LMFDB - Embedded newform 7098.2.a.cq.1.2

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			1.2
Root			$-2.29987$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.86789 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.86789 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.86789 q^{10} +2.24284 q^{11} +1.00000 q^{12} -1.00000 q^{14} -3.86789 q^{15} +1.00000 q^{16} +0.139361 q^{17} -1.00000 q^{18} -3.18995 q^{19} -3.86789 q^{20} +1.00000 q^{21} -2.24284 q^{22} +1.05473 q^{23} -1.00000 q^{24} +9.96056 q^{25} +1.00000 q^{27} +1.00000 q^{28} -6.34879 q^{29} +3.86789 q^{30} +3.91164 q^{31} -1.00000 q^{32} +2.24284 q^{33} -0.139361 q^{34} -3.86789 q^{35} +1.00000 q^{36} -3.02354 q^{37} +3.18995 q^{38} +3.86789 q^{40} -11.8139 q^{41} -1.00000 q^{42} +8.07597 q^{43} +2.24284 q^{44} -3.86789 q^{45} -1.05473 q^{46} -6.28681 q^{47} +1.00000 q^{48} +1.00000 q^{49} -9.96056 q^{50} +0.139361 q^{51} +8.90676 q^{53} -1.00000 q^{54} -8.67506 q^{55} -1.00000 q^{56} -3.18995 q^{57} +6.34879 q^{58} +0.140899 q^{59} -3.86789 q^{60} -7.35955 q^{61} -3.91164 q^{62} +1.00000 q^{63} +1.00000 q^{64} -2.24284 q^{66} +12.0213 q^{67} +0.139361 q^{68} +1.05473 q^{69} +3.86789 q^{70} +11.5292 q^{71} -1.00000 q^{72} +2.39940 q^{73} +3.02354 q^{74} +9.96056 q^{75} -3.18995 q^{76} +2.24284 q^{77} +7.06021 q^{79} -3.86789 q^{80} +1.00000 q^{81} +11.8139 q^{82} -16.0286 q^{83} +1.00000 q^{84} -0.539031 q^{85} -8.07597 q^{86} -6.34879 q^{87} -2.24284 q^{88} -3.37495 q^{89} +3.86789 q^{90} +1.05473 q^{92} +3.91164 q^{93} +6.28681 q^{94} +12.3384 q^{95} -1.00000 q^{96} -7.74831 q^{97} -1.00000 q^{98} +2.24284 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−3.86789	−1.72977	−0.864886	−	0.501968i	$-0.832609\pi$
$5$	−3.86789	−1.72977	−0.864886	+	0.501968i	$0.832609\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.86789	1.22313
$11$	2.24284	0.676242	0.338121	−	0.941103i	$-0.390209\pi$
$11$	2.24284	0.676242	0.338121	+	0.941103i	$0.390209\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	−3.86789	−0.998685
$16$	1.00000	0.250000
$17$	0.139361	0.0337999	0.0169000	−	0.999857i	$-0.494620\pi$
$17$	0.139361	0.0337999	0.0169000	+	0.999857i	$0.494620\pi$
$18$	−1.00000	−0.235702
$19$	−3.18995	−0.731825	−0.365913	−	0.930649i	$-0.619243\pi$
$19$	−3.18995	−0.731825	−0.365913	+	0.930649i	$0.619243\pi$
$20$	−3.86789	−0.864886
$21$	1.00000	0.218218
$22$	−2.24284	−0.478175
$23$	1.05473	0.219927	0.109963	−	0.993936i	$-0.464927\pi$
$23$	1.05473	0.219927	0.109963	+	0.993936i	$0.464927\pi$
$24$	−1.00000	−0.204124
$25$	9.96056	1.99211
$26$	0	0
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	−6.34879	−1.17894	−0.589470	−	0.807790i	$-0.700663\pi$
$29$	−6.34879	−1.17894	−0.589470	+	0.807790i	$0.700663\pi$
$30$	3.86789	0.706177
$31$	3.91164	0.702552	0.351276	−	0.936272i	$-0.385748\pi$
$31$	3.91164	0.702552	0.351276	+	0.936272i	$0.385748\pi$
$32$	−1.00000	−0.176777
$33$	2.24284	0.390428
$34$	−0.139361	−0.0239001
$35$	−3.86789	−0.653792
$36$	1.00000	0.166667
$37$	−3.02354	−0.497067	−0.248533	−	0.968623i	$-0.579949\pi$
$37$	−3.02354	−0.497067	−0.248533	+	0.968623i	$0.579949\pi$
$38$	3.18995	0.517479
$39$	0	0
$40$	3.86789	0.611567
$41$	−11.8139	−1.84502	−0.922509	−	0.385976i	$-0.873865\pi$
$41$	−11.8139	−1.84502	−0.922509	+	0.385976i	$0.873865\pi$
$42$	−1.00000	−0.154303
$43$	8.07597	1.23157	0.615787	−	0.787913i	$-0.288838\pi$
$43$	8.07597	1.23157	0.615787	+	0.787913i	$0.288838\pi$
$44$	2.24284	0.338121
$45$	−3.86789	−0.576591
$46$	−1.05473	−0.155512
$47$	−6.28681	−0.917025	−0.458512	−	0.888688i	$-0.651618\pi$
$47$	−6.28681	−0.917025	−0.458512	+	0.888688i	$0.651618\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−9.96056	−1.40864
$51$	0.139361	0.0195144
$52$	0	0
$53$	8.90676	1.22344	0.611719	−	0.791075i	$-0.290478\pi$
$53$	8.90676	1.22344	0.611719	+	0.791075i	$0.290478\pi$
$54$	−1.00000	−0.136083
$55$	−8.67506	−1.16974
$56$	−1.00000	−0.133631
$57$	−3.18995	−0.422519
$58$	6.34879	0.833636
$59$	0.140899	0.0183435	0.00917176	−	0.999958i	$-0.497080\pi$
$59$	0.140899	0.0183435	0.00917176	+	0.999958i	$0.497080\pi$
$60$	−3.86789	−0.499342
$61$	−7.35955	−0.942294	−0.471147	−	0.882055i	$-0.656160\pi$
$61$	−7.35955	−0.942294	−0.471147	+	0.882055i	$0.656160\pi$
$62$	−3.91164	−0.496779
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−2.24284	−0.276075
$67$	12.0213	1.46863	0.734316	−	0.678808i	$-0.237503\pi$
$67$	12.0213	1.46863	0.734316	+	0.678808i	$0.237503\pi$
$68$	0.139361	0.0169000
$69$	1.05473	0.126975
$70$	3.86789	0.462301
$71$	11.5292	1.36826	0.684131	−	0.729359i	$-0.260182\pi$
$71$	11.5292	1.36826	0.684131	+	0.729359i	$0.260182\pi$
$72$	−1.00000	−0.117851
$73$	2.39940	0.280829	0.140414	−	0.990093i	$-0.455157\pi$
$73$	2.39940	0.280829	0.140414	+	0.990093i	$0.455157\pi$
$74$	3.02354	0.351479
$75$	9.96056	1.15015
$76$	−3.18995	−0.365913
$77$	2.24284	0.255595
$78$	0	0
$79$	7.06021	0.794336	0.397168	−	0.917746i	$-0.369993\pi$
$79$	7.06021	0.794336	0.397168	+	0.917746i	$0.369993\pi$
$80$	−3.86789	−0.432443
$81$	1.00000	0.111111
$82$	11.8139	1.30462
$83$	−16.0286	−1.75937	−0.879685	−	0.475556i	$-0.842247\pi$
$83$	−16.0286	−1.75937	−0.879685	+	0.475556i	$0.842247\pi$
$84$	1.00000	0.109109
$85$	−0.539031	−0.0584661
$86$	−8.07597	−0.870854
$87$	−6.34879	−0.680661
$88$	−2.24284	−0.239088
