141$	4.50967	0.379783
$142$	−9.25671	−0.776806
$143$	−0.297667	−0.0248921
$144$	−4.90673	−0.408894
$145$	10.9094	0.905979
$146$	28.8829	2.39036
$147$	1.00000	0.0824786
$148$	4.47490	0.367835
$149$	−19.7609	−1.61887	−0.809437	−	0.587207i	$-0.800227\pi$
$149$	−19.7609	−1.61887	−0.809437	+	0.587207i	$0.800227\pi$
$150$	−5.53890	−0.452249
$151$	7.89570	0.642543	0.321272	−	0.946987i	$-0.395890\pi$
$151$	7.89570	0.642543	0.321272	+	0.946987i	$0.395890\pi$
$152$	4.01289	0.325489
$153$	4.93727	0.399155
$154$	−0.153548	−0.0123733
$155$	8.76540	0.704054
$156$	−4.60091	−0.368368
$157$	18.3445	1.46405	0.732024	−	0.681279i	$-0.238576\pi$
$157$	18.3445	1.46405	0.732024	+	0.681279i	$0.238576\pi$
$158$	−18.8354	−1.49846
$159$	−0.234825	−0.0186229
$160$	8.93821	0.706628
$161$	3.91903	0.308862
$162$	1.81808	0.142842
$163$	20.4515	1.60189	0.800944	−	0.598739i	$-0.204331\pi$
$163$	20.4515	1.60189	0.800944	+	0.598739i	$0.204331\pi$
$164$	−12.7727	−0.997380
$165$	−0.118041	−0.00918945
$166$	−10.0497	−0.780011
$167$	22.4305	1.73572	0.867861	−	0.496807i	$-0.165494\pi$
$167$	22.4305	1.73572	0.867861	+	0.496807i	$0.165494\pi$
$168$	1.26282	0.0974289
$169$	−0.577899	−0.0444538
$170$	−12.5458	−0.962219
$171$	−3.17772	−0.243006
$172$	13.8830	1.05857
$173$	23.4089	1.77975	0.889873	−	0.456208i	$-0.150793\pi$
$173$	23.4089	1.77975	0.889873	+	0.456208i	$0.150793\pi$
$174$	−14.1911	−1.07582
$175$	3.04657	0.230299
$176$	−0.414405	−0.0312369
$177$	−2.23465	−0.167967
$178$	−27.3150	−2.04734
$179$	−12.0263	−0.898887	−0.449443	−	0.893309i	$-0.648378\pi$
$179$	−12.0263	−0.898887	−0.449443	+	0.893309i	$0.648378\pi$
$180$	−1.82451	−0.135991
$181$	−14.7462	−1.09607	−0.548037	−	0.836454i	$-0.684625\pi$
$181$	−14.7462	−1.09607	−0.548037	+	0.836454i	$0.684625\pi$
$182$	6.40782	0.474979
$183$	8.26515	0.610977
$184$	4.94904	0.364848
$185$	−4.79111	−0.352250
$186$	−11.4021	−0.836044
$187$	0.416984	0.0304929
$188$	5.88696	0.429351
$189$	−1.00000	−0.0727393
$190$	8.07471	0.585801
$191$	−15.1077	−1.09315	−0.546577	−	0.837409i	$-0.684069\pi$
$191$	−15.1077	−1.09315	−0.546577	+	0.837409i	$0.684069\pi$
$192$	−1.81346	−0.130875
$193$	−4.11572	−0.296256	−0.148128	−	0.988968i	$-0.547325\pi$
$193$	−4.11572	−0.296256	−0.148128	+	0.988968i	$0.547325\pi$
$194$	−16.6014	−1.19191
$195$	4.92602	0.352760
$196$	1.30541	0.0932434
$197$	−8.76996	−0.624834	−0.312417	−	0.949945i	$-0.601139\pi$
$197$	−8.76996	−0.624834	−0.312417	+	0.949945i	$0.601139\pi$
$198$	0.153548	0.0109122
$199$	−19.9853	−1.41672	−0.708360	−	0.705851i	$-0.750565\pi$
$199$	−19.9853	−1.41672	−0.708360	+	0.705851i	$0.750565\pi$
$200$	3.84728	0.272044
$201$	−3.74734	−0.264317
$202$	22.0019	1.54805
$203$	7.80555	0.547842
$204$	6.44515	0.451251
$205$	13.6753	0.955122
$206$	−10.5509	−0.735116
$207$	−3.91903	−0.272391
$208$	17.2938	1.19911
$209$	−0.268379	−0.0185641
$210$	2.54104	0.175348
$211$	6.14263	0.422876	0.211438	−	0.977391i	$-0.432185\pi$
$211$	6.14263	0.422876	0.211438	+	0.977391i	$0.432185\pi$
$212$	−0.306543	−0.0210534
$213$	−5.09148	−0.348863
$214$	−0.665241	−0.0454750
$215$	−14.8641	−1.01372
$216$	−1.26282	−0.0859242
$217$	6.27152	0.425739
$218$	−26.4320	−1.79020
$219$	15.8865	1.07351
$220$	−0.154091	−0.0103888
$221$	−17.4014	−1.17055
$222$	6.23232	0.418286
$223$	−6.16516	−0.412850	−0.206425	−	0.978462i	$-0.566183\pi$
$223$	−6.16516	−0.412850	−0.206425	+	0.978462i	$0.566183\pi$
$224$	6.39517	0.427295
$225$	−3.04657	−0.203105
$226$	−12.9866	−0.863858
$227$	24.5032	1.62633	0.813167	−	0.582030i	$-0.197742\pi$
$227$	24.5032	1.62633	0.813167	+	0.582030i	$0.197742\pi$
$228$	−4.14822	−0.274722
$229$	−1.24111	−0.0820148	−0.0410074	−	0.999159i	$-0.513057\pi$
$229$	−1.24111	−0.0820148	−0.0410074	+	0.999159i	$0.513057\pi$
$230$	9.95840	0.656638
$231$	−0.0844564	−0.00555682
$232$	9.85702	0.647145
$233$	24.8114	1.62545	0.812723	−	0.582650i	$-0.197984\pi$
$233$	24.8114	1.62545	0.812723	+	0.582650i	$0.197984\pi$
$234$	−6.40782	−0.418892
$235$	−6.30295	−0.411159
$236$	−2.91713	−0.189889
$237$	−10.3600	−0.672957
$238$	−8.97635	−0.581850
$239$	19.9316	1.28927	0.644633	−	0.764492i	$-0.277010\pi$
$239$	19.9316	1.28927	0.644633	+	0.764492i	$0.277010\pi$
$240$	6.85789	0.442675
$241$	1.78751	0.115144	0.0575718	−	0.998341i	$-0.481664\pi$
$241$	1.78751	0.115144	0.0575718	+	0.998341i	$0.481664\pi$
$242$	−19.9859	−1.28474
$243$	1.00000	0.0641500
$244$	10.7894	0.690720
$245$	−1.39765	−0.0892927
$246$	−17.7889	−1.13418
$247$	11.1999	0.712630
$248$	7.91982	0.502909
$249$	−5.52767	−0.350302
$250$	20.4467	1.29316
$251$	19.0011	1.19934	0.599671	−	0.800247i	$-0.295298\pi$
$251$	19.0011	1.19934	0.599671	+	0.800247i	$0.295298\pi$
$252$	−1.30541	−0.0822330
