LMFDB - Embedded newform 7098.2.a.cq.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7098,2,Mod(1,7098)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7098, 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("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7098.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:	$56.6778153547$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.6148961.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 11x^{4} + 12x^{3} + 32x^{2} - 16x - 29 $ x^6 - 2x^5 - 11x^4 + 12x^3 + 32x^2 - 16*x - 29
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			1.1
Root			$1.63026$ of defining polynomial
Character	$\chi$	$=$	7098.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.93763 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.93763 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.93763 q^{10} -5.95254 q^{11} +1.00000 q^{12} -1.00000 q^{14} -3.93763 q^{15} +1.00000 q^{16} +5.27740 q^{17} -1.00000 q^{18} +4.12422 q^{19} -3.93763 q^{20} +1.00000 q^{21} +5.95254 q^{22} -6.25102 q^{23} -1.00000 q^{24} +10.5049 q^{25} +1.00000 q^{27} +1.00000 q^{28} +1.98716 q^{29} +3.93763 q^{30} +8.86180 q^{31} -1.00000 q^{32} -5.95254 q^{33} -5.27740 q^{34} -3.93763 q^{35} +1.00000 q^{36} -4.03290 q^{37} -4.12422 q^{38} +3.93763 q^{40} -4.03511 q^{41} -1.00000 q^{42} -9.79142 q^{43} -5.95254 q^{44} -3.93763 q^{45} +6.25102 q^{46} -0.0488343 q^{47} +1.00000 q^{48} +1.00000 q^{49} -10.5049 q^{50} +5.27740 q^{51} -1.32042 q^{53} -1.00000 q^{54} +23.4389 q^{55} -1.00000 q^{56} +4.12422 q^{57} -1.98716 q^{58} -1.86716 q^{59} -3.93763 q^{60} +10.2395 q^{61} -8.86180 q^{62} +1.00000 q^{63} +1.00000 q^{64} +5.95254 q^{66} -15.5361 q^{67} +5.27740 q^{68} -6.25102 q^{69} +3.93763 q^{70} +10.5057 q^{71} -1.00000 q^{72} +6.79637 q^{73} +4.03290 q^{74} +10.5049 q^{75} +4.12422 q^{76} -5.95254 q^{77} +9.36407 q^{79} -3.93763 q^{80} +1.00000 q^{81} +4.03511 q^{82} +12.8885 q^{83} +1.00000 q^{84} -20.7804 q^{85} +9.79142 q^{86} +1.98716 q^{87} +5.95254 q^{88} +4.89017 q^{89} +3.93763 q^{90} -6.25102 q^{92} +8.86180 q^{93} +0.0488343 q^{94} -16.2396 q^{95} -1.00000 q^{96} +5.77720 q^{97} -1.00000 q^{98} -5.95254 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} - 9 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 - 9 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8 + 6 * q^9	$ 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} - 9 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8} + 6 q^{9} + 9 q^{10} - 10 q^{11} + 6 q^{12} - 6 q^{14} - 9 q^{15} + 6 q^{16} + 4 q^{17} - 6 q^{18} - 2 q^{19} - 9 q^{20} + 6 q^{21} + 10 q^{22} - 6 q^{24} + 9 q^{25} + 6 q^{27} + 6 q^{28} - 4 q^{29} + 9 q^{30} - 9 q^{31} - 6 q^{32} - 10 q^{33} - 4 q^{34} - 9 q^{35} + 6 q^{36} - 9 q^{37} + 2 q^{38} + 9 q^{40} - 25 q^{41} - 6 q^{42} + 19 q^{43} - 10 q^{44} - 9 q^{45} - 21 q^{47} + 6 q^{48} + 6 q^{49} - 9 q^{50} + 4 q^{51} - 4 q^{53} - 6 q^{54} + 21 q^{55} - 6 q^{56} - 2 q^{57} + 4 q^{58} - 20 q^{59} - 9 q^{60} + 3 q^{61} + 9 q^{62} + 6 q^{63} + 6 q^{64} + 10 q^{66} - 24 q^{67} + 4 q^{68} + 9 q^{70} - 13 q^{71} - 6 q^{72} + 9 q^{73} + 9 q^{74} + 9 q^{75} - 2 q^{76} - 10 q^{77} + 28 q^{79} - 9 q^{80} + 6 q^{81} + 25 q^{82} - 15 q^{83} + 6 q^{84} - 17 q^{85} - 19 q^{86} - 4 q^{87} + 10 q^{88} - 11 q^{89} + 9 q^{90} - 9 q^{93} + 21 q^{94} - 6 q^{96} - 2 q^{97} - 6 q^{98} - 10 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 - 9 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8 + 6 * q^9 + 9 * q^10 - 10 * q^11 + 6 * q^12 - 6 * q^14 - 9 * q^15 + 6 * q^16 + 4 * q^17 - 6 * q^18 - 2 * q^19 - 9 * q^20 + 6 * q^21 + 10 * q^22 - 6 * q^24 + 9 * q^25 + 6 * q^27 + 6 * q^28 - 4 * q^29 + 9 * q^30 - 9 * q^31 - 6 * q^32 - 10 * q^33 - 4 * q^34 - 9 * q^35 + 6 * q^36 - 9 * q^37 + 2 * q^38 + 9 * q^40 - 25 * q^41 - 6 * q^42 + 19 * q^43 - 10 * q^44 - 9 * q^45 - 21 * q^47 + 6 * q^48 + 6 * q^49 - 9 * q^50 + 4 * q^51 - 4 * q^53 - 6 * q^54 + 21 * q^55 - 6 * q^56 - 2 * q^57 + 4 * q^58 - 20 * q^59 - 9 * q^60 + 3 * q^61 + 9 * q^62 + 6 * q^63 + 6 * q^64 + 10 * q^66 - 24 * q^67 + 4 * q^68 + 9 * q^70 - 13 * q^71 - 6 * q^72 + 9 * q^73 + 9 * q^74 + 9 * q^75 - 2 * q^76 - 10 * q^77 + 28 * q^79 - 9 * q^80 + 6 * q^81 + 25 * q^82 - 15 * q^83 + 6 * q^84 - 17 * q^85 - 19 * q^86 - 4 * q^87 + 10 * q^88 - 11 * q^89 + 9 * q^90 - 9 * q^93 + 21 * q^94 - 6 * q^96 - 2 * q^97 - 6 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−3.93763	−1.76096	−0.880480	−	0.474083i	$-0.842780\pi$
$5$	−3.93763	−1.76096	−0.880480	+	0.474083i	$0.842780\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.93763	1.24519
$11$	−5.95254	−1.79476	−0.897379	−	0.441260i	$-0.854532\pi$
$11$	−5.95254	−1.79476	−0.897379	+	0.441260i	$0.854532\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	−3.93763	−1.01669
$16$	1.00000	0.250000
$17$	5.27740	1.27996	0.639979	−	0.768392i	$-0.278943\pi$
$17$	5.27740	1.27996	0.639979	+	0.768392i	$0.278943\pi$
$18$	−1.00000	−0.235702
$19$	4.12422	0.946161	0.473080	−	0.881019i	$-0.343142\pi$
$19$	4.12422	0.946161	0.473080	+	0.881019i	$0.343142\pi$
$20$	−3.93763	−0.880480
$21$	1.00000	0.218218
$22$	5.95254	1.26909
$23$	−6.25102	−1.30343	−0.651714	−	0.758465i	$-0.725950\pi$
$23$	−6.25102	−1.30343	−0.651714	+	0.758465i	$0.725950\pi$
$24$	−1.00000	−0.204124
$25$	10.5049	2.10098
$26$	0	0
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	1.98716	0.369005	0.184503	−	0.982832i	$-0.440933\pi$
$29$	1.98716	0.369005	0.184503	+	0.982832i	$0.440933\pi$
$30$	3.93763	0.718909
$31$	8.86180	1.59163	0.795813	−	0.605543i	$-0.207044\pi$
$31$	8.86180	1.59163	0.795813	+	0.605543i	$0.207044\pi$
$32$	−1.00000	−0.176777
$33$	−5.95254	−1.03620
$34$	−5.27740	−0.905067
$35$	−3.93763	−0.665580
$36$	1.00000	0.166667
$37$	−4.03290	−0.663005	−0.331502	−	0.943454i	$-0.607555\pi$
$37$	−4.03290	−0.663005	−0.331502	+	0.943454i	$0.607555\pi$
$38$	−4.12422	−0.669037
$39$	0	0
$40$	3.93763	0.622593