$89$	−3.37495	−0.357744	−0.178872	−	0.983872i	$-0.557245\pi$
$89$	−3.37495	−0.357744	−0.178872	+	0.983872i	$0.557245\pi$
$90$	3.86789	0.407711
$91$	0	0
$92$	1.05473	0.109963
$93$	3.91164	0.405619
$94$	6.28681	0.648434
$95$	12.3384	1.26589
$96$	−1.00000	−0.102062
$97$	−7.74831	−0.786722	−0.393361	−	0.919384i	$-0.628688\pi$
$97$	−7.74831	−0.786722	−0.393361	+	0.919384i	$0.628688\pi$
$98$	−1.00000	−0.101015
$99$	2.24284	0.225414
$100$	9.96056	0.996056
$101$	11.0146	1.09599	0.547995	−	0.836482i	$-0.315391\pi$
$101$	11.0146	1.09599	0.547995	+	0.836482i	$0.315391\pi$
$102$	−0.139361	−0.0137988
$103$	−7.70449	−0.759146	−0.379573	−	0.925162i	$-0.623929\pi$
$103$	−7.70449	−0.759146	−0.379573	+	0.925162i	$0.623929\pi$
$104$	0	0
$105$	−3.86789	−0.377467
$106$	−8.90676	−0.865101
$107$	−10.9871	−1.06217	−0.531083	−	0.847320i	$-0.678215\pi$
$107$	−10.9871	−1.06217	−0.531083	+	0.847320i	$0.678215\pi$
$108$	1.00000	0.0962250
$109$	−14.7856	−1.41620	−0.708101	−	0.706111i	$-0.750448\pi$
$109$	−14.7856	−1.41620	−0.708101	+	0.706111i	$0.750448\pi$
$110$	8.67506	0.827134
$111$	−3.02354	−0.286981
$112$	1.00000	0.0944911
$113$	−0.462379	−0.0434969	−0.0217485	−	0.999763i	$-0.506923\pi$
$113$	−0.462379	−0.0434969	−0.0217485	+	0.999763i	$0.506923\pi$
$114$	3.18995	0.298766
$115$	−4.07958	−0.380423
$116$	−6.34879	−0.589470
$117$	0	0
$118$	−0.140899	−0.0129708
$119$	0.139361	0.0127752
$120$	3.86789	0.353088
$121$	−5.96967	−0.542697
$122$	7.35955	0.666302
$123$	−11.8139	−1.06522
$124$	3.91164	0.351276
$125$	−19.1869	−1.71613
$126$	−1.00000	−0.0890871
$127$	17.2718	1.53262	0.766311	−	0.642470i	$-0.222090\pi$
$127$	17.2718	1.53262	0.766311	+	0.642470i	$0.222090\pi$
$128$	−1.00000	−0.0883883
$129$	8.07597	0.711050
$130$	0	0
$131$	2.76749	0.241797	0.120898	−	0.992665i	$-0.461422\pi$
$131$	2.76749	0.241797	0.120898	+	0.992665i	$0.461422\pi$
$132$	2.24284	0.195214
$133$	−3.18995	−0.276604
$134$	−12.0213	−1.03848
$135$	−3.86789	−0.332895
$136$	−0.139361	−0.0119501
$137$	10.1598	0.868010	0.434005	−	0.900910i	$-0.357100\pi$
$137$	10.1598	0.868010	0.434005	+	0.900910i	$0.357100\pi$
$138$	−1.05473	−0.0897846
$139$	−16.7430	−1.42012	−0.710062	−	0.704139i	$-0.751333\pi$
$139$	−16.7430	−1.42012	−0.710062	+	0.704139i	$0.751333\pi$
$140$	−3.86789	−0.326896
$141$	−6.28681	−0.529445
$142$	−11.5292	−0.967507
$143$	0	0
$144$	1.00000	0.0833333
$145$	24.5564	2.03930
$146$	−2.39940	−0.198576
$147$	1.00000	0.0824786
$148$	−3.02354	−0.248533
$149$	1.87669	0.153744	0.0768722	−	0.997041i	$-0.475507\pi$
$149$	1.87669	0.153744	0.0768722	+	0.997041i	$0.475507\pi$
$150$	−9.96056	−0.813276
$151$	3.92238	0.319198	0.159599	−	0.987182i	$-0.448980\pi$
$151$	3.92238	0.319198	0.159599	+	0.987182i	$0.448980\pi$
$152$	3.18995	0.258739
$153$	0.139361	0.0112666
$154$	−2.24284	−0.180733
$155$	−15.1298	−1.21525
$156$	0	0
$157$	10.3473	0.825807	0.412903	−	0.910775i	$-0.364515\pi$
$157$	10.3473	0.825807	0.412903	+	0.910775i	$0.364515\pi$
$158$	−7.06021	−0.561680
$159$	8.90676	0.706352
$160$	3.86789	0.305783
$161$	1.05473	0.0831244
$162$	−1.00000	−0.0785674
$163$	−4.02161	−0.314997	−0.157498	−	0.987519i	$-0.550343\pi$
$163$	−4.02161	−0.314997	−0.157498	+	0.987519i	$0.550343\pi$
$164$	−11.8139	−0.922509
$165$	−8.67506	−0.675352
$166$	16.0286	1.24406
$167$	24.0977	1.86474	0.932369	−	0.361509i	$-0.117738\pi$
$167$	24.0977	1.86474	0.932369	+	0.361509i	$0.117738\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	0.539031	0.0413418
$171$	−3.18995	−0.243942
$172$	8.07597	0.615787
$173$	−22.1817	−1.68644	−0.843221	−	0.537567i	$-0.819343\pi$
$173$	−22.1817	−1.68644	−0.843221	+	0.537567i	$0.819343\pi$
$174$	6.34879	0.481300
$175$	9.96056	0.752948
$176$	2.24284	0.169060
$177$	0.140899	0.0105906
$178$	3.37495	0.252963
$179$	−24.6368	−1.84144	−0.920721	−	0.390221i	$-0.872398\pi$
$179$	−24.6368	−1.84144	−0.920721	+	0.390221i	$0.872398\pi$
$180$	−3.86789	−0.288295
$181$	5.10254	0.379269	0.189635	−	0.981855i	$-0.439270\pi$
$181$	5.10254	0.379269	0.189635	+	0.981855i	$0.439270\pi$
$182$	0	0
$183$	−7.35955	−0.544034
$184$	−1.05473	−0.0777558
$185$	11.6947	0.859812
$186$	−3.91164	−0.286816
$187$	0.312563	0.0228569
$188$	−6.28681	−0.458512
$189$	1.00000	0.0727393
$190$	−12.3384	−0.895120
$191$	8.61491	0.623353	0.311676	−	0.950188i	$-0.399110\pi$
$191$	8.61491	0.623353	0.311676	+	0.950188i	$0.399110\pi$
$192$	1.00000	0.0721688
$193$	−4.77251	−0.343533	−0.171766	−	0.985138i	$-0.554947\pi$
$193$	−4.77251	−0.343533	−0.171766	+	0.985138i	$0.554947\pi$
$194$	7.74831	0.556296
$195$	0	0
$196$	1.00000	0.0714286
$197$	20.7284	1.47684	0.738419	−	0.674342i	$-0.235573\pi$
$197$	20.7284	1.47684	0.738419	+	0.674342i	$0.235573\pi$
$198$	−2.24284	−0.159392
$199$	23.0544	1.63428	0.817141	−	0.576438i	$-0.195558\pi$
$199$	23.0544	1.63428	0.817141	+	0.576438i	$0.195558\pi$
$200$	−9.96056	−0.704318
$201$	12.0213	0.847915
$202$	−11.0146	−0.774982
$203$	−6.34879	−0.445597
$204$	0.139361	0.00975719
$205$	45.6948	3.19146
$206$	7.70449	0.536797
$207$	1.05473	0.0733088
$208$	0	0
$209$	−7.15455	−0.494891
$210$	3.86789	0.266910
$211$	−24.8756	−1.71250	−0.856252	−	0.516558i	$-0.827213\pi$
$211$	−24.8756	−1.71250	−0.856252	+	0.516558i	$0.827213\pi$
$212$	8.90676	0.611719
$213$	11.5292	0.789966
$214$	10.9871	0.751065
$215$	−31.2370	−2.13034
$216$	−1.00000	−0.0680414
$217$	3.91164	0.265540
$218$	14.7856	1.00141
