LMFDB - Embedded newform 7098.2.a.ct.1.5

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:	$0$
Dimension:	$6$
Coefficient field:	6.6.48406561.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 17x^{4} + 39x^{3} + 111x^{2} - 131x - 281 $ x^6 - 3x^5 - 17x^4 + 39x^3 + 111x^2 - 131*x - 281
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			1.5
Root			$3.10863$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.10863 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.10863 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.10863 q^{10} +1.55496 q^{11} +1.00000 q^{12} +1.00000 q^{14} +3.10863 q^{15} +1.00000 q^{16} -1.24698 q^{17} +1.00000 q^{18} -4.73805 q^{19} +3.10863 q^{20} +1.00000 q^{21} +1.55496 q^{22} +5.10817 q^{23} +1.00000 q^{24} +4.66359 q^{25} +1.00000 q^{27} +1.00000 q^{28} -1.05926 q^{29} +3.10863 q^{30} -2.46553 q^{31} +1.00000 q^{32} +1.55496 q^{33} -1.24698 q^{34} +3.10863 q^{35} +1.00000 q^{36} +7.92429 q^{37} -4.73805 q^{38} +3.10863 q^{40} +2.71654 q^{41} +1.00000 q^{42} -2.63128 q^{43} +1.55496 q^{44} +3.10863 q^{45} +5.10817 q^{46} +5.06412 q^{47} +1.00000 q^{48} +1.00000 q^{49} +4.66359 q^{50} -1.24698 q^{51} -7.09392 q^{53} +1.00000 q^{54} +4.83379 q^{55} +1.00000 q^{56} -4.73805 q^{57} -1.05926 q^{58} -3.41870 q^{59} +3.10863 q^{60} +13.2814 q^{61} -2.46553 q^{62} +1.00000 q^{63} +1.00000 q^{64} +1.55496 q^{66} -8.48684 q^{67} -1.24698 q^{68} +5.10817 q^{69} +3.10863 q^{70} -5.31350 q^{71} +1.00000 q^{72} +9.45056 q^{73} +7.92429 q^{74} +4.66359 q^{75} -4.73805 q^{76} +1.55496 q^{77} +11.1942 q^{79} +3.10863 q^{80} +1.00000 q^{81} +2.71654 q^{82} -4.40061 q^{83} +1.00000 q^{84} -3.87640 q^{85} -2.63128 q^{86} -1.05926 q^{87} +1.55496 q^{88} +5.76399 q^{89} +3.10863 q^{90} +5.10817 q^{92} -2.46553 q^{93} +5.06412 q^{94} -14.7289 q^{95} +1.00000 q^{96} +10.8007 q^{97} +1.00000 q^{98} +1.55496 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 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 + 3 * 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} + 3 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} + 3 q^{10} + 10 q^{11} + 6 q^{12} + 6 q^{14} + 3 q^{15} + 6 q^{16} + 2 q^{17} + 6 q^{18} + 2 q^{19} + 3 q^{20} + 6 q^{21} + 10 q^{22} + 4 q^{23} + 6 q^{24} + 13 q^{25} + 6 q^{27} + 6 q^{28} + 2 q^{29} + 3 q^{30} + 9 q^{31} + 6 q^{32} + 10 q^{33} + 2 q^{34} + 3 q^{35} + 6 q^{36} + 7 q^{37} + 2 q^{38} + 3 q^{40} + 11 q^{41} + 6 q^{42} - 5 q^{43} + 10 q^{44} + 3 q^{45} + 4 q^{46} + 5 q^{47} + 6 q^{48} + 6 q^{49} + 13 q^{50} + 2 q^{51} - 6 q^{53} + 6 q^{54} + 5 q^{55} + 6 q^{56} + 2 q^{57} + 2 q^{58} + 28 q^{59} + 3 q^{60} + 23 q^{61} + 9 q^{62} + 6 q^{63} + 6 q^{64} + 10 q^{66} - 10 q^{67} + 2 q^{68} + 4 q^{69} + 3 q^{70} + 21 q^{71} + 6 q^{72} - 7 q^{73} + 7 q^{74} + 13 q^{75} + 2 q^{76} + 10 q^{77} - 14 q^{79} + 3 q^{80} + 6 q^{81} + 11 q^{82} + 17 q^{83} + 6 q^{84} + q^{85} - 5 q^{86} + 2 q^{87} + 10 q^{88} + 17 q^{89} + 3 q^{90} + 4 q^{92} + 9 q^{93} + 5 q^{94} - 22 q^{95} + 6 q^{96} + 6 q^{98} + 10 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 + 3 * q^10 + 10 * q^11 + 6 * q^12 + 6 * q^14 + 3 * q^15 + 6 * q^16 + 2 * q^17 + 6 * q^18 + 2 * q^19 + 3 * q^20 + 6 * q^21 + 10 * q^22 + 4 * q^23 + 6 * q^24 + 13 * q^25 + 6 * q^27 + 6 * q^28 + 2 * q^29 + 3 * q^30 + 9 * q^31 + 6 * q^32 + 10 * q^33 + 2 * q^34 + 3 * q^35 + 6 * q^36 + 7 * q^37 + 2 * q^38 + 3 * q^40 + 11 * q^41 + 6 * q^42 - 5 * q^43 + 10 * q^44 + 3 * q^45 + 4 * q^46 + 5 * q^47 + 6 * q^48 + 6 * q^49 + 13 * q^50 + 2 * q^51 - 6 * q^53 + 6 * q^54 + 5 * q^55 + 6 * q^56 + 2 * q^57 + 2 * q^58 + 28 * q^59 + 3 * q^60 + 23 * q^61 + 9 * q^62 + 6 * q^63 + 6 * q^64 + 10 * q^66 - 10 * q^67 + 2 * q^68 + 4 * q^69 + 3 * q^70 + 21 * q^71 + 6 * q^72 - 7 * q^73 + 7 * q^74 + 13 * q^75 + 2 * q^76 + 10 * q^77 - 14 * q^79 + 3 * q^80 + 6 * q^81 + 11 * q^82 + 17 * q^83 + 6 * q^84 + q^85 - 5 * q^86 + 2 * q^87 + 10 * q^88 + 17 * q^89 + 3 * q^90 + 4 * q^92 + 9 * q^93 + 5 * q^94 - 22 * q^95 + 6 * q^96 + 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
$5$	3.10863	1.39022	0.695111	−	0.718902i	$-0.255355\pi$
$5$	3.10863	1.39022	0.695111	+	0.718902i	$0.255355\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.10863	0.983036
$11$	1.55496	0.468838	0.234419	−	0.972136i	$-0.424681\pi$
$11$	1.55496	0.468838	0.234419	+	0.972136i	$0.424681\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	3.10863	0.802645
$16$	1.00000	0.250000
$17$	−1.24698	−0.302437	−0.151218	−	0.988500i	$-0.548320\pi$
$17$	−1.24698	−0.302437	−0.151218	+	0.988500i	$0.548320\pi$
$18$	1.00000	0.235702
$19$	−4.73805	−1.08698	−0.543492	−	0.839414i	$-0.682898\pi$
$19$	−4.73805	−1.08698	−0.543492	+	0.839414i	$0.682898\pi$
$20$	3.10863	0.695111
$21$	1.00000	0.218218
$22$	1.55496	0.331518
$23$	5.10817	1.06513	0.532564	−	0.846390i	$-0.321229\pi$
$23$	5.10817	1.06513	0.532564	+	0.846390i	$0.321229\pi$
$24$	1.00000	0.204124
$25$	4.66359	0.932718
$26$	0	0
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	−1.05926	−0.196699	−0.0983494	−	0.995152i	$-0.531356\pi$
$29$	−1.05926	−0.196699	−0.0983494	+	0.995152i	$0.531356\pi$
$30$	3.10863	0.567556
$31$	−2.46553	−0.442822	−0.221411	−	0.975181i	$-0.571066\pi$
$31$	−2.46553	−0.442822	−0.221411	+	0.975181i	$0.571066\pi$
$32$	1.00000	0.176777
$33$	1.55496	0.270683
$34$	−1.24698	−0.213855
$35$	3.10863	0.525455
$36$	1.00000	0.166667
$37$	7.92429	1.30274	0.651372	−	0.758758i	$-0.274194\pi$
$37$	7.92429	1.30274	0.651372	+	0.758758i	$0.274194\pi$
$38$	−4.73805	−0.768614
$39$	0	0
$40$	3.10863	0.491518
$41$	2.71654	0.424252	0.212126	−	0.977242i	$-0.431961\pi$
$41$	2.71654	0.424252	0.212126	+	0.977242i	$0.431961\pi$
$42$	1.00000	0.154303
$43$	−2.63128	−0.401266	−0.200633	−	0.979666i	$-0.564300\pi$
$43$	−2.63128	−0.401266	−0.200633	+	0.979666i	$0.564300\pi$