$253$	−0.330987	−0.0208090
$254$	1.81808	0.114076
$255$	−6.90059	−0.432132
$256$	20.8865	1.30541
$257$	−5.27896	−0.329293	−0.164646	−	0.986353i	$-0.552648\pi$
$257$	−5.27896	−0.329293	−0.164646	+	0.986353i	$0.552648\pi$
$258$	19.3353	1.20376
$259$	−3.42797	−0.213004
$260$	6.43047	0.398801
$261$	−7.80555	−0.483151
$262$	39.7393	2.45510
$263$	−22.2560	−1.37236	−0.686181	−	0.727431i	$-0.740714\pi$
$263$	−22.2560	−1.37236	−0.686181	+	0.727431i	$0.740714\pi$
$264$	−0.106653	−0.00656407
$265$	0.328204	0.0201614
$266$	5.77734	0.354231
$267$	−15.0241	−0.919460
$268$	−4.89181	−0.298815
$269$	8.70678	0.530862	0.265431	−	0.964130i	$-0.414486\pi$
$269$	8.70678	0.530862	0.265431	+	0.964130i	$0.414486\pi$
$270$	−2.54104	−0.154643
$271$	10.9473	0.665002	0.332501	−	0.943103i	$-0.392107\pi$
$271$	10.9473	0.665002	0.332501	+	0.943103i	$0.392107\pi$
$272$	−24.2258	−1.46891
$273$	3.52450	0.213312
$274$	19.6900	1.18952
$275$	−0.257302	−0.0155159
$276$	−5.11593	−0.307943
$277$	−21.4950	−1.29151	−0.645756	−	0.763544i	$-0.723458\pi$
$277$	−21.4950	−1.29151	−0.645756	+	0.763544i	$0.723458\pi$
$278$	−25.8109	−1.54803
$279$	−6.27152	−0.375466
$280$	−1.76499	−0.105478
$281$	16.9237	1.00958	0.504790	−	0.863242i	$-0.331570\pi$
$281$	16.9237	1.00958	0.504790	+	0.863242i	$0.331570\pi$
$282$	8.19894	0.488240
$283$	−11.0667	−0.657850	−0.328925	−	0.944356i	$-0.606686\pi$
$283$	−11.0667	−0.657850	−0.328925	+	0.944356i	$0.606686\pi$
$284$	−6.64646	−0.394395
$285$	4.44134	0.263082
$286$	−0.541181	−0.0320007
$287$	9.78445	0.577558
$288$	−6.39517	−0.376839
$289$	7.37666	0.433921
$290$	19.8342	1.16470
$291$	−9.13128	−0.535285
$292$	20.7383	1.21362
$293$	−24.7793	−1.44762	−0.723811	−	0.689999i	$-0.757611\pi$
$293$	−24.7793	−1.44762	−0.723811	+	0.689999i	$0.757611\pi$
$294$	1.81808	0.106032
$295$	3.12326	0.181843
$296$	−4.32892	−0.251614
$297$	0.0844564	0.00490066
$298$	−35.9268	−2.08118
$299$	13.8126	0.798804
$300$	−3.97702	−0.229613
$301$	−10.6350	−0.612992
$302$	14.3550	0.826038
$303$	12.1017	0.695226
$304$	15.5922	0.894273
$305$	−11.5518	−0.661454
$306$	8.97635	0.513144
$307$	22.2886	1.27208	0.636038	−	0.771658i	$-0.280572\pi$
$307$	22.2886	1.27208	0.636038	+	0.771658i	$0.280572\pi$
$308$	−0.110250	−0.00628208
$309$	−5.80333	−0.330140
$310$	15.9362	0.905115
$311$	9.48282	0.537721	0.268861	−	0.963179i	$-0.413353\pi$
$311$	9.48282	0.537721	0.268861	+	0.963179i	$0.413353\pi$
$312$	4.45082	0.251978
$313$	5.82224	0.329092	0.164546	−	0.986369i	$-0.447384\pi$
$313$	5.82224	0.329092	0.164546	+	0.986369i	$0.447384\pi$
$314$	33.3517	1.88214
$315$	1.39765	0.0787488
$316$	−13.5241	−0.760789
$317$	28.5643	1.60433	0.802166	−	0.597100i	$-0.203681\pi$
$317$	28.5643	1.60433	0.802166	+	0.597100i	$0.203681\pi$
$318$	−0.426931	−0.0239411
$319$	−0.659228	−0.0369097
$320$	2.53458	0.141687
$321$	−0.365904	−0.0204227
$322$	7.12509	0.397066
$323$	−15.6893	−0.872973
$324$	1.30541	0.0725227
$325$	10.7376	0.595617
$326$	37.1825	2.05935
$327$	−14.5385	−0.803978
$328$	12.3560	0.682248
$329$	−4.50967	−0.248626
$330$	−0.214607	−0.0118137
$331$	−27.6246	−1.51839	−0.759193	−	0.650866i	$-0.774406\pi$
$331$	−27.6246	−1.51839	−0.759193	+	0.650866i	$0.774406\pi$
$332$	−7.21586	−0.396022
$333$	3.42797	0.187852
$334$	40.7803	2.23140
$335$	5.23748	0.286154
$336$	4.90673	0.267684
$337$	12.0879	0.658467	0.329234	−	0.944248i	$-0.393210\pi$
$337$	12.0879	0.658467	0.329234	+	0.944248i	$0.393210\pi$
$338$	−1.05067	−0.0571487
$339$	−7.14306	−0.387958
$340$	−9.00808	−0.488532
$341$	−0.529670	−0.0286833
$342$	−5.77734	−0.312403
$343$	−1.00000	−0.0539949
$344$	−13.4301	−0.724105
$345$	5.47743	0.294895
$346$	42.5592	2.28800
$347$	−11.5304	−0.618985	−0.309492	−	0.950902i	$-0.600159\pi$
$347$	−11.5304	−0.618985	−0.309492	+	0.950902i	$0.600159\pi$
$348$	−10.1894	−0.546210
$349$	−32.9671	−1.76469	−0.882345	−	0.470603i	$-0.844036\pi$
$349$	−32.9671	−1.76469	−0.882345	+	0.470603i	$0.844036\pi$
$350$	5.53890	0.296067
$351$	−3.52450	−0.188124
$352$	−0.540113	−0.0287881
$353$	12.8554	0.684222	0.342111	−	0.939660i	$-0.388858\pi$
$353$	12.8554	0.684222	0.342111	+	0.939660i	$0.388858\pi$
$354$	−4.06277	−0.215934
$355$	7.11612	0.377684
$356$	−19.6126	−1.03946
$357$	−4.93727	−0.261308
$358$	−21.8647	−1.15559
$359$	21.9370	1.15779	0.578896	−	0.815402i	$-0.303484\pi$
$359$	21.9370	1.15779	0.578896	+	0.815402i	$0.303484\pi$
$360$	1.76499	0.0930230
$361$	−8.90212	−0.468532
$362$	−26.8097	−1.40909
$363$	−10.9929	−0.576976
$364$	4.60091	0.241153
$365$	−22.2038	−1.16220
$366$	15.0267	0.785457
$367$	−16.7528	−0.874487	−0.437244	−	0.899343i	$-0.644045\pi$
$367$	−16.7528	−0.874487	−0.437244	+	0.899343i	$0.644045\pi$
$368$	19.2296	1.00241
$369$	−9.78445	−0.509358