$219$	2.39940	0.162137
$220$	−8.67506	−0.584872
$221$	0	0
$222$	3.02354	0.202927
$223$	1.66144	0.111258	0.0556292	−	0.998451i	$-0.482284\pi$
$223$	1.66144	0.111258	0.0556292	+	0.998451i	$0.482284\pi$
$224$	−1.00000	−0.0668153
$225$	9.96056	0.664037
$226$	0.462379	0.0307570
$227$	0.338882	0.0224924	0.0112462	−	0.999937i	$-0.496420\pi$
$227$	0.338882	0.0224924	0.0112462	+	0.999937i	$0.496420\pi$
$228$	−3.18995	−0.211260
$229$	−10.8351	−0.716005	−0.358003	−	0.933721i	$-0.616542\pi$
$229$	−10.8351	−0.716005	−0.358003	+	0.933721i	$0.616542\pi$
$230$	4.07958	0.269000
$231$	2.24284	0.147568
$232$	6.34879	0.416818
$233$	−23.1718	−1.51803	−0.759016	−	0.651072i	$-0.774320\pi$
$233$	−23.1718	−1.51803	−0.759016	+	0.651072i	$0.774320\pi$
$234$	0	0
$235$	24.3167	1.58624
$236$	0.140899	0.00917176
$237$	7.06021	0.458610
$238$	−0.139361	−0.00903340
$239$	−22.0531	−1.42649	−0.713247	−	0.700913i	$-0.752776\pi$
$239$	−22.0531	−1.42649	−0.713247	+	0.700913i	$0.752776\pi$
$240$	−3.86789	−0.249671
$241$	−16.3750	−1.05481	−0.527404	−	0.849614i	$-0.676835\pi$
$241$	−16.3750	−1.05481	−0.527404	+	0.849614i	$0.676835\pi$
$242$	5.96967	0.383745
$243$	1.00000	0.0641500
$244$	−7.35955	−0.471147
$245$	−3.86789	−0.247110
$246$	11.8139	0.753225
$247$	0	0
$248$	−3.91164	−0.248390
$249$	−16.0286	−1.01577
$250$	19.1869	1.21349
$251$	14.6666	0.925747	0.462874	−	0.886424i	$-0.346818\pi$
$251$	14.6666	0.925747	0.462874	+	0.886424i	$0.346818\pi$
$252$	1.00000	0.0629941
$253$	2.36559	0.148724
$254$	−17.2718	−1.08373
$255$	−0.539031	−0.0337554
$256$	1.00000	0.0625000
$257$	−16.7051	−1.04204	−0.521018	−	0.853546i	$-0.674448\pi$
$257$	−16.7051	−1.04204	−0.521018	+	0.853546i	$0.674448\pi$
$258$	−8.07597	−0.502788
$259$	−3.02354	−0.187873
$260$	0	0
$261$	−6.34879	−0.392980
$262$	−2.76749	−0.170976
$263$	−17.9218	−1.10511	−0.552554	−	0.833477i	$-0.686347\pi$
$263$	−17.9218	−1.10511	−0.552554	+	0.833477i	$0.686347\pi$
$264$	−2.24284	−0.138037
$265$	−34.4504	−2.11627
$266$	3.18995	0.195588
$267$	−3.37495	−0.206544
$268$	12.0213	0.734316
$269$	−8.91367	−0.543476	−0.271738	−	0.962371i	$-0.587598\pi$
$269$	−8.91367	−0.543476	−0.271738	+	0.962371i	$0.587598\pi$
$270$	3.86789	0.235392
$271$	18.0947	1.09917	0.549586	−	0.835437i	$-0.314785\pi$
$271$	18.0947	1.09917	0.549586	+	0.835437i	$0.314785\pi$
$272$	0.139361	0.00844998
$273$	0	0
$274$	−10.1598	−0.613776
$275$	22.3399	1.34715
$276$	1.05473	0.0634873
$277$	−17.8010	−1.06956	−0.534778	−	0.844992i	$-0.679605\pi$
$277$	−17.8010	−1.06956	−0.534778	+	0.844992i	$0.679605\pi$
$278$	16.7430	1.00418
$279$	3.91164	0.234184
$280$	3.86789	0.231151
$281$	−26.6085	−1.58733	−0.793664	−	0.608356i	$-0.791829\pi$
$281$	−26.6085	−1.58733	−0.793664	+	0.608356i	$0.791829\pi$
$282$	6.28681	0.374374
$283$	−2.43370	−0.144668	−0.0723342	−	0.997380i	$-0.523045\pi$
$283$	−2.43370	−0.144668	−0.0723342	+	0.997380i	$0.523045\pi$
$284$	11.5292	0.684131
$285$	12.3384	0.730862
$286$	0	0
$287$	−11.8139	−0.697351
$288$	−1.00000	−0.0589256
$289$	−16.9806	−0.998858
$290$	−24.5564	−1.44200
$291$	−7.74831	−0.454214
$292$	2.39940	0.140414
$293$	−30.1152	−1.75935	−0.879674	−	0.475578i	$-0.842239\pi$
$293$	−30.1152	−1.75935	−0.879674	+	0.475578i	$0.842239\pi$
$294$	−1.00000	−0.0583212
$295$	−0.544983	−0.0317301
$296$	3.02354	0.175740
$297$	2.24284	0.130143
$298$	−1.87669	−0.108714
$299$	0	0
$300$	9.96056	0.575073
$301$	8.07597	0.465491
$302$	−3.92238	−0.225707
$303$	11.0146	0.632770
$304$	−3.18995	−0.182956
$305$	28.4659	1.62995
$306$	−0.139361	−0.00796671
$307$	0.551365	0.0314681	0.0157340	−	0.999876i	$-0.494991\pi$
$307$	0.551365	0.0314681	0.0157340	+	0.999876i	$0.494991\pi$
$308$	2.24284	0.127798
$309$	−7.70449	−0.438293
$310$	15.1298	0.859315
$311$	−26.9438	−1.52784	−0.763922	−	0.645309i	$-0.776729\pi$
$311$	−26.9438	−1.52784	−0.763922	+	0.645309i	$0.776729\pi$
$312$	0	0
$313$	−24.9518	−1.41036	−0.705179	−	0.709029i	$-0.749133\pi$
$313$	−24.9518	−1.41036	−0.705179	+	0.709029i	$0.749133\pi$
$314$	−10.3473	−0.583933
$315$	−3.86789	−0.217931
$316$	7.06021	0.397168
$317$	−1.75675	−0.0986688	−0.0493344	−	0.998782i	$-0.515710\pi$
$317$	−1.75675	−0.0986688	−0.0493344	+	0.998782i	$0.515710\pi$
$318$	−8.90676	−0.499466
$319$	−14.2393	−0.797248
$320$	−3.86789	−0.216222
$321$	−10.9871	−0.613242
$322$	−1.05473	−0.0587778
$323$	−0.444554	−0.0247356
$324$	1.00000	0.0555556
$325$	0	0
$326$	4.02161	0.222736
$327$	−14.7856	−0.817645
$328$	11.8139	0.652312
$329$	−6.28681	−0.346603
$330$	8.67506	0.477546
$331$	25.3386	1.39274	0.696368	−	0.717685i	$-0.254798\pi$
$331$	25.3386	1.39274	0.696368	+	0.717685i	$0.254798\pi$
$332$	−16.0286	−0.879685
$333$	−3.02354	−0.165689
$334$	−24.0977	−1.31857
$335$	−46.4969	−2.54040
$336$	1.00000	0.0545545
$337$	−20.6628	−1.12558	−0.562788	−	0.826601i	$-0.690271\pi$
$337$	−20.6628	−1.12558	−0.562788	+	0.826601i	$0.690271\pi$
$338$	0	0
$339$	−0.462379	−0.0251130
$340$	−0.539031	−0.0292331
$341$	8.77319	0.475095
$342$	3.18995	0.172493
$343$	1.00000	0.0539949
$344$	−8.07597	−0.435427
$345$	−4.07958	−0.219637
$346$	22.1817	1.19249
$347$	−25.7221	−1.38083	−0.690417	−	0.723412i	$-0.742573\pi$
$347$	−25.7221	−1.38083	−0.690417	+	0.723412i	$0.742573\pi$
$348$	−6.34879	−0.340331
$349$	19.3295	1.03468	0.517342	−	0.855779i	$-0.326922\pi$
$349$	19.3295	1.03468	0.517342	+	0.855779i	$0.326922\pi$
$350$	−9.96056	−0.532414
