LMFDB - Embedded newform 7098.2.a.by.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7098, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$56.6778153547$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.73205 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.73205 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.73205 q^{10} +5.19615 q^{11} +1.00000 q^{12} +1.00000 q^{14} -2.73205 q^{15} +1.00000 q^{16} -5.73205 q^{17} +1.00000 q^{18} -6.46410 q^{19} -2.73205 q^{20} +1.00000 q^{21} +5.19615 q^{22} -0.535898 q^{23} +1.00000 q^{24} +2.46410 q^{25} +1.00000 q^{27} +1.00000 q^{28} -10.4641 q^{29} -2.73205 q^{30} -6.73205 q^{31} +1.00000 q^{32} +5.19615 q^{33} -5.73205 q^{34} -2.73205 q^{35} +1.00000 q^{36} -3.26795 q^{37} -6.46410 q^{38} -2.73205 q^{40} -1.53590 q^{41} +1.00000 q^{42} -5.26795 q^{43} +5.19615 q^{44} -2.73205 q^{45} -0.535898 q^{46} +9.92820 q^{47} +1.00000 q^{48} +1.00000 q^{49} +2.46410 q^{50} -5.73205 q^{51} +3.92820 q^{53} +1.00000 q^{54} -14.1962 q^{55} +1.00000 q^{56} -6.46410 q^{57} -10.4641 q^{58} -4.92820 q^{59} -2.73205 q^{60} +0.267949 q^{61} -6.73205 q^{62} +1.00000 q^{63} +1.00000 q^{64} +5.19615 q^{66} +10.0000 q^{67} -5.73205 q^{68} -0.535898 q^{69} -2.73205 q^{70} -10.7321 q^{71} +1.00000 q^{72} -5.46410 q^{73} -3.26795 q^{74} +2.46410 q^{75} -6.46410 q^{76} +5.19615 q^{77} +9.00000 q^{79} -2.73205 q^{80} +1.00000 q^{81} -1.53590 q^{82} +12.7321 q^{83} +1.00000 q^{84} +15.6603 q^{85} -5.26795 q^{86} -10.4641 q^{87} +5.19615 q^{88} -10.8564 q^{89} -2.73205 q^{90} -0.535898 q^{92} -6.73205 q^{93} +9.92820 q^{94} +17.6603 q^{95} +1.00000 q^{96} +3.80385 q^{97} +1.00000 q^{98} +5.19615 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{12} + 2 q^{14} - 2 q^{15} + 2 q^{16} - 8 q^{17} + 2 q^{18} - 6 q^{19} - 2 q^{20} + 2 q^{21} - 8 q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{27} + 2 q^{28} - 14 q^{29} - 2 q^{30} - 10 q^{31} + 2 q^{32} - 8 q^{34} - 2 q^{35} + 2 q^{36} - 10 q^{37} - 6 q^{38} - 2 q^{40} - 10 q^{41} + 2 q^{42} - 14 q^{43} - 2 q^{45} - 8 q^{46} + 6 q^{47} + 2 q^{48} + 2 q^{49} - 2 q^{50} - 8 q^{51} - 6 q^{53} + 2 q^{54} - 18 q^{55} + 2 q^{56} - 6 q^{57} - 14 q^{58} + 4 q^{59} - 2 q^{60} + 4 q^{61} - 10 q^{62} + 2 q^{63} + 2 q^{64} + 20 q^{67} - 8 q^{68} - 8 q^{69} - 2 q^{70} - 18 q^{71} + 2 q^{72} - 4 q^{73} - 10 q^{74} - 2 q^{75} - 6 q^{76} + 18 q^{79} - 2 q^{80} + 2 q^{81} - 10 q^{82} + 22 q^{83} + 2 q^{84} + 14 q^{85} - 14 q^{86} - 14 q^{87} + 6 q^{89} - 2 q^{90} - 8 q^{92} - 10 q^{93} + 6 q^{94} + 18 q^{95} + 2 q^{96} + 18 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^12 + 2 * q^14 - 2 * q^15 + 2 * q^16 - 8 * q^17 + 2 * q^18 - 6 * q^19 - 2 * q^20 + 2 * q^21 - 8 * q^23 + 2 * q^24 - 2 * q^25 + 2 * q^27 + 2 * q^28 - 14 * q^29 - 2 * q^30 - 10 * q^31 + 2 * q^32 - 8 * q^34 - 2 * q^35 + 2 * q^36 - 10 * q^37 - 6 * q^38 - 2 * q^40 - 10 * q^41 + 2 * q^42 - 14 * q^43 - 2 * q^45 - 8 * q^46 + 6 * q^47 + 2 * q^48 + 2 * q^49 - 2 * q^50 - 8 * q^51 - 6 * q^53 + 2 * q^54 - 18 * q^55 + 2 * q^56 - 6 * q^57 - 14 * q^58 + 4 * q^59 - 2 * q^60 + 4 * q^61 - 10 * q^62 + 2 * q^63 + 2 * q^64 + 20 * q^67 - 8 * q^68 - 8 * q^69 - 2 * q^70 - 18 * q^71 + 2 * q^72 - 4 * q^73 - 10 * q^74 - 2 * q^75 - 6 * q^76 + 18 * q^79 - 2 * q^80 + 2 * q^81 - 10 * q^82 + 22 * q^83 + 2 * q^84 + 14 * q^85 - 14 * q^86 - 14 * q^87 + 6 * q^89 - 2 * q^90 - 8 * q^92 - 10 * q^93 + 6 * q^94 + 18 * q^95 + 2 * q^96 + 18 * q^97 + 2 * q^98

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
$5$	−2.73205	−1.22181	−0.610905	−	0.791704i	$-0.709194\pi$
$5$	−2.73205	−1.22181	−0.610905	+	0.791704i	$0.709194\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.73205	−0.863950
$11$	5.19615	1.56670	0.783349	−	0.621582i	$-0.213510\pi$
$11$	5.19615	1.56670	0.783349	+	0.621582i	$0.213510\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	−2.73205	−0.705412
$16$	1.00000	0.250000
$17$	−5.73205	−1.39023	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	−5.73205	−1.39023	−0.695113	+	0.718900i	$0.744646\pi$
$18$	1.00000	0.235702
$19$	−6.46410	−1.48297	−0.741483	−	0.670971i	$-0.765877\pi$
$19$	−6.46410	−1.48297	−0.741483	+	0.670971i	$0.765877\pi$
$20$	−2.73205	−0.610905
$21$	1.00000	0.218218
$22$	5.19615	1.10782