$41$	−4.03511	−0.630178	−0.315089	−	0.949062i	$-0.602034\pi$
$41$	−4.03511	−0.630178	−0.315089	+	0.949062i	$0.602034\pi$
$42$	−1.00000	−0.154303
$43$	−9.79142	−1.49318	−0.746589	−	0.665286i	$-0.768310\pi$
$43$	−9.79142	−1.49318	−0.746589	+	0.665286i	$0.768310\pi$
$44$	−5.95254	−0.897379
$45$	−3.93763	−0.586987
$46$	6.25102	0.921662
$47$	−0.0488343	−0.00712322	−0.00356161	−	0.999994i	$-0.501134\pi$
$47$	−0.0488343	−0.00712322	−0.00356161	+	0.999994i	$0.501134\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−10.5049	−1.48562
$51$	5.27740	0.738984
$52$	0	0
$53$	−1.32042	−0.181373	−0.0906865	−	0.995879i	$-0.528906\pi$
$53$	−1.32042	−0.181373	−0.0906865	+	0.995879i	$0.528906\pi$
$54$	−1.00000	−0.136083
$55$	23.4389	3.16050
$56$	−1.00000	−0.133631
$57$	4.12422	0.546266
$58$	−1.98716	−0.260926
$59$	−1.86716	−0.243084	−0.121542	−	0.992586i	$-0.538784\pi$
$59$	−1.86716	−0.243084	−0.121542	+	0.992586i	$0.538784\pi$
$60$	−3.93763	−0.508345
$61$	10.2395	1.31104	0.655520	−	0.755178i	$-0.272450\pi$
$61$	10.2395	1.31104	0.655520	+	0.755178i	$0.272450\pi$
$62$	−8.86180	−1.12545
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	5.95254	0.732707
$67$	−15.5361	−1.89803	−0.949016	−	0.315229i	$-0.897919\pi$
$67$	−15.5361	−1.89803	−0.949016	+	0.315229i	$0.897919\pi$
$68$	5.27740	0.639979
$69$	−6.25102	−0.752534
$70$	3.93763	0.470636
$71$	10.5057	1.24679	0.623396	−	0.781906i	$-0.285752\pi$
$71$	10.5057	1.24679	0.623396	+	0.781906i	$0.285752\pi$
$72$	−1.00000	−0.117851
$73$	6.79637	0.795455	0.397728	−	0.917504i	$-0.369799\pi$
$73$	6.79637	0.795455	0.397728	+	0.917504i	$0.369799\pi$
$74$	4.03290	0.468815
$75$	10.5049	1.21300
$76$	4.12422	0.473080
$77$	−5.95254	−0.678355
$78$	0	0
$79$	9.36407	1.05354	0.526770	−	0.850008i	$-0.323403\pi$
$79$	9.36407	1.05354	0.526770	+	0.850008i	$0.323403\pi$
$80$	−3.93763	−0.440240
$81$	1.00000	0.111111
$82$	4.03511	0.445603
$83$	12.8885	1.41470	0.707348	−	0.706866i	$-0.249892\pi$
$83$	12.8885	1.41470	0.707348	+	0.706866i	$0.249892\pi$
$84$	1.00000	0.109109
$85$	−20.7804	−2.25396
$86$	9.79142	1.05584
$87$	1.98716	0.213045
$88$	5.95254	0.634543
$89$	4.89017	0.518357	0.259178	−	0.965829i	$-0.416548\pi$
$89$	4.89017	0.518357	0.259178	+	0.965829i	$0.416548\pi$
$90$	3.93763	0.415062
$91$	0	0
$92$	−6.25102	−0.651714
$93$	8.86180	0.918925
$94$	0.0488343	0.00503687
$95$	−16.2396	−1.66615
$96$	−1.00000	−0.102062
$97$	5.77720	0.586586	0.293293	−	0.956023i	$-0.405249\pi$
$97$	5.77720	0.586586	0.293293	+	0.956023i	$0.405249\pi$
$98$	−1.00000	−0.101015
$99$	−5.95254	−0.598253
$100$	10.5049	1.05049
$101$	−0.110425	−0.0109877	−0.00549383	−	0.999985i	$-0.501749\pi$
$101$	−0.110425	−0.0109877	−0.00549383	+	0.999985i	$0.501749\pi$
$102$	−5.27740	−0.522541
$103$	−12.5145	−1.23309	−0.616545	−	0.787319i	$-0.711468\pi$
$103$	−12.5145	−1.23309	−0.616545	+	0.787319i	$0.711468\pi$
$104$	0	0
$105$	−3.93763	−0.384273
$106$	1.32042	0.128250
$107$	6.69454	0.647185	0.323593	−	0.946197i	$-0.395109\pi$
$107$	6.69454	0.647185	0.323593	+	0.946197i	$0.395109\pi$
$108$	1.00000	0.0962250
$109$	3.01315	0.288608	0.144304	−	0.989533i	$-0.453906\pi$
$109$	3.01315	0.288608	0.144304	+	0.989533i	$0.453906\pi$
$110$	−23.4389	−2.23481
$111$	−4.03290	−0.382786
$112$	1.00000	0.0944911
$113$	−5.32437	−0.500875	−0.250437	−	0.968133i	$-0.580574\pi$
$113$	−5.32437	−0.500875	−0.250437	+	0.968133i	$0.580574\pi$
$114$	−4.12422	−0.386268
$115$	24.6142	2.29528
$116$	1.98716	0.184503
$117$	0	0
$118$	1.86716	0.171886
$119$	5.27740	0.483779
$120$	3.93763	0.359454
$121$	24.4327	2.22116
$122$	−10.2395	−0.927045
$123$	−4.03511	−0.363833
$124$	8.86180	0.795813
$125$	−21.6762	−1.93878
$126$	−1.00000	−0.0890871
$127$	−19.1192	−1.69655	−0.848276	−	0.529555i	$-0.822359\pi$
$127$	−19.1192	−1.69655	−0.848276	+	0.529555i	$0.822359\pi$
$128$	−1.00000	−0.0883883
$129$	−9.79142	−0.862086
$130$	0	0
$131$	−8.95315	−0.782241	−0.391120	−	0.920340i	$-0.627912\pi$
$131$	−8.95315	−0.782241	−0.391120	+	0.920340i	$0.627912\pi$
$132$	−5.95254	−0.518102
$133$	4.12422	0.357615
$134$	15.5361	1.34211
$135$	−3.93763	−0.338897
$136$	−5.27740	−0.452534
$137$	14.9023	1.27319	0.636595	−	0.771198i	$-0.280342\pi$
$137$	14.9023	1.27319	0.636595	+	0.771198i	$0.280342\pi$
$138$	6.25102	0.532122
$139$	−22.0903	−1.87367	−0.936837	−	0.349767i	$-0.886261\pi$
$139$	−22.0903	−1.87367	−0.936837	+	0.349767i	$0.886261\pi$
$140$	−3.93763	−0.332790
$141$	−0.0488343	−0.00411259
$142$	−10.5057	−0.881616
$143$	0	0
$144$	1.00000	0.0833333
$145$	−7.82468	−0.649804
$146$	−6.79637	−0.562472
$147$	1.00000	0.0824786
$148$	−4.03290	−0.331502
$149$	8.69435	0.712269	0.356134	−	0.934435i	$-0.384095\pi$
$149$	8.69435	0.712269	0.356134	+	0.934435i	$0.384095\pi$
$150$	−10.5049	−0.857721
$151$	−2.91278	−0.237039	−0.118520	−	0.992952i	$-0.537815\pi$
$151$	−2.91278	−0.237039	−0.118520	+	0.992952i	$0.537815\pi$
$152$	−4.12422	−0.334518
$153$	5.27740	0.426653
$154$	5.95254	0.479669
$155$	−34.8944	−2.80279
$156$	0	0
$157$	4.11582	0.328478	0.164239	−	0.986421i	$-0.447483\pi$
$157$	4.11582	0.328478	0.164239	+	0.986421i	$0.447483\pi$
$158$	−9.36407	−0.744965
$159$	−1.32042	−0.104716
$160$	3.93763	0.311297
$161$	−6.25102	−0.492649
$162$	−1.00000	−0.0785674
$163$	−23.5642	−1.84569	−0.922845	−	0.385171i	$-0.874143\pi$
$163$	−23.5642	−1.84569	−0.922845	+	0.385171i	$0.874143\pi$
$164$	−4.03511	−0.315089
$165$	23.4389	1.82471
$166$	−12.8885	−1.00034
$167$	−17.3082	−1.33935	−0.669674	−	0.742656i	$-0.733566\pi$
$167$	−17.3082	−1.33935	−0.669674	+	0.742656i	$0.733566\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	20.7804	1.59379
$171$	4.12422	0.315387
$172$	−9.79142	−0.746589
$173$	18.0884	1.37523	0.687617	−	0.726073i	$-0.258657\pi$
$173$	18.0884	1.37523	0.687617	+	0.726073i	$0.258657\pi$
$174$	−1.98716	−0.150646
$175$	10.5049	0.794096
$176$	−5.95254	−0.448690
$177$	−1.86716	−0.140345
$178$	−4.89017	−0.366533
$179$	−21.0936	−1.57661	−0.788306	−	0.615284i	$-0.789041\pi$