$370$	−8.71062	−0.452843
$371$	0.234825	0.0121915
$372$	−8.18689	−0.424471
$373$	−14.6000	−0.755961	−0.377980	−	0.925814i	$-0.623381\pi$
$373$	−14.6000	−0.755961	−0.377980	+	0.925814i	$0.623381\pi$
$374$	0.758110	0.0392009
$375$	11.2463	0.580757
$376$	−5.69492	−0.293693
$377$	27.5106	1.41687
$378$	−1.81808	−0.0935118
$379$	1.91231	0.0982286	0.0491143	−	0.998793i	$-0.484360\pi$
$379$	1.91231	0.0982286	0.0491143	+	0.998793i	$0.484360\pi$
$380$	5.79776	0.297419
$381$	1.00000	0.0512316
$382$	−27.4669	−1.40533
$383$	−14.6000	−0.746025	−0.373012	−	0.927826i	$-0.621675\pi$
$383$	−14.6000	−0.746025	−0.373012	+	0.927826i	$0.621675\pi$
$384$	9.49332	0.484454
$385$	0.118041	0.00601591
$386$	−7.48270	−0.380859
$387$	10.6350	0.540608
$388$	−11.9200	−0.605149
$389$	−1.62130	−0.0822033	−0.0411017	−	0.999155i	$-0.513087\pi$
$389$	−1.62130	−0.0822033	−0.0411017	+	0.999155i	$0.513087\pi$
$390$	8.95590	0.453499
$391$	−19.3493	−0.978536
$392$	−1.26282	−0.0637822
$393$	21.8579	1.10258
$394$	−15.9445	−0.803271
$395$	14.4797	0.728554
$396$	0.110250	0.00554027
$397$	−38.7222	−1.94341	−0.971705	−	0.236197i	$-0.924099\pi$
$397$	−38.7222	−1.94341	−0.971705	+	0.236197i	$0.924099\pi$
$398$	−36.3348	−1.82130
$399$	3.17772	0.159085
$400$	14.9487	0.747434
$401$	−12.5099	−0.624716	−0.312358	−	0.949964i	$-0.601119\pi$
$401$	−12.5099	−0.624716	−0.312358	+	0.949964i	$0.601119\pi$
$402$	−6.81295	−0.339799
$403$	22.1040	1.10108
$404$	15.7977	0.785965
$405$	−1.39765	−0.0694499
$406$	14.1911	0.704292
$407$	0.289514	0.0143507
$408$	−6.23490	−0.308674
$409$	−1.09186	−0.0539888	−0.0269944	−	0.999636i	$-0.508594\pi$
$409$	−1.09186	−0.0539888	−0.0269944	+	0.999636i	$0.508594\pi$
$410$	24.8627	1.22788
$411$	10.8301	0.534211
$412$	−7.57571	−0.373228
$413$	2.23465	0.109960
$414$	−7.12509	−0.350179
$415$	7.72576	0.379243
$416$	22.5398	1.10510
$417$	−14.1968	−0.695220
$418$	−0.487933	−0.0238656
$419$	25.5953	1.25041	0.625207	−	0.780459i	$-0.285015\pi$
$419$	25.5953	1.25041	0.625207	+	0.780459i	$0.285015\pi$
$420$	1.82451	0.0890268
$421$	26.7270	1.30260	0.651298	−	0.758822i	$-0.274225\pi$
$421$	26.7270	1.30260	0.651298	+	0.758822i	$0.274225\pi$
$422$	11.1678	0.543639
$423$	4.50967	0.219268
$424$	0.296543	0.0144014
$425$	−15.0417	−0.729632
$426$	−9.25671	−0.448489
$427$	−8.26515	−0.399979
$428$	−0.477653	−0.0230883
$429$	−0.297667	−0.0143715
$430$	−27.0240	−1.30321
$431$	−20.1905	−0.972544	−0.486272	−	0.873808i	$-0.661644\pi$
$431$	−20.1905	−0.972544	−0.486272	+	0.873808i	$0.661644\pi$
$432$	−4.90673	−0.236075
$433$	21.9651	1.05557	0.527787	−	0.849377i	$-0.323022\pi$
$433$	21.9651	1.05557	0.527787	+	0.849377i	$0.323022\pi$
$434$	11.4021	0.547319
$435$	10.9094	0.523067
$436$	−18.9786	−0.908911
$437$	12.4536	0.595734
$438$	28.8829	1.38008
$439$	12.8006	0.610939	0.305470	−	0.952202i	$-0.401187\pi$
$439$	12.8006	0.610939	0.305470	+	0.952202i	$0.401187\pi$
$440$	0.149064	0.00710637
$441$	1.00000	0.0476190
$442$	−31.6371	−1.50482
$443$	−35.3169	−1.67795	−0.838977	−	0.544166i	$-0.816846\pi$
$443$	−35.3169	−1.67795	−0.838977	+	0.544166i	$0.816846\pi$
$444$	4.47490	0.212370
$445$	20.9985	0.995422
$446$	−11.2087	−0.530749
$447$	−19.7609	−0.934657
$448$	1.81346	0.0856778
$449$	−9.48179	−0.447473	−0.223737	−	0.974650i	$-0.571826\pi$
$449$	−9.48179	−0.447473	−0.223737	+	0.974650i	$0.571826\pi$
$450$	−5.53890	−0.261106
$451$	−0.826360	−0.0389118
$452$	−9.32461	−0.438593
$453$	7.89570	0.370973
$454$	44.5487	2.09077
$455$	−4.92602	−0.230936
$456$	4.01289	0.187921
$457$	14.4625	0.676528	0.338264	−	0.941051i	$-0.390160\pi$
$457$	14.4625	0.676528	0.338264	+	0.941051i	$0.390160\pi$
$458$	−2.25643	−0.105436
$459$	4.93727	0.230452
$460$	7.15028	0.333384
$461$	−16.5198	−0.769404	−0.384702	−	0.923041i	$-0.625696\pi$
$461$	−16.5198	−0.769404	−0.384702	+	0.923041i	$0.625696\pi$
$462$	−0.153548	−0.00714372
$463$	−21.0251	−0.977120	−0.488560	−	0.872530i	$-0.662478\pi$
$463$	−21.0251	−0.977120	−0.488560	+	0.872530i	$0.662478\pi$
$464$	38.2997	1.77802
$465$	8.76540	0.406486
$466$	45.1090	2.08963
$467$	−3.24697	−0.150252	−0.0751260	−	0.997174i	$-0.523936\pi$
$467$	−3.24697	−0.150252	−0.0751260	+	0.997174i	$0.523936\pi$
$468$	−4.60091	−0.212677
$469$	3.74734	0.173036
$470$	−11.4593	−0.528576
$471$	18.3445	0.845268
$472$	2.82197	0.129892
$473$	0.898196	0.0412991
$474$	−18.8354	−0.865137
$475$	9.68113	0.444201
$476$	−6.44515	−0.295413
$477$	−0.234825	−0.0107519
$478$	36.2372	1.65745
$479$	−37.5282	−1.71471	−0.857353	−	0.514729i	$-0.827892\pi$
$479$	−37.5282	−1.71471	−0.857353	+	0.514729i	$0.827892\pi$
$480$	8.93821	0.407972
$481$	−12.0819	−0.550887
$482$	3.24983	0.148026
$483$	3.91903	0.178322
$484$	−14.3502	−0.652281