$23$	−0.535898	−0.111743	−0.0558713	−	0.998438i	$-0.517794\pi$
$23$	−0.535898	−0.111743	−0.0558713	+	0.998438i	$0.517794\pi$
$24$	1.00000	0.204124
$25$	2.46410	0.492820
$26$	0	0
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	−10.4641	−1.94313	−0.971567	−	0.236763i	$-0.923914\pi$
$29$	−10.4641	−1.94313	−0.971567	+	0.236763i	$0.923914\pi$
$30$	−2.73205	−0.498802
$31$	−6.73205	−1.20911	−0.604556	−	0.796563i	$-0.706649\pi$
$31$	−6.73205	−1.20911	−0.604556	+	0.796563i	$0.706649\pi$
$32$	1.00000	0.176777
$33$	5.19615	0.904534
$34$	−5.73205	−0.983039
$35$	−2.73205	−0.461801
$36$	1.00000	0.166667
$37$	−3.26795	−0.537248	−0.268624	−	0.963245i	$-0.586569\pi$
$37$	−3.26795	−0.537248	−0.268624	+	0.963245i	$0.586569\pi$
$38$	−6.46410	−1.04862
$39$	0	0
$40$	−2.73205	−0.431975
$41$	−1.53590	−0.239867	−0.119934	−	0.992782i	$-0.538268\pi$
$41$	−1.53590	−0.239867	−0.119934	+	0.992782i	$0.538268\pi$
$42$	1.00000	0.154303
$43$	−5.26795	−0.803355	−0.401677	−	0.915781i	$-0.631573\pi$
$43$	−5.26795	−0.803355	−0.401677	+	0.915781i	$0.631573\pi$
$44$	5.19615	0.783349
$45$	−2.73205	−0.407270
$46$	−0.535898	−0.0790139
$47$	9.92820	1.44818	0.724089	−	0.689707i	$-0.242261\pi$
$47$	9.92820	1.44818	0.724089	+	0.689707i	$0.242261\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	2.46410	0.348477
$51$	−5.73205	−0.802648
$52$	0	0
$53$	3.92820	0.539580	0.269790	−	0.962919i	$-0.413046\pi$
$53$	3.92820	0.539580	0.269790	+	0.962919i	$0.413046\pi$
$54$	1.00000	0.136083
$55$	−14.1962	−1.91421
$56$	1.00000	0.133631
$57$	−6.46410	−0.856191
$58$	−10.4641	−1.37400
$59$	−4.92820	−0.641597	−0.320799	−	0.947147i	$-0.603951\pi$
$59$	−4.92820	−0.641597	−0.320799	+	0.947147i	$0.603951\pi$
$60$	−2.73205	−0.352706
$61$	0.267949	0.0343074	0.0171537	−	0.999853i	$-0.494540\pi$
$61$	0.267949	0.0343074	0.0171537	+	0.999853i	$0.494540\pi$
$62$	−6.73205	−0.854971
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	5.19615	0.639602
$67$	10.0000	1.22169	0.610847	−	0.791748i	$-0.290829\pi$
$67$	10.0000	1.22169	0.610847	+	0.791748i	$0.290829\pi$
$68$	−5.73205	−0.695113
$69$	−0.535898	−0.0645146
$70$	−2.73205	−0.326543
$71$	−10.7321	−1.27366	−0.636830	−	0.771004i	$-0.719755\pi$
$71$	−10.7321	−1.27366	−0.636830	+	0.771004i	$0.719755\pi$
$72$	1.00000	0.117851
$73$	−5.46410	−0.639525	−0.319762	−	0.947498i	$-0.603603\pi$
$73$	−5.46410	−0.639525	−0.319762	+	0.947498i	$0.603603\pi$
$74$	−3.26795	−0.379891
$75$	2.46410	0.284530
$76$	−6.46410	−0.741483
$77$	5.19615	0.592157
$78$	0	0
$79$	9.00000	1.01258	0.506290	−	0.862364i	$-0.331017\pi$
$79$	9.00000	1.01258	0.506290	+	0.862364i	$0.331017\pi$
$80$	−2.73205	−0.305453
$81$	1.00000	0.111111
$82$	−1.53590	−0.169612
$83$	12.7321	1.39752	0.698762	−	0.715354i	$-0.253735\pi$
$83$	12.7321	1.39752	0.698762	+	0.715354i	$0.253735\pi$
$84$	1.00000	0.109109
$85$	15.6603	1.69859
$86$	−5.26795	−0.568058
$87$	−10.4641	−1.12187
$88$	5.19615	0.553912
$89$	−10.8564	−1.15078	−0.575388	−	0.817880i	$-0.695149\pi$
$89$	−10.8564	−1.15078	−0.575388	+	0.817880i	$0.695149\pi$
$90$	−2.73205	−0.287983
$91$	0	0
$92$	−0.535898	−0.0558713
$93$	−6.73205	−0.698081
$94$	9.92820	1.02402
$95$	17.6603	1.81190
$96$	1.00000	0.102062
$97$	3.80385	0.386222	0.193111	−	0.981177i	$-0.438142\pi$
$97$	3.80385	0.386222	0.193111	+	0.981177i	$0.438142\pi$
$98$	1.00000	0.101015
$99$	5.19615	0.522233
$100$	2.46410	0.246410
$101$	−8.92820	−0.888389	−0.444195	−	0.895930i	$-0.646510\pi$
$101$	−8.92820	−0.888389	−0.444195	+	0.895930i	$0.646510\pi$
$102$	−5.73205	−0.567558
$103$	−5.80385	−0.571870	−0.285935	−	0.958249i	$-0.592304\pi$
$103$	−5.80385	−0.571870	−0.285935	+	0.958249i	$0.592304\pi$
$104$	0	0
$105$	−2.73205	−0.266621
$106$	3.92820	0.381541
$107$	−19.9282	−1.92653	−0.963266	−	0.268549i	$-0.913456\pi$
$107$	−19.9282	−1.92653	−0.963266	+	0.268549i	$0.913456\pi$
$108$	1.00000	0.0962250
$109$	14.7321	1.41107	0.705537	−	0.708673i	$-0.250706\pi$
$109$	14.7321	1.41107	0.705537	+	0.708673i	$0.250706\pi$
$110$	−14.1962	−1.35355
$111$	−3.26795	−0.310180
$112$	1.00000	0.0944911
$113$	−9.66025	−0.908760	−0.454380	−	0.890808i	$-0.650139\pi$
$113$	−9.66025	−0.908760	−0.454380	+	0.890808i	$0.650139\pi$
$114$	−6.46410	−0.605419
$115$	1.46410	0.136528
$116$	−10.4641	−0.971567
$117$	0	0
$118$	−4.92820	−0.453678