$179$	−21.0936	−1.57661	−0.788306	+	0.615284i	$0.789041\pi$
$180$	−3.93763	−0.293493
$181$	−9.67145	−0.718874	−0.359437	−	0.933169i	$-0.617031\pi$
$181$	−9.67145	−0.718874	−0.359437	+	0.933169i	$0.617031\pi$
$182$	0	0
$183$	10.2395	0.756929
$184$	6.25102	0.460831
$185$	15.8801	1.16752
$186$	−8.86180	−0.649778
$187$	−31.4140	−2.29722
$188$	−0.0488343	−0.00356161
$189$	1.00000	0.0727393
$190$	16.2396	1.17815
$191$	3.57978	0.259024	0.129512	−	0.991578i	$-0.458659\pi$
$191$	3.57978	0.259024	0.129512	+	0.991578i	$0.458659\pi$
$192$	1.00000	0.0721688
$193$	−7.32890	−0.527546	−0.263773	−	0.964585i	$-0.584967\pi$
$193$	−7.32890	−0.527546	−0.263773	+	0.964585i	$0.584967\pi$
$194$	−5.77720	−0.414779
$195$	0	0
$196$	1.00000	0.0714286
$197$	−19.9531	−1.42160	−0.710801	−	0.703394i	$-0.751667\pi$
$197$	−19.9531	−1.42160	−0.710801	+	0.703394i	$0.751667\pi$
$198$	5.95254	0.423029
$199$	0.0540891	0.00383427	0.00191714	−	0.999998i	$-0.499390\pi$
$199$	0.0540891	0.00383427	0.00191714	+	0.999998i	$0.499390\pi$
$200$	−10.5049	−0.742809
$201$	−15.5361	−1.09583
$202$	0.110425	0.00776945
$203$	1.98716	0.139471
$204$	5.27740	0.369492
$205$	15.8887	1.10972
$206$	12.5145	0.871927
$207$	−6.25102	−0.434476
$208$	0	0
$209$	−24.5496	−1.69813
$210$	3.93763	0.271722
$211$	5.13943	0.353813	0.176906	−	0.984228i	$-0.443391\pi$
$211$	5.13943	0.353813	0.176906	+	0.984228i	$0.443391\pi$
$212$	−1.32042	−0.0906865
$213$	10.5057	0.719836
$214$	−6.69454	−0.457629
$215$	38.5549	2.62943
$216$	−1.00000	−0.0680414
$217$	8.86180	0.601578
$218$	−3.01315	−0.204077
$219$	6.79637	0.459256
$220$	23.4389	1.58025
$221$	0	0
$222$	4.03290	0.270671
$223$	−15.9842	−1.07038	−0.535191	−	0.844731i	$-0.679760\pi$
$223$	−15.9842	−1.07038	−0.535191	+	0.844731i	$0.679760\pi$
$224$	−1.00000	−0.0668153
$225$	10.5049	0.700327
$226$	5.32437	0.354172
$227$	4.72939	0.313900	0.156950	−	0.987607i	$-0.449834\pi$
$227$	4.72939	0.313900	0.156950	+	0.987607i	$0.449834\pi$
$228$	4.12422	0.273133
$229$	−8.24798	−0.545042	−0.272521	−	0.962150i	$-0.587857\pi$
$229$	−8.24798	−0.545042	−0.272521	+	0.962150i	$0.587857\pi$
$230$	−24.6142	−1.62301
$231$	−5.95254	−0.391648
$232$	−1.98716	−0.130463
$233$	−7.51568	−0.492368	−0.246184	−	0.969223i	$-0.579177\pi$
$233$	−7.51568	−0.492368	−0.246184	+	0.969223i	$0.579177\pi$
$234$	0	0
$235$	0.192291	0.0125437
$236$	−1.86716	−0.121542
$237$	9.36407	0.608262
$238$	−5.27740	−0.342083
$239$	10.7008	0.692180	0.346090	−	0.938201i	$-0.387509\pi$
$239$	10.7008	0.692180	0.346090	+	0.938201i	$0.387509\pi$
$240$	−3.93763	−0.254173
$241$	−4.74363	−0.305564	−0.152782	−	0.988260i	$-0.548823\pi$
$241$	−4.74363	−0.305564	−0.152782	+	0.988260i	$0.548823\pi$
$242$	−24.4327	−1.57060
$243$	1.00000	0.0641500
$244$	10.2395	0.655520
$245$	−3.93763	−0.251566
$246$	4.03511	0.257269
$247$	0	0
$248$	−8.86180	−0.562725
$249$	12.8885	0.816775
$250$	21.6762	1.37093
$251$	−19.2761	−1.21670	−0.608350	−	0.793669i	$-0.708168\pi$
$251$	−19.2761	−1.21670	−0.608350	+	0.793669i	$0.708168\pi$
$252$	1.00000	0.0629941
$253$	37.2094	2.33934
$254$	19.1192	1.19964
$255$	−20.7804	−1.30132
$256$	1.00000	0.0625000
$257$	2.72367	0.169898	0.0849489	−	0.996385i	$-0.472927\pi$
$257$	2.72367	0.169898	0.0849489	+	0.996385i	$0.472927\pi$
$258$	9.79142	0.609587
$259$	−4.03290	−0.250592
$260$	0	0
$261$	1.98716	0.123002
$262$	8.95315	0.553128
$263$	−6.87522	−0.423944	−0.211972	−	0.977276i	$-0.567989\pi$
$263$	−6.87522	−0.423944	−0.211972	+	0.977276i	$0.567989\pi$
$264$	5.95254	0.366354
$265$	5.19930	0.319391
$266$	−4.12422	−0.252872
$267$	4.89017	0.299273
$268$	−15.5361	−0.949016
$269$	−14.7284	−0.898008	−0.449004	−	0.893530i	$-0.648221\pi$
$269$	−14.7284	−0.898008	−0.449004	+	0.893530i	$0.648221\pi$
$270$	3.93763	0.239636
$271$	9.90086	0.601434	0.300717	−	0.953713i	$-0.402774\pi$
$271$	9.90086	0.601434	0.300717	+	0.953713i	$0.402774\pi$
$272$	5.27740	0.319990
$273$	0	0
$274$	−14.9023	−0.900282
$275$	−62.5308	−3.77075
$276$	−6.25102	−0.376267
$277$	3.11461	0.187139	0.0935693	−	0.995613i	$-0.470172\pi$
$277$	3.11461	0.187139	0.0935693	+	0.995613i	$0.470172\pi$
$278$	22.0903	1.32489
$279$	8.86180	0.530542
$280$	3.93763	0.235318
$281$	−4.85588	−0.289677	−0.144839	−	0.989455i	$-0.546266\pi$
$281$	−4.85588	−0.289677	−0.144839	+	0.989455i	$0.546266\pi$
$282$	0.0488343	0.00290804
$283$	17.1764	1.02103	0.510515	−	0.859869i	$-0.329455\pi$
$283$	17.1764	1.02103	0.510515	+	0.859869i	$0.329455\pi$
$284$	10.5057	0.623396
$285$	−16.2396	−0.961953
$286$	0	0
$287$	−4.03511	−0.238185
$288$	−1.00000	−0.0589256
$289$	10.8510	0.638293
$290$	7.82468	0.459481
$291$	5.77720	0.338666
$292$	6.79637	0.397728
$293$	17.3422	1.01314	0.506571	−	0.862198i	$-0.330913\pi$
$293$	17.3422	1.01314	0.506571	+	0.862198i	$0.330913\pi$
$294$	−1.00000	−0.0583212
$295$	7.35220	0.428061
$296$	4.03290	0.234408
$297$	−5.95254	−0.345401
$298$	−8.69435	−0.503650
$299$	0	0
$300$	10.5049	0.606501
$301$	−9.79142	−0.564368
$302$	2.91278	0.167612
$303$	−0.110425	−0.00634373
$304$	4.12422	0.236540
$305$	−40.3195	−2.30869
$306$	−5.27740	−0.301689
$307$	−21.3546	−1.21877	−0.609385	−	0.792874i	$-0.708584\pi$
$307$	−21.3546	−1.21877	−0.609385	+	0.792874i	$0.708584\pi$
$308$	−5.95254	−0.339177
$309$	−12.5145	−0.711925
$310$	34.8944	1.98187
$311$	25.4708	1.44432	0.722159	−	0.691727i	$-0.243150\pi$
$311$	25.4708	1.44432	0.722159	+	0.691727i	$0.243150\pi$
$312$	0	0
$313$	−26.0909	−1.47474	−0.737372	−	0.675487i	$-0.763933\pi$
$313$	−26.0909	−1.47474	−0.737372	+	0.675487i	$0.763933\pi$
$314$	−4.11582	−0.232269
$315$	−3.93763	−0.221860
$316$	9.36407	0.526770
$317$	−27.5033	−1.54474	−0.772371	−	0.635172i	$-0.780929\pi$
$317$	−27.5033	−1.54474	−0.772371	+	0.635172i	$0.780929\pi$
$318$	1.32042	0.0740452
$319$	−11.8286	−0.662276
$320$	−3.93763	−0.220120
$321$	6.69454	0.373653
$322$	6.25102	0.348356
$323$	21.7652	1.21105
$324$	1.00000	0.0555556
$325$	0	0
$326$	23.5642	1.30510
$327$	3.01315	0.166628