$351$	0	0
$352$	−2.24284	−0.119544
$353$	−14.9866	−0.797654	−0.398827	−	0.917026i	$-0.630583\pi$
$353$	−14.9866	−0.797654	−0.398827	+	0.917026i	$0.630583\pi$
$354$	−0.140899	−0.00748871
$355$	−44.5936	−2.36678
$356$	−3.37495	−0.178872
$357$	0.139361	0.00737574
$358$	24.6368	1.30210
$359$	0.508545	0.0268400	0.0134200	−	0.999910i	$-0.495728\pi$
$359$	0.508545	0.0268400	0.0134200	+	0.999910i	$0.495728\pi$
$360$	3.86789	0.203856
$361$	−8.82421	−0.464432
$362$	−5.10254	−0.268184
$363$	−5.96967	−0.313326
$364$	0	0
$365$	−9.28062	−0.485770
$366$	7.35955	0.384690
$367$	32.4060	1.69158	0.845790	−	0.533515i	$-0.179129\pi$
$367$	32.4060	1.69158	0.845790	+	0.533515i	$0.179129\pi$
$368$	1.05473	0.0549816
$369$	−11.8139	−0.615006
$370$	−11.6947	−0.607979
$371$	8.90676	0.462416
$372$	3.91164	0.202809
$373$	−16.9364	−0.876933	−0.438467	−	0.898747i	$-0.644478\pi$
$373$	−16.9364	−0.876933	−0.438467	+	0.898747i	$0.644478\pi$
$374$	−0.312563	−0.0161623
$375$	−19.1869	−0.990807
$376$	6.28681	0.324217
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	17.3124	0.889277	0.444639	−	0.895710i	$-0.353332\pi$
$379$	17.3124	0.889277	0.444639	+	0.895710i	$0.353332\pi$
$380$	12.3384	0.632945
$381$	17.2718	0.884860
$382$	−8.61491	−0.440777
$383$	26.1955	1.33853	0.669264	−	0.743024i	$-0.266609\pi$
$383$	26.1955	1.33853	0.669264	+	0.743024i	$0.266609\pi$
$384$	−1.00000	−0.0510310
$385$	−8.67506	−0.442122
$386$	4.77251	0.242914
$387$	8.07597	0.410525
$388$	−7.74831	−0.393361
$389$	−12.3683	−0.627096	−0.313548	−	0.949572i	$-0.601518\pi$
$389$	−12.3683	−0.627096	−0.313548	+	0.949572i	$0.601518\pi$
$390$	0	0
$391$	0.146988	0.00743350
$392$	−1.00000	−0.0505076
$393$	2.76749	0.139602
$394$	−20.7284	−1.04428
$395$	−27.3081	−1.37402
$396$	2.24284	0.112707
$397$	31.5113	1.58151	0.790753	−	0.612135i	$-0.209689\pi$
$397$	31.5113	1.58151	0.790753	+	0.612135i	$0.209689\pi$
$398$	−23.0544	−1.15561
$399$	−3.18995	−0.159697
$400$	9.96056	0.498028
$401$	−11.2879	−0.563691	−0.281846	−	0.959460i	$-0.590947\pi$
$401$	−11.2879	−0.563691	−0.281846	+	0.959460i	$0.590947\pi$
$402$	−12.0213	−0.599566
$403$	0	0
$404$	11.0146	0.547995
$405$	−3.86789	−0.192197
$406$	6.34879	0.315085
$407$	−6.78131	−0.336137
$408$	−0.139361	−0.00689938
$409$	−28.1324	−1.39106	−0.695528	−	0.718499i	$-0.744829\pi$
$409$	−28.1324	−1.39106	−0.695528	+	0.718499i	$0.744829\pi$
$410$	−45.6948	−2.25670
$411$	10.1598	0.501146
$412$	−7.70449	−0.379573
$413$	0.140899	0.00693320
$414$	−1.05473	−0.0518372
$415$	61.9970	3.04331
$416$	0	0
$417$	−16.7430	−0.819910
$418$	7.15455	0.349941
$419$	26.8087	1.30969	0.654844	−	0.755764i	$-0.272734\pi$
$419$	26.8087	1.30969	0.654844	+	0.755764i	$0.272734\pi$
$420$	−3.86789	−0.188734
$421$	−18.7350	−0.913090	−0.456545	−	0.889700i	$-0.650913\pi$
$421$	−18.7350	−0.913090	−0.456545	+	0.889700i	$0.650913\pi$
$422$	24.8756	1.21092
$423$	−6.28681	−0.305675
$424$	−8.90676	−0.432550
$425$	1.38811	0.0673332
$426$	−11.5292	−0.558591
$427$	−7.35955	−0.356154
$428$	−10.9871	−0.531083
$429$	0	0
$430$	31.2370	1.50638
$431$	−6.57093	−0.316510	−0.158255	−	0.987398i	$-0.550587\pi$
$431$	−6.57093	−0.316510	−0.158255	+	0.987398i	$0.550587\pi$
$432$	1.00000	0.0481125
$433$	5.84123	0.280711	0.140356	−	0.990101i	$-0.455175\pi$
$433$	5.84123	0.280711	0.140356	+	0.990101i	$0.455175\pi$
$434$	−3.91164	−0.187765
$435$	24.5564	1.17739
$436$	−14.7856	−0.708101
$437$	−3.36454	−0.160948
$438$	−2.39940	−0.114648
$439$	−3.21503	−0.153445	−0.0767225	−	0.997052i	$-0.524446\pi$
$439$	−3.21503	−0.153445	−0.0767225	+	0.997052i	$0.524446\pi$
$440$	8.67506	0.413567
$441$	1.00000	0.0476190
$442$	0	0
$443$	−25.9746	−1.23409	−0.617046	−	0.786927i	$-0.711671\pi$
$443$	−25.9746	−1.23409	−0.617046	+	0.786927i	$0.711671\pi$
$444$	−3.02354	−0.143491
$445$	13.0539	0.618816
$446$	−1.66144	−0.0786716
$447$	1.87669	0.0887644
$448$	1.00000	0.0472456
$449$	10.3628	0.489052	0.244526	−	0.969643i	$-0.421368\pi$
$449$	10.3628	0.489052	0.244526	+	0.969643i	$0.421368\pi$
$450$	−9.96056	−0.469545
$451$	−26.4966	−1.24768
$452$	−0.462379	−0.0217485
$453$	3.92238	0.184289
$454$	−0.338882	−0.0159045
$455$	0	0
$456$	3.18995	0.149383
$457$	−11.5925	−0.542275	−0.271137	−	0.962541i	$-0.587400\pi$
$457$	−11.5925	−0.542275	−0.271137	+	0.962541i	$0.587400\pi$
$458$	10.8351	0.506292
$459$	0.139361	0.00650479
$460$	−4.07958	−0.190211
$461$	−26.0552	−1.21351	−0.606756	−	0.794888i	$-0.707530\pi$
$461$	−26.0552	−1.21351	−0.606756	+	0.794888i	$0.707530\pi$
$462$	−2.24284	−0.104346
$463$	4.21320	0.195804	0.0979021	−	0.995196i	$-0.468787\pi$
$463$	4.21320	0.195804	0.0979021	+	0.995196i	$0.468787\pi$
$464$	−6.34879	−0.294735
$465$	−15.1298	−0.701628
$466$	23.1718	1.07341
$467$	−27.1787	−1.25768	−0.628841	−	0.777534i	$-0.716470\pi$
$467$	−27.1787	−1.25768	−0.628841	+	0.777534i	$0.716470\pi$
$468$	0	0
$469$	12.0213	0.555090
$470$	−24.3167	−1.12164
$471$	10.3473	0.476780
$472$	−0.140899	−0.00648542
$473$	18.1131	0.832842
$474$	−7.06021	−0.324286
$475$	−31.7737	−1.45788
$476$	0.139361	0.00638758
$477$	8.90676	0.407813
$478$	22.0531	1.00868
$479$	−5.50802	−0.251668	−0.125834	−	0.992051i	$-0.540161\pi$
$479$	−5.50802	−0.251668	−0.125834	+	0.992051i	$0.540161\pi$
$480$	3.86789	0.176544
$481$	0	0
$482$	16.3750	0.745862
$483$	1.05473	0.0479919
$484$	−5.96967	−0.271349
$485$	29.9696	1.36085