$44$	1.55496	0.234419
$45$	3.10863	0.463407
$46$	5.10817	0.753159
$47$	5.06412	0.738678	0.369339	−	0.929295i	$-0.379584\pi$
$47$	5.06412	0.738678	0.369339	+	0.929295i	$0.379584\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	4.66359	0.659531
$51$	−1.24698	−0.174612
$52$	0	0
$53$	−7.09392	−0.974425	−0.487212	−	0.873284i	$-0.661986\pi$
$53$	−7.09392	−0.974425	−0.487212	+	0.873284i	$0.661986\pi$
$54$	1.00000	0.136083
$55$	4.83379	0.651788
$56$	1.00000	0.133631
$57$	−4.73805	−0.627570
$58$	−1.05926	−0.139087
$59$	−3.41870	−0.445077	−0.222539	−	0.974924i	$-0.571434\pi$
$59$	−3.41870	−0.445077	−0.222539	+	0.974924i	$0.571434\pi$
$60$	3.10863	0.401323
$61$	13.2814	1.70051	0.850254	−	0.526373i	$-0.176448\pi$
$61$	13.2814	1.70051	0.850254	+	0.526373i	$0.176448\pi$
$62$	−2.46553	−0.313122
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	1.55496	0.191402
$67$	−8.48684	−1.03683	−0.518416	−	0.855128i	$-0.673478\pi$
$67$	−8.48684	−1.03683	−0.518416	+	0.855128i	$0.673478\pi$
$68$	−1.24698	−0.151218
$69$	5.10817	0.614952
$70$	3.10863	0.371553
$71$	−5.31350	−0.630596	−0.315298	−	0.948993i	$-0.602104\pi$
$71$	−5.31350	−0.630596	−0.315298	+	0.948993i	$0.602104\pi$
$72$	1.00000	0.117851
$73$	9.45056	1.10610	0.553052	−	0.833147i	$-0.313463\pi$
$73$	9.45056	1.10610	0.553052	+	0.833147i	$0.313463\pi$
$74$	7.92429	0.921180
$75$	4.66359	0.538505
$76$	−4.73805	−0.543492
$77$	1.55496	0.177204
$78$	0	0
$79$	11.1942	1.25945	0.629725	−	0.776818i	$-0.283167\pi$
$79$	11.1942	1.25945	0.629725	+	0.776818i	$0.283167\pi$
$80$	3.10863	0.347556
$81$	1.00000	0.111111
$82$	2.71654	0.299991
$83$	−4.40061	−0.483030	−0.241515	−	0.970397i	$-0.577644\pi$
$83$	−4.40061	−0.483030	−0.241515	+	0.970397i	$0.577644\pi$
$84$	1.00000	0.109109
$85$	−3.87640	−0.420455
$86$	−2.63128	−0.283738
$87$	−1.05926	−0.113564
$88$	1.55496	0.165759
$89$	5.76399	0.610982	0.305491	−	0.952195i	$-0.401179\pi$
$89$	5.76399	0.610982	0.305491	+	0.952195i	$0.401179\pi$
$90$	3.10863	0.327679
$91$	0	0
$92$	5.10817	0.532564
$93$	−2.46553	−0.255663
$94$	5.06412	0.522325
$95$	−14.7289	−1.51115
$96$	1.00000	0.102062
$97$	10.8007	1.09664	0.548322	−	0.836267i	$-0.315267\pi$
$97$	10.8007	1.09664	0.548322	+	0.836267i	$0.315267\pi$
$98$	1.00000	0.101015
$99$	1.55496	0.156279
$100$	4.66359	0.466359
$101$	8.82958	0.878576	0.439288	−	0.898346i	$-0.355231\pi$
$101$	8.82958	0.878576	0.439288	+	0.898346i	$0.355231\pi$
$102$	−1.24698	−0.123469
$103$	1.89793	0.187009	0.0935044	−	0.995619i	$-0.470193\pi$
$103$	1.89793	0.187009	0.0935044	+	0.995619i	$0.470193\pi$
$104$	0	0
$105$	3.10863	0.303371
$106$	−7.09392	−0.689022
$107$	−3.58727	−0.346795	−0.173397	−	0.984852i	$-0.555474\pi$
$107$	−3.58727	−0.346795	−0.173397	+	0.984852i	$0.555474\pi$
$108$	1.00000	0.0962250
$109$	−20.3167	−1.94599	−0.972995	−	0.230826i	$-0.925857\pi$
$109$	−20.3167	−1.94599	−0.972995	+	0.230826i	$0.925857\pi$
$110$	4.83379	0.460884
$111$	7.92429	0.752140
$112$	1.00000	0.0944911
$113$	−6.85060	−0.644450	−0.322225	−	0.946663i	$-0.604431\pi$
$113$	−6.85060	−0.644450	−0.322225	+	0.946663i	$0.604431\pi$
$114$	−4.73805	−0.443759
$115$	15.8794	1.48076
$116$	−1.05926	−0.0983494
$117$	0	0
$118$	−3.41870	−0.314717
$119$	−1.24698	−0.114310
$120$	3.10863	0.283778
$121$	−8.58211	−0.780191
$122$	13.2814	1.20244
$123$	2.71654	0.244942
$124$	−2.46553	−0.221411
$125$	−1.04578	−0.0935370
$126$	1.00000	0.0890871
$127$	8.46378	0.751039	0.375520	−	0.926814i	$-0.377464\pi$
$127$	8.46378	0.751039	0.375520	+	0.926814i	$0.377464\pi$
$128$	1.00000	0.0883883
$129$	−2.63128	−0.231671
$130$	0	0
$131$	−5.07860	−0.443719	−0.221860	−	0.975079i	$-0.571213\pi$
$131$	−5.07860	−0.443719	−0.221860	+	0.975079i	$0.571213\pi$
$132$	1.55496	0.135342
$133$	−4.73805	−0.410841
$134$	−8.48684	−0.733151
$135$	3.10863	0.267548
$136$	−1.24698	−0.106928
$137$	20.8764	1.78359	0.891795	−	0.452440i	$-0.149446\pi$
$137$	20.8764	1.78359	0.891795	+	0.452440i	$0.149446\pi$
$138$	5.10817	0.434837
$139$	17.7255	1.50346	0.751729	−	0.659472i	$-0.229220\pi$
$139$	17.7255	1.50346	0.751729	+	0.659472i	$0.229220\pi$
$140$	3.10863	0.262727
$141$	5.06412	0.426476
$142$	−5.31350	−0.445899
$143$	0	0
$144$	1.00000	0.0833333
$145$	−3.29284	−0.273455
$146$	9.45056	0.782134
$147$	1.00000	0.0824786
$148$	7.92429	0.651372
$149$	0.829877	0.0679862	0.0339931	−	0.999422i	$-0.489178\pi$
$149$	0.829877	0.0679862	0.0339931	+	0.999422i	$0.489178\pi$
$150$	4.66359	0.380780
$151$	−3.39170	−0.276012	−0.138006	−	0.990431i	$-0.544069\pi$
$151$	−3.39170	−0.276012	−0.138006	+	0.990431i	$0.544069\pi$
$152$	−4.73805	−0.384307
$153$	−1.24698	−0.100812
$154$	1.55496	0.125302
$155$	−7.66442	−0.615621
$156$	0	0
$157$	−23.7381	−1.89450	−0.947251	−	0.320492i	$-0.896152\pi$
$157$	−23.7381	−1.89450	−0.947251	+	0.320492i	$0.896152\pi$
$158$	11.1942	0.890566
$159$	−7.09392	−0.562584
$160$	3.10863	0.245759
$161$	5.10817	0.402580
$162$	1.00000	0.0785674
$163$	−6.35482	−0.497748	−0.248874	−	0.968536i	$-0.580060\pi$
$163$	−6.35482	−0.497748	−0.248874	+	0.968536i	$0.580060\pi$
$164$	2.71654	0.212126
$165$	4.83379	0.376310
$166$	−4.40061	−0.341554
$167$	−7.50114	−0.580456	−0.290228	−	0.956958i	$-0.593731\pi$
$167$	−7.50114	−0.580456	−0.290228	+	0.956958i	$0.593731\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	−3.87640	−0.297306
$171$	−4.73805	−0.362328
$172$	−2.63128	−0.200633
$173$	−16.1881	−1.23076	−0.615378	−	0.788232i	$-0.710997\pi$
$173$	−16.1881	−1.23076	−0.615378	+	0.788232i	$0.710997\pi$
$174$	−1.05926	−0.0803020
$175$	4.66359	0.352534
$176$	1.55496	0.117209
$177$	−3.41870	−0.256966
$178$	5.76399	0.432030
$179$	1.95421	0.146064	0.0730322	−	0.997330i	$-0.476732\pi$
$179$	1.95421	0.146064	0.0730322	+	0.997330i	$0.476732\pi$
$180$	3.10863	0.231704
$181$	−1.81969	−0.135256	−0.0676281	−	0.997711i	$-0.521543\pi$
$181$	−1.81969	−0.135256	−0.0676281	+	0.997711i	$0.521543\pi$