$328$	4.03511	0.222801
$329$	−0.0488343	−0.00269232
$330$	−23.4389	−1.29027
$331$	−1.96485	−0.107998	−0.0539988	−	0.998541i	$-0.517197\pi$
$331$	−1.96485	−0.107998	−0.0539988	+	0.998541i	$0.517197\pi$
$332$	12.8885	0.707348
$333$	−4.03290	−0.221002
$334$	17.3082	0.947062
$335$	61.1752	3.34236
$336$	1.00000	0.0545545
$337$	−35.0864	−1.91128	−0.955640	−	0.294538i	$-0.904834\pi$
$337$	−35.0864	−1.91128	−0.955640	+	0.294538i	$0.904834\pi$
$338$	0	0
$339$	−5.32437	−0.289180
$340$	−20.7804	−1.12698
$341$	−52.7502	−2.85658
$342$	−4.12422	−0.223012
$343$	1.00000	0.0539949
$344$	9.79142	0.527918
$345$	24.6142	1.32518
$346$	−18.0884	−0.972438
$347$	−32.3227	−1.73518	−0.867588	−	0.497284i	$-0.834331\pi$
$347$	−32.3227	−1.73518	−0.867588	+	0.497284i	$0.834331\pi$
$348$	1.98716	0.106523
$349$	−14.7193	−0.787908	−0.393954	−	0.919130i	$-0.628893\pi$
$349$	−14.7193	−0.787908	−0.393954	+	0.919130i	$0.628893\pi$
$350$	−10.5049	−0.561511
$351$	0	0
$352$	5.95254	0.317271
$353$	8.68310	0.462155	0.231077	−	0.972935i	$-0.425775\pi$
$353$	8.68310	0.462155	0.231077	+	0.972935i	$0.425775\pi$
$354$	1.86716	0.0992387
$355$	−41.3674	−2.19555
$356$	4.89017	0.259178
$357$	5.27740	0.279310
$358$	21.0936	1.11483
$359$	−7.28242	−0.384351	−0.192176	−	0.981361i	$-0.561554\pi$
$359$	−7.28242	−0.384351	−0.192176	+	0.981361i	$0.561554\pi$
$360$	3.93763	0.207531
$361$	−1.99082	−0.104780
$362$	9.67145	0.508320
$363$	24.4327	1.28239
$364$	0	0
$365$	−26.7616	−1.40076
$366$	−10.2395	−0.535230
$367$	31.1358	1.62527	0.812637	−	0.582770i	$-0.198031\pi$
$367$	31.1358	1.62527	0.812637	+	0.582770i	$0.198031\pi$
$368$	−6.25102	−0.325857
$369$	−4.03511	−0.210059
$370$	−15.8801	−0.825565
$371$	−1.32042	−0.0685526
$372$	8.86180	0.459463
$373$	6.91060	0.357817	0.178909	−	0.983866i	$-0.442743\pi$
$373$	6.91060	0.357817	0.178909	+	0.983866i	$0.442743\pi$
$374$	31.4140	1.62438
$375$	−21.6762	−1.11936
$376$	0.0488343	0.00251844
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	11.6048	0.596099	0.298049	−	0.954550i	$-0.403664\pi$
$379$	11.6048	0.596099	0.298049	+	0.954550i	$0.403664\pi$
$380$	−16.2396	−0.833076
$381$	−19.1192	−0.979504
$382$	−3.57978	−0.183157
$383$	−11.7207	−0.598898	−0.299449	−	0.954112i	$-0.596803\pi$
$383$	−11.7207	−0.598898	−0.299449	+	0.954112i	$0.596803\pi$
$384$	−1.00000	−0.0510310
$385$	23.4389	1.19456
$386$	7.32890	0.373031
$387$	−9.79142	−0.497726
$388$	5.77720	0.293293
$389$	5.14645	0.260935	0.130468	−	0.991453i	$-0.458352\pi$
$389$	5.14645	0.260935	0.130468	+	0.991453i	$0.458352\pi$
$390$	0	0
$391$	−32.9891	−1.66833
$392$	−1.00000	−0.0505076
$393$	−8.95315	−0.451627
$394$	19.9531	1.00522
$395$	−36.8722	−1.85524
$396$	−5.95254	−0.299126
$397$	−36.6409	−1.83895	−0.919476	−	0.393146i	$-0.871387\pi$
$397$	−36.6409	−1.83895	−0.919476	+	0.393146i	$0.871387\pi$
$398$	−0.0540891	−0.00271124
$399$	4.12422	0.206469
$400$	10.5049	0.525245
$401$	−1.32884	−0.0663592	−0.0331796	−	0.999449i	$-0.510563\pi$
$401$	−1.32884	−0.0663592	−0.0331796	+	0.999449i	$0.510563\pi$
$402$	15.5361	0.774868
$403$	0	0
$404$	−0.110425	−0.00549383
$405$	−3.93763	−0.195662
$406$	−1.98716	−0.0986209
$407$	24.0060	1.18993
$408$	−5.27740	−0.261270
$409$	−6.80036	−0.336256	−0.168128	−	0.985765i	$-0.553772\pi$
$409$	−6.80036	−0.336256	−0.168128	+	0.985765i	$0.553772\pi$
$410$	−15.8887	−0.784689
$411$	14.9023	0.735077
$412$	−12.5145	−0.616545
$413$	−1.86716	−0.0918772
$414$	6.25102	0.307221
$415$	−50.7501	−2.49122
$416$	0	0
$417$	−22.0903	−1.08177
$418$	24.5496	1.20076
$419$	−7.97625	−0.389665	−0.194833	−	0.980837i	$-0.562416\pi$
$419$	−7.97625	−0.389665	−0.194833	+	0.980837i	$0.562416\pi$
$420$	−3.93763	−0.192136
$421$	−21.5780	−1.05165	−0.525823	−	0.850594i	$-0.676242\pi$
$421$	−21.5780	−1.05165	−0.525823	+	0.850594i	$0.676242\pi$
$422$	−5.13943	−0.250183
$423$	−0.0488343	−0.00237441
$424$	1.32042	0.0641250
$425$	55.4386	2.68917
$426$	−10.5057	−0.509001
$427$	10.2395	0.495526
$428$	6.69454	0.323593
$429$	0	0
$430$	−38.5549	−1.85928
$431$	−37.7673	−1.81919	−0.909593	−	0.415499i	$-0.863607\pi$
$431$	−37.7673	−1.81919	−0.909593	+	0.415499i	$0.863607\pi$
$432$	1.00000	0.0481125
$433$	−34.1954	−1.64333	−0.821663	−	0.569974i	$-0.806953\pi$
$433$	−34.1954	−1.64333	−0.821663	+	0.569974i	$0.806953\pi$
$434$	−8.86180	−0.425380
$435$	−7.82468	−0.375164
$436$	3.01315	0.144304
$437$	−25.7806	−1.23325
$438$	−6.79637	−0.324743
$439$	22.7429	1.08546	0.542729	−	0.839908i	$-0.317391\pi$
$439$	22.7429	1.08546	0.542729	+	0.839908i	$0.317391\pi$
$440$	−23.4389	−1.11740
$441$	1.00000	0.0476190
$442$	0	0
$443$	16.2310	0.771157	0.385579	−	0.922675i	$-0.374002\pi$
$443$	16.2310	0.771157	0.385579	+	0.922675i	$0.374002\pi$
$444$	−4.03290	−0.191393
$445$	−19.2556	−0.912805
$446$	15.9842	0.756875
$447$	8.69435	0.411228
$448$	1.00000	0.0472456
$449$	−3.87770	−0.183000	−0.0915000	−	0.995805i	$-0.529166\pi$
$449$	−3.87770	−0.183000	−0.0915000	+	0.995805i	$0.529166\pi$
$450$	−10.5049	−0.495206
$451$	24.0191	1.13102
$452$	−5.32437	−0.250437
$453$	−2.91278	−0.136855
$454$	−4.72939	−0.221961
$455$	0	0
$456$	−4.12422	−0.193134
$457$	34.2245	1.60095	0.800477	−	0.599364i	$-0.204580\pi$
$457$	34.2245	1.60095	0.800477	+	0.599364i	$0.204580\pi$
$458$	8.24798	0.385403
$459$	5.27740	0.246328
$460$	24.6142	1.14764
$461$	−18.4058	−0.857242	−0.428621	−	0.903484i	$-0.641000\pi$
$461$	−18.4058	−0.857242	−0.428621	+	0.903484i	$0.641000\pi$
$462$	5.95254	0.276937
$463$	−18.4653	−0.858155	−0.429077	−	0.903268i	$-0.641161\pi$
$463$	−18.4653	−0.858155	−0.429077	+	0.903268i	$0.641161\pi$
$464$	1.98716	0.0922514
$465$	−34.8944	−1.61819
$466$	7.51568	0.348157
$467$	−9.04300	−0.418460	−0.209230	−	0.977866i	$-0.567096\pi$
$467$	−9.04300	−0.418460	−0.209230	+	0.977866i	$0.567096\pi$
$468$	0	0
$469$	−15.5361	−0.717388
$470$	−0.192291	−0.00886974
$471$	4.11582	0.189647
$472$	1.86716	0.0859432
$473$	58.2838	2.67989
$474$	−9.36407	−0.430106
$475$	43.3245	1.98786