$119$	−5.73205	−0.525456
$120$	−2.73205	−0.249401
$121$	16.0000	1.45455
$122$	0.267949	0.0242590
$123$	−1.53590	−0.138487
$124$	−6.73205	−0.604556
$125$	6.92820	0.619677
$126$	1.00000	0.0890871
$127$	−6.39230	−0.567225	−0.283613	−	0.958939i	$-0.591533\pi$
$127$	−6.39230	−0.567225	−0.283613	+	0.958939i	$0.591533\pi$
$128$	1.00000	0.0883883
$129$	−5.26795	−0.463817
$130$	0	0
$131$	−1.07180	−0.0936433	−0.0468217	−	0.998903i	$-0.514909\pi$
$131$	−1.07180	−0.0936433	−0.0468217	+	0.998903i	$0.514909\pi$
$132$	5.19615	0.452267
$133$	−6.46410	−0.560509
$134$	10.0000	0.863868
$135$	−2.73205	−0.235137
$136$	−5.73205	−0.491519
$137$	−12.5359	−1.07101	−0.535507	−	0.844531i	$-0.679879\pi$
$137$	−12.5359	−1.07101	−0.535507	+	0.844531i	$0.679879\pi$
$138$	−0.535898	−0.0456187
$139$	−21.0526	−1.78565	−0.892827	−	0.450399i	$-0.851282\pi$
$139$	−21.0526	−1.78565	−0.892827	+	0.450399i	$0.851282\pi$
$140$	−2.73205	−0.230900
$141$	9.92820	0.836106
$142$	−10.7321	−0.900614
$143$	0	0
$144$	1.00000	0.0833333
$145$	28.5885	2.37414
$146$	−5.46410	−0.452212
$147$	1.00000	0.0824786
$148$	−3.26795	−0.268624
$149$	8.00000	0.655386	0.327693	−	0.944784i	$-0.393729\pi$
$149$	8.00000	0.655386	0.327693	+	0.944784i	$0.393729\pi$
$150$	2.46410	0.201193
$151$	−9.19615	−0.748372	−0.374186	−	0.927354i	$-0.622078\pi$
$151$	−9.19615	−0.748372	−0.374186	+	0.927354i	$0.622078\pi$
$152$	−6.46410	−0.524308
$153$	−5.73205	−0.463409
$154$	5.19615	0.418718
$155$	18.3923	1.47731
$156$	0	0
$157$	−4.53590	−0.362004	−0.181002	−	0.983483i	$-0.557934\pi$
$157$	−4.53590	−0.362004	−0.181002	+	0.983483i	$0.557934\pi$
$158$	9.00000	0.716002
$159$	3.92820	0.311527
$160$	−2.73205	−0.215988
$161$	−0.535898	−0.0422347
$162$	1.00000	0.0785674
$163$	17.1244	1.34128	0.670642	−	0.741782i	$-0.266019\pi$
$163$	17.1244	1.34128	0.670642	+	0.741782i	$0.266019\pi$
$164$	−1.53590	−0.119934
$165$	−14.1962	−1.10517
$166$	12.7321	0.988199
$167$	18.9282	1.46471	0.732354	−	0.680924i	$-0.238422\pi$
$167$	18.9282	1.46471	0.732354	+	0.680924i	$0.238422\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	15.6603	1.20109
$171$	−6.46410	−0.494322
$172$	−5.26795	−0.401677
$173$	−8.19615	−0.623142	−0.311571	−	0.950223i	$-0.600855\pi$
$173$	−8.19615	−0.623142	−0.311571	+	0.950223i	$0.600855\pi$
$174$	−10.4641	−0.793281
$175$	2.46410	0.186269
$176$	5.19615	0.391675
$177$	−4.92820	−0.370426
$178$	−10.8564	−0.813722
$179$	3.46410	0.258919	0.129460	−	0.991585i	$-0.458676\pi$
$179$	3.46410	0.258919	0.129460	+	0.991585i	$0.458676\pi$
$180$	−2.73205	−0.203635
$181$	−17.7321	−1.31801	−0.659006	−	0.752137i	$-0.729023\pi$
$181$	−17.7321	−1.31801	−0.659006	+	0.752137i	$0.729023\pi$
$182$	0	0
$183$	0.267949	0.0198074
$184$	−0.535898	−0.0395070
$185$	8.92820	0.656415
$186$	−6.73205	−0.493618
$187$	−29.7846	−2.17807
$188$	9.92820	0.724089
$189$	1.00000	0.0727393
$190$	17.6603	1.28121
$191$	2.19615	0.158908	0.0794540	−	0.996839i	$-0.474682\pi$
$191$	2.19615	0.158908	0.0794540	+	0.996839i	$0.474682\pi$
$192$	1.00000	0.0721688
$193$	23.5885	1.69793	0.848967	−	0.528446i	$-0.177225\pi$
$193$	23.5885	1.69793	0.848967	+	0.528446i	$0.177225\pi$
$194$	3.80385	0.273100
$195$	0	0
$196$	1.00000	0.0714286
$197$	3.73205	0.265898	0.132949	−	0.991123i	$-0.457555\pi$
$197$	3.73205	0.265898	0.132949	+	0.991123i	$0.457555\pi$
$198$	5.19615	0.369274
$199$	−6.58846	−0.467043	−0.233522	−	0.972352i	$-0.575025\pi$
$199$	−6.58846	−0.467043	−0.233522	+	0.972352i	$0.575025\pi$
$200$	2.46410	0.174238
$201$	10.0000	0.705346
$202$	−8.92820	−0.628186
$203$	−10.4641	−0.734436
$204$	−5.73205	−0.401324
$205$	4.19615	0.293072
$206$	−5.80385	−0.404373
$207$	−0.535898	−0.0372475
$208$	0	0
$209$	−33.5885	−2.32336
$210$	−2.73205	−0.188529
$211$	11.0718	0.762214	0.381107	−	0.924531i	$-0.375543\pi$
$211$	11.0718	0.762214	0.381107	+	0.924531i	$0.375543\pi$
$212$	3.92820	0.269790
$213$	−10.7321	−0.735348
$214$	−19.9282	−1.36226
$215$	14.3923	0.981547
$216$	1.00000	0.0680414
$217$	−6.73205	−0.457001
$218$	14.7321	0.997780
$219$	−5.46410	−0.369230
$220$	−14.1962	−0.957104
$221$	0	0
$222$	−3.26795	−0.219330
$223$	1.46410	0.0980435	0.0490217	−	0.998798i	$-0.484390\pi$
$223$	1.46410	0.0980435	0.0490217	+	0.998798i	$0.484390\pi$
$224$	1.00000	0.0668153
$225$	2.46410	0.164273