$182$	0	0
$183$	13.2814	0.981788
$184$	5.10817	0.376580
$185$	24.6337	1.81110
$186$	−2.46553	−0.180781
$187$	−1.93900	−0.141794
$188$	5.06412	0.369339
$189$	1.00000	0.0727393
$190$	−14.7289	−1.06854
$191$	−23.3210	−1.68745	−0.843723	−	0.536779i	$-0.819641\pi$
$191$	−23.3210	−1.68745	−0.843723	+	0.536779i	$0.819641\pi$
$192$	1.00000	0.0721688
$193$	7.99277	0.575332	0.287666	−	0.957731i	$-0.407121\pi$
$193$	7.99277	0.575332	0.287666	+	0.957731i	$0.407121\pi$
$194$	10.8007	0.775444
$195$	0	0
$196$	1.00000	0.0714286
$197$	−2.24858	−0.160205	−0.0801024	−	0.996787i	$-0.525525\pi$
$197$	−2.24858	−0.160205	−0.0801024	+	0.996787i	$0.525525\pi$
$198$	1.55496	0.110506
$199$	−25.4768	−1.80600	−0.903001	−	0.429638i	$-0.858641\pi$
$199$	−25.4768	−1.80600	−0.903001	+	0.429638i	$0.858641\pi$
$200$	4.66359	0.329766
$201$	−8.48684	−0.598615
$202$	8.82958	0.621247
$203$	−1.05926	−0.0743452
$204$	−1.24698	−0.0873060
$205$	8.44471	0.589804
$206$	1.89793	0.132235
$207$	5.10817	0.355043
$208$	0	0
$209$	−7.36747	−0.509619
$210$	3.10863	0.214516
$211$	2.01914	0.139003	0.0695016	−	0.997582i	$-0.477859\pi$
$211$	2.01914	0.139003	0.0695016	+	0.997582i	$0.477859\pi$
$212$	−7.09392	−0.487212
$213$	−5.31350	−0.364075
$214$	−3.58727	−0.245221
$215$	−8.17967	−0.557849
$216$	1.00000	0.0680414
$217$	−2.46553	−0.167371
$218$	−20.3167	−1.37602
$219$	9.45056	0.638610
$220$	4.83379	0.325894
$221$	0	0
$222$	7.92429	0.531843
$223$	−13.1491	−0.880532	−0.440266	−	0.897867i	$-0.645116\pi$
$223$	−13.1491	−0.880532	−0.440266	+	0.897867i	$0.645116\pi$
$224$	1.00000	0.0668153
$225$	4.66359	0.310906
$226$	−6.85060	−0.455695
$227$	1.90722	0.126587	0.0632935	−	0.997995i	$-0.479840\pi$
$227$	1.90722	0.126587	0.0632935	+	0.997995i	$0.479840\pi$
$228$	−4.73805	−0.313785
$229$	−1.32344	−0.0874554	−0.0437277	−	0.999043i	$-0.513923\pi$
$229$	−1.32344	−0.0874554	−0.0437277	+	0.999043i	$0.513923\pi$
$230$	15.8794	1.04706
$231$	1.55496	0.102309
$232$	−1.05926	−0.0695435
$233$	−23.7561	−1.55631	−0.778157	−	0.628069i	$-0.783845\pi$
$233$	−23.7561	−1.55631	−0.778157	+	0.628069i	$0.783845\pi$
$234$	0	0
$235$	15.7425	1.02693
$236$	−3.41870	−0.222539
$237$	11.1942	0.727144
$238$	−1.24698	−0.0808297
$239$	27.3308	1.76789	0.883943	−	0.467595i	$-0.154879\pi$
$239$	27.3308	1.76789	0.883943	+	0.467595i	$0.154879\pi$
$240$	3.10863	0.200661
$241$	2.68328	0.172846	0.0864228	−	0.996259i	$-0.472456\pi$
$241$	2.68328	0.172846	0.0864228	+	0.996259i	$0.472456\pi$
$242$	−8.58211	−0.551679
$243$	1.00000	0.0641500
$244$	13.2814	0.850254
$245$	3.10863	0.198603
$246$	2.71654	0.173200
$247$	0	0
$248$	−2.46553	−0.156561
$249$	−4.40061	−0.278877
$250$	−1.04578	−0.0661407
$251$	−30.8962	−1.95015	−0.975077	−	0.221867i	$-0.928785\pi$
$251$	−30.8962	−1.95015	−0.975077	+	0.221867i	$0.928785\pi$
$252$	1.00000	0.0629941
$253$	7.94300	0.499372
$254$	8.46378	0.531065
$255$	−3.87640	−0.242750
$256$	1.00000	0.0625000
$257$	27.6822	1.72677	0.863385	−	0.504546i	$-0.168340\pi$
$257$	27.6822	1.72677	0.863385	+	0.504546i	$0.168340\pi$
$258$	−2.63128	−0.163816
$259$	7.92429	0.492391
$260$	0	0
$261$	−1.05926	−0.0655663
$262$	−5.07860	−0.313757
$263$	21.8601	1.34795	0.673975	−	0.738754i	$-0.264586\pi$
$263$	21.8601	1.34795	0.673975	+	0.738754i	$0.264586\pi$
$264$	1.55496	0.0957011
$265$	−22.0524	−1.35467
$266$	−4.73805	−0.290509
$267$	5.76399	0.352751
$268$	−8.48684	−0.518416
$269$	−17.0766	−1.04118	−0.520590	−	0.853807i	$-0.674288\pi$
$269$	−17.0766	−1.04118	−0.520590	+	0.853807i	$0.674288\pi$
$270$	3.10863	0.189185
$271$	27.8718	1.69309	0.846547	−	0.532315i	$-0.178678\pi$
$271$	27.8718	1.69309	0.846547	+	0.532315i	$0.178678\pi$
$272$	−1.24698	−0.0756092
$273$	0	0
$274$	20.8764	1.26119
$275$	7.25169	0.437293
$276$	5.10817	0.307476
$277$	−31.9253	−1.91820	−0.959102	−	0.283061i	$-0.908650\pi$
$277$	−31.9253	−1.91820	−0.959102	+	0.283061i	$0.908650\pi$
$278$	17.7255	1.06311
$279$	−2.46553	−0.147607
$280$	3.10863	0.185776
$281$	−11.3692	−0.678229	−0.339114	−	0.940745i	$-0.610127\pi$
$281$	−11.3692	−0.678229	−0.339114	+	0.940745i	$0.610127\pi$
$282$	5.06412	0.301564
$283$	−16.6264	−0.988334	−0.494167	−	0.869367i	$-0.664527\pi$
$283$	−16.6264	−0.988334	−0.494167	+	0.869367i	$0.664527\pi$
$284$	−5.31350	−0.315298
$285$	−14.7289	−0.872462
$286$	0	0
$287$	2.71654	0.160352
$288$	1.00000	0.0589256
$289$	−15.4450	−0.908532
$290$	−3.29284	−0.193362
$291$	10.8007	0.633147
$292$	9.45056	0.553052
$293$	−5.41358	−0.316265	−0.158132	−	0.987418i	$-0.550547\pi$
$293$	−5.41358	−0.316265	−0.158132	+	0.987418i	$0.550547\pi$
$294$	1.00000	0.0583212
$295$	−10.6275	−0.618757
$296$	7.92429	0.460590
$297$	1.55496	0.0902278
$298$	0.829877	0.0480735
$299$	0	0
$300$	4.66359	0.269252
$301$	−2.63128	−0.151664
$302$	−3.39170	−0.195170
$303$	8.82958	0.507246
$304$	−4.73805	−0.271746
$305$	41.2869	2.36408
$306$	−1.24698	−0.0712851
$307$	6.53538	0.372994	0.186497	−	0.982456i	$-0.440287\pi$
$307$	6.53538	0.372994	0.186497	+	0.982456i	$0.440287\pi$
$308$	1.55496	0.0886020
$309$	1.89793	0.107970
$310$	−7.66442	−0.435310
$311$	−27.7921	−1.57595	−0.787973	−	0.615710i	$-0.788869\pi$
$311$	−27.7921	−1.57595	−0.787973	+	0.615710i	$0.788869\pi$
$312$	0	0
$313$	−4.35209	−0.245995	−0.122997	−	0.992407i	$-0.539251\pi$
$313$	−4.35209	−0.245995	−0.122997	+	0.992407i	$0.539251\pi$
$314$	−23.7381	−1.33962
$315$	3.10863	0.175152
$316$	11.1942	0.629725
$317$	12.5835	0.706761	0.353381	−	0.935480i	$-0.385032\pi$
$317$	12.5835	0.706761	0.353381	+	0.935480i	$0.385032\pi$
$318$	−7.09392	−0.397807
$319$	−1.64710	−0.0922198
$320$	3.10863	0.173778
$321$	−3.58727	−0.200222
$322$	5.10817	0.284667
$323$	5.90825	0.328744
$324$	1.00000	0.0555556
$325$	0	0
$326$	−6.35482	−0.351961
$327$	−20.3167	−1.12352
$328$	2.71654	0.149996
$329$	5.06412	0.279194
$330$	4.83379	0.266091