$486$	−1.00000	−0.0453609
$487$	−4.98323	−0.225812	−0.112906	−	0.993606i	$-0.536016\pi$
$487$	−4.98323	−0.225812	−0.112906	+	0.993606i	$0.536016\pi$
$488$	7.35955	0.333151
$489$	−4.02161	−0.181863
$490$	3.86789	0.174733
$491$	−5.28048	−0.238305	−0.119152	−	0.992876i	$-0.538018\pi$
$491$	−5.28048	−0.238305	−0.119152	+	0.992876i	$0.538018\pi$
$492$	−11.8139	−0.532611
$493$	−0.884770	−0.0398481
$494$	0	0
$495$	−8.67506	−0.389915
$496$	3.91164	0.175638
$497$	11.5292	0.517154
$498$	16.0286	0.718260
$499$	8.54700	0.382616	0.191308	−	0.981530i	$-0.438727\pi$
$499$	8.54700	0.382616	0.191308	+	0.981530i	$0.438727\pi$
$500$	−19.1869	−0.858064
$501$	24.0977	1.07661
$502$	−14.6666	−0.654602
$503$	−0.223190	−0.00995153	−0.00497577	−	0.999988i	$-0.501584\pi$
$503$	−0.223190	−0.00995153	−0.00497577	+	0.999988i	$0.501584\pi$
$504$	−1.00000	−0.0445435
$505$	−42.6031	−1.89581
$506$	−2.36559	−0.105163
$507$	0	0
$508$	17.2718	0.766311
$509$	6.01539	0.266628	0.133314	−	0.991074i	$-0.457438\pi$
$509$	6.01539	0.266628	0.133314	+	0.991074i	$0.457438\pi$
$510$	0.539031	0.0238687
$511$	2.39940	0.106143
$512$	−1.00000	−0.0441942
$513$	−3.18995	−0.140840
$514$	16.7051	0.736831
$515$	29.8001	1.31315
$516$	8.07597	0.355525
$517$	−14.1003	−0.620130
$518$	3.02354	0.132847
$519$	−22.1817	−0.973668
$520$	0	0
$521$	−22.2178	−0.973381	−0.486691	−	0.873574i	$-0.661796\pi$
$521$	−22.2178	−0.973381	−0.486691	+	0.873574i	$0.661796\pi$
$522$	6.34879	0.277879
$523$	−15.2139	−0.665255	−0.332628	−	0.943058i	$-0.607935\pi$
$523$	−15.2139	−0.665255	−0.332628	+	0.943058i	$0.607935\pi$
$524$	2.76749	0.120898
$525$	9.96056	0.434715
$526$	17.9218	0.781429
$527$	0.545129	0.0237462
$528$	2.24284	0.0976071
$529$	−21.8875	−0.951632
$530$	34.4504	1.49643
$531$	0.140899	0.00611451
$532$	−3.18995	−0.138302
$533$	0	0
$534$	3.37495	0.146048
$535$	42.4970	1.83731
$536$	−12.0213	−0.519240
$537$	−24.6368	−1.06316
$538$	8.91367	0.384296
$539$	2.24284	0.0966060
$540$	−3.86789	−0.166447
$541$	−30.4739	−1.31017	−0.655087	−	0.755554i	$-0.727368\pi$
$541$	−30.4739	−1.31017	−0.655087	+	0.755554i	$0.727368\pi$
$542$	−18.0947	−0.777232
$543$	5.10254	0.218971
$544$	−0.139361	−0.00597504
$545$	57.1890	2.44971
$546$	0	0
$547$	−10.7680	−0.460408	−0.230204	−	0.973142i	$-0.573939\pi$
$547$	−10.7680	−0.460408	−0.230204	+	0.973142i	$0.573939\pi$
$548$	10.1598	0.434005
$549$	−7.35955	−0.314098
$550$	−22.3399	−0.952579
$551$	20.2523	0.862778
$552$	−1.05473	−0.0448923
$553$	7.06021	0.300231
$554$	17.8010	0.756291
$555$	11.6947	0.496413
$556$	−16.7430	−0.710062
$557$	−12.1663	−0.515502	−0.257751	−	0.966211i	$-0.582981\pi$
$557$	−12.1663	−0.515502	−0.257751	+	0.966211i	$0.582981\pi$
$558$	−3.91164	−0.165593
$559$	0	0
$560$	−3.86789	−0.163448
$561$	0.312563	0.0131964
$562$	26.6085	1.12241
$563$	15.3757	0.648008	0.324004	−	0.946056i	$-0.394971\pi$
$563$	15.3757	0.648008	0.324004	+	0.946056i	$0.394971\pi$
$564$	−6.28681	−0.264722
$565$	1.78843	0.0752398
$566$	2.43370	0.102296
$567$	1.00000	0.0419961
$568$	−11.5292	−0.483754
$569$	37.1485	1.55735	0.778674	−	0.627429i	$-0.215893\pi$
$569$	37.1485	1.55735	0.778674	+	0.627429i	$0.215893\pi$
$570$	−12.3384	−0.516798
$571$	8.86859	0.371139	0.185569	−	0.982631i	$-0.440587\pi$
$571$	8.86859	0.371139	0.185569	+	0.982631i	$0.440587\pi$
$572$	0	0
$573$	8.61491	0.359893
$574$	11.8139	0.493102
$575$	10.5057	0.438118
$576$	1.00000	0.0416667
$577$	−16.8429	−0.701177	−0.350589	−	0.936530i	$-0.614018\pi$
$577$	−16.8429	−0.701177	−0.350589	+	0.936530i	$0.614018\pi$
$578$	16.9806	0.706299
$579$	−4.77251	−0.198339
$580$	24.5564	1.01965
$581$	−16.0286	−0.664980
$582$	7.74831	0.321178
$583$	19.9764	0.827340
$584$	−2.39940	−0.0992880
$585$	0	0
$586$	30.1152	1.24405
$587$	16.3655	0.675475	0.337737	−	0.941240i	$-0.390338\pi$
$587$	16.3655	0.675475	0.337737	+	0.941240i	$0.390338\pi$
$588$	1.00000	0.0412393
$589$	−12.4780	−0.514145
$590$	0.544983	0.0224366
$591$	20.7284	0.852653
$592$	−3.02354	−0.124267
$593$	28.3867	1.16570	0.582852	−	0.812579i	$-0.301937\pi$
$593$	28.3867	1.16570	0.582852	+	0.812579i	$0.301937\pi$
$594$	−2.24284	−0.0920248
$595$	−0.539031	−0.0220981
$596$	1.87669	0.0768722
$597$	23.0544	0.943553
$598$	0	0
$599$	8.92546	0.364685	0.182342	−	0.983235i	$-0.441632\pi$
$599$	8.92546	0.364685	0.182342	+	0.983235i	$0.441632\pi$
$600$	−9.96056	−0.406638
$601$	−29.0218	−1.18382	−0.591912	−	0.806003i	$-0.701627\pi$
$601$	−29.0218	−1.18382	−0.591912	+	0.806003i	$0.701627\pi$
$602$	−8.07597	−0.329152
$603$	12.0213	0.489544
$604$	3.92238	0.159599
$605$	23.0900	0.938742
$606$	−11.0146	−0.447436
$607$	15.3453	0.622845	0.311423	−	0.950272i	$-0.399195\pi$
$607$	15.3453	0.622845	0.311423	+	0.950272i	$0.399195\pi$
$608$	3.18995	0.129370
$609$	−6.34879	−0.257266
$610$	−28.4659	−1.15255
$611$	0	0
$612$	0.139361	0.00563332
$613$	−48.0959	−1.94257	−0.971287	−	0.237910i	$-0.923538\pi$
$613$	−48.0959	−1.94257	−0.971287	+	0.237910i	$0.923538\pi$
$614$	−0.551365	−0.0222513
$615$	45.6948	1.84259
$616$	−2.24284	−0.0903666
$617$	−22.9255	−0.922946	−0.461473	−	0.887154i	$-0.652679\pi$
$617$	−22.9255	−0.922946	−0.461473	+	0.887154i	$0.652679\pi$
$618$	7.70449	0.309920
$619$	8.54959	0.343637	0.171818	−	0.985129i	$-0.445036\pi$
$619$	8.54959	0.343637	0.171818	+	0.985129i	$0.445036\pi$
$620$	−15.1298	−0.607627
$621$	1.05473	0.0423249
$622$	26.9438	1.08035