$226$	−9.66025	−0.642591
$227$	−21.3205	−1.41509	−0.707546	−	0.706667i	$-0.750198\pi$
$227$	−21.3205	−1.41509	−0.707546	+	0.706667i	$0.750198\pi$
$228$	−6.46410	−0.428096
$229$	3.39230	0.224170	0.112085	−	0.993699i	$-0.464247\pi$
$229$	3.39230	0.224170	0.112085	+	0.993699i	$0.464247\pi$
$230$	1.46410	0.0965400
$231$	5.19615	0.341882
$232$	−10.4641	−0.687002
$233$	12.5885	0.824697	0.412349	−	0.911026i	$-0.364709\pi$
$233$	12.5885	0.824697	0.412349	+	0.911026i	$0.364709\pi$
$234$	0	0
$235$	−27.1244	−1.76940
$236$	−4.92820	−0.320799
$237$	9.00000	0.584613
$238$	−5.73205	−0.371554
$239$	−4.58846	−0.296803	−0.148401	−	0.988927i	$-0.547413\pi$
$239$	−4.58846	−0.296803	−0.148401	+	0.988927i	$0.547413\pi$
$240$	−2.73205	−0.176353
$241$	−2.92820	−0.188622	−0.0943111	−	0.995543i	$-0.530065\pi$
$241$	−2.92820	−0.188622	−0.0943111	+	0.995543i	$0.530065\pi$
$242$	16.0000	1.02852
$243$	1.00000	0.0641500
$244$	0.267949	0.0171537
$245$	−2.73205	−0.174544
$246$	−1.53590	−0.0979253
$247$	0	0
$248$	−6.73205	−0.427486
$249$	12.7321	0.806861
$250$	6.92820	0.438178
$251$	−27.5167	−1.73684	−0.868418	−	0.495833i	$-0.834863\pi$
$251$	−27.5167	−1.73684	−0.868418	+	0.495833i	$0.834863\pi$
$252$	1.00000	0.0629941
$253$	−2.78461	−0.175067
$254$	−6.39230	−0.401089
$255$	15.6603	0.980683
$256$	1.00000	0.0625000
$257$	13.0526	0.814196	0.407098	−	0.913384i	$-0.366541\pi$
$257$	13.0526	0.814196	0.407098	+	0.913384i	$0.366541\pi$
$258$	−5.26795	−0.327968
$259$	−3.26795	−0.203060
$260$	0	0
$261$	−10.4641	−0.647712
$262$	−1.07180	−0.0662158
$263$	−21.1244	−1.30258	−0.651292	−	0.758827i	$-0.725773\pi$
$263$	−21.1244	−1.30258	−0.651292	+	0.758827i	$0.725773\pi$
$264$	5.19615	0.319801
$265$	−10.7321	−0.659265
$266$	−6.46410	−0.396339
$267$	−10.8564	−0.664401
$268$	10.0000	0.610847
$269$	−4.00000	−0.243884	−0.121942	−	0.992537i	$-0.538912\pi$
$269$	−4.00000	−0.243884	−0.121942	+	0.992537i	$0.538912\pi$
$270$	−2.73205	−0.166267
$271$	9.66025	0.586819	0.293409	−	0.955987i	$-0.405210\pi$
$271$	9.66025	0.586819	0.293409	+	0.955987i	$0.405210\pi$
$272$	−5.73205	−0.347557
$273$	0	0
$274$	−12.5359	−0.757321
$275$	12.8038	0.772101
$276$	−0.535898	−0.0322573
$277$	6.39230	0.384076	0.192038	−	0.981387i	$-0.438490\pi$
$277$	6.39230	0.384076	0.192038	+	0.981387i	$0.438490\pi$
$278$	−21.0526	−1.26265
$279$	−6.73205	−0.403037
$280$	−2.73205	−0.163271
$281$	−9.26795	−0.552879	−0.276440	−	0.961031i	$-0.589155\pi$
$281$	−9.26795	−0.552879	−0.276440	+	0.961031i	$0.589155\pi$
$282$	9.92820	0.591216
$283$	9.85641	0.585903	0.292951	−	0.956127i	$-0.405363\pi$
$283$	9.85641	0.585903	0.292951	+	0.956127i	$0.405363\pi$
$284$	−10.7321	−0.636830
$285$	17.6603	1.04610
$286$	0	0
$287$	−1.53590	−0.0906612
$288$	1.00000	0.0589256
$289$	15.8564	0.932730
$290$	28.5885	1.67877
$291$	3.80385	0.222985
$292$	−5.46410	−0.319762
$293$	14.9282	0.872115	0.436057	−	0.899919i	$-0.356374\pi$
$293$	14.9282	0.872115	0.436057	+	0.899919i	$0.356374\pi$
$294$	1.00000	0.0583212
$295$	13.4641	0.783910
$296$	−3.26795	−0.189946
$297$	5.19615	0.301511
$298$	8.00000	0.463428
$299$	0	0
$300$	2.46410	0.142265
$301$	−5.26795	−0.303640
$302$	−9.19615	−0.529179
$303$	−8.92820	−0.512912
$304$	−6.46410	−0.370742
$305$	−0.732051	−0.0419171
$306$	−5.73205	−0.327680
$307$	5.00000	0.285365	0.142683	−	0.989769i	$-0.454427\pi$
$307$	5.00000	0.285365	0.142683	+	0.989769i	$0.454427\pi$
$308$	5.19615	0.296078
$309$	−5.80385	−0.330169
$310$	18.3923	1.04461
$311$	−25.1962	−1.42874	−0.714371	−	0.699767i	$-0.753287\pi$
$311$	−25.1962	−1.42874	−0.714371	+	0.699767i	$0.753287\pi$
$312$	0	0
$313$	31.1244	1.75925	0.879626	−	0.475665i	$-0.157793\pi$
$313$	31.1244	1.75925	0.879626	+	0.475665i	$0.157793\pi$
$314$	−4.53590	−0.255976
$315$	−2.73205	−0.153934
$316$	9.00000	0.506290
$317$	−26.7846	−1.50437	−0.752187	−	0.658950i	$-0.771001\pi$
$317$	−26.7846	−1.50437	−0.752187	+	0.658950i	$0.771001\pi$
$318$	3.92820	0.220283
$319$	−54.3731	−3.04431
$320$	−2.73205	−0.152726
$321$	−19.9282	−1.11228
$322$	−0.535898	−0.0298644
$323$	37.0526	2.06166
$324$	1.00000	0.0555556
$325$	0	0
$326$	17.1244	0.948430
$327$	14.7321	0.814684
$328$	−1.53590	−0.0848058
$329$	9.92820	0.547360
$330$	−14.1962	−0.781472
$331$	34.7846	1.91194	0.955968	−	0.293472i	$-0.0948109\pi$