$331$	19.8866	1.09307	0.546533	−	0.837437i	$-0.315947\pi$
$331$	19.8866	1.09307	0.546533	+	0.837437i	$0.315947\pi$
$332$	−4.40061	−0.241515
$333$	7.92429	0.434248
$334$	−7.50114	−0.410444
$335$	−26.3825	−1.44143
$336$	1.00000	0.0545545
$337$	0.500733	0.0272767	0.0136383	−	0.999907i	$-0.495659\pi$
$337$	0.500733	0.0272767	0.0136383	+	0.999907i	$0.495659\pi$
$338$	0	0
$339$	−6.85060	−0.372074
$340$	−3.87640	−0.210227
$341$	−3.83379	−0.207611
$342$	−4.73805	−0.256205
$343$	1.00000	0.0539949
$344$	−2.63128	−0.141869
$345$	15.8794	0.854920
$346$	−16.1881	−0.870276
$347$	−24.7464	−1.32846	−0.664229	−	0.747530i	$-0.731240\pi$
$347$	−24.7464	−1.32846	−0.664229	+	0.747530i	$0.731240\pi$
$348$	−1.05926	−0.0567821
$349$	−4.30578	−0.230483	−0.115241	−	0.993338i	$-0.536764\pi$
$349$	−4.30578	−0.230483	−0.115241	+	0.993338i	$0.536764\pi$
$350$	4.66359	0.249279
$351$	0	0
$352$	1.55496	0.0828795
$353$	−4.18501	−0.222746	−0.111373	−	0.993779i	$-0.535525\pi$
$353$	−4.18501	−0.222746	−0.111373	+	0.993779i	$0.535525\pi$
$354$	−3.41870	−0.181702
$355$	−16.5177	−0.876668
$356$	5.76399	0.305491
$357$	−1.24698	−0.0659972
$358$	1.95421	0.103283
$359$	−6.33135	−0.334156	−0.167078	−	0.985944i	$-0.553433\pi$
$359$	−6.33135	−0.334156	−0.167078	+	0.985944i	$0.553433\pi$
$360$	3.10863	0.163839
$361$	3.44914	0.181533
$362$	−1.81969	−0.0956406
$363$	−8.58211	−0.450444
$364$	0	0
$365$	29.3783	1.53773
$366$	13.2814	0.694229
$367$	19.8935	1.03843	0.519216	−	0.854643i	$-0.326224\pi$
$367$	19.8935	1.03843	0.519216	+	0.854643i	$0.326224\pi$
$368$	5.10817	0.266282
$369$	2.71654	0.141417
$370$	24.6337	1.28064
$371$	−7.09392	−0.368298
$372$	−2.46553	−0.127832
$373$	−35.9969	−1.86385	−0.931923	−	0.362655i	$-0.881870\pi$
$373$	−35.9969	−1.86385	−0.931923	+	0.362655i	$0.881870\pi$
$374$	−1.93900	−0.100263
$375$	−1.04578	−0.0540036
$376$	5.06412	0.261162
$377$	0	0
$378$	1.00000	0.0514344
$379$	29.5252	1.51661	0.758304	−	0.651901i	$-0.226028\pi$
$379$	29.5252	1.51661	0.758304	+	0.651901i	$0.226028\pi$
$380$	−14.7289	−0.755574
$381$	8.46378	0.433613
$382$	−23.3210	−1.19320
$383$	−0.770083	−0.0393494	−0.0196747	−	0.999806i	$-0.506263\pi$
$383$	−0.770083	−0.0393494	−0.0196747	+	0.999806i	$0.506263\pi$
$384$	1.00000	0.0510310
$385$	4.83379	0.246353
$386$	7.99277	0.406821
$387$	−2.63128	−0.133755
$388$	10.8007	0.548322
$389$	18.6621	0.946208	0.473104	−	0.881006i	$-0.343133\pi$
$389$	18.6621	0.946208	0.473104	+	0.881006i	$0.343133\pi$
$390$	0	0
$391$	−6.36979	−0.322134
$392$	1.00000	0.0505076
$393$	−5.07860	−0.256181
$394$	−2.24858	−0.113282
$395$	34.7988	1.75092
$396$	1.55496	0.0781396
$397$	17.7403	0.890360	0.445180	−	0.895441i	$-0.353140\pi$
$397$	17.7403	0.890360	0.445180	+	0.895441i	$0.353140\pi$
$398$	−25.4768	−1.27704
$399$	−4.73805	−0.237199
$400$	4.66359	0.233179
$401$	18.1461	0.906172	0.453086	−	0.891467i	$-0.350323\pi$
$401$	18.1461	0.906172	0.453086	+	0.891467i	$0.350323\pi$
$402$	−8.48684	−0.423285
$403$	0	0
$404$	8.82958	0.439288
$405$	3.10863	0.154469
$406$	−1.05926	−0.0525700
$407$	12.3219	0.610776
$408$	−1.24698	−0.0617347
$409$	0.936649	0.0463143	0.0231572	−	0.999732i	$-0.492628\pi$
$409$	0.936649	0.0463143	0.0231572	+	0.999732i	$0.492628\pi$
$410$	8.44471	0.417054
$411$	20.8764	1.02976
$412$	1.89793	0.0935044
$413$	−3.41870	−0.168223
$414$	5.10817	0.251053
$415$	−13.6799	−0.671519
$416$	0	0
$417$	17.7255	0.868022
$418$	−7.36747	−0.360355
$419$	−10.0234	−0.489675	−0.244838	−	0.969564i	$-0.578735\pi$
$419$	−10.0234	−0.489675	−0.244838	+	0.969564i	$0.578735\pi$
$420$	3.10863	0.151686
$421$	−19.7171	−0.960951	−0.480475	−	0.877008i	$-0.659536\pi$
$421$	−19.7171	−0.960951	−0.480475	+	0.877008i	$0.659536\pi$
$422$	2.01914	0.0982902
$423$	5.06412	0.246226
$424$	−7.09392	−0.344511
$425$	−5.81540	−0.282088
$426$	−5.31350	−0.257440
$427$	13.2814	0.642731
$428$	−3.58727	−0.173397
$429$	0	0
$430$	−8.17967	−0.394459
$431$	−31.5252	−1.51852	−0.759259	−	0.650789i	$-0.774438\pi$
$431$	−31.5252	−1.51852	−0.759259	+	0.650789i	$0.774438\pi$
$432$	1.00000	0.0481125
$433$	19.6284	0.943281	0.471641	−	0.881791i	$-0.343662\pi$
$433$	19.6284	0.943281	0.471641	+	0.881791i	$0.343662\pi$
$434$	−2.46553	−0.118349
$435$	−3.29284	−0.157879
$436$	−20.3167	−0.972995
$437$	−24.2028	−1.15778
$438$	9.45056	0.451565
$439$	34.8525	1.66342	0.831708	−	0.555213i	$-0.187363\pi$
$439$	34.8525	1.66342	0.831708	+	0.555213i	$0.187363\pi$
$440$	4.83379	0.230442
$441$	1.00000	0.0476190
$442$	0	0
$443$	−9.65305	−0.458630	−0.229315	−	0.973352i	$-0.573649\pi$
$443$	−9.65305	−0.458630	−0.229315	+	0.973352i	$0.573649\pi$
$444$	7.92429	0.376070
$445$	17.9181	0.849401
$446$	−13.1491	−0.622630
$447$	0.829877	0.0392518
$448$	1.00000	0.0472456
$449$	15.2830	0.721249	0.360625	−	0.932711i	$-0.382564\pi$
$449$	15.2830	0.721249	0.360625	+	0.932711i	$0.382564\pi$
$450$	4.66359	0.219844
$451$	4.22410	0.198905
$452$	−6.85060	−0.322225
$453$	−3.39170	−0.159356
$454$	1.90722	0.0895105
$455$	0	0
$456$	−4.73805	−0.221880
$457$	16.0318	0.749937	0.374968	−	0.927038i	$-0.377654\pi$
$457$	16.0318	0.749937	0.374968	+	0.927038i	$0.377654\pi$
$458$	−1.32344	−0.0618403
$459$	−1.24698	−0.0582040
$460$	15.8794	0.740382
$461$	28.6119	1.33259	0.666294	−	0.745689i	$-0.267879\pi$
$461$	28.6119	1.33259	0.666294	+	0.745689i	$0.267879\pi$
$462$	1.55496	0.0723432
$463$	−35.8620	−1.66665	−0.833325	−	0.552783i	$-0.813566\pi$
$463$	−35.8620	−1.66665	−0.833325	+	0.552783i	$0.813566\pi$
$464$	−1.05926	−0.0491747
$465$	−7.66442	−0.355429
$466$	−23.7561	−1.10048
$467$	−14.9263	−0.690708	−0.345354	−	0.938473i	$-0.612241\pi$
$467$	−14.9263	−0.690708	−0.345354	+	0.938473i	$0.612241\pi$
$468$	0	0
$469$	−8.48684	−0.391886
$470$	15.7425	0.726147
$471$	−23.7381	−1.09379
$472$	−3.41870	−0.157359
$473$	−4.09153	−0.188129
$474$	11.1942	0.514169
$475$	−22.0963	−1.01385
$476$	−1.24698	−0.0571552