$485$	12.7624	0.579509
$486$	1.81808	0.0824697
$487$	−40.2962	−1.82600	−0.912998	−	0.407964i	$-0.866239\pi$
$487$	−40.2962	−1.82600	−0.912998	+	0.407964i	$0.866239\pi$
$488$	−10.4374	−0.472480
$489$	20.4515	0.924851
$490$	−2.54104	−0.114792
$491$	−23.9030	−1.07873	−0.539364	−	0.842072i	$-0.681335\pi$
$491$	−23.9030	−1.07873	−0.539364	+	0.842072i	$0.681335\pi$
$492$	−12.7727	−0.575838
$493$	−38.5381	−1.73567
$494$	20.3622	0.916140
$495$	−0.118041	−0.00530553
$496$	30.7726	1.38173
$497$	5.09148	0.228384
$498$	−10.0497	−0.450339
$499$	4.38382	0.196247	0.0981233	−	0.995174i	$-0.468716\pi$
$499$	4.38382	0.196247	0.0981233	+	0.995174i	$0.468716\pi$
$500$	14.6810	0.656555
$501$	22.4305	1.00212
$502$	34.5456	1.54184
$503$	26.1847	1.16752	0.583758	−	0.811927i	$-0.301582\pi$
$503$	26.1847	1.16752	0.583758	+	0.811927i	$0.301582\pi$
$504$	1.26282	0.0562506
$505$	−16.9140	−0.752663
$506$	−0.601760	−0.0267515
$507$	−0.577899	−0.0256654
$508$	1.30541	0.0579181
$509$	3.82171	0.169394	0.0846972	−	0.996407i	$-0.473008\pi$
$509$	3.82171	0.169394	0.0846972	+	0.996407i	$0.473008\pi$
$510$	−12.5458	−0.555538
$511$	−15.8865	−0.702777
$512$	18.9867	0.839100
$513$	−3.17772	−0.140300
$514$	−9.59757	−0.423331
$515$	8.11103	0.357415
$516$	13.8830	0.611167
$517$	0.380871	0.0167507
$518$	−6.23232	−0.273833
$519$	23.4089	1.02754
$520$	−6.22070	−0.272796
$521$	15.3809	0.673850	0.336925	−	0.941531i	$-0.390613\pi$
$521$	15.3809	0.673850	0.336925	+	0.941531i	$0.390613\pi$
$522$	−14.1911	−0.621127
$523$	10.9314	0.477998	0.238999	−	0.971020i	$-0.423181\pi$
$523$	10.9314	0.477998	0.238999	+	0.971020i	$0.423181\pi$
$524$	28.5335	1.24649
$525$	3.04657	0.132963
$526$	−40.4631	−1.76427
$527$	−30.9642	−1.34882
$528$	−0.414405	−0.0180346
$529$	−7.64124	−0.332228
$530$	0.596701	0.0259190
$531$	−2.23465	−0.0969755
$532$	4.14822	0.179848
$533$	34.4853	1.49372
$534$	−27.3150	−1.18203
$535$	0.511406	0.0221100
$536$	4.73223	0.204401
$537$	−12.0263	−0.518973
$538$	15.8296	0.682463
$539$	0.0844564	0.00363780
$540$	−1.82451	−0.0785142
$541$	−40.3414	−1.73441	−0.867206	−	0.497949i	$-0.834087\pi$
$541$	−40.3414	−1.73441	−0.867206	+	0.497949i	$0.834087\pi$
$542$	19.9031	0.854910
$543$	−14.7462	−0.632819
$544$	−31.5747	−1.35375
$545$	20.3197	0.870400
$546$	6.40782	0.274229
$547$	−38.2345	−1.63479	−0.817396	−	0.576077i	$-0.804583\pi$
$547$	−38.2345	−1.63479	−0.817396	+	0.576077i	$0.804583\pi$
$548$	14.1377	0.603935
$549$	8.26515	0.352748
$550$	−0.467796	−0.0199469
$551$	24.8038	1.05668
$552$	4.94904	0.210645
$553$	10.3600	0.440554
$554$	−39.0797	−1.66034
$555$	−4.79111	−0.203371
$556$	−18.5326	−0.785957
$557$	24.3805	1.03304	0.516518	−	0.856276i	$-0.327228\pi$
$557$	24.3805	1.03304	0.516518	+	0.856276i	$0.327228\pi$
$558$	−11.4021	−0.482690
$559$	−37.4831	−1.58537
$560$	−6.85789	−0.289799
$561$	0.416984	0.0176051
$562$	30.7685	1.29789
$563$	−11.0319	−0.464938	−0.232469	−	0.972604i	$-0.574680\pi$
$563$	−11.0319	−0.464938	−0.232469	+	0.972604i	$0.574680\pi$
$564$	5.88696	0.247886
$565$	9.98351	0.420009
$566$	−20.1202	−0.845716
$567$	−1.00000	−0.0419961
$568$	6.42964	0.269782
$569$	41.4077	1.73590	0.867950	−	0.496651i	$-0.165437\pi$
$569$	41.4077	1.73590	0.867950	+	0.496651i	$0.165437\pi$
$570$	8.07471	0.338212
$571$	−20.0004	−0.836991	−0.418495	−	0.908219i	$-0.637442\pi$
$571$	−20.0004	−0.836991	−0.418495	+	0.908219i	$0.637442\pi$
$572$	−0.388576	−0.0162472
$573$	−15.1077	−0.631132
$574$	17.7889	0.742494
$575$	11.9396	0.497915
$576$	−1.81346	−0.0755607
$577$	29.2882	1.21928	0.609642	−	0.792677i	$-0.291313\pi$
$577$	29.2882	1.21928	0.609642	+	0.792677i	$0.291313\pi$
$578$	13.4113	0.557838
$579$	−4.11572	−0.171043
$580$	14.2413	0.591336
$581$	5.52767	0.229326
$582$	−16.6014	−0.688149
$583$	−0.0198325	−0.000821378 0
$584$	−20.0618	−0.830164
$585$	4.92602	0.203666
$586$	−45.0507	−1.86103
$587$	21.2041	0.875187	0.437593	−	0.899173i	$-0.355831\pi$
$587$	21.2041	0.875187	0.437593	+	0.899173i	$0.355831\pi$
$588$	1.30541	0.0538341
$589$	19.9291	0.821165
$590$	5.67834	0.233773
$591$	−8.76996	−0.360748
$592$	−16.8201	−0.691303
$593$	−37.6147	−1.54465	−0.772325	−	0.635227i	$-0.780906\pi$
$593$	−37.6147	−1.54465	−0.772325	+	0.635227i	$0.780906\pi$
$594$	0.153548	0.00630017
$595$	6.90059	0.282897
$596$	−25.7960	−1.05664
$597$	−19.9853	−0.817944
$598$	25.1124	1.02692
$599$	−25.3004	−1.03375	−0.516873	−	0.856062i	$-0.672904\pi$
$599$	−25.3004	−1.03375	−0.516873	+	0.856062i	$0.672904\pi$
$600$	3.84728	0.157064
$601$	22.2166	0.906235	0.453118	−	0.891451i	$-0.350312\pi$
$601$	22.2166	0.906235	0.453118	+	0.891451i	$0.350312\pi$
$602$	−19.3353	−0.788048
$603$	−3.74734	−0.152603
$604$	10.3071	0.419390
$605$	15.3642	0.624644