$623$	−3.37495	−0.135215
$624$	0	0
$625$	24.4100	0.976399
$626$	24.9518	0.997274
$627$	−7.15455	−0.285725
$628$	10.3473	0.412903
$629$	−0.421362	−0.0168008
$630$	3.86789	0.154100
$631$	39.5572	1.57475	0.787373	−	0.616477i	$-0.211441\pi$
$631$	39.5572	1.57475	0.787373	+	0.616477i	$0.211441\pi$
$632$	−7.06021	−0.280840
$633$	−24.8756	−0.988715
$634$	1.75675	0.0697694
$635$	−66.8053	−2.65109
$636$	8.90676	0.353176
$637$	0	0
$638$	14.2393	0.563740
$639$	11.5292	0.456087
$640$	3.86789	0.152892
$641$	48.2978	1.90765	0.953824	−	0.300366i	$-0.0971087\pi$
$641$	48.2978	1.90765	0.953824	+	0.300366i	$0.0971087\pi$
$642$	10.9871	0.433628
$643$	22.8990	0.903048	0.451524	−	0.892259i	$-0.350881\pi$
$643$	22.8990	0.903048	0.451524	+	0.892259i	$0.350881\pi$
$644$	1.05473	0.0415622
$645$	−31.2370	−1.22995
$646$	0.444554	0.0174907
$647$	14.7982	0.581776	0.290888	−	0.956757i	$-0.406049\pi$
$647$	14.7982	0.581776	0.290888	+	0.956757i	$0.406049\pi$
$648$	−1.00000	−0.0392837
$649$	0.316015	0.0124047
$650$	0	0
$651$	3.91164	0.153309
$652$	−4.02161	−0.157498
$653$	38.8845	1.52167	0.760835	−	0.648946i	$-0.224790\pi$
$653$	38.8845	1.52167	0.760835	+	0.648946i	$0.224790\pi$
$654$	14.7856	0.578162
$655$	−10.7044	−0.418254
$656$	−11.8139	−0.461254
$657$	2.39940	0.0936096
$658$	6.28681	0.245085
$659$	27.3178	1.06415	0.532075	−	0.846698i	$-0.321413\pi$
$659$	27.3178	1.06415	0.532075	+	0.846698i	$0.321413\pi$
$660$	−8.67506	−0.337676
$661$	−40.6662	−1.58173	−0.790866	−	0.611989i	$-0.790370\pi$
$661$	−40.6662	−1.58173	−0.790866	+	0.611989i	$0.790370\pi$
$662$	−25.3386	−0.984814
$663$	0	0
$664$	16.0286	0.622032
$665$	12.3384	0.478462
$666$	3.02354	0.117160
$667$	−6.69626	−0.259280
$668$	24.0977	0.932369
$669$	1.66144	0.0642351
$670$	46.4969	1.79633
$671$	−16.5063	−0.637218
$672$	−1.00000	−0.0385758
$673$	27.8723	1.07440	0.537199	−	0.843456i	$-0.319483\pi$
$673$	27.8723	1.07440	0.537199	+	0.843456i	$0.319483\pi$
$674$	20.6628	0.795902
$675$	9.96056	0.383382
$676$	0	0
$677$	−46.5331	−1.78841	−0.894206	−	0.447656i	$-0.852259\pi$
$677$	−46.5331	−1.78841	−0.894206	+	0.447656i	$0.852259\pi$
$678$	0.462379	0.0177575
$679$	−7.74831	−0.297353
$680$	0.539031	0.0206709
$681$	0.338882	0.0129860
$682$	−8.77319	−0.335943
$683$	−15.9747	−0.611253	−0.305627	−	0.952151i	$-0.598866\pi$
$683$	−15.9747	−0.611253	−0.305627	+	0.952151i	$0.598866\pi$
$684$	−3.18995	−0.121971
$685$	−39.2970	−1.50146
$686$	−1.00000	−0.0381802
$687$	−10.8351	−0.413386
$688$	8.07597	0.307894
$689$	0	0
$690$	4.07958	0.155307
$691$	23.4458	0.891919	0.445959	−	0.895053i	$-0.352863\pi$
$691$	23.4458	0.891919	0.445959	+	0.895053i	$0.352863\pi$
$692$	−22.1817	−0.843221
$693$	2.24284	0.0851985
$694$	25.7221	0.976397
$695$	64.7602	2.45649
$696$	6.34879	0.240650
$697$	−1.64639	−0.0623614
$698$	−19.3295	−0.731632
$699$	−23.1718	−0.876436
$700$	9.96056	0.376474
$701$	−2.74217	−0.103570	−0.0517851	−	0.998658i	$-0.516491\pi$
$701$	−2.74217	−0.103570	−0.0517851	+	0.998658i	$0.516491\pi$
$702$	0	0
$703$	9.64494	0.363766
$704$	2.24284	0.0845302
$705$	24.3167	0.915819
$706$	14.9866	0.564027
$707$	11.0146	0.414245
$708$	0.140899	0.00529532
$709$	40.4098	1.51762	0.758811	−	0.651310i	$-0.225780\pi$
$709$	40.4098	1.51762	0.758811	+	0.651310i	$0.225780\pi$
$710$	44.5936	1.67357
$711$	7.06021	0.264779
$712$	3.37495	0.126482
$713$	4.12573	0.154510
$714$	−0.139361	−0.00521544
$715$	0	0
$716$	−24.6368	−0.920721
$717$	−22.0531	−0.823587
$718$	−0.508545	−0.0189787
$719$	14.5158	0.541348	0.270674	−	0.962671i	$-0.412753\pi$
$719$	14.5158	0.541348	0.270674	+	0.962671i	$0.412753\pi$
$720$	−3.86789	−0.144148
$721$	−7.70449	−0.286930
$722$	8.82421	0.328403
$723$	−16.3750	−0.608994
$724$	5.10254	0.189635
$725$	−63.2375	−2.34858
$726$	5.96967	0.221555
$727$	−30.0166	−1.11325	−0.556627	−	0.830762i	$-0.687905\pi$
$727$	−30.0166	−1.11325	−0.556627	+	0.830762i	$0.687905\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	9.28062	0.343491
$731$	1.12547	0.0416271
$732$	−7.35955	−0.272017
$733$	−31.5831	−1.16655	−0.583275	−	0.812275i	$-0.698229\pi$
$733$	−31.5831	−1.16655	−0.583275	+	0.812275i	$0.698229\pi$
$734$	−32.4060	−1.19613
$735$	−3.86789	−0.142669
$736$	−1.05473	−0.0388779
$737$	26.9618	0.993150
$738$	11.8139	0.434875
$739$	−32.2913	−1.18786	−0.593928	−	0.804518i	$-0.702424\pi$
$739$	−32.2913	−1.18786	−0.593928	+	0.804518i	$0.702424\pi$
$740$	11.6947	0.429906
$741$	0	0
$742$	−8.90676	−0.326977
$743$	−37.6673	−1.38188	−0.690939	−	0.722913i	$-0.742803\pi$
$743$	−37.6673	−1.38188	−0.690939	+	0.722913i	$0.742803\pi$
$744$	−3.91164	−0.143408
$745$	−7.25883	−0.265943
$746$	16.9364	0.620086
$747$	−16.0286	−0.586457
$748$	0.312563	0.0114285
$749$	−10.9871	−0.401461
$750$	19.1869	0.700606
$751$	5.32524	0.194321	0.0971603	−	0.995269i	$-0.469024\pi$
$751$	5.32524	0.194321	0.0971603	+	0.995269i	$0.469024\pi$
$752$	−6.28681	−0.229256
$753$	14.6666	0.534480
$754$	0	0
$755$	−15.1713	−0.552141
$756$	1.00000	0.0363696
$757$	−22.6684	−0.823898	−0.411949	−	0.911207i	$-0.635152\pi$
$757$	−22.6684	−0.823898	−0.411949	+	0.911207i	$0.635152\pi$
$758$	−17.3124	−0.628814
$759$	2.36559	0.0858656
$760$	−12.3384	−0.447560
$761$	−10.3154	−0.373934	−0.186967	−	0.982366i	$-0.559866\pi$
$761$	−10.3154	−0.373934	−0.186967	+	0.982366i	$0.559866\pi$
$762$	−17.2718	−0.625690
$763$	−14.7856	−0.535274
$764$	8.61491	0.311676