$477$	−7.09392	−0.324808
$478$	27.3308	1.25008
$479$	−14.4348	−0.659541	−0.329771	−	0.944061i	$-0.606971\pi$
$479$	−14.4348	−0.659541	−0.329771	+	0.944061i	$0.606971\pi$
$480$	3.10863	0.141889
$481$	0	0
$482$	2.68328	0.122220
$483$	5.10817	0.232430
$484$	−8.58211	−0.390096
$485$	33.5754	1.52458
$486$	1.00000	0.0453609
$487$	−24.8740	−1.12715	−0.563575	−	0.826065i	$-0.690575\pi$
$487$	−24.8740	−1.12715	−0.563575	+	0.826065i	$0.690575\pi$
$488$	13.2814	0.601220
$489$	−6.35482	−0.287375
$490$	3.10863	0.140434
$491$	−10.6142	−0.479014	−0.239507	−	0.970895i	$-0.576986\pi$
$491$	−10.6142	−0.479014	−0.239507	+	0.970895i	$0.576986\pi$
$492$	2.71654	0.122471
$493$	1.32087	0.0594890
$494$	0	0
$495$	4.83379	0.217263
$496$	−2.46553	−0.110705
$497$	−5.31350	−0.238343
$498$	−4.40061	−0.197196
$499$	0.950418	0.0425465	0.0212733	−	0.999774i	$-0.493228\pi$
$499$	0.950418	0.0425465	0.0212733	+	0.999774i	$0.493228\pi$
$500$	−1.04578	−0.0467685
$501$	−7.50114	−0.335126
$502$	−30.8962	−1.37897
$503$	34.9853	1.55992	0.779958	−	0.625832i	$-0.215240\pi$
$503$	34.9853	1.55992	0.779958	+	0.625832i	$0.215240\pi$
$504$	1.00000	0.0445435
$505$	27.4479	1.22142
$506$	7.94300	0.353109
$507$	0	0
$508$	8.46378	0.375520
$509$	26.0425	1.15431	0.577157	−	0.816634i	$-0.304162\pi$
$509$	26.0425	1.15431	0.577157	+	0.816634i	$0.304162\pi$
$510$	−3.87640	−0.171650
$511$	9.45056	0.418068
$512$	1.00000	0.0441942
$513$	−4.73805	−0.209190
$514$	27.6822	1.22101
$515$	5.89997	0.259984
$516$	−2.63128	−0.115836
$517$	7.87450	0.346320
$518$	7.92429	0.348173
$519$	−16.1881	−0.710578
$520$	0	0
$521$	39.0890	1.71252	0.856261	−	0.516544i	$-0.172782\pi$
$521$	39.0890	1.71252	0.856261	+	0.516544i	$0.172782\pi$
$522$	−1.05926	−0.0463624
$523$	−6.41000	−0.280290	−0.140145	−	0.990131i	$-0.544757\pi$
$523$	−6.41000	−0.280290	−0.140145	+	0.990131i	$0.544757\pi$
$524$	−5.07860	−0.221860
$525$	4.66359	0.203536
$526$	21.8601	0.953144
$527$	3.07446	0.133926
$528$	1.55496	0.0676709
$529$	3.09343	0.134497
$530$	−22.0524	−0.957894
$531$	−3.41870	−0.148359
$532$	−4.73805	−0.205421
$533$	0	0
$534$	5.76399	0.249432
$535$	−11.1515	−0.482122
$536$	−8.48684	−0.366576
$537$	1.95421	0.0843303
$538$	−17.0766	−0.736225
$539$	1.55496	0.0669768
$540$	3.10863	0.133774
$541$	20.7891	0.893792	0.446896	−	0.894586i	$-0.352529\pi$
$541$	20.7891	0.893792	0.446896	+	0.894586i	$0.352529\pi$
$542$	27.8718	1.19720
$543$	−1.81969	−0.0780902
$544$	−1.24698	−0.0534638
$545$	−63.1572	−2.70536
$546$	0	0
$547$	12.9402	0.553284	0.276642	−	0.960973i	$-0.410778\pi$
$547$	12.9402	0.553284	0.276642	+	0.960973i	$0.410778\pi$
$548$	20.8764	0.891795
$549$	13.2814	0.566836
$550$	7.25169	0.309213
$551$	5.01881	0.213808
$552$	5.10817	0.217418
$553$	11.1942	0.476028
$554$	−31.9253	−1.35637
$555$	24.6337	1.04564
$556$	17.7255	0.751729
$557$	−24.0823	−1.02040	−0.510200	−	0.860056i	$-0.670429\pi$
$557$	−24.0823	−1.02040	−0.510200	+	0.860056i	$0.670429\pi$
$558$	−2.46553	−0.104374
$559$	0	0
$560$	3.10863	0.131364
$561$	−1.93900	−0.0818647
$562$	−11.3692	−0.479580
$563$	−27.0146	−1.13853	−0.569266	−	0.822154i	$-0.692772\pi$
$563$	−27.0146	−1.13853	−0.569266	+	0.822154i	$0.692772\pi$
$564$	5.06412	0.213238
$565$	−21.2960	−0.895929
$566$	−16.6264	−0.698858
$567$	1.00000	0.0419961
$568$	−5.31350	−0.222949
$569$	−17.1952	−0.720859	−0.360429	−	0.932787i	$-0.617370\pi$
$569$	−17.1952	−0.720859	−0.360429	+	0.932787i	$0.617370\pi$
$570$	−14.7289	−0.616924
$571$	−21.5316	−0.901071	−0.450536	−	0.892758i	$-0.648767\pi$
$571$	−21.5316	−0.901071	−0.450536	+	0.892758i	$0.648767\pi$
$572$	0	0
$573$	−23.3210	−0.974247
$574$	2.71654	0.113386
$575$	23.8224	0.993464
$576$	1.00000	0.0416667
$577$	−30.2104	−1.25767	−0.628837	−	0.777537i	$-0.716469\pi$
$577$	−30.2104	−1.25767	−0.628837	+	0.777537i	$0.716469\pi$
$578$	−15.4450	−0.642429
$579$	7.99277	0.332168
$580$	−3.29284	−0.136728
$581$	−4.40061	−0.182568
$582$	10.8007	0.447703
$583$	−11.0307	−0.456847
$584$	9.45056	0.391067
$585$	0	0
$586$	−5.41358	−0.223633
$587$	−39.7362	−1.64009	−0.820045	−	0.572299i	$-0.806052\pi$
$587$	−39.7362	−1.64009	−0.820045	+	0.572299i	$0.806052\pi$
$588$	1.00000	0.0412393
$589$	11.6818	0.481340
$590$	−10.6275	−0.437527
$591$	−2.24858	−0.0924943
$592$	7.92429	0.325686
$593$	37.1150	1.52413	0.762066	−	0.647499i	$-0.224185\pi$
$593$	37.1150	1.52413	0.762066	+	0.647499i	$0.224185\pi$
$594$	1.55496	0.0638007
$595$	−3.87640	−0.158917
$596$	0.829877	0.0339931
$597$	−25.4768	−1.04270
$598$	0	0
$599$	10.5957	0.432928	0.216464	−	0.976291i	$-0.430548\pi$
$599$	10.5957	0.432928	0.216464	+	0.976291i	$0.430548\pi$
$600$	4.66359	0.190390
$601$	0.577212	0.0235450	0.0117725	−	0.999931i	$-0.496253\pi$
$601$	0.577212	0.0235450	0.0117725	+	0.999931i	$0.496253\pi$
$602$	−2.63128	−0.107243
$603$	−8.48684	−0.345611
$604$	−3.39170	−0.138006
$605$	−26.6786	−1.08464
$606$	8.82958	0.358677
$607$	3.75798	0.152532	0.0762659	−	0.997088i	$-0.475700\pi$
$607$	3.75798	0.152532	0.0762659	+	0.997088i	$0.475700\pi$
$608$	−4.73805	−0.192153
$609$	−1.05926	−0.0429232
$610$	41.2869	1.67166
$611$	0	0
$612$	−1.24698	−0.0504062
$613$	8.92496	0.360476	0.180238	−	0.983623i	$-0.442313\pi$
$613$	8.92496	0.360476	0.180238	+	0.983623i	$0.442313\pi$
$614$	6.53538	0.263746
$615$	8.44471	0.340524
$616$	1.55496	0.0626510
$617$	−8.90864	−0.358648	−0.179324	−	0.983790i	$-0.557391\pi$
$617$	−8.90864	−0.358648	−0.179324	+	0.983790i	$0.557391\pi$
$618$	1.89793	0.0763460
$619$	−8.63105	−0.346911	−0.173456	−	0.984842i	$-0.555493\pi$
$619$	−8.63105	−0.346911	−0.173456	+	0.984842i	$0.555493\pi$
$620$	−7.66442	−0.307810
$621$	5.10817	0.204984
$622$	−27.7921	−1.11436
$623$	5.76399	0.230930
$624$	0	0
$625$	−26.5689	−1.06276
$626$	−4.35209	−0.173945
$627$	−7.36747	−0.294229
$628$	−23.7381	−0.947251
$629$	−9.88142	−0.393998
$630$	3.10863	0.123851