$606$	22.0019	0.893766
$607$	26.6139	1.08023	0.540113	−	0.841592i	$-0.318381\pi$
$607$	26.6139	1.08023	0.540113	+	0.841592i	$0.318381\pi$
$608$	20.3220	0.824167
$609$	7.80555	0.316297
$610$	−21.0021	−0.850349
$611$	−15.8943	−0.643016
$612$	6.44515	0.260530
$613$	−32.9527	−1.33095	−0.665474	−	0.746421i	$-0.731771\pi$
$613$	−32.9527	−1.33095	−0.665474	+	0.746421i	$0.731771\pi$
$614$	40.5224	1.63535
$615$	13.6753	0.551440
$616$	0.106653	0.00429719
$617$	−42.6655	−1.71765	−0.858824	−	0.512271i	$-0.828804\pi$
$617$	−42.6655	−1.71765	−0.858824	+	0.512271i	$0.828804\pi$
$618$	−10.5509	−0.424420
$619$	−27.3570	−1.09957	−0.549786	−	0.835306i	$-0.685291\pi$
$619$	−27.3570	−1.09957	−0.549786	+	0.835306i	$0.685291\pi$
$620$	11.4424	0.459539
$621$	−3.91903	−0.157265
$622$	17.2405	0.691281
$623$	15.0241	0.601928
$624$	17.2938	0.692304
$625$	−0.485568	−0.0194227
$626$	10.5853	0.423073
$627$	−0.268379	−0.0107180
$628$	23.9470	0.955590
$629$	16.9248	0.674838
$630$	2.54104	0.101237
$631$	17.0826	0.680049	0.340024	−	0.940417i	$-0.389565\pi$
$631$	17.0826	0.680049	0.340024	+	0.940417i	$0.389565\pi$
$632$	13.0829	0.520410
$633$	6.14263	0.244148
$634$	51.9322	2.06249
$635$	−1.39765	−0.0554641
$636$	−0.306543	−0.0121552
$637$	−3.52450	−0.139646
$638$	−1.19853	−0.0474502
$639$	−5.09148	−0.201416
$640$	−13.2684	−0.524478
$641$	32.1820	1.27111	0.635557	−	0.772054i	$-0.280770\pi$
$641$	32.1820	1.27111	0.635557	+	0.772054i	$0.280770\pi$
$642$	−0.665241	−0.0262550
$643$	−5.32118	−0.209847	−0.104923	−	0.994480i	$-0.533460\pi$
$643$	−5.32118	−0.209847	−0.104923	+	0.994480i	$0.533460\pi$
$644$	5.11593	0.201596
$645$	−14.8641	−0.585272
$646$	−28.5243	−1.12227
$647$	2.44907	0.0962827	0.0481414	−	0.998841i	$-0.484670\pi$
$647$	2.44907	0.0962827	0.0481414	+	0.998841i	$0.484670\pi$
$648$	−1.26282	−0.0496084
$649$	−0.188731	−0.00740832
$650$	19.5219	0.765710
$651$	6.27152	0.245800
$652$	26.6976	1.04556
$653$	−30.1572	−1.18014	−0.590070	−	0.807352i	$-0.700900\pi$
$653$	−30.1572	−1.18014	−0.590070	+	0.807352i	$0.700900\pi$
$654$	−26.4320	−1.03357
$655$	−30.5497	−1.19368
$656$	48.0096	1.87446
$657$	15.8865	0.619791
$658$	−8.19894	−0.319628
$659$	−33.1094	−1.28976	−0.644880	−	0.764284i	$-0.723093\pi$
$659$	−33.1094	−1.28976	−0.644880	+	0.764284i	$0.723093\pi$
$660$	−0.154091	−0.00599799
$661$	−38.7669	−1.50786	−0.753928	−	0.656957i	$-0.771843\pi$
$661$	−38.7669	−1.50786	−0.753928	+	0.656957i	$0.771843\pi$
$662$	−50.2237	−1.95200
$663$	−17.4014	−0.675815
$664$	6.98047	0.270895
$665$	−4.44134	−0.172228
$666$	6.23232	0.241498
$667$	30.5901	1.18445
$668$	29.2809	1.13291
$669$	−6.16516	−0.238359
$670$	9.52214	0.367872
$671$	0.698045	0.0269477
$672$	6.39517	0.246699
$673$	−21.3247	−0.822006	−0.411003	−	0.911634i	$-0.634821\pi$
$673$	−21.3247	−0.822006	−0.411003	+	0.911634i	$0.634821\pi$
$674$	21.9767	0.846509
$675$	−3.04657	−0.117263
$676$	−0.754394	−0.0290152
$677$	10.7266	0.412257	0.206129	−	0.978525i	$-0.433913\pi$
$677$	10.7266	0.412257	0.206129	+	0.978525i	$0.433913\pi$
$678$	−12.9866	−0.498749
$679$	9.13128	0.350426
$680$	8.71422	0.334175
$681$	24.5032	0.938964
$682$	−0.962982	−0.0368745
$683$	−14.7316	−0.563688	−0.281844	−	0.959460i	$-0.590946\pi$
$683$	−14.7316	−0.563688	−0.281844	+	0.959460i	$0.590946\pi$
$684$	−4.14822	−0.158611
$685$	−15.1368	−0.578346
$686$	−1.81808	−0.0694145
$687$	−1.24111	−0.0473513
$688$	−52.1831	−1.98946
$689$	0.827642	0.0315306
$690$	9.95840	0.379110
$691$	−26.0749	−0.991934	−0.495967	−	0.868341i	$-0.665186\pi$
$691$	−26.0749	−0.991934	−0.495967	+	0.868341i	$0.665186\pi$
$692$	30.5582	1.16165
$693$	−0.0844564	−0.00320823
$694$	−20.9632	−0.795751
$695$	19.8422	0.752656
$696$	9.85702	0.373629
$697$	−48.3085	−1.82982
$698$	−59.9368	−2.26864
$699$	24.8114	0.938452
$700$	3.97702	0.150317
$701$	−3.42272	−0.129275	−0.0646373	−	0.997909i	$-0.520589\pi$
$701$	−3.42272	−0.129275	−0.0646373	+	0.997909i	$0.520589\pi$
$702$	−6.40782	−0.241847
$703$	−10.8931	−0.410842
$704$	−0.153158	−0.00577236
$705$	−6.30295	−0.237383
$706$	23.3721	0.879619
$707$	−12.1017	−0.455132
$708$	−2.91713	−0.109632
$709$	15.4309	0.579520	0.289760	−	0.957099i	$-0.406425\pi$
$709$	15.4309	0.579520	0.289760	+	0.957099i	$0.406425\pi$
$710$	12.9377	0.485542
$711$	−10.3600	−0.388532
$712$	18.9728	0.711035
$713$	24.5783	0.920463
$714$	−8.97635	−0.335931
$715$	0.416034	0.0155588
$716$	−15.6992	−0.586707
$717$	19.9316	0.744358
$718$	39.8832	1.48843
$719$	0.647747	0.0241569	0.0120784	−	0.999927i	$-0.496155\pi$
$719$	0.647747	0.0241569	0.0120784	+	0.999927i	$0.496155\pi$
$720$	6.85789	0.255579
$721$	5.80333	0.216127
$722$	−16.1847	−0.602334
$723$	1.78751	0.0664782
$724$	−19.2498	−0.715412