$476$	5.27740	0.241889
$477$	−1.32042	−0.0604577
$478$	−10.7008	−0.489445
$479$	−0.516444	−0.0235969	−0.0117985	−	0.999930i	$-0.503756\pi$
$479$	−0.516444	−0.0235969	−0.0117985	+	0.999930i	$0.503756\pi$
$480$	3.93763	0.179727
$481$	0	0
$482$	4.74363	0.216067
$483$	−6.25102	−0.284431
$484$	24.4327	1.11058
$485$	−22.7485	−1.03295
$486$	−1.00000	−0.0453609
$487$	−13.9052	−0.630107	−0.315053	−	0.949074i	$-0.602022\pi$
$487$	−13.9052	−0.630107	−0.315053	+	0.949074i	$0.602022\pi$
$488$	−10.2395	−0.463523
$489$	−23.5642	−1.06561
$490$	3.93763	0.177884
$491$	−25.0053	−1.12847	−0.564236	−	0.825613i	$-0.690829\pi$
$491$	−25.0053	−1.12847	−0.564236	+	0.825613i	$0.690829\pi$
$492$	−4.03511	−0.181917
$493$	10.4870	0.472312
$494$	0	0
$495$	23.4389	1.05350
$496$	8.86180	0.397906
$497$	10.5057	0.471243
$498$	−12.8885	−0.577547
$499$	22.6065	1.01201	0.506003	−	0.862532i	$-0.331122\pi$
$499$	22.6065	1.01201	0.506003	+	0.862532i	$0.331122\pi$
$500$	−21.6762	−0.969391
$501$	−17.3082	−0.773273
$502$	19.2761	0.860337
$503$	44.2715	1.97397	0.986984	−	0.160820i	$-0.0514139\pi$
$503$	44.2715	1.97397	0.986984	+	0.160820i	$0.0514139\pi$
$504$	−1.00000	−0.0445435
$505$	0.434811	0.0193488
$506$	−37.2094	−1.65416
$507$	0	0
$508$	−19.1192	−0.848276
$509$	22.4164	0.993589	0.496795	−	0.867868i	$-0.334510\pi$
$509$	22.4164	0.993589	0.496795	+	0.867868i	$0.334510\pi$
$510$	20.7804	0.920173
$511$	6.79637	0.300654
$512$	−1.00000	−0.0441942
$513$	4.12422	0.182089
$514$	−2.72367	−0.120136
$515$	49.2774	2.17142
$516$	−9.79142	−0.431043
$517$	0.290688	0.0127845
$518$	4.03290	0.177195
$519$	18.0884	0.793992
$520$	0	0
$521$	−26.8789	−1.17759	−0.588793	−	0.808284i	$-0.700397\pi$
$521$	−26.8789	−1.17759	−0.588793	+	0.808284i	$0.700397\pi$
$522$	−1.98716	−0.0869754
$523$	1.07834	0.0471526	0.0235763	−	0.999722i	$-0.492495\pi$
$523$	1.07834	0.0471526	0.0235763	+	0.999722i	$0.492495\pi$
$524$	−8.95315	−0.391120
$525$	10.5049	0.458471
$526$	6.87522	0.299774
$527$	46.7673	2.03721
$528$	−5.95254	−0.259051
$529$	16.0752	0.698923
$530$	−5.19930	−0.225843
$531$	−1.86716	−0.0810281
$532$	4.12422	0.178808
$533$	0	0
$534$	−4.89017	−0.211618
$535$	−26.3606	−1.13967
$536$	15.5361	0.671055
$537$	−21.0936	−0.910257
$538$	14.7284	0.634988
$539$	−5.95254	−0.256394
$540$	−3.93763	−0.169448
$541$	42.0378	1.80735	0.903673	−	0.428223i	$-0.140860\pi$
$541$	42.0378	1.80735	0.903673	+	0.428223i	$0.140860\pi$
$542$	−9.90086	−0.425278
$543$	−9.67145	−0.415042
$544$	−5.27740	−0.226267
$545$	−11.8647	−0.508227
$546$	0	0
$547$	39.0481	1.66958	0.834789	−	0.550571i	$-0.185590\pi$
$547$	39.0481	1.66958	0.834789	+	0.550571i	$0.185590\pi$
$548$	14.9023	0.636595
$549$	10.2395	0.437013
$550$	62.5308	2.66632
$551$	8.19546	0.349138
$552$	6.25102	0.266061
$553$	9.36407	0.398201
$554$	−3.11461	−0.132327
$555$	15.8801	0.674071
$556$	−22.0903	−0.936837
$557$	27.4079	1.16131	0.580656	−	0.814149i	$-0.302796\pi$
$557$	27.4079	1.16131	0.580656	+	0.814149i	$0.302796\pi$
$558$	−8.86180	−0.375150
$559$	0	0
$560$	−3.93763	−0.166395
$561$	−31.4140	−1.32630
$562$	4.85588	0.204833
$563$	4.69061	0.197686	0.0988428	−	0.995103i	$-0.468486\pi$
$563$	4.69061	0.197686	0.0988428	+	0.995103i	$0.468486\pi$
$564$	−0.0488343	−0.00205630
$565$	20.9654	0.882020
$566$	−17.1764	−0.721978
$567$	1.00000	0.0419961
$568$	−10.5057	−0.440808
$569$	−18.8870	−0.791783	−0.395892	−	0.918297i	$-0.629564\pi$
$569$	−18.8870	−0.791783	−0.395892	+	0.918297i	$0.629564\pi$
$570$	16.2396	0.680203
$571$	5.67161	0.237349	0.118675	−	0.992933i	$-0.462135\pi$
$571$	5.67161	0.237349	0.118675	+	0.992933i	$0.462135\pi$
$572$	0	0
$573$	3.57978	0.149547
$574$	4.03511	0.168422
$575$	−65.6663	−2.73848
$576$	1.00000	0.0416667
$577$	28.3707	1.18109	0.590544	−	0.807006i	$-0.298913\pi$
$577$	28.3707	1.18109	0.590544	+	0.807006i	$0.298913\pi$
$578$	−10.8510	−0.451341
$579$	−7.32890	−0.304579
$580$	−7.82468	−0.324902
$581$	12.8885	0.534705
$582$	−5.77720	−0.239473
$583$	7.85983	0.325521
$584$	−6.79637	−0.281236
$585$	0	0
$586$	−17.3422	−0.716400
$587$	1.18639	0.0489675	0.0244837	−	0.999700i	$-0.492206\pi$
$587$	1.18639	0.0489675	0.0244837	+	0.999700i	$0.492206\pi$
$588$	1.00000	0.0412393
$589$	36.5480	1.50593
$590$	−7.35220	−0.302685
$591$	−19.9531	−0.820762
$592$	−4.03290	−0.165751
$593$	5.16818	0.212232	0.106116	−	0.994354i	$-0.466159\pi$
$593$	5.16818	0.212232	0.106116	+	0.994354i	$0.466159\pi$
$594$	5.95254	0.244236
$595$	−20.7804	−0.851915
$596$	8.69435	0.356134
$597$	0.0540891	0.00221372
$598$	0	0
$599$	31.1360	1.27218	0.636091	−	0.771614i	$-0.280550\pi$
$599$	31.1360	1.27218	0.636091	+	0.771614i	$0.280550\pi$
$600$	−10.5049	−0.428861
$601$	−4.98647	−0.203402	−0.101701	−	0.994815i	$-0.532429\pi$
$601$	−4.98647	−0.203402	−0.101701	+	0.994815i	$0.532429\pi$
$602$	9.79142	0.399068
$603$	−15.5361	−0.632677
$604$	−2.91278	−0.118520
$605$	−96.2070	−3.91137
$606$	0.110425	0.00448569
$607$	−36.4538	−1.47961	−0.739807	−	0.672819i	$-0.765083\pi$
$607$	−36.4538	−1.47961	−0.739807	+	0.672819i	$0.765083\pi$
$608$	−4.12422	−0.167259
$609$	1.98716	0.0805236
$610$	40.3195	1.63249
$611$	0	0
$612$	5.27740	0.213326
$613$	16.3320	0.659642	0.329821	−	0.944043i	$-0.393012\pi$
$613$	16.3320	0.659642	0.329821	+	0.944043i	$0.393012\pi$
$614$	21.3546	0.861801
$615$	15.8887	0.640696
$616$	5.95254	0.239835
$617$	−34.3259	−1.38191	−0.690955	−	0.722898i	$-0.742810\pi$
$617$	−34.3259	−1.38191	−0.690955	+	0.722898i	$0.742810\pi$
$618$	12.5145	0.503407
$619$	−11.3755	−0.457222	−0.228611	−	0.973518i	$-0.573418\pi$
$619$	−11.3755	−0.457222	−0.228611	+	0.973518i	$0.573418\pi$
$620$	−34.8944	−1.40139
$621$	−6.25102	−0.250845
$622$	−25.4708	−1.02129
$623$	4.89017	0.195920
$624$	0	0
$625$	32.8284	1.31314
$626$	26.0909	1.04280
$627$	−24.5496	−0.980416
$628$	4.11582	0.164239
$629$	−21.2832	−0.848618
$630$	3.93763	0.156879
$631$	−24.1271	−0.960484	−0.480242	−	0.877136i	$-0.659451\pi$
$631$	−24.1271	−0.960484	−0.480242	+	0.877136i	$0.659451\pi$