$331$	34.7846	1.91194	0.955968	+	0.293472i	$0.0948109\pi$
$332$	12.7321	0.698762
$333$	−3.26795	−0.179083
$334$	18.9282	1.03571
$335$	−27.3205	−1.49268
$336$	1.00000	0.0545545
$337$	11.0000	0.599208	0.299604	−	0.954064i	$-0.403145\pi$
$337$	11.0000	0.599208	0.299604	+	0.954064i	$0.403145\pi$
$338$	0	0
$339$	−9.66025	−0.524673
$340$	15.6603	0.849297
$341$	−34.9808	−1.89431
$342$	−6.46410	−0.349539
$343$	1.00000	0.0539949
$344$	−5.26795	−0.284029
$345$	1.46410	0.0788246
$346$	−8.19615	−0.440628
$347$	0.464102	0.0249143	0.0124571	−	0.999922i	$-0.496035\pi$
$347$	0.464102	0.0249143	0.0124571	+	0.999922i	$0.496035\pi$
$348$	−10.4641	−0.560935
$349$	−33.8564	−1.81229	−0.906146	−	0.422965i	$-0.860989\pi$
$349$	−33.8564	−1.81229	−0.906146	+	0.422965i	$0.860989\pi$
$350$	2.46410	0.131712
$351$	0	0
$352$	5.19615	0.276956
$353$	−3.32051	−0.176733	−0.0883664	−	0.996088i	$-0.528165\pi$
$353$	−3.32051	−0.176733	−0.0883664	+	0.996088i	$0.528165\pi$
$354$	−4.92820	−0.261931
$355$	29.3205	1.55617
$356$	−10.8564	−0.575388
$357$	−5.73205	−0.303372
$358$	3.46410	0.183083
$359$	−24.4449	−1.29015	−0.645075	−	0.764119i	$-0.723174\pi$
$359$	−24.4449	−1.29015	−0.645075	+	0.764119i	$0.723174\pi$
$360$	−2.73205	−0.143992
$361$	22.7846	1.19919
$362$	−17.7321	−0.931976
$363$	16.0000	0.839782
$364$	0	0
$365$	14.9282	0.781378
$366$	0.267949	0.0140059
$367$	−21.3205	−1.11292	−0.556461	−	0.830874i	$-0.687841\pi$
$367$	−21.3205	−1.11292	−0.556461	+	0.830874i	$0.687841\pi$
$368$	−0.535898	−0.0279356
$369$	−1.53590	−0.0799557
$370$	8.92820	0.464155
$371$	3.92820	0.203942
$372$	−6.73205	−0.349041
$373$	9.12436	0.472441	0.236221	−	0.971699i	$-0.424091\pi$
$373$	9.12436	0.472441	0.236221	+	0.971699i	$0.424091\pi$
$374$	−29.7846	−1.54013
$375$	6.92820	0.357771
$376$	9.92820	0.512008
$377$	0	0
$378$	1.00000	0.0514344
$379$	2.05256	0.105433	0.0527164	−	0.998610i	$-0.483212\pi$
$379$	2.05256	0.105433	0.0527164	+	0.998610i	$0.483212\pi$
$380$	17.6603	0.905952
$381$	−6.39230	−0.327488
$382$	2.19615	0.112365
$383$	−31.0000	−1.58403	−0.792013	−	0.610504i	$-0.790967\pi$
$383$	−31.0000	−1.58403	−0.792013	+	0.610504i	$0.790967\pi$
$384$	1.00000	0.0510310
$385$	−14.1962	−0.723503
$386$	23.5885	1.20062
$387$	−5.26795	−0.267785
$388$	3.80385	0.193111
$389$	−14.5359	−0.736999	−0.368500	−	0.929628i	$-0.620128\pi$
$389$	−14.5359	−0.736999	−0.368500	+	0.929628i	$0.620128\pi$
$390$	0	0
$391$	3.07180	0.155347
$392$	1.00000	0.0505076
$393$	−1.07180	−0.0540650
$394$	3.73205	0.188018
$395$	−24.5885	−1.23718
$396$	5.19615	0.261116
$397$	−0.607695	−0.0304993	−0.0152497	−	0.999884i	$-0.504854\pi$
$397$	−0.607695	−0.0304993	−0.0152497	+	0.999884i	$0.504854\pi$
$398$	−6.58846	−0.330250
$399$	−6.46410	−0.323610
$400$	2.46410	0.123205
$401$	24.9282	1.24486	0.622428	−	0.782677i	$-0.286147\pi$
$401$	24.9282	1.24486	0.622428	+	0.782677i	$0.286147\pi$
$402$	10.0000	0.498755
$403$	0	0
$404$	−8.92820	−0.444195
$405$	−2.73205	−0.135757
$406$	−10.4641	−0.519325
$407$	−16.9808	−0.841705
$408$	−5.73205	−0.283779
$409$	−14.5885	−0.721353	−0.360676	−	0.932691i	$-0.617454\pi$
$409$	−14.5885	−0.721353	−0.360676	+	0.932691i	$0.617454\pi$
$410$	4.19615	0.207233
$411$	−12.5359	−0.618350
$412$	−5.80385	−0.285935
$413$	−4.92820	−0.242501
$414$	−0.535898	−0.0263380
$415$	−34.7846	−1.70751
$416$	0	0
$417$	−21.0526	−1.03095
$418$	−33.5885	−1.64287
$419$	16.5885	0.810399	0.405200	−	0.914228i	$-0.367202\pi$
$419$	16.5885	0.810399	0.405200	+	0.914228i	$0.367202\pi$
$420$	−2.73205	−0.133310
$421$	−9.32051	−0.454254	−0.227127	−	0.973865i	$-0.572933\pi$
$421$	−9.32051	−0.454254	−0.227127	+	0.973865i	$0.572933\pi$
$422$	11.0718	0.538967
$423$	9.92820	0.482726
$424$	3.92820	0.190770
$425$	−14.1244	−0.685132
$426$	−10.7321	−0.519970
$427$	0.267949	0.0129670
$428$	−19.9282	−0.963266
$429$	0	0
$430$	14.3923	0.694059
$431$	−11.1244	−0.535841	−0.267921	−	0.963441i	$-0.586337\pi$
$431$	−11.1244	−0.535841	−0.267921	+	0.963441i	$0.586337\pi$
$432$	1.00000	0.0481125
$433$	39.8564	1.91538	0.957688	−	0.287807i	$-0.0929263\pi$
$433$	39.8564	1.91538	0.957688	+	0.287807i	$0.0929263\pi$
$434$	−6.73205	−0.323149
$435$	28.5885	1.37071
$436$	14.7321	0.705537
$437$	3.46410	0.165710
$438$	−5.46410	−0.261085