$631$	−22.0935	−0.879528	−0.439764	−	0.898113i	$-0.644938\pi$
$631$	−22.0935	−0.879528	−0.439764	+	0.898113i	$0.644938\pi$
$632$	11.1942	0.445283
$633$	2.01914	0.0802536
$634$	12.5835	0.499756
$635$	26.3108	1.04411
$636$	−7.09392	−0.281292
$637$	0	0
$638$	−1.64710	−0.0652092
$639$	−5.31350	−0.210199
$640$	3.10863	0.122879
$641$	10.0871	0.398416	0.199208	−	0.979957i	$-0.436163\pi$
$641$	10.0871	0.398416	0.199208	+	0.979957i	$0.436163\pi$
$642$	−3.58727	−0.141578
$643$	8.84091	0.348652	0.174326	−	0.984688i	$-0.444225\pi$
$643$	8.84091	0.348652	0.174326	+	0.984688i	$0.444225\pi$
$644$	5.10817	0.201290
$645$	−8.17967	−0.322074
$646$	5.90825	0.232457
$647$	1.73856	0.0683497	0.0341748	−	0.999416i	$-0.489120\pi$
$647$	1.73856	0.0683497	0.0341748	+	0.999416i	$0.489120\pi$
$648$	1.00000	0.0392837
$649$	−5.31594	−0.208669
$650$	0	0
$651$	−2.46553	−0.0966316
$652$	−6.35482	−0.248874
$653$	−45.8052	−1.79250	−0.896248	−	0.443554i	$-0.853717\pi$
$653$	−45.8052	−1.79250	−0.896248	+	0.443554i	$0.853717\pi$
$654$	−20.3167	−0.794447
$655$	−15.7875	−0.616868
$656$	2.71654	0.106063
$657$	9.45056	0.368701
$658$	5.06412	0.197420
$659$	11.7599	0.458099	0.229050	−	0.973415i	$-0.426438\pi$
$659$	11.7599	0.458099	0.229050	+	0.973415i	$0.426438\pi$
$660$	4.83379	0.188155
$661$	−13.5257	−0.526089	−0.263044	−	0.964784i	$-0.584727\pi$
$661$	−13.5257	−0.526089	−0.263044	+	0.964784i	$0.584727\pi$
$662$	19.8866	0.772915
$663$	0	0
$664$	−4.40061	−0.170777
$665$	−14.7289	−0.571161
$666$	7.92429	0.307060
$667$	−5.41086	−0.209509
$668$	−7.50114	−0.290228
$669$	−13.1491	−0.508375
$670$	−26.3825	−1.01924
$671$	20.6520	0.797262
$672$	1.00000	0.0385758
$673$	12.0762	0.465505	0.232752	−	0.972536i	$-0.425227\pi$
$673$	12.0762	0.465505	0.232752	+	0.972536i	$0.425227\pi$
$674$	0.500733	0.0192875
$675$	4.66359	0.179502
$676$	0	0
$677$	4.22192	0.162262	0.0811308	−	0.996703i	$-0.474147\pi$
$677$	4.22192	0.162262	0.0811308	+	0.996703i	$0.474147\pi$
$678$	−6.85060	−0.263096
$679$	10.8007	0.414492
$680$	−3.87640	−0.148653
$681$	1.90722	0.0730850
$682$	−3.83379	−0.146803
$683$	46.8330	1.79201	0.896007	−	0.444039i	$-0.146455\pi$
$683$	46.8330	1.79201	0.896007	+	0.444039i	$0.146455\pi$
$684$	−4.73805	−0.181164
$685$	64.8970	2.47959
$686$	1.00000	0.0381802
$687$	−1.32344	−0.0504924
$688$	−2.63128	−0.100316
$689$	0	0
$690$	15.8794	0.604519
$691$	−19.2883	−0.733762	−0.366881	−	0.930268i	$-0.619574\pi$
$691$	−19.2883	−0.733762	−0.366881	+	0.930268i	$0.619574\pi$
$692$	−16.1881	−0.615378
$693$	1.55496	0.0590680
$694$	−24.7464	−0.939361
$695$	55.1021	2.09014
$696$	−1.05926	−0.0401510
$697$	−3.38747	−0.128309
$698$	−4.30578	−0.162976
$699$	−23.7561	−0.898539
$700$	4.66359	0.176267
$701$	−16.9306	−0.639459	−0.319729	−	0.947509i	$-0.603592\pi$
$701$	−16.9306	−0.639459	−0.319729	+	0.947509i	$0.603592\pi$
$702$	0	0
$703$	−37.5457	−1.41606
$704$	1.55496	0.0586047
$705$	15.7425	0.592897
$706$	−4.18501	−0.157505
$707$	8.82958	0.332070
$708$	−3.41870	−0.128483
$709$	−7.93895	−0.298153	−0.149077	−	0.988826i	$-0.547630\pi$
$709$	−7.93895	−0.298153	−0.149077	+	0.988826i	$0.547630\pi$
$710$	−16.5177	−0.619898
$711$	11.1942	0.419817
$712$	5.76399	0.216015
$713$	−12.5943	−0.471662
$714$	−1.24698	−0.0466670
$715$	0	0
$716$	1.95421	0.0730322
$717$	27.3308	1.02069
$718$	−6.33135	−0.236284
$719$	31.5702	1.17737	0.588684	−	0.808363i	$-0.299646\pi$
$719$	31.5702	1.17737	0.588684	+	0.808363i	$0.299646\pi$
$720$	3.10863	0.115852
$721$	1.89793	0.0706827
$722$	3.44914	0.128364
$723$	2.68328	0.0997924
$724$	−1.81969	−0.0676281
$725$	−4.93993	−0.183465
$726$	−8.58211	−0.318512
$727$	10.8589	0.402733	0.201367	−	0.979516i	$-0.435462\pi$
$727$	10.8589	0.402733	0.201367	+	0.979516i	$0.435462\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	29.3783	1.08734
$731$	3.28115	0.121358
$732$	13.2814	0.490894
$733$	2.22682	0.0822495	0.0411247	−	0.999154i	$-0.486906\pi$
$733$	2.22682	0.0822495	0.0411247	+	0.999154i	$0.486906\pi$
$734$	19.8935	0.734282
$735$	3.10863	0.114664
$736$	5.10817	0.188290
$737$	−13.1967	−0.486106
$738$	2.71654	0.0999971
$739$	39.5399	1.45450	0.727249	−	0.686374i	$-0.240799\pi$
$739$	39.5399	1.45450	0.727249	+	0.686374i	$0.240799\pi$
$740$	24.6337	0.905552
$741$	0	0
$742$	−7.09392	−0.260426
$743$	−35.0085	−1.28434	−0.642169	−	0.766563i	$-0.721965\pi$
$743$	−35.0085	−1.28434	−0.642169	+	0.766563i	$0.721965\pi$
$744$	−2.46553	−0.0903906
$745$	2.57978	0.0945159
$746$	−35.9969	−1.31794
$747$	−4.40061	−0.161010
$748$	−1.93900	−0.0708969
$749$	−3.58727	−0.131076
$750$	−1.04578	−0.0381863
$751$	3.08816	0.112689	0.0563443	−	0.998411i	$-0.482056\pi$
$751$	3.08816	0.112689	0.0563443	+	0.998411i	$0.482056\pi$
$752$	5.06412	0.184670
$753$	−30.8962	−1.12592
$754$	0	0
$755$	−10.5435	−0.383719
$756$	1.00000	0.0363696
$757$	−31.1069	−1.13060	−0.565300	−	0.824885i	$-0.691240\pi$
$757$	−31.1069	−1.13060	−0.565300	+	0.824885i	$0.691240\pi$
$758$	29.5252	1.07240
$759$	7.94300	0.288312
$760$	−14.7289	−0.534272
$761$	34.3881	1.24657	0.623284	−	0.781996i	$-0.285798\pi$
$761$	34.3881	1.24657	0.623284	+	0.781996i	$0.285798\pi$
$762$	8.46378	0.306611
$763$	−20.3167	−0.735515
$764$	−23.3210	−0.843723
$765$	−3.87640	−0.140152
$766$	−0.770083	−0.0278242
$767$	0	0
$768$	1.00000	0.0360844
$769$	28.7352	1.03622	0.518109	−	0.855314i	$-0.326636\pi$
$769$	28.7352	1.03622	0.518109	+	0.855314i	$0.326636\pi$
$770$	4.83379	0.174198
$771$	27.6822	0.996951
$772$	7.99277	0.287666
$773$	−43.0766	−1.54936	−0.774679	−	0.632354i	$-0.782089\pi$
$773$	−43.0766	−1.54936	−0.774679	+	0.632354i	$0.782089\pi$
$774$	−2.63128	−0.0945793
$775$	−11.4982	−0.413028
$776$	10.8007	0.387722
$777$	7.92429	0.284282
$778$	18.6621	0.669070
$779$	−12.8711	−0.461155
$780$	0	0
$781$	−8.26226	−0.295647
$782$	−6.36979	−0.227783
$783$	−1.05926	−0.0378547
$784$	1.00000	0.0357143
$785$	−73.7929	−2.63378