$632$	−9.36407	−0.372483
$633$	5.13943	0.204274
$634$	27.5033	1.09230
$635$	75.2841	2.98756
$636$	−1.32042	−0.0523579
$637$	0	0
$638$	11.8286	0.468300
$639$	10.5057	0.415598
$640$	3.93763	0.155648
$641$	−44.7726	−1.76841	−0.884206	−	0.467097i	$-0.845300\pi$
$641$	−44.7726	−1.76841	−0.884206	+	0.467097i	$0.845300\pi$
$642$	−6.69454	−0.264212
$643$	7.24447	0.285694	0.142847	−	0.989745i	$-0.454374\pi$
$643$	7.24447	0.285694	0.142847	+	0.989745i	$0.454374\pi$
$644$	−6.25102	−0.246325
$645$	38.5549	1.51810
$646$	−21.7652	−0.856339
$647$	−35.1871	−1.38335	−0.691674	−	0.722209i	$-0.743127\pi$
$647$	−35.1871	−1.38335	−0.691674	+	0.722209i	$0.743127\pi$
$648$	−1.00000	−0.0392837
$649$	11.1144	0.436277
$650$	0	0
$651$	8.86180	0.347321
$652$	−23.5642	−0.922845
$653$	35.3124	1.38188	0.690941	−	0.722911i	$-0.257196\pi$
$653$	35.3124	1.38188	0.690941	+	0.722911i	$0.257196\pi$
$654$	−3.01315	−0.117824
$655$	35.2542	1.37749
$656$	−4.03511	−0.157544
$657$	6.79637	0.265152
$658$	0.0488343	0.00190376
$659$	2.49125	0.0970455	0.0485228	−	0.998822i	$-0.484549\pi$
$659$	2.49125	0.0970455	0.0485228	+	0.998822i	$0.484549\pi$
$660$	23.4389	0.912357
$661$	−8.25195	−0.320964	−0.160482	−	0.987039i	$-0.551305\pi$
$661$	−8.25195	−0.320964	−0.160482	+	0.987039i	$0.551305\pi$
$662$	1.96485	0.0763659
$663$	0	0
$664$	−12.8885	−0.500170
$665$	−16.2396	−0.629746
$666$	4.03290	0.156272
$667$	−12.4217	−0.480972
$668$	−17.3082	−0.669674
$669$	−15.9842	−0.617986
$670$	−61.1752	−2.36340
$671$	−60.9513	−2.35300
$672$	−1.00000	−0.0385758
$673$	−16.2767	−0.627421	−0.313711	−	0.949519i	$-0.601572\pi$
$673$	−16.2767	−0.627421	−0.313711	+	0.949519i	$0.601572\pi$
$674$	35.0864	1.35148
$675$	10.5049	0.404334
$676$	0	0
$677$	5.10063	0.196033	0.0980167	−	0.995185i	$-0.468750\pi$
$677$	5.10063	0.196033	0.0980167	+	0.995185i	$0.468750\pi$
$678$	5.32437	0.204481
$679$	5.77720	0.221709
$680$	20.7804	0.796893
$681$	4.72939	0.181230
$682$	52.7502	2.01991
$683$	4.01643	0.153685	0.0768423	−	0.997043i	$-0.475516\pi$
$683$	4.01643	0.153685	0.0768423	+	0.997043i	$0.475516\pi$
$684$	4.12422	0.157693
$685$	−58.6797	−2.24204
$686$	−1.00000	−0.0381802
$687$	−8.24798	−0.314680
$688$	−9.79142	−0.373294
$689$	0	0
$690$	−24.6142	−0.937046
$691$	−18.4845	−0.703183	−0.351592	−	0.936153i	$-0.614359\pi$
$691$	−18.4845	−0.703183	−0.351592	+	0.936153i	$0.614359\pi$
$692$	18.0884	0.687617
$693$	−5.95254	−0.226118
$694$	32.3227	1.22695
$695$	86.9833	3.29946
$696$	−1.98716	−0.0753229
$697$	−21.2949	−0.806601
$698$	14.7193	0.557135
$699$	−7.51568	−0.284269
$700$	10.5049	0.397048
$701$	29.2002	1.10288	0.551439	−	0.834215i	$-0.314079\pi$
$701$	29.2002	1.10288	0.551439	+	0.834215i	$0.314079\pi$
$702$	0	0
$703$	−16.6326	−0.627309
$704$	−5.95254	−0.224345
$705$	0.192291	0.00724211
$706$	−8.68310	−0.326793
$707$	−0.110425	−0.00415294
$708$	−1.86716	−0.0701724
$709$	−15.3209	−0.575387	−0.287693	−	0.957723i	$-0.592888\pi$
$709$	−15.3209	−0.575387	−0.287693	+	0.957723i	$0.592888\pi$
$710$	41.3674	1.55249
$711$	9.36407	0.351180
$712$	−4.89017	−0.183267
$713$	−55.3953	−2.07457
$714$	−5.27740	−0.197502
$715$	0	0
$716$	−21.0936	−0.788306
$717$	10.7008	0.399630
$718$	7.28242	0.271778
$719$	13.6080	0.507493	0.253746	−	0.967271i	$-0.418337\pi$
$719$	13.6080	0.507493	0.253746	+	0.967271i	$0.418337\pi$
$720$	−3.93763	−0.146747
$721$	−12.5145	−0.466065
$722$	1.99082	0.0740906
$723$	−4.74363	−0.176418
$724$	−9.67145	−0.359437
$725$	20.8749	0.775273
$726$	−24.4327	−0.906784
$727$	−26.8716	−0.996612	−0.498306	−	0.867001i	$-0.666044\pi$
$727$	−26.8716	−0.996612	−0.498306	+	0.867001i	$0.666044\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	26.7616	0.990490
$731$	−51.6733	−1.91120
$732$	10.2395	0.378465
$733$	−0.898361	−0.0331817	−0.0165909	−	0.999862i	$-0.505281\pi$
$733$	−0.898361	−0.0331817	−0.0165909	+	0.999862i	$0.505281\pi$
$734$	−31.1358	−1.14924
$735$	−3.93763	−0.145242
$736$	6.25102	0.230416
$737$	92.4790	3.40651
$738$	4.03511	0.148534
$739$	−31.2596	−1.14990	−0.574952	−	0.818187i	$-0.694979\pi$
$739$	−31.2596	−1.14990	−0.574952	+	0.818187i	$0.694979\pi$
$740$	15.8801	0.583762
$741$	0	0
$742$	1.32042	0.0484740
$743$	13.9519	0.511845	0.255922	−	0.966697i	$-0.417621\pi$
$743$	13.9519	0.511845	0.255922	+	0.966697i	$0.417621\pi$
$744$	−8.86180	−0.324889
$745$	−34.2351	−1.25428
$746$	−6.91060	−0.253015
$747$	12.8885	0.471565
$748$	−31.4140	−1.14861
$749$	6.69454	0.244613
$750$	21.6762	0.791504
$751$	−16.7544	−0.611376	−0.305688	−	0.952132i	$-0.598886\pi$
$751$	−16.7544	−0.611376	−0.305688	+	0.952132i	$0.598886\pi$
$752$	−0.0488343	−0.00178080
$753$	−19.2761	−0.702462
$754$	0	0
$755$	11.4695	0.417416
$756$	1.00000	0.0363696
$757$	35.8731	1.30383	0.651916	−	0.758292i	$-0.273966\pi$
$757$	35.8731	1.30383	0.651916	+	0.758292i	$0.273966\pi$
$758$	−11.6048	−0.421506
$759$	37.2094	1.35062
$760$	16.2396	0.589073
$761$	42.2683	1.53223	0.766113	−	0.642706i	$-0.222188\pi$
$761$	42.2683	1.53223	0.766113	+	0.642706i	$0.222188\pi$
$762$	19.1192	0.692614
$763$	3.01315	0.109083
$764$	3.57978	0.129512
$765$	−20.7804	−0.751318
$766$	11.7207	0.423485
$767$	0	0
$768$	1.00000	0.0360844
$769$	−30.5737	−1.10252	−0.551258	−	0.834335i	$-0.685852\pi$
$769$	−30.5737	−1.10252	−0.551258	+	0.834335i	$0.685852\pi$
$770$	−23.4389	−0.844679
$771$	2.72367	0.0980906
$772$	−7.32890	−0.263773
$773$	−9.01791	−0.324352	−0.162176	−	0.986762i	$-0.551851\pi$
$773$	−9.01791	−0.324352	−0.162176	+	0.986762i	$0.551851\pi$
$774$	9.79142	0.351945
$775$	93.0923	3.34397
$776$	−5.77720	−0.207389
$777$	−4.03290	−0.144679
$778$	−5.14645	−0.184509
$779$	−16.6417	−0.596249
$780$	0	0
$781$	−62.5354	−2.23769
$782$	32.9891	1.17969
$783$	1.98716	0.0710151
$784$	1.00000	0.0357143
$785$	−16.2066	−0.578437
$786$	8.95315	0.319348
$787$	−14.6046	−0.520599	−0.260300	−	0.965528i	$-0.583821\pi$
$787$	−14.6046	−0.520599	−0.260300	+	0.965528i	$0.583821\pi$
$788$	−19.9531	−0.710801
$789$	−6.87522	−0.244764