$439$	−11.3205	−0.540298	−0.270149	−	0.962818i	$-0.587073\pi$
$439$	−11.3205	−0.540298	−0.270149	+	0.962818i	$0.587073\pi$
$440$	−14.1962	−0.676775
$441$	1.00000	0.0476190
$442$	0	0
$443$	−25.0000	−1.18779	−0.593893	−	0.804544i	$-0.702410\pi$
$443$	−25.0000	−1.18779	−0.593893	+	0.804544i	$0.702410\pi$
$444$	−3.26795	−0.155090
$445$	29.6603	1.40603
$446$	1.46410	0.0693272
$447$	8.00000	0.378387
$448$	1.00000	0.0472456
$449$	−22.9808	−1.08453	−0.542265	−	0.840208i	$-0.682433\pi$
$449$	−22.9808	−1.08453	−0.542265	+	0.840208i	$0.682433\pi$
$450$	2.46410	0.116159
$451$	−7.98076	−0.375799
$452$	−9.66025	−0.454380
$453$	−9.19615	−0.432073
$454$	−21.3205	−1.00062
$455$	0	0
$456$	−6.46410	−0.302709
$457$	25.7128	1.20279	0.601397	−	0.798950i	$-0.294611\pi$
$457$	25.7128	1.20279	0.601397	+	0.798950i	$0.294611\pi$
$458$	3.39230	0.158512
$459$	−5.73205	−0.267549
$460$	1.46410	0.0682641
$461$	6.92820	0.322679	0.161339	−	0.986899i	$-0.448419\pi$
$461$	6.92820	0.322679	0.161339	+	0.986899i	$0.448419\pi$
$462$	5.19615	0.241747
$463$	−32.6603	−1.51785	−0.758925	−	0.651178i	$-0.774275\pi$
$463$	−32.6603	−1.51785	−0.758925	+	0.651178i	$0.774275\pi$
$464$	−10.4641	−0.485784
$465$	18.3923	0.852923
$466$	12.5885	0.583149
$467$	−5.07180	−0.234695	−0.117347	−	0.993091i	$-0.537439\pi$
$467$	−5.07180	−0.234695	−0.117347	+	0.993091i	$0.537439\pi$
$468$	0	0
$469$	10.0000	0.461757
$470$	−27.1244	−1.25115
$471$	−4.53590	−0.209003
$472$	−4.92820	−0.226839
$473$	−27.3731	−1.25861
$474$	9.00000	0.413384
$475$	−15.9282	−0.730836
$476$	−5.73205	−0.262728
$477$	3.92820	0.179860
$478$	−4.58846	−0.209871
$479$	22.8564	1.04434	0.522168	−	0.852843i	$-0.325123\pi$
$479$	22.8564	1.04434	0.522168	+	0.852843i	$0.325123\pi$
$480$	−2.73205	−0.124700
$481$	0	0
$482$	−2.92820	−0.133376
$483$	−0.535898	−0.0243842
$484$	16.0000	0.727273
$485$	−10.3923	−0.471890
$486$	1.00000	0.0453609
$487$	−29.4449	−1.33427	−0.667137	−	0.744935i	$-0.732480\pi$
$487$	−29.4449	−1.33427	−0.667137	+	0.744935i	$0.732480\pi$
$488$	0.267949	0.0121295
$489$	17.1244	0.774390
$490$	−2.73205	−0.123421
$491$	14.3923	0.649516	0.324758	−	0.945797i	$-0.394717\pi$
$491$	14.3923	0.649516	0.324758	+	0.945797i	$0.394717\pi$
$492$	−1.53590	−0.0692436
$493$	59.9808	2.70140
$494$	0	0
$495$	−14.1962	−0.638070
$496$	−6.73205	−0.302278
$497$	−10.7321	−0.481398
$498$	12.7321	0.570537
$499$	−10.5885	−0.474004	−0.237002	−	0.971509i	$-0.576165\pi$
$499$	−10.5885	−0.474004	−0.237002	+	0.971509i	$0.576165\pi$
$500$	6.92820	0.309839
$501$	18.9282	0.845650
$502$	−27.5167	−1.22813
$503$	−17.0718	−0.761194	−0.380597	−	0.924741i	$-0.624281\pi$
$503$	−17.0718	−0.761194	−0.380597	+	0.924741i	$0.624281\pi$
$504$	1.00000	0.0445435
$505$	24.3923	1.08544
$506$	−2.78461	−0.123791
$507$	0	0
$508$	−6.39230	−0.283613
$509$	−12.3397	−0.546950	−0.273475	−	0.961879i	$-0.588173\pi$
$509$	−12.3397	−0.546950	−0.273475	+	0.961879i	$0.588173\pi$
$510$	15.6603	0.693448
$511$	−5.46410	−0.241718
$512$	1.00000	0.0441942
$513$	−6.46410	−0.285397
$514$	13.0526	0.575724
$515$	15.8564	0.698717
$516$	−5.26795	−0.231909
$517$	51.5885	2.26886
$518$	−3.26795	−0.143585
$519$	−8.19615	−0.359771
$520$	0	0
$521$	9.58846	0.420078	0.210039	−	0.977693i	$-0.432641\pi$
$521$	9.58846	0.420078	0.210039	+	0.977693i	$0.432641\pi$
$522$	−10.4641	−0.458001
$523$	−14.8038	−0.647327	−0.323664	−	0.946172i	$-0.604915\pi$
$523$	−14.8038	−0.647327	−0.323664	+	0.946172i	$0.604915\pi$
$524$	−1.07180	−0.0468217
$525$	2.46410	0.107542
$526$	−21.1244	−0.921066
$527$	38.5885	1.68094
$528$	5.19615	0.226134
$529$	−22.7128	−0.987514
$530$	−10.7321	−0.466170
$531$	−4.92820	−0.213866
$532$	−6.46410	−0.280254
$533$	0	0
$534$	−10.8564	−0.469803
$535$	54.4449	2.35386
$536$	10.0000	0.431934
$537$	3.46410	0.149487
$538$	−4.00000	−0.172452
$539$	5.19615	0.223814
$540$	−2.73205	−0.117569
$541$	30.0526	1.29206	0.646030	−	0.763312i	$-0.276428\pi$
$541$	30.0526	1.29206	0.646030	+	0.763312i	$0.276428\pi$
$542$	9.66025	0.414943
$543$	−17.7321	−0.760955
$544$	−5.73205	−0.245760
$545$	−40.2487	−1.72407
$546$	0	0
$547$	6.19615	0.264928	0.132464	−	0.991188i	$-0.457711\pi$
$547$	6.19615	0.264928	0.132464	+	0.991188i	$0.457711\pi$
$548$	−12.5359	−0.535507
$549$	0.267949	0.0114358
$550$	12.8038	0.545958
$551$	67.6410	2.88160