$786$	−5.07860	−0.181148
$787$	−12.5432	−0.447117	−0.223558	−	0.974691i	$-0.571767\pi$
$787$	−12.5432	−0.447117	−0.223558	+	0.974691i	$0.571767\pi$
$788$	−2.24858	−0.0801024
$789$	21.8601	0.778239
$790$	34.7988	1.23808
$791$	−6.85060	−0.243579
$792$	1.55496	0.0552530
$793$	0	0
$794$	17.7403	0.629580
$795$	−22.0524	−0.782117
$796$	−25.4768	−0.903001
$797$	35.9473	1.27332	0.636659	−	0.771146i	$-0.280316\pi$
$797$	35.9473	1.27332	0.636659	+	0.771146i	$0.280316\pi$
$798$	−4.73805	−0.167725
$799$	−6.31486	−0.223404
$800$	4.66359	0.164883
$801$	5.76399	0.203661
$802$	18.1461	0.640761
$803$	14.6952	0.518583
$804$	−8.48684	−0.299308
$805$	15.8794	0.559676
$806$	0	0
$807$	−17.0766	−0.601125
$808$	8.82958	0.310623
$809$	38.3283	1.34755	0.673776	−	0.738936i	$-0.264671\pi$
$809$	38.3283	1.34755	0.673776	+	0.738936i	$0.264671\pi$
$810$	3.10863	0.109226
$811$	−55.4449	−1.94693	−0.973466	−	0.228831i	$-0.926510\pi$
$811$	−55.4449	−1.94693	−0.973466	+	0.228831i	$0.926510\pi$
$812$	−1.05926	−0.0371726
$813$	27.8718	0.977508
$814$	12.3219	0.431884
$815$	−19.7548	−0.691980
$816$	−1.24698	−0.0436530
$817$	12.4671	0.436170
$818$	0.936649	0.0327492
$819$	0	0
$820$	8.44471	0.294902
$821$	30.7208	1.07216	0.536082	−	0.844166i	$-0.319904\pi$
$821$	30.7208	1.07216	0.536082	+	0.844166i	$0.319904\pi$
$822$	20.8764	0.728148
$823$	−29.4586	−1.02686	−0.513431	−	0.858131i	$-0.671626\pi$
$823$	−29.4586	−1.02686	−0.513431	+	0.858131i	$0.671626\pi$
$824$	1.89793	0.0661176
$825$	7.25169	0.252471
$826$	−3.41870	−0.118952
$827$	39.5955	1.37687	0.688435	−	0.725298i	$-0.258298\pi$
$827$	39.5955	1.37687	0.688435	+	0.725298i	$0.258298\pi$
$828$	5.10817	0.177521
$829$	52.6258	1.82777	0.913884	−	0.405975i	$-0.133068\pi$
$829$	52.6258	1.82777	0.913884	+	0.405975i	$0.133068\pi$
$830$	−13.6799	−0.474836
$831$	−31.9253	−1.10748
$832$	0	0
$833$	−1.24698	−0.0432053
$834$	17.7255	0.613784
$835$	−23.3183	−0.806962
$836$	−7.36747	−0.254809
$837$	−2.46553	−0.0852211
$838$	−10.0234	−0.346253
$839$	−31.0141	−1.07073	−0.535363	−	0.844622i	$-0.679825\pi$
$839$	−31.0141	−1.07073	−0.535363	+	0.844622i	$0.679825\pi$
$840$	3.10863	0.107258
$841$	−27.8780	−0.961310
$842$	−19.7171	−0.679495
$843$	−11.3692	−0.391576
$844$	2.01914	0.0695016
$845$	0	0
$846$	5.06412	0.174108
$847$	−8.58211	−0.294885
$848$	−7.09392	−0.243606
$849$	−16.6264	−0.570615
$850$	−5.81540	−0.199467
$851$	40.4786	1.38759
$852$	−5.31350	−0.182037
$853$	55.8464	1.91214	0.956072	−	0.293133i	$-0.0946979\pi$
$853$	55.8464	1.91214	0.956072	+	0.293133i	$0.0946979\pi$
$854$	13.2814	0.454480
$855$	−14.7289	−0.503716
$856$	−3.58727	−0.122610
$857$	26.7950	0.915299	0.457650	−	0.889133i	$-0.348691\pi$
$857$	26.7950	0.915299	0.457650	+	0.889133i	$0.348691\pi$
$858$	0	0
$859$	13.5325	0.461724	0.230862	−	0.972986i	$-0.425845\pi$
$859$	13.5325	0.461724	0.230862	+	0.972986i	$0.425845\pi$
$860$	−8.17967	−0.278924
$861$	2.71654	0.0925793
$862$	−31.5252	−1.07375
$863$	34.8946	1.18783	0.593914	−	0.804529i	$-0.297582\pi$
$863$	34.8946	1.18783	0.593914	+	0.804529i	$0.297582\pi$
$864$	1.00000	0.0340207
$865$	−50.3228	−1.71103
$866$	19.6284	0.667000
$867$	−15.4450	−0.524541
$868$	−2.46553	−0.0836855
$869$	17.4066	0.590478
$870$	−3.29284	−0.111638
$871$	0	0
$872$	−20.3167	−0.688011
$873$	10.8007	0.365548
$874$	−24.2028	−0.818672
$875$	−1.04578	−0.0353537
$876$	9.45056	0.319305
$877$	51.7834	1.74860	0.874300	−	0.485386i	$-0.161321\pi$
$877$	51.7834	1.74860	0.874300	+	0.485386i	$0.161321\pi$
$878$	34.8525	1.17621
$879$	−5.41358	−0.182596
$880$	4.83379	0.162947
$881$	−2.60278	−0.0876900	−0.0438450	−	0.999038i	$-0.513961\pi$
$881$	−2.60278	−0.0876900	−0.0438450	+	0.999038i	$0.513961\pi$
$882$	1.00000	0.0336718
$883$	−38.5127	−1.29605	−0.648027	−	0.761617i	$-0.724406\pi$
$883$	−38.5127	−1.29605	−0.648027	+	0.761617i	$0.724406\pi$
$884$	0	0
$885$	−10.6275	−0.357239
$886$	−9.65305	−0.324300
$887$	15.6703	0.526156	0.263078	−	0.964775i	$-0.415262\pi$
$887$	15.6703	0.526156	0.263078	+	0.964775i	$0.415262\pi$
$888$	7.92429	0.265922
$889$	8.46378	0.283866
$890$	17.9181	0.600617
$891$	1.55496	0.0520931
$892$	−13.1491	−0.440266
$893$	−23.9941	−0.802931
$894$	0.829877	0.0277552
$895$	6.07491	0.203062
$896$	1.00000	0.0334077
$897$	0	0
$898$	15.2830	0.510000
$899$	2.61162	0.0871025
$900$	4.66359	0.155453
$901$	8.84597	0.294702
$902$	4.22410	0.140647
$903$	−2.63128	−0.0875634
$904$	−6.85060	−0.227848
$905$	−5.65673	−0.188036
$906$	−3.39170	−0.112682
$907$	−30.6745	−1.01853	−0.509265	−	0.860610i	$-0.670083\pi$
$907$	−30.6745	−1.01853	−0.509265	+	0.860610i	$0.670083\pi$
$908$	1.90722	0.0632935
$909$	8.82958	0.292859
$910$	0	0
$911$	32.8588	1.08866	0.544331	−	0.838870i	$-0.316784\pi$
$911$	32.8588	1.08866	0.544331	+	0.838870i	$0.316784\pi$
$912$	−4.73805	−0.156893
$913$	−6.84277	−0.226463
$914$	16.0318	0.530285
$915$	41.2869	1.36490
$916$	−1.32344	−0.0437277
$917$	−5.07860	−0.167710
$918$	−1.24698	−0.0411565
$919$	−10.6383	−0.350925	−0.175462	−	0.984486i	$-0.556142\pi$
$919$	−10.6383	−0.350925	−0.175462	+	0.984486i	$0.556142\pi$
$920$	15.8794	0.523529
$921$	6.53538	0.215348
$922$	28.6119	0.942282
$923$	0	0
$924$	1.55496	0.0511544
$925$	36.9556	1.21509
$926$	−35.8620	−1.17850
$927$	1.89793	0.0623363
$928$	−1.05926	−0.0347718
$929$	3.54100	0.116176	0.0580882	−	0.998311i	$-0.481500\pi$
$929$	3.54100	0.116176	0.0580882	+	0.998311i	$0.481500\pi$
$930$	−7.66442	−0.251326
$931$	−4.73805	−0.155283
$932$	−23.7561	−0.778157
$933$	−27.7921	−0.909873
$934$	−14.9263	−0.488404
$935$	−6.02764	−0.197125
$936$	0	0
$937$	−15.5489	−0.507959	−0.253980	−	0.967210i	$-0.581740\pi$
$937$	−15.5489	−0.507959	−0.253980	+	0.967210i	$0.581740\pi$
$938$	−8.48684	−0.277105
$939$	−4.35209	−0.142025
$940$	15.7425	0.513464
$941$	34.3011	1.11818	0.559092	−	0.829106i	$-0.311150\pi$
$941$	34.3011	1.11818	0.559092	+	0.829106i	$0.311150\pi$