$790$	36.8722	1.31185
$791$	−5.32437	−0.189313
$792$	5.95254	0.211514
$793$	0	0
$794$	36.6409	1.30034
$795$	5.19930	0.184400
$796$	0.0540891	0.00191714
$797$	10.2013	0.361348	0.180674	−	0.983543i	$-0.442172\pi$
$797$	10.2013	0.361348	0.180674	+	0.983543i	$0.442172\pi$
$798$	−4.12422	−0.145996
$799$	−0.257718	−0.00911742
$800$	−10.5049	−0.371404
$801$	4.89017	0.172786
$802$	1.32884	0.0469230
$803$	−40.4557	−1.42765
$804$	−15.5361	−0.547915
$805$	24.6142	0.867536
$806$	0	0
$807$	−14.7284	−0.518465
$808$	0.110425	0.00388472
$809$	30.7815	1.08222	0.541109	−	0.840952i	$-0.318005\pi$
$809$	30.7815	1.08222	0.541109	+	0.840952i	$0.318005\pi$
$810$	3.93763	0.138354
$811$	49.4249	1.73554	0.867771	−	0.496965i	$-0.165552\pi$
$811$	49.4249	1.73554	0.867771	+	0.496965i	$0.165552\pi$
$812$	1.98716	0.0697355
$813$	9.90086	0.347238
$814$	−24.0060	−0.841410
$815$	92.7870	3.25019
$816$	5.27740	0.184746
$817$	−40.3819	−1.41279
$818$	6.80036	0.237769
$819$	0	0
$820$	15.8887	0.554859
$821$	27.0510	0.944088	0.472044	−	0.881575i	$-0.343516\pi$
$821$	27.0510	0.944088	0.472044	+	0.881575i	$0.343516\pi$
$822$	−14.9023	−0.519778
$823$	20.1613	0.702778	0.351389	−	0.936229i	$-0.385709\pi$
$823$	20.1613	0.702778	0.351389	+	0.936229i	$0.385709\pi$
$824$	12.5145	0.435963
$825$	−62.5308	−2.17704
$826$	1.86716	0.0649670
$827$	−23.7405	−0.825538	−0.412769	−	0.910836i	$-0.635438\pi$
$827$	−23.7405	−0.825538	−0.412769	+	0.910836i	$0.635438\pi$
$828$	−6.25102	−0.217238
$829$	−29.8227	−1.03578	−0.517892	−	0.855446i	$-0.673283\pi$
$829$	−29.8227	−1.03578	−0.517892	+	0.855446i	$0.673283\pi$
$830$	50.7501	1.76156
$831$	3.11461	0.108045
$832$	0	0
$833$	5.27740	0.182851
$834$	22.0903	0.764924
$835$	68.1531	2.35854
$836$	−24.5496	−0.849065
$837$	8.86180	0.306308
$838$	7.97625	0.275535
$839$	19.6410	0.678082	0.339041	−	0.940772i	$-0.389898\pi$
$839$	19.6410	0.678082	0.339041	+	0.940772i	$0.389898\pi$
$840$	3.93763	0.135861
$841$	−25.0512	−0.863835
$842$	21.5780	0.743625
$843$	−4.85588	−0.167245
$844$	5.13943	0.176906
$845$	0	0
$846$	0.0488343	0.00167896
$847$	24.4327	0.839519
$848$	−1.32042	−0.0453433
$849$	17.1764	0.589492
$850$	−55.4386	−1.90153
$851$	25.2097	0.864179
$852$	10.5057	0.359918
$853$	−2.43093	−0.0832333	−0.0416167	−	0.999134i	$-0.513251\pi$
$853$	−2.43093	−0.0832333	−0.0416167	+	0.999134i	$0.513251\pi$
$854$	−10.2395	−0.350390
$855$	−16.2396	−0.555384
$856$	−6.69454	−0.228815
$857$	−35.0880	−1.19858	−0.599292	−	0.800531i	$-0.704551\pi$
$857$	−35.0880	−1.19858	−0.599292	+	0.800531i	$0.704551\pi$
$858$	0	0
$859$	−37.7688	−1.28866	−0.644328	−	0.764749i	$-0.722863\pi$
$859$	−37.7688	−1.28866	−0.644328	+	0.764749i	$0.722863\pi$
$860$	38.5549	1.31471
$861$	−4.03511	−0.137516
$862$	37.7673	1.28636
$863$	−4.38475	−0.149259	−0.0746293	−	0.997211i	$-0.523777\pi$
$863$	−4.38475	−0.149259	−0.0746293	+	0.997211i	$0.523777\pi$
$864$	−1.00000	−0.0340207
$865$	−71.2253	−2.42173
$866$	34.1954	1.16201
$867$	10.8510	0.368519
$868$	8.86180	0.300789
$869$	−55.7400	−1.89085
$870$	7.82468	0.265281
$871$	0	0
$872$	−3.01315	−0.102038
$873$	5.77720	0.195529
$874$	25.7806	0.872041
$875$	−21.6762	−0.732791
$876$	6.79637	0.229628
$877$	−3.94067	−0.133067	−0.0665335	−	0.997784i	$-0.521194\pi$
$877$	−3.94067	−0.133067	−0.0665335	+	0.997784i	$0.521194\pi$
$878$	−22.7429	−0.767535
$879$	17.3422	0.584938
$880$	23.4389	0.790124
$881$	−4.52048	−0.152299	−0.0761495	−	0.997096i	$-0.524263\pi$
$881$	−4.52048	−0.152299	−0.0761495	+	0.997096i	$0.524263\pi$
$882$	−1.00000	−0.0336718
$883$	−39.6799	−1.33534	−0.667668	−	0.744460i	$-0.732707\pi$
$883$	−39.6799	−1.33534	−0.667668	+	0.744460i	$0.732707\pi$
$884$	0	0
$885$	7.35220	0.247141
$886$	−16.2310	−0.545290
$887$	−12.7770	−0.429009	−0.214505	−	0.976723i	$-0.568814\pi$
$887$	−12.7770	−0.429009	−0.214505	+	0.976723i	$0.568814\pi$
$888$	4.03290	0.135335
$889$	−19.1192	−0.641236
$890$	19.2556	0.645451
$891$	−5.95254	−0.199418
$892$	−15.9842	−0.535191
$893$	−0.201403	−0.00673971
$894$	−8.69435	−0.290782
$895$	83.0588	2.77635
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	3.87770	0.129401
$899$	17.6098	0.587319
$900$	10.5049	0.350163
$901$	−6.96836	−0.232150
$902$	−24.0191	−0.799750
$903$	−9.79142	−0.325838
$904$	5.32437	0.177086
$905$	38.0826	1.26591
$906$	2.91278	0.0967708
$907$	56.5076	1.87630	0.938152	−	0.346223i	$-0.112536\pi$
$907$	56.5076	1.87630	0.938152	+	0.346223i	$0.112536\pi$
$908$	4.72939	0.156950
$909$	−0.110425	−0.00366255
$910$	0	0
$911$	−24.2044	−0.801926	−0.400963	−	0.916094i	$-0.631324\pi$
$911$	−24.2044	−0.801926	−0.400963	+	0.916094i	$0.631324\pi$
$912$	4.12422	0.136567
$913$	−76.7193	−2.53904
$914$	−34.2245	−1.13205
$915$	−40.3195	−1.33292
$916$	−8.24798	−0.272521
$917$	−8.95315	−0.295659
$918$	−5.27740	−0.174180
$919$	−1.67355	−0.0552054	−0.0276027	−	0.999619i	$-0.508787\pi$
$919$	−1.67355	−0.0552054	−0.0276027	+	0.999619i	$0.508787\pi$
$920$	−24.6142	−0.811505
$921$	−21.3546	−0.703658
$922$	18.4058	0.606161
$923$	0	0
$924$	−5.95254	−0.195824
$925$	−42.3652	−1.39296
$926$	18.4653	0.606807
$927$	−12.5145	−0.411030
$928$	−1.98716	−0.0652316
$929$	12.2642	0.402375	0.201188	−	0.979553i	$-0.435520\pi$
$929$	12.2642	0.402375	0.201188	+	0.979553i	$0.435520\pi$
$930$	34.8944	1.14423
$931$	4.12422	0.135166
$932$	−7.51568	−0.246184
$933$	25.4708	0.833877
$934$	9.04300	0.295896
$935$	123.696	4.04530
$936$	0	0
$937$	20.3760	0.665656	0.332828	−	0.942988i	$-0.391997\pi$
$937$	20.3760	0.665656	0.332828	+	0.942988i	$0.391997\pi$
$938$	15.5361	0.507270
$939$	−26.0909	−0.851444
$940$	0.192291	0.00627185
$941$	−36.7270	−1.19727	−0.598633	−	0.801023i	$-0.704289\pi$
$941$	−36.7270	−1.19727	−0.598633	+	0.801023i	$0.704289\pi$
$942$	−4.11582	−0.134101
$943$	25.2235	0.821391
$944$	−1.86716	−0.0607710
$945$	−3.93763	−0.128091
$946$	−58.2838	−1.89497
$947$	−7.99772	−0.259891	−0.129946	−	0.991521i	$-0.541480\pi$
$947$	−7.99772	−0.259891	−0.129946	+	0.991521i	$0.541480\pi$