$725$	23.7801	0.883172
$726$	−19.9859	−0.741746
$727$	22.4181	0.831442	0.415721	−	0.909492i	$-0.363529\pi$
$727$	22.4181	0.831442	0.415721	+	0.909492i	$0.363529\pi$
$728$	−4.45082	−0.164958
$729$	1.00000	0.0370370
$730$	−40.3682	−1.49409
$731$	52.5080	1.94208
$732$	10.7894	0.398787
$733$	−22.0750	−0.815358	−0.407679	−	0.913125i	$-0.633662\pi$
$733$	−22.0750	−0.815358	−0.407679	+	0.913125i	$0.633662\pi$
$734$	−30.4578	−1.12422
$735$	−1.39765	−0.0515532
$736$	25.0628	0.923828
$737$	−0.316487	−0.0116579
$738$	−17.7889	−0.654818
$739$	−15.2742	−0.561871	−0.280936	−	0.959727i	$-0.590645\pi$
$739$	−15.2742	−0.561871	−0.280936	+	0.959727i	$0.590645\pi$
$740$	−6.25436	−0.229915
$741$	11.1999	0.411437
$742$	0.426931	0.0156731
$743$	−16.5688	−0.607851	−0.303925	−	0.952696i	$-0.598297\pi$
$743$	−16.5688	−0.607851	−0.303925	+	0.952696i	$0.598297\pi$
$744$	7.91982	0.290355
$745$	27.6188	1.01187
$746$	−26.5440	−0.971845
$747$	−5.52767	−0.202247
$748$	0.544335	0.0199028
$749$	0.365904	0.0133698
$750$	20.4467	0.746606
$751$	−25.6803	−0.937089	−0.468544	−	0.883440i	$-0.655221\pi$
$751$	−25.6803	−0.937089	−0.468544	+	0.883440i	$0.655221\pi$
$752$	−22.1277	−0.806915
$753$	19.0011	0.692440
$754$	50.0165	1.82149
$755$	−11.0354	−0.401621
$756$	−1.30541	−0.0474772
$757$	2.68605	0.0976262	0.0488131	−	0.998808i	$-0.484456\pi$
$757$	2.68605	0.0976262	0.0488131	+	0.998808i	$0.484456\pi$
$758$	3.47672	0.126280
$759$	−0.330987	−0.0120141
$760$	−5.60863	−0.203446
$761$	32.2716	1.16984	0.584922	−	0.811090i	$-0.301125\pi$
$761$	32.2716	1.16984	0.584922	+	0.811090i	$0.301125\pi$
$762$	1.81808	0.0658620
$763$	14.5385	0.526327
$764$	−19.7217	−0.713505
$765$	−6.90059	−0.249491
$766$	−26.5439	−0.959071
$767$	7.87602	0.284387
$768$	20.8865	0.753677
$769$	33.0914	1.19331	0.596654	−	0.802499i	$-0.296497\pi$
$769$	33.0914	1.19331	0.596654	+	0.802499i	$0.296497\pi$
$770$	0.214607	0.00773390
$771$	−5.27896	−0.190117
$772$	−5.37269	−0.193367
$773$	−41.8362	−1.50474	−0.752372	−	0.658738i	$-0.771091\pi$
$773$	−41.8362	−1.50474	−0.752372	+	0.658738i	$0.771091\pi$
$774$	19.3353	0.694993
$775$	19.1066	0.686330
$776$	11.5312	0.413946
$777$	−3.42797	−0.122978
$778$	−2.94766	−0.105679
$779$	31.0922	1.11399
$780$	6.43047	0.230248
$781$	−0.430008	−0.0153869
$782$	−35.1785	−1.25798
$783$	−7.80555	−0.278947
$784$	−4.90673	−0.175240
$785$	−25.6392	−0.915101
$786$	39.7393	1.41746
$787$	−49.6735	−1.77067	−0.885335	−	0.464954i	$-0.846071\pi$
$787$	−49.6735	−1.77067	−0.885335	+	0.464954i	$0.846071\pi$
$788$	−11.4484	−0.407831
$789$	−22.2560	−0.792333
$790$	26.3253	0.936611
$791$	7.14306	0.253978
$792$	−0.106653	−0.00378977
$793$	−29.1305	−1.03445
$794$	−70.3999	−2.49840
$795$	0.328204	0.0116402
$796$	−26.0890	−0.924699
$797$	−47.6456	−1.68769	−0.843847	−	0.536584i	$-0.819714\pi$
$797$	−47.6456	−1.68769	−0.843847	+	0.536584i	$0.819714\pi$
$798$	5.77734	0.204516
$799$	22.2655	0.787696
$800$	19.4833	0.688839
$801$	−15.0241	−0.530850
$802$	−22.7440	−0.803120
$803$	1.34172	0.0473481
$804$	−4.89181	−0.172521
$805$	−5.47743	−0.193054
$806$	40.1868	1.41552
$807$	8.70678	0.306493
$808$	−15.2823	−0.537631
$809$	−25.8849	−0.910064	−0.455032	−	0.890475i	$-0.650372\pi$
$809$	−25.8849	−0.910064	−0.455032	+	0.890475i	$0.650372\pi$
$810$	−2.54104	−0.0892830
$811$	−10.3199	−0.362382	−0.181191	−	0.983448i	$-0.557995\pi$
$811$	−10.3199	−0.362382	−0.181191	+	0.983448i	$0.557995\pi$
$812$	10.1894	0.357579
$813$	10.9473	0.383939
$814$	0.526360	0.0184489
$815$	−28.5841	−1.00126
$816$	−24.2258	−0.848074
$817$	−33.7951	−1.18234
$818$	−1.98508	−0.0694066
$819$	3.52450	0.123156
$820$	17.8518	0.623412
$821$	−14.2032	−0.495696	−0.247848	−	0.968799i	$-0.579723\pi$
$821$	−14.2032	−0.495696	−0.247848	+	0.968799i	$0.579723\pi$
$822$	19.6900	0.686769
$823$	56.7644	1.97868	0.989342	−	0.145612i	$-0.0465152\pi$
$823$	56.7644	1.97868	0.989342	+	0.145612i	$0.0465152\pi$
$824$	7.32857	0.255303
$825$	−0.257302	−0.00895812
$826$	4.06277	0.141362
$827$	19.9274	0.692944	0.346472	−	0.938060i	$-0.387380\pi$
$827$	19.9274	0.692944	0.346472	+	0.938060i	$0.387380\pi$
$828$	−5.11593	−0.177791
$829$	−9.92254	−0.344624	−0.172312	−	0.985042i	$-0.555124\pi$
$829$	−9.92254	−0.344624	−0.172312	+	0.985042i	$0.555124\pi$
$830$	14.0460	0.487545
$831$	−21.4950	−0.745655
$832$	6.39153	0.221586
$833$	4.93727	0.171066
$834$	−25.8109	−0.893757
$835$	−31.3500	−1.08491
$836$	−0.350343	−0.0121169
$837$	−6.27152	−0.216775
$838$	46.5343	1.60750
$839$	51.1367	1.76543	0.882717	−	0.469904i	$-0.155712\pi$
$839$	51.1367	1.76543	0.882717	+	0.469904i	$0.155712\pi$
$840$	−1.76499	−0.0608978
$841$	31.9265	1.10092
$842$	48.5918	1.67459
$843$	16.9237	0.582882
$844$	8.01864	0.276013