$942$	−23.7381	−0.773427
$943$	13.8765	0.451882
$944$	−3.41870	−0.111269
$945$	3.10863	0.101124
$946$	−4.09153	−0.133027
$947$	−45.7712	−1.48737	−0.743683	−	0.668533i	$-0.766923\pi$
$947$	−45.7712	−1.48737	−0.743683	+	0.668533i	$0.766923\pi$
$948$	11.1942	0.363572
$949$	0	0
$950$	−22.0963	−0.716900
$951$	12.5835	0.408049
$952$	−1.24698	−0.0404148
$953$	38.1938	1.23722	0.618609	−	0.785699i	$-0.287697\pi$
$953$	38.1938	1.23722	0.618609	+	0.785699i	$0.287697\pi$
$954$	−7.09392	−0.229674
$955$	−72.4963	−2.34592
$956$	27.3308	0.883943
$957$	−1.64710	−0.0532431
$958$	−14.4348	−0.466366
$959$	20.8764	0.674134
$960$	3.10863	0.100331
$961$	−24.9212	−0.803909
$962$	0	0
$963$	−3.58727	−0.115598
$964$	2.68328	0.0864228
$965$	24.8466	0.799839
$966$	5.10817	0.164353
$967$	−1.46535	−0.0471223	−0.0235612	−	0.999722i	$-0.507500\pi$
$967$	−1.46535	−0.0471223	−0.0235612	+	0.999722i	$0.507500\pi$
$968$	−8.58211	−0.275839
$969$	5.90825	0.189800
$970$	33.5754	1.07804
$971$	−15.1475	−0.486106	−0.243053	−	0.970013i	$-0.578149\pi$
$971$	−15.1475	−0.486106	−0.243053	+	0.970013i	$0.578149\pi$
$972$	1.00000	0.0320750
$973$	17.7255	0.568254
$974$	−24.8740	−0.797016
$975$	0	0
$976$	13.2814	0.425127
$977$	30.6974	0.982098	0.491049	−	0.871132i	$-0.336614\pi$
$977$	30.6974	0.982098	0.491049	+	0.871132i	$0.336614\pi$
$978$	−6.35482	−0.203205
$979$	8.96277	0.286451
$980$	3.10863	0.0993016
$981$	−20.3167	−0.648663
$982$	−10.6142	−0.338714
$983$	13.4997	0.430574	0.215287	−	0.976551i	$-0.430931\pi$
$983$	13.4997	0.430574	0.215287	+	0.976551i	$0.430931\pi$
$984$	2.71654	0.0866000
$985$	−6.99001	−0.222720
$986$	1.32087	0.0420651
$987$	5.06412	0.161193
$988$	0	0
$989$	−13.4410	−0.427400
$990$	4.83379	0.153628
$991$	−39.7612	−1.26306	−0.631529	−	0.775352i	$-0.717572\pi$
$991$	−39.7612	−1.26306	−0.631529	+	0.775352i	$0.717572\pi$
$992$	−2.46553	−0.0782806
$993$	19.8866	0.631082
$994$	−5.31350	−0.168534
$995$	−79.1980	−2.51075
$996$	−4.40061	−0.139439
$997$	5.54069	0.175475	0.0877377	−	0.996144i	$-0.472036\pi$
$997$	5.54069	0.175475	0.0877377	+	0.996144i	$0.472036\pi$
$998$	0.950418	0.0300849
$999$	7.92429	0.250713

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cr.1.2	✓	6	13.12	even	2
7098.2.a.ct.1.5	yes	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.10863 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.10863 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.10863 q^{10} +1.55496 q^{11} +1.00000 q^{12} +1.00000 q^{14} +3.10863 q^{15} +1.00000 q^{16} -1.24698 q^{17} +1.00000 q^{18} -4.73805 q^{19} +3.10863 q^{20} +1.00000 q^{21} +1.55496 q^{22} +5.10817 q^{23} +1.00000 q^{24} +4.66359 q^{25} +1.00000 q^{27} +1.00000 q^{28} -1.05926 q^{29} +3.10863 q^{30} -2.46553 q^{31} +1.00000 q^{32} +1.55496 q^{33} -1.24698 q^{34} +3.10863 q^{35} +1.00000 q^{36} +7.92429 q^{37} -4.73805 q^{38} +3.10863 q^{40} +2.71654 q^{41} +1.00000 q^{42} -2.63128 q^{43} +1.55496 q^{44} +3.10863 q^{45} +5.10817 q^{46} +5.06412 q^{47} +1.00000 q^{48} +1.00000 q^{49} +4.66359 q^{50} -1.24698 q^{51} -7.09392 q^{53} +1.00000 q^{54} +4.83379 q^{55} +1.00000 q^{56} -4.73805 q^{57} -1.05926 q^{58} -3.41870 q^{59} +3.10863 q^{60} +13.2814 q^{61} -2.46553 q^{62} +1.00000 q^{63} +1.00000 q^{64} +1.55496 q^{66} -8.48684 q^{67} -1.24698 q^{68} +5.10817 q^{69} +3.10863 q^{70} -5.31350 q^{71} +1.00000 q^{72} +9.45056 q^{73} +7.92429 q^{74} +4.66359 q^{75} -4.73805 q^{76} +1.55496 q^{77} +11.1942 q^{79} +3.10863 q^{80} +1.00000 q^{81} +2.71654 q^{82} -4.40061 q^{83} +1.00000 q^{84} -3.87640 q^{85} -2.63128 q^{86} -1.05926 q^{87} +1.55496 q^{88} +5.76399 q^{89} +3.10863 q^{90} +5.10817 q^{92} -2.46553 q^{93} +5.06412 q^{94} -14.7289 q^{95} +1.00000 q^{96} +10.8007 q^{97} +1.00000 q^{98} +1.55496 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} + 3 q^{10} + 10 q^{11} + 6 q^{12} + 6 q^{14} + 3 q^{15} + 6 q^{16} + 2 q^{17} + 6 q^{18} + 2 q^{19} + 3 q^{20} + 6 q^{21} + 10 q^{22} + 4 q^{23} + 6 q^{24} + 13 q^{25} + 6 q^{27} + 6 q^{28} + 2 q^{29} + 3 q^{30} + 9 q^{31} + 6 q^{32} + 10 q^{33} + 2 q^{34} + 3 q^{35} + 6 q^{36} + 7 q^{37} + 2 q^{38} + 3 q^{40} + 11 q^{41} + 6 q^{42} - 5 q^{43} + 10 q^{44} + 3 q^{45} + 4 q^{46} + 5 q^{47} + 6 q^{48} + 6 q^{49} + 13 q^{50} + 2 q^{51} - 6 q^{53} + 6 q^{54} + 5 q^{55} + 6 q^{56} + 2 q^{57} + 2 q^{58} + 28 q^{59} + 3 q^{60} + 23 q^{61} + 9 q^{62} + 6 q^{63} + 6 q^{64} + 10 q^{66} - 10 q^{67} + 2 q^{68} + 4 q^{69} + 3 q^{70} + 21 q^{71} + 6 q^{72} - 7 q^{73} + 7 q^{74} + 13 q^{75} + 2 q^{76} + 10 q^{77} - 14 q^{79} + 3 q^{80} + 6 q^{81} + 11 q^{82} + 17 q^{83} + 6 q^{84} + q^{85} - 5 q^{86} + 2 q^{87} + 10 q^{88} + 17 q^{89} + 3 q^{90} + 4 q^{92} + 9 q^{93} + 5 q^{94} - 22 q^{95} + 6 q^{96} + 6 q^{98} + 10 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 + 3 * q^10 + 10 * q^11 + 6 * q^12 + 6 * q^14 + 3 * q^15 + 6 * q^16 + 2 * q^17 + 6 * q^18 + 2 * q^19 + 3 * q^20 + 6 * q^21 + 10 * q^22 + 4 * q^23 + 6 * q^24 + 13 * q^25 + 6 * q^27 + 6 * q^28 + 2 * q^29 + 3 * q^30 + 9 * q^31 + 6 * q^32 + 10 * q^33 + 2 * q^34 + 3 * q^35 + 6 * q^36 + 7 * q^37 + 2 * q^38 + 3 * q^40 + 11 * q^41 + 6 * q^42 - 5 * q^43 + 10 * q^44 + 3 * q^45 + 4 * q^46 + 5 * q^47 + 6 * q^48 + 6 * q^49 + 13 * q^50 + 2 * q^51 - 6 * q^53 + 6 * q^54 + 5 * q^55 + 6 * q^56 + 2 * q^57 + 2 * q^58 + 28 * q^59 + 3 * q^60 + 23 * q^61 + 9 * q^62 + 6 * q^63 + 6 * q^64 + 10 * q^66 - 10 * q^67 + 2 * q^68 + 4 * q^69 + 3 * q^70 + 21 * q^71 + 6 * q^72 - 7 * q^73 + 7 * q^74 + 13 * q^75 + 2 * q^76 + 10 * q^77 - 14 * q^79 + 3 * q^80 + 6 * q^81 + 11 * q^82 + 17 * q^83 + 6 * q^84 + q^85 - 5 * q^86 + 2 * q^87 + 10 * q^88 + 17 * q^89 + 3 * q^90 + 4 * q^92 + 9 * q^93 + 5 * q^94 - 22 * q^95 + 6 * q^96 + 6 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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