$948$	9.36407	0.304131
$949$	0	0
$950$	−43.3245	−1.40563
$951$	−27.5033	−0.891857
$952$	−5.27740	−0.171042
$953$	−0.0745675	−0.00241548	−0.00120774	−	0.999999i	$-0.500384\pi$
$953$	−0.0745675	−0.00241548	−0.00120774	+	0.999999i	$0.500384\pi$
$954$	1.32042	0.0427500
$955$	−14.0958	−0.456130
$956$	10.7008	0.346090
$957$	−11.8286	−0.382365
$958$	0.516444	0.0166856
$959$	14.9023	0.481221
$960$	−3.93763	−0.127086
$961$	47.5314	1.53327
$962$	0	0
$963$	6.69454	0.215728
$964$	−4.74363	−0.152782
$965$	28.8585	0.928987
$966$	6.25102	0.201123
$967$	6.94212	0.223244	0.111622	−	0.993751i	$-0.464395\pi$
$967$	6.94212	0.223244	0.111622	+	0.993751i	$0.464395\pi$
$968$	−24.4327	−0.785298
$969$	21.7652	0.699198
$970$	22.7485	0.730409
$971$	−45.8237	−1.47055	−0.735276	−	0.677768i	$-0.762947\pi$
$971$	−45.8237	−1.47055	−0.735276	+	0.677768i	$0.762947\pi$
$972$	1.00000	0.0320750
$973$	−22.0903	−0.708182
$974$	13.9052	0.445553
$975$	0	0
$976$	10.2395	0.327760
$977$	−37.3193	−1.19395	−0.596975	−	0.802260i	$-0.703631\pi$
$977$	−37.3193	−1.19395	−0.596975	+	0.802260i	$0.703631\pi$
$978$	23.5642	0.753500
$979$	−29.1089	−0.930325
$980$	−3.93763	−0.125783
$981$	3.01315	0.0962026
$982$	25.0053	0.797951
$983$	−18.7748	−0.598822	−0.299411	−	0.954124i	$-0.596790\pi$
$983$	−18.7748	−0.598822	−0.299411	+	0.954124i	$0.596790\pi$
$984$	4.03511	0.128634
$985$	78.5679	2.50338
$986$	−10.4870	−0.333975
$987$	−0.0488343	−0.00155441
$988$	0	0
$989$	61.2063	1.94625
$990$	−23.4389	−0.744936
$991$	19.5044	0.619577	0.309788	−	0.950806i	$-0.399742\pi$
$991$	19.5044	0.619577	0.309788	+	0.950806i	$0.399742\pi$
$992$	−8.86180	−0.281362
$993$	−1.96485	−0.0623525
$994$	−10.5057	−0.333219
$995$	−0.212983	−0.00675200
$996$	12.8885	0.408387
$997$	−7.92510	−0.250990	−0.125495	−	0.992094i	$-0.540052\pi$
$997$	−7.92510	−0.250990	−0.125495	+	0.992094i	$0.540052\pi$
$998$	−22.6065	−0.715596
$999$	−4.03290	−0.127595

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.cq.1.1	✓	6
13.12	even	2		7098.2.a.cu.1.6	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cq.1.1	✓	6	1.1	even	1	trivial
7098.2.a.cu.1.6	yes	6	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7098.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.93763 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.93763 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.93763 q^{10} -5.95254 q^{11} +1.00000 q^{12} -1.00000 q^{14} -3.93763 q^{15} +1.00000 q^{16} +5.27740 q^{17} -1.00000 q^{18} +4.12422 q^{19} -3.93763 q^{20} +1.00000 q^{21} +5.95254 q^{22} -6.25102 q^{23} -1.00000 q^{24} +10.5049 q^{25} +1.00000 q^{27} +1.00000 q^{28} +1.98716 q^{29} +3.93763 q^{30} +8.86180 q^{31} -1.00000 q^{32} -5.95254 q^{33} -5.27740 q^{34} -3.93763 q^{35} +1.00000 q^{36} -4.03290 q^{37} -4.12422 q^{38} +3.93763 q^{40} -4.03511 q^{41} -1.00000 q^{42} -9.79142 q^{43} -5.95254 q^{44} -3.93763 q^{45} +6.25102 q^{46} -0.0488343 q^{47} +1.00000 q^{48} +1.00000 q^{49} -10.5049 q^{50} +5.27740 q^{51} -1.32042 q^{53} -1.00000 q^{54} +23.4389 q^{55} -1.00000 q^{56} +4.12422 q^{57} -1.98716 q^{58} -1.86716 q^{59} -3.93763 q^{60} +10.2395 q^{61} -8.86180 q^{62} +1.00000 q^{63} +1.00000 q^{64} +5.95254 q^{66} -15.5361 q^{67} +5.27740 q^{68} -6.25102 q^{69} +3.93763 q^{70} +10.5057 q^{71} -1.00000 q^{72} +6.79637 q^{73} +4.03290 q^{74} +10.5049 q^{75} +4.12422 q^{76} -5.95254 q^{77} +9.36407 q^{79} -3.93763 q^{80} +1.00000 q^{81} +4.03511 q^{82} +12.8885 q^{83} +1.00000 q^{84} -20.7804 q^{85} +9.79142 q^{86} +1.98716 q^{87} +5.95254 q^{88} +4.89017 q^{89} +3.93763 q^{90} -6.25102 q^{92} +8.86180 q^{93} +0.0488343 q^{94} -16.2396 q^{95} -1.00000 q^{96} +5.77720 q^{97} -1.00000 q^{98} -5.95254 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} - 9 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 - 9 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} - 9 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8} + 6 q^{9} + 9 q^{10} - 10 q^{11} + 6 q^{12} - 6 q^{14} - 9 q^{15} + 6 q^{16} + 4 q^{17} - 6 q^{18} - 2 q^{19} - 9 q^{20} + 6 q^{21} + 10 q^{22} - 6 q^{24} + 9 q^{25} + 6 q^{27} + 6 q^{28} - 4 q^{29} + 9 q^{30} - 9 q^{31} - 6 q^{32} - 10 q^{33} - 4 q^{34} - 9 q^{35} + 6 q^{36} - 9 q^{37} + 2 q^{38} + 9 q^{40} - 25 q^{41} - 6 q^{42} + 19 q^{43} - 10 q^{44} - 9 q^{45} - 21 q^{47} + 6 q^{48} + 6 q^{49} - 9 q^{50} + 4 q^{51} - 4 q^{53} - 6 q^{54} + 21 q^{55} - 6 q^{56} - 2 q^{57} + 4 q^{58} - 20 q^{59} - 9 q^{60} + 3 q^{61} + 9 q^{62} + 6 q^{63} + 6 q^{64} + 10 q^{66} - 24 q^{67} + 4 q^{68} + 9 q^{70} - 13 q^{71} - 6 q^{72} + 9 q^{73} + 9 q^{74} + 9 q^{75} - 2 q^{76} - 10 q^{77} + 28 q^{79} - 9 q^{80} + 6 q^{81} + 25 q^{82} - 15 q^{83} + 6 q^{84} - 17 q^{85} - 19 q^{86} - 4 q^{87} + 10 q^{88} - 11 q^{89} + 9 q^{90} - 9 q^{93} + 21 q^{94} - 6 q^{96} - 2 q^{97} - 6 q^{98} - 10 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 - 9 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8 + 6 * q^9 + 9 * q^10 - 10 * q^11 + 6 * q^12 - 6 * q^14 - 9 * q^15 + 6 * q^16 + 4 * q^17 - 6 * q^18 - 2 * q^19 - 9 * q^20 + 6 * q^21 + 10 * q^22 - 6 * q^24 + 9 * q^25 + 6 * q^27 + 6 * q^28 - 4 * q^29 + 9 * q^30 - 9 * q^31 - 6 * q^32 - 10 * q^33 - 4 * q^34 - 9 * q^35 + 6 * q^36 - 9 * q^37 + 2 * q^38 + 9 * q^40 - 25 * q^41 - 6 * q^42 + 19 * q^43 - 10 * q^44 - 9 * q^45 - 21 * q^47 + 6 * q^48 + 6 * q^49 - 9 * q^50 + 4 * q^51 - 4 * q^53 - 6 * q^54 + 21 * q^55 - 6 * q^56 - 2 * q^57 + 4 * q^58 - 20 * q^59 - 9 * q^60 + 3 * q^61 + 9 * q^62 + 6 * q^63 + 6 * q^64 + 10 * q^66 - 24 * q^67 + 4 * q^68 + 9 * q^70 - 13 * q^71 - 6 * q^72 + 9 * q^73 + 9 * q^74 + 9 * q^75 - 2 * q^76 - 10 * q^77 + 28 * q^79 - 9 * q^80 + 6 * q^81 + 25 * q^82 - 15 * q^83 + 6 * q^84 - 17 * q^85 - 19 * q^86 - 4 * q^87 + 10 * q^88 - 11 * q^89 + 9 * q^90 - 9 * q^93 + 21 * q^94 - 6 * q^96 - 2 * q^97 - 6 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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