$765$	−0.539031	−0.0194887
$766$	−26.1955	−0.946483
$767$	0	0
$768$	1.00000	0.0360844
$769$	−36.4505	−1.31444	−0.657220	−	0.753699i	$-0.728268\pi$
$769$	−36.4505	−1.31444	−0.657220	+	0.753699i	$0.728268\pi$
$770$	8.67506	0.312627
$771$	−16.7051	−0.601620
$772$	−4.77251	−0.171766
$773$	−32.1023	−1.15464	−0.577320	−	0.816518i	$-0.695902\pi$
$773$	−32.1023	−1.15464	−0.577320	+	0.816518i	$0.695902\pi$
$774$	−8.07597	−0.290285
$775$	38.9622	1.39956
$776$	7.74831	0.278148
$777$	−3.02354	−0.108469
$778$	12.3683	0.443424
$779$	37.6857	1.35023
$780$	0	0
$781$	25.8581	0.925276
$782$	−0.146988	−0.00525628
$783$	−6.34879	−0.226887
$784$	1.00000	0.0357143
$785$	−40.0223	−1.42846
$786$	−2.76749	−0.0987132
$787$	2.80320	0.0999234	0.0499617	−	0.998751i	$-0.484090\pi$
$787$	2.80320	0.0999234	0.0499617	+	0.998751i	$0.484090\pi$
$788$	20.7284	0.738419
$789$	−17.9218	−0.638034
$790$	27.3081	0.971579
$791$	−0.462379	−0.0164403
$792$	−2.24284	−0.0796959
$793$	0	0
$794$	−31.5113	−1.11829
$795$	−34.4504	−1.22183
$796$	23.0544	0.817141
$797$	−32.5356	−1.15247	−0.576236	−	0.817283i	$-0.695479\pi$
$797$	−32.5356	−1.15247	−0.576236	+	0.817283i	$0.695479\pi$
$798$	3.18995	0.112923
$799$	−0.876133	−0.0309954
$800$	−9.96056	−0.352159
$801$	−3.37495	−0.119248
$802$	11.2879	0.398590
$803$	5.38148	0.189908
$804$	12.0213	0.423957
$805$	−4.07958	−0.143786
$806$	0	0
$807$	−8.91367	−0.313776
$808$	−11.0146	−0.387491
$809$	33.0597	1.16232	0.581159	−	0.813790i	$-0.302600\pi$
$809$	33.0597	1.16232	0.581159	+	0.813790i	$0.302600\pi$
$810$	3.86789	0.135904
$811$	19.8406	0.696697	0.348348	−	0.937365i	$-0.386743\pi$
$811$	19.8406	0.696697	0.348348	+	0.937365i	$0.386743\pi$
$812$	−6.34879	−0.222799
$813$	18.0947	0.634607
$814$	6.78131	0.237685
$815$	15.5551	0.544872
$816$	0.139361	0.00487860
$817$	−25.7620	−0.901297
$818$	28.1324	0.983625
$819$	0	0
$820$	45.6948	1.59573
$821$	43.0221	1.50148	0.750741	−	0.660597i	$-0.229697\pi$
$821$	43.0221	1.50148	0.750741	+	0.660597i	$0.229697\pi$
$822$	−10.1598	−0.354364
$823$	−20.0391	−0.698521	−0.349260	−	0.937026i	$-0.613567\pi$
$823$	−20.0391	−0.698521	−0.349260	+	0.937026i	$0.613567\pi$
$824$	7.70449	0.268399
$825$	22.3399	0.777777
$826$	−0.140899	−0.00490251
$827$	−31.4823	−1.09475	−0.547373	−	0.836889i	$-0.684372\pi$
$827$	−31.4823	−1.09475	−0.547373	+	0.836889i	$0.684372\pi$
$828$	1.05473	0.0366544
$829$	8.84242	0.307110	0.153555	−	0.988140i	$-0.450928\pi$
$829$	8.84242	0.307110	0.153555	+	0.988140i	$0.450928\pi$
$830$	−61.9970	−2.15195
$831$	−17.8010	−0.617509
$832$	0	0
$833$	0.139361	0.00482856
$834$	16.7430	0.579764
$835$	−93.2073	−3.22557
$836$	−7.15455	−0.247445
$837$	3.91164	0.135206
$838$	−26.8087	−0.926090
$839$	22.7336	0.784850	0.392425	−	0.919784i	$-0.371636\pi$
$839$	22.7336	0.784850	0.392425	+	0.919784i	$0.371636\pi$
$840$	3.86789	0.133455
$841$	11.3071	0.389899
$842$	18.7350	0.645652
$843$	−26.6085	−0.916444
$844$	−24.8756	−0.856252
$845$	0	0
$846$	6.28681	0.216145
$847$	−5.96967	−0.205120
$848$	8.90676	0.305859
$849$	−2.43370	−0.0835244
$850$	−1.38811	−0.0476118
$851$	−3.18902	−0.109318
$852$	11.5292	0.394983
$853$	19.1797	0.656702	0.328351	−	0.944556i	$-0.393507\pi$
$853$	19.1797	0.656702	0.328351	+	0.944556i	$0.393507\pi$
$854$	7.35955	0.251839
$855$	12.3384	0.421964
$856$	10.9871	0.375532
$857$	35.2664	1.20468	0.602338	−	0.798241i	$-0.294236\pi$
$857$	35.2664	1.20468	0.602338	+	0.798241i	$0.294236\pi$
$858$	0	0
$859$	4.08052	0.139226	0.0696128	−	0.997574i	$-0.477824\pi$
$859$	4.08052	0.139226	0.0696128	+	0.997574i	$0.477824\pi$
$860$	−31.2370	−1.06517
$861$	−11.8139	−0.402616
$862$	6.57093	0.223807
$863$	−13.0268	−0.443437	−0.221718	−	0.975111i	$-0.571167\pi$
$863$	−13.0268	−0.443437	−0.221718	+	0.975111i	$0.571167\pi$
$864$	−1.00000	−0.0340207
$865$	85.7963	2.91716
$866$	−5.84123	−0.198493
$867$	−16.9806	−0.576691
$868$	3.91164	0.132770
$869$	15.8349	0.537163
$870$	−24.5564	−0.832540
$871$	0	0
$872$	14.7856	0.500703
$873$	−7.74831	−0.262241
$874$	3.36454	0.113807
$875$	−19.1869	−0.648636
$876$	2.39940	0.0810683
$877$	−2.57514	−0.0869563	−0.0434781	−	0.999054i	$-0.513844\pi$
$877$	−2.57514	−0.0869563	−0.0434781	+	0.999054i	$0.513844\pi$
$878$	3.21503	0.108502
$879$	−30.1152	−1.01576
$880$	−8.67506	−0.292436
$881$	17.5766	0.592172	0.296086	−	0.955161i	$-0.404319\pi$
$881$	17.5766	0.592172	0.296086	+	0.955161i	$0.404319\pi$
$882$	−1.00000	−0.0336718
$883$	−1.49250	−0.0502266	−0.0251133	−	0.999685i	$-0.507995\pi$
$883$	−1.49250	−0.0502266	−0.0251133	+	0.999685i	$0.507995\pi$
$884$	0	0
$885$	−0.544983	−0.0183194
$886$	25.9746	0.872634
$887$	22.4040	0.752251	0.376126	−	0.926569i	$-0.377256\pi$
$887$	22.4040	0.752251	0.376126	+	0.926569i	$0.377256\pi$
$888$	3.02354	0.101463
$889$	17.2718	0.579277
$890$	−13.0539	−0.437569
$891$	2.24284	0.0751380
$892$	1.66144	0.0556292
$893$	20.0546	0.671102
$894$	−1.87669	−0.0627659
$895$	95.2925	3.18528
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	−10.3628	−0.345812
$899$	−24.8342	−0.828267
$900$	9.96056	0.332019
$901$	1.24125	0.0413521
$902$	26.4966	0.882242
$903$	8.07597	0.268751
$904$	0.462379	0.0153785
$905$	−19.7361	−0.656049
$906$	−3.92238	−0.130312
$907$	5.77228	0.191665	0.0958327	−	0.995397i	$-0.469449\pi$
$907$	5.77228	0.191665	0.0958327	+	0.995397i	$0.469449\pi$
$908$	0.338882	0.0112462