$845$	0.807702	0.0277858
$846$	8.19894	0.281885
$847$	10.9929	0.377719
$848$	1.15222	0.0395675
$849$	−11.0667	−0.379810
$850$	−27.3471	−0.937997
$851$	−13.4343	−0.460522
$852$	−6.64646	−0.227704
$853$	−37.5651	−1.28620	−0.643102	−	0.765781i	$-0.722353\pi$
$853$	−37.5651	−1.28620	−0.643102	+	0.765781i	$0.722353\pi$
$854$	−15.0267	−0.514203
$855$	4.44134	0.151891
$856$	0.462071	0.0157933
$857$	−21.4442	−0.732521	−0.366261	−	0.930512i	$-0.619362\pi$
$857$	−21.4442	−0.732521	−0.366261	+	0.930512i	$0.619362\pi$
$858$	−0.541181	−0.0184756
$859$	−3.57663	−0.122033	−0.0610166	−	0.998137i	$-0.519434\pi$
$859$	−3.57663	−0.122033	−0.0610166	+	0.998137i	$0.519434\pi$
$860$	−19.4037	−0.661659
$861$	9.78445	0.333453
$862$	−36.7080	−1.25028
$863$	2.03377	0.0692303	0.0346151	−	0.999401i	$-0.488979\pi$
$863$	2.03377	0.0692303	0.0346151	+	0.999401i	$0.488979\pi$
$864$	−6.39517	−0.217568
$865$	−32.7175	−1.11243
$866$	39.9342	1.35702
$867$	7.37666	0.250524
$868$	8.18689	0.277881
$869$	−0.874972	−0.0296814
$870$	19.8342	0.672443
$871$	13.2075	0.447519
$872$	18.3595	0.621731
$873$	−9.13128	−0.309047
$874$	22.6415	0.765861
$875$	−11.2463	−0.380194
$876$	20.7383	0.700683
$877$	34.8009	1.17514	0.587572	−	0.809172i	$-0.300084\pi$
$877$	34.8009	1.17514	0.587572	+	0.809172i	$0.300084\pi$
$878$	23.2725	0.785409
$879$	−24.7793	−0.835785
$880$	0.579193	0.0195246
$881$	46.1355	1.55435	0.777173	−	0.629287i	$-0.216653\pi$
$881$	46.1355	1.55435	0.777173	+	0.629287i	$0.216653\pi$
$882$	1.81808	0.0612179
$883$	2.96916	0.0999203	0.0499602	−	0.998751i	$-0.484091\pi$
$883$	2.96916	0.0999203	0.0499602	+	0.998751i	$0.484091\pi$
$884$	−22.7159	−0.764020
$885$	3.12326	0.104987
$886$	−64.2088	−2.15714
$887$	41.6884	1.39976	0.699880	−	0.714260i	$-0.253237\pi$
$887$	41.6884	1.39976	0.699880	+	0.714260i	$0.253237\pi$
$888$	−4.32892	−0.145269
$889$	−1.00000	−0.0335389
$890$	38.1768	1.27969
$891$	0.0844564	0.00282940
$892$	−8.04805	−0.269469
$893$	−14.3305	−0.479551
$894$	−35.9268	−1.20157
$895$	16.8086	0.561848
$896$	−9.49332	−0.317150
$897$	13.8126	0.461189
$898$	−17.2386	−0.575261
$899$	48.9526	1.63266
$900$	−3.97702	−0.132567
$901$	−1.15940	−0.0386251
$902$	−1.50239	−0.0500240
$903$	−10.6350	−0.353911
$904$	9.02042	0.300015
$905$	20.6100	0.685100
$906$	14.3550	0.476913
$907$	−33.2816	−1.10510	−0.552549	−	0.833480i	$-0.686345\pi$
$907$	−33.2816	−1.10510	−0.552549	+	0.833480i	$0.686345\pi$
$908$	31.9867	1.06151
$909$	12.1017	0.401389
$910$	−8.95590	−0.296885
$911$	41.8018	1.38496	0.692478	−	0.721439i	$-0.256519\pi$
$911$	41.8018	1.38496	0.692478	+	0.721439i	$0.256519\pi$
$912$	15.5922	0.516309
$913$	−0.466847	−0.0154504
$914$	26.2940	0.869728
$915$	−11.5518	−0.381891
$916$	−1.62015	−0.0535314
$917$	−21.8579	−0.721811
$918$	8.97635	0.296264
$919$	8.93340	0.294686	0.147343	−	0.989085i	$-0.452928\pi$
$919$	8.93340	0.294686	0.147343	+	0.989085i	$0.452928\pi$
$920$	−6.91703	−0.228048
$921$	22.2886	0.734434
$922$	−30.0343	−0.989127
$923$	17.9449	0.590665
$924$	−0.110250	−0.00362696
$925$	−10.4436	−0.343382
$926$	−38.2253	−1.25616
$927$	−5.80333	−0.190606
$928$	49.9178	1.63863
$929$	43.2613	1.41936	0.709679	−	0.704525i	$-0.248840\pi$
$929$	43.2613	1.41936	0.709679	+	0.704525i	$0.248840\pi$
$930$	15.9362	0.522568
$931$	−3.17772	−0.104145
$932$	32.3890	1.06094
$933$	9.48282	0.310454
$934$	−5.90325	−0.193160
$935$	−0.582799	−0.0190596
$936$	4.45082	0.145480
$937$	7.34205	0.239854	0.119927	−	0.992783i	$-0.461734\pi$
$937$	7.34205	0.239854	0.119927	+	0.992783i	$0.461734\pi$
$938$	6.81295	0.222451
$939$	5.82224	0.190002
$940$	−8.22792	−0.268365
$941$	−50.7589	−1.65469	−0.827346	−	0.561692i	$-0.810151\pi$
$941$	−50.7589	−1.65469	−0.827346	+	0.561692i	$0.810151\pi$
$942$	33.3517	1.08666
$943$	38.3455	1.24870
$944$	10.9648	0.356874
$945$	1.39765	0.0454656
$946$	1.63299	0.0530931
$947$	26.6858	0.867171	0.433585	−	0.901112i	$-0.357248\pi$
$947$	26.6858	0.867171	0.433585	+	0.901112i	$0.357248\pi$
$948$	−13.5241	−0.439242
$949$	−55.9919	−1.81757
$950$	17.6011	0.571054
$951$	28.5643	0.926262
$952$	6.23490	0.202074
$953$	−6.47952	−0.209892	−0.104946	−	0.994478i	$-0.533467\pi$
$953$	−6.47952	−0.209892	−0.104946	+	0.994478i	$0.533467\pi$
$954$	−0.426931	−0.0138224
$955$	21.1153	0.683274
$956$	26.0188	0.841509
$957$	−0.659228	−0.0213098
$958$	−68.2291	−2.20438
$959$	−10.8301	−0.349723
$960$	2.53458	0.0818033
$961$	8.33198	0.268773
$962$	−21.9658	−0.708207
$963$	−0.365904	−0.0117911
$964$	2.33343	0.0751547
$965$	5.75234	0.185174
$966$	7.12509	0.229246
$967$	14.2378	0.457857	0.228929	−	0.973443i	$-0.426478\pi$
$967$	14.2378	0.457857	0.228929	+	0.973443i	$0.426478\pi$
$968$	13.8820	0.446186
$969$	−15.6893	−0.504011