$552$	−0.535898	−0.0228093
$553$	9.00000	0.382719
$554$	6.39230	0.271583
$555$	8.92820	0.378981
$556$	−21.0526	−0.892827
$557$	−16.2679	−0.689295	−0.344648	−	0.938732i	$-0.612002\pi$
$557$	−16.2679	−0.689295	−0.344648	+	0.938732i	$0.612002\pi$
$558$	−6.73205	−0.284990
$559$	0	0
$560$	−2.73205	−0.115450
$561$	−29.7846	−1.25751
$562$	−9.26795	−0.390945
$563$	3.66025	0.154261	0.0771307	−	0.997021i	$-0.475424\pi$
$563$	3.66025	0.154261	0.0771307	+	0.997021i	$0.475424\pi$
$564$	9.92820	0.418053
$565$	26.3923	1.11033
$566$	9.85641	0.414296
$567$	1.00000	0.0419961
$568$	−10.7321	−0.450307
$569$	−15.6603	−0.656512	−0.328256	−	0.944589i	$-0.606461\pi$
$569$	−15.6603	−0.656512	−0.328256	+	0.944589i	$0.606461\pi$
$570$	17.6603	0.739707
$571$	5.51666	0.230865	0.115433	−	0.993315i	$-0.463175\pi$
$571$	5.51666	0.230865	0.115433	+	0.993315i	$0.463175\pi$
$572$	0	0
$573$	2.19615	0.0917456
$574$	−1.53590	−0.0641072
$575$	−1.32051	−0.0550690
$576$	1.00000	0.0416667
$577$	2.58846	0.107759	0.0538794	−	0.998547i	$-0.482841\pi$
$577$	2.58846	0.107759	0.0538794	+	0.998547i	$0.482841\pi$
$578$	15.8564	0.659540
$579$	23.5885	0.980303
$580$	28.5885	1.18707
$581$	12.7321	0.528214
$582$	3.80385	0.157675
$583$	20.4115	0.845360
$584$	−5.46410	−0.226106
$585$	0	0
$586$	14.9282	0.616678
$587$	19.1244	0.789347	0.394673	−	0.918822i	$-0.370858\pi$
$587$	19.1244	0.789347	0.394673	+	0.918822i	$0.370858\pi$
$588$	1.00000	0.0412393
$589$	43.5167	1.79307
$590$	13.4641	0.554308
$591$	3.73205	0.153516
$592$	−3.26795	−0.134312
$593$	37.0000	1.51941	0.759704	−	0.650269i	$-0.225344\pi$
$593$	37.0000	1.51941	0.759704	+	0.650269i	$0.225344\pi$
$594$	5.19615	0.213201
$595$	15.6603	0.642008
$596$	8.00000	0.327693
$597$	−6.58846	−0.269648
$598$	0	0
$599$	35.5692	1.45332	0.726659	−	0.686998i	$-0.241072\pi$
$599$	35.5692	1.45332	0.726659	+	0.686998i	$0.241072\pi$
$600$	2.46410	0.100597
$601$	38.3013	1.56234	0.781171	−	0.624317i	$-0.214623\pi$
$601$	38.3013	1.56234	0.781171	+	0.624317i	$0.214623\pi$
$602$	−5.26795	−0.214706
$603$	10.0000	0.407231
$604$	−9.19615	−0.374186
$605$	−43.7128	−1.77718
$606$	−8.92820	−0.362683
$607$	−8.33975	−0.338500	−0.169250	−	0.985573i	$-0.554135\pi$
$607$	−8.33975	−0.338500	−0.169250	+	0.985573i	$0.554135\pi$
$608$	−6.46410	−0.262154
$609$	−10.4641	−0.424027
$610$	−0.732051	−0.0296399
$611$	0	0
$612$	−5.73205	−0.231704
$613$	7.71281	0.311518	0.155759	−	0.987795i	$-0.450218\pi$
$613$	7.71281	0.311518	0.155759	+	0.987795i	$0.450218\pi$
$614$	5.00000	0.201784
$615$	4.19615	0.169205
$616$	5.19615	0.209359
$617$	−24.1962	−0.974100	−0.487050	−	0.873374i	$-0.661927\pi$
$617$	−24.1962	−0.974100	−0.487050	+	0.873374i	$0.661927\pi$
$618$	−5.80385	−0.233465
$619$	9.39230	0.377509	0.188754	−	0.982024i	$-0.439555\pi$
$619$	9.39230	0.377509	0.188754	+	0.982024i	$0.439555\pi$
$620$	18.3923	0.738653
$621$	−0.535898	−0.0215049
$622$	−25.1962	−1.01027
$623$	−10.8564	−0.434953
$624$	0	0
$625$	−31.2487	−1.24995
$626$	31.1244	1.24398
$627$	−33.5885	−1.34139
$628$	−4.53590	−0.181002
$629$	18.7321	0.746896
$630$	−2.73205	−0.108848
$631$	26.1244	1.03999	0.519997	−	0.854168i	$-0.325933\pi$
$631$	26.1244	1.03999	0.519997	+	0.854168i	$0.325933\pi$
$632$	9.00000	0.358001
$633$	11.0718	0.440064
$634$	−26.7846	−1.06375
$635$	17.4641	0.693042
$636$	3.92820	0.155763
$637$	0	0
$638$	−54.3731	−2.15265
$639$	−10.7321	−0.424553
$640$	−2.73205	−0.107994
$641$	17.3205	0.684119	0.342059	−	0.939678i	$-0.388876\pi$
$641$	17.3205	0.684119	0.342059	+	0.939678i	$0.388876\pi$
$642$	−19.9282	−0.786503
$643$	32.3205	1.27460	0.637298	−	0.770617i	$-0.280052\pi$
$643$	32.3205	1.27460	0.637298	+	0.770617i	$0.280052\pi$
$644$	−0.535898	−0.0211174
$645$	14.3923	0.566696
$646$	37.0526	1.45781
$647$	−20.2679	−0.796815	−0.398408	−	0.917208i	$-0.630437\pi$
$647$	−20.2679	−0.796815	−0.398408	+	0.917208i	$0.630437\pi$
$648$	1.00000	0.0392837
$649$	−25.6077	−1.00519
$650$	0	0
$651$	−6.73205	−0.263850
$652$	17.1244	0.670642
$653$	40.7128	1.59322	0.796608	−	0.604497i	$-0.206626\pi$
$653$	40.7128	1.59322	0.796608	+	0.604497i	$0.206626\pi$
$654$	14.7321	0.576069
$655$	2.92820	0.114414
$656$	−1.53590	−0.0599668
$657$	−5.46410	−0.213175
$658$	9.92820	0.387042
$659$	35.2487	1.37309	0.686547	−	0.727085i	$-0.259125\pi$