$909$	11.0146	0.365330
$910$	0	0
$911$	−5.97933	−0.198104	−0.0990520	−	0.995082i	$-0.531581\pi$
$911$	−5.97933	−0.198104	−0.0990520	+	0.995082i	$0.531581\pi$
$912$	−3.18995	−0.105630
$913$	−35.9497	−1.18976
$914$	11.5925	0.383446
$915$	28.4659	0.941054
$916$	−10.8351	−0.358003
$917$	2.76749	0.0913907
$918$	−0.139361	−0.00459958
$919$	−50.7209	−1.67313	−0.836565	−	0.547868i	$-0.815440\pi$
$919$	−50.7209	−1.67313	−0.836565	+	0.547868i	$0.815440\pi$
$920$	4.07958	0.134500
$921$	0.551365	0.0181681
$922$	26.0552	0.858083
$923$	0	0
$924$	2.24284	0.0737840
$925$	−30.1161	−0.990212
$926$	−4.21320	−0.138454
$927$	−7.70449	−0.253049
$928$	6.34879	0.208409
$929$	−10.0913	−0.331083	−0.165542	−	0.986203i	$-0.552937\pi$
$929$	−10.0913	−0.331083	−0.165542	+	0.986203i	$0.552937\pi$
$930$	15.1298	0.496126
$931$	−3.18995	−0.104546
$932$	−23.1718	−0.759016
$933$	−26.9438	−0.882101
$934$	27.1787	0.889315
$935$	−1.20896	−0.0395372
$936$	0	0
$937$	45.3366	1.48108	0.740542	−	0.672010i	$-0.234569\pi$
$937$	45.3366	1.48108	0.740542	+	0.672010i	$0.234569\pi$
$938$	−12.0213	−0.392508
$939$	−24.9518	−0.814271
$940$	24.3167	0.793122
$941$	−40.1238	−1.30800	−0.653999	−	0.756495i	$-0.726910\pi$
$941$	−40.1238	−1.30800	−0.653999	+	0.756495i	$0.726910\pi$
$942$	−10.3473	−0.337134
$943$	−12.4605	−0.405768
$944$	0.140899	0.00458588
$945$	−3.86789	−0.125822
$946$	−18.1131	−0.588908
$947$	13.2272	0.429826	0.214913	−	0.976633i	$-0.431053\pi$
$947$	13.2272	0.429826	0.214913	+	0.976633i	$0.431053\pi$
$948$	7.06021	0.229305
$949$	0	0
$950$	31.7737	1.03088
$951$	−1.75675	−0.0569665
$952$	−0.139361	−0.00451670
$953$	−5.57685	−0.180652	−0.0903260	−	0.995912i	$-0.528791\pi$
$953$	−5.57685	−0.180652	−0.0903260	+	0.995912i	$0.528791\pi$
$954$	−8.90676	−0.288367
$955$	−33.3215	−1.07826
$956$	−22.0531	−0.713247
$957$	−14.2393	−0.460292
$958$	5.50802	0.177956
$959$	10.1598	0.328077
$960$	−3.86789	−0.124836
$961$	−15.6990	−0.506421
$962$	0	0
$963$	−10.9871	−0.354055
$964$	−16.3750	−0.527404
$965$	18.4595	0.594234
$966$	−1.05473	−0.0339354
$967$	−26.6772	−0.857882	−0.428941	−	0.903332i	$-0.641113\pi$
$967$	−26.6772	−0.857882	−0.428941	+	0.903332i	$0.641113\pi$
$968$	5.96967	0.191872
$969$	−0.444554	−0.0142811
$970$	−29.9696	−0.962266
$971$	11.6045	0.372406	0.186203	−	0.982511i	$-0.440382\pi$
$971$	11.6045	0.372406	0.186203	+	0.982511i	$0.440382\pi$
$972$	1.00000	0.0320750
$973$	−16.7430	−0.536757
$974$	4.98323	0.159673
$975$	0	0
$976$	−7.35955	−0.235573
$977$	−13.1162	−0.419624	−0.209812	−	0.977742i	$-0.567285\pi$
$977$	−13.1162	−0.419624	−0.209812	+	0.977742i	$0.567285\pi$
$978$	4.02161	0.128597
$979$	−7.56948	−0.241922
$980$	−3.86789	−0.123555
$981$	−14.7856	−0.472067
$982$	5.28048	0.168507
$983$	39.2505	1.25190	0.625948	−	0.779865i	$-0.284712\pi$
$983$	39.2505	1.25190	0.625948	+	0.779865i	$0.284712\pi$
$984$	11.8139	0.376613
$985$	−80.1752	−2.55459
$986$	0.884770	0.0281768
$987$	−6.28681	−0.200111
$988$	0	0
$989$	8.51797	0.270856
$990$	8.67506	0.275711
$991$	32.9814	1.04769	0.523844	−	0.851814i	$-0.324498\pi$
$991$	32.9814	1.04769	0.523844	+	0.851814i	$0.324498\pi$
$992$	−3.91164	−0.124195
$993$	25.3386	0.804097
$994$	−11.5292	−0.365683
$995$	−89.1718	−2.82693
$996$	−16.0286	−0.507887
$997$	−50.2260	−1.59067	−0.795337	−	0.606167i	$-0.792706\pi$
$997$	−50.2260	−1.59067	−0.795337	+	0.606167i	$0.792706\pi$
$998$	−8.54700	−0.270551
$999$	−3.02354	−0.0956605

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.cq.1.2	✓	6
13.12	even	2		7098.2.a.cu.1.5	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cq.1.2	✓	6	1.1	even	1	trivial
7098.2.a.cu.1.5	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.86789 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.86789 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.86789 q^{10} +2.24284 q^{11} +1.00000 q^{12} -1.00000 q^{14} -3.86789 q^{15} +1.00000 q^{16} +0.139361 q^{17} -1.00000 q^{18} -3.18995 q^{19} -3.86789 q^{20} +1.00000 q^{21} -2.24284 q^{22} +1.05473 q^{23} -1.00000 q^{24} +9.96056 q^{25} +1.00000 q^{27} +1.00000 q^{28} -6.34879 q^{29} +3.86789 q^{30} +3.91164 q^{31} -1.00000 q^{32} +2.24284 q^{33} -0.139361 q^{34} -3.86789 q^{35} +1.00000 q^{36} -3.02354 q^{37} +3.18995 q^{38} +3.86789 q^{40} -11.8139 q^{41} -1.00000 q^{42} +8.07597 q^{43} +2.24284 q^{44} -3.86789 q^{45} -1.05473 q^{46} -6.28681 q^{47} +1.00000 q^{48} +1.00000 q^{49} -9.96056 q^{50} +0.139361 q^{51} +8.90676 q^{53} -1.00000 q^{54} -8.67506 q^{55} -1.00000 q^{56} -3.18995 q^{57} +6.34879 q^{58} +0.140899 q^{59} -3.86789 q^{60} -7.35955 q^{61} -3.91164 q^{62} +1.00000 q^{63} +1.00000 q^{64} -2.24284 q^{66} +12.0213 q^{67} +0.139361 q^{68} +1.05473 q^{69} +3.86789 q^{70} +11.5292 q^{71} -1.00000 q^{72} +2.39940 q^{73} +3.02354 q^{74} +9.96056 q^{75} -3.18995 q^{76} +2.24284 q^{77} +7.06021 q^{79} -3.86789 q^{80} +1.00000 q^{81} +11.8139 q^{82} -16.0286 q^{83} +1.00000 q^{84} -0.539031 q^{85} -8.07597 q^{86} -6.34879 q^{87} -2.24284 q^{88} -3.37495 q^{89} +3.86789 q^{90} +1.05473 q^{92} +3.91164 q^{93} +6.28681 q^{94} +12.3384 q^{95} -1.00000 q^{96} -7.74831 q^{97} -1.00000 q^{98} +2.24284 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} - 9 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 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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