$970$	23.2030	0.745002
$971$	−19.2850	−0.618885	−0.309442	−	0.950918i	$-0.600142\pi$
$971$	−19.2850	−0.618885	−0.309442	+	0.950918i	$0.600142\pi$
$972$	1.30541	0.0418710
$973$	14.1968	0.455128
$974$	−73.2617	−2.34746
$975$	10.7376	0.343880
$976$	−40.5548	−1.29813
$977$	3.08393	0.0986638	0.0493319	−	0.998782i	$-0.484291\pi$
$977$	3.08393	0.0986638	0.0493319	+	0.998782i	$0.484291\pi$
$978$	37.1825	1.18897
$979$	−1.26888	−0.0405536
$980$	−1.82451	−0.0582817
$981$	−14.5385	−0.464177
$982$	−43.4576	−1.38679
$983$	25.0025	0.797454	0.398727	−	0.917070i	$-0.369452\pi$
$983$	25.0025	0.797454	0.398727	+	0.917070i	$0.369452\pi$
$984$	12.3560	0.393896
$985$	12.2574	0.390552
$986$	−70.0653	−2.23133
$987$	−4.50967	−0.143544
$988$	14.6204	0.465137
$989$	−41.6789	−1.32531
$990$	−0.214607	−0.00682066
$991$	8.99880	0.285856	0.142928	−	0.989733i	$-0.454348\pi$
$991$	8.99880	0.285856	0.142928	+	0.989733i	$0.454348\pi$
$992$	40.1074	1.27341
$993$	−27.6246	−0.876640
$994$	9.25671	0.293605
$995$	27.9325	0.885519
$996$	−7.21586	−0.228643
$997$	−32.2384	−1.02100	−0.510501	−	0.859877i	$-0.670540\pi$
$997$	−32.2384	−1.02100	−0.510501	+	0.859877i	$0.670540\pi$
$998$	7.97012	0.252290
$999$	3.42797	0.108456

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.k.1.10	✓	11
3.2	odd	2		8001.2.a.m.1.2		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.k.1.10	✓	11	1.1	even	1	trivial
8001.2.a.m.1.2		11	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2667 = 3 \cdot 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2667.a (trivial)

\(f(q)\)	\(=\)	\(q+1.81808 q^{2} +1.00000 q^{3} +1.30541 q^{4} -1.39765 q^{5} +1.81808 q^{6} -1.00000 q^{7} -1.26282 q^{8} +1.00000 q^{9} -2.54104 q^{10} +0.0844564 q^{11} +1.30541 q^{12} -3.52450 q^{13} -1.81808 q^{14} -1.39765 q^{15} -4.90673 q^{16} +4.93727 q^{17} +1.81808 q^{18} -3.17772 q^{19} -1.82451 q^{20} -1.00000 q^{21} +0.153548 q^{22} -3.91903 q^{23} -1.26282 q^{24} -3.04657 q^{25} -6.40782 q^{26} +1.00000 q^{27} -1.30541 q^{28} -7.80555 q^{29} -2.54104 q^{30} -6.27152 q^{31} -6.39517 q^{32} +0.0844564 q^{33} +8.97635 q^{34} +1.39765 q^{35} +1.30541 q^{36} +3.42797 q^{37} -5.77734 q^{38} -3.52450 q^{39} +1.76499 q^{40} -9.78445 q^{41} -1.81808 q^{42} +10.6350 q^{43} +0.110250 q^{44} -1.39765 q^{45} -7.12509 q^{46} +4.50967 q^{47} -4.90673 q^{48} +1.00000 q^{49} -5.53890 q^{50} +4.93727 q^{51} -4.60091 q^{52} -0.234825 q^{53} +1.81808 q^{54} -0.118041 q^{55} +1.26282 q^{56} -3.17772 q^{57} -14.1911 q^{58} -2.23465 q^{59} -1.82451 q^{60} +8.26515 q^{61} -11.4021 q^{62} -1.00000 q^{63} -1.81346 q^{64} +4.92602 q^{65} +0.153548 q^{66} -3.74734 q^{67} +6.44515 q^{68} -3.91903 q^{69} +2.54104 q^{70} -5.09148 q^{71} -1.26282 q^{72} +15.8865 q^{73} +6.23232 q^{74} -3.04657 q^{75} -4.14822 q^{76} -0.0844564 q^{77} -6.40782 q^{78} -10.3600 q^{79} +6.85789 q^{80} +1.00000 q^{81} -17.7889 q^{82} -5.52767 q^{83} -1.30541 q^{84} -6.90059 q^{85} +19.3353 q^{86} -7.80555 q^{87} -0.106653 q^{88} -15.0241 q^{89} -2.54104 q^{90} +3.52450 q^{91} -5.11593 q^{92} -6.27152 q^{93} +8.19894 q^{94} +4.44134 q^{95} -6.39517 q^{96} -9.13128 q^{97} +1.81808 q^{98} +0.0844564 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 2 q^{2} + 11 q^{3} + 12 q^{4} + q^{5} - 2 q^{6} - 11 q^{7} - 15 q^{8} + 11 q^{9} - 12 q^{10} - 7 q^{11} + 12 q^{12} - 24 q^{13} + 2 q^{14} + q^{15} - 6 q^{16} - 15 q^{17} - 2 q^{18} - 19 q^{19}+ \cdots - 7 q^{99}+O(q^{100}) \) 11 * q - 2 * q^2 + 11 * q^3 + 12 * q^4 + q^5 - 2 * q^6 - 11 * q^7 - 15 * q^8 + 11 * q^9 - 12 * q^10 - 7 * q^11 + 12 * q^12 - 24 * q^13 + 2 * q^14 + q^15 - 6 * q^16 - 15 * q^17 - 2 * q^18 - 19 * q^19 + 3 * q^20 - 11 * q^21 - 3 * q^22 - 11 * q^23 - 15 * q^24 + 10 * q^25 + 10 * q^26 + 11 * q^27 - 12 * q^28 - 10 * q^29 - 12 * q^30 - 20 * q^31 - 27 * q^32 - 7 * q^33 - 9 * q^34 - q^35 + 12 * q^36 - 22 * q^37 + 8 * q^38 - 24 * q^39 - 29 * q^40 + 9 * q^41 + 2 * q^42 - 17 * q^43 - 9 * q^44 + q^45 - 18 * q^46 - 7 * q^47 - 6 * q^48 + 11 * q^49 - 47 * q^50 - 15 * q^51 - 66 * q^52 - 28 * q^53 - 2 * q^54 - 24 * q^55 + 15 * q^56 - 19 * q^57 - 39 * q^58 + 35 * q^59 + 3 * q^60 - 6 * q^61 + 18 * q^62 - 11 * q^63 + 11 * q^64 - 43 * q^65 - 3 * q^66 - 22 * q^67 - 12 * q^68 - 11 * q^69 + 12 * q^70 - 22 * q^71 - 15 * q^72 - 29 * q^73 + 14 * q^74 + 10 * q^75 + 10 * q^76 + 7 * q^77 + 10 * q^78 - 20 * q^79 + 66 * q^80 + 11 * q^81 - 24 * q^82 + 17 * q^83 - 12 * q^84 - 50 * q^85 - 12 * q^86 - 10 * q^87 + 2 * q^88 - q^89 - 12 * q^90 + 24 * q^91 - 22 * q^92 - 20 * q^93 + q^94 + 10 * q^95 - 27 * q^96 - 45 * q^97 - 2 * q^98 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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