$659$	35.2487	1.37309	0.686547	+	0.727085i	$0.259125\pi$
$660$	−14.1962	−0.552584
$661$	−29.4641	−1.14602	−0.573010	−	0.819548i	$-0.694225\pi$
$661$	−29.4641	−1.14602	−0.573010	+	0.819548i	$0.694225\pi$
$662$	34.7846	1.35194
$663$	0	0
$664$	12.7321	0.494099
$665$	17.6603	0.684835
$666$	−3.26795	−0.126630
$667$	5.60770	0.217131
$668$	18.9282	0.732354
$669$	1.46410	0.0566054
$670$	−27.3205	−1.05548
$671$	1.39230	0.0537493
$672$	1.00000	0.0385758
$673$	25.6410	0.988389	0.494194	−	0.869351i	$-0.335463\pi$
$673$	25.6410	0.988389	0.494194	+	0.869351i	$0.335463\pi$
$674$	11.0000	0.423704
$675$	2.46410	0.0948433
$676$	0	0
$677$	46.7321	1.79606	0.898029	−	0.439936i	$-0.144999\pi$
$677$	46.7321	1.79606	0.898029	+	0.439936i	$0.144999\pi$
$678$	−9.66025	−0.371000
$679$	3.80385	0.145978
$680$	15.6603	0.600543
$681$	−21.3205	−0.817004
$682$	−34.9808	−1.33948
$683$	17.3205	0.662751	0.331375	−	0.943499i	$-0.392487\pi$
$683$	17.3205	0.662751	0.331375	+	0.943499i	$0.392487\pi$
$684$	−6.46410	−0.247161
$685$	34.2487	1.30858
$686$	1.00000	0.0381802
$687$	3.39230	0.129425
$688$	−5.26795	−0.200839
$689$	0	0
$690$	1.46410	0.0557374
$691$	50.9282	1.93740	0.968700	−	0.248234i	$-0.0798502\pi$
$691$	50.9282	1.93740	0.968700	+	0.248234i	$0.0798502\pi$
$692$	−8.19615	−0.311571
$693$	5.19615	0.197386
$694$	0.464102	0.0176171
$695$	57.5167	2.18173
$696$	−10.4641	−0.396641
$697$	8.80385	0.333470
$698$	−33.8564	−1.28148
$699$	12.5885	0.476139
$700$	2.46410	0.0931343
$701$	−15.7846	−0.596176	−0.298088	−	0.954538i	$-0.596349\pi$
$701$	−15.7846	−0.596176	−0.298088	+	0.954538i	$0.596349\pi$
$702$	0	0
$703$	21.1244	0.796720
$704$	5.19615	0.195837
$705$	−27.1244	−1.02156
$706$	−3.32051	−0.124969
$707$	−8.92820	−0.335780
$708$	−4.92820	−0.185213
$709$	−21.3731	−0.802682	−0.401341	−	0.915929i	$-0.631456\pi$
$709$	−21.3731	−0.802682	−0.401341	+	0.915929i	$0.631456\pi$
$710$	29.3205	1.10038
$711$	9.00000	0.337526
$712$	−10.8564	−0.406861
$713$	3.60770	0.135109
$714$	−5.73205	−0.214517
$715$	0	0
$716$	3.46410	0.129460
$717$	−4.58846	−0.171359
$718$	−24.4449	−0.912274
$719$	−19.4449	−0.725171	−0.362586	−	0.931951i	$-0.618106\pi$
$719$	−19.4449	−0.725171	−0.362586	+	0.931951i	$0.618106\pi$
$720$	−2.73205	−0.101818
$721$	−5.80385	−0.216147
$722$	22.7846	0.847955
$723$	−2.92820	−0.108901
$724$	−17.7321	−0.659006
$725$	−25.7846	−0.957616
$726$	16.0000	0.593816
$727$	−24.3923	−0.904661	−0.452330	−	0.891851i	$-0.649407\pi$
$727$	−24.3923	−0.904661	−0.452330	+	0.891851i	$0.649407\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	14.9282	0.552518
$731$	30.1962	1.11685
$732$	0.267949	0.00990369
$733$	15.7846	0.583018	0.291509	−	0.956568i	$-0.405843\pi$
$733$	15.7846	0.583018	0.291509	+	0.956568i	$0.405843\pi$
$734$	−21.3205	−0.786954
$735$	−2.73205	−0.100773
$736$	−0.535898	−0.0197535
$737$	51.9615	1.91403
$738$	−1.53590	−0.0565372
$739$	−23.1769	−0.852577	−0.426288	−	0.904587i	$-0.640179\pi$
$739$	−23.1769	−0.852577	−0.426288	+	0.904587i	$0.640179\pi$
$740$	8.92820	0.328207
$741$	0	0
$742$	3.92820	0.144209
$743$	−24.0526	−0.882403	−0.441201	−	0.897408i	$-0.645448\pi$
$743$	−24.0526	−0.882403	−0.441201	+	0.897408i	$0.645448\pi$
$744$	−6.73205	−0.246809
$745$	−21.8564	−0.800757
$746$	9.12436	0.334066
$747$	12.7321	0.465841
$748$	−29.7846	−1.08903
$749$	−19.9282	−0.728161
$750$	6.92820	0.252982
$751$	32.8564	1.19895	0.599474	−	0.800394i	$-0.295377\pi$
$751$	32.8564	1.19895	0.599474	+	0.800394i	$0.295377\pi$
$752$	9.92820	0.362044
$753$	−27.5167	−1.00276
$754$	0	0
$755$	25.1244	0.914369
$756$	1.00000	0.0363696
$757$	5.80385	0.210944	0.105472	−	0.994422i	$-0.466365\pi$
$757$	5.80385	0.210944	0.105472	+	0.994422i	$0.466365\pi$
$758$	2.05256	0.0745523
$759$	−2.78461	−0.101075
$760$	17.6603	0.640605
$761$	30.2487	1.09651	0.548257	−	0.836310i	$-0.315291\pi$
$761$	30.2487	1.09651	0.548257	+	0.836310i	$0.315291\pi$
$762$	−6.39230	−0.231569
$763$	14.7321	0.533336
$764$	2.19615	0.0794540
$765$	15.6603	0.566198
$766$	−31.0000	−1.12008
$767$	0	0
$768$	1.00000	0.0360844
$769$	−46.7321	−1.68520	−0.842600	−	0.538539i	$-0.818976\pi$
$769$	−46.7321	−1.68520	−0.842600	+	0.538539i	$0.818976\pi$
$770$	−14.1962	−0.511594
$771$	13.0526	0.470076
$772$	23.5885	0.848967
$773$	43.1769	1.55297	0.776483	−	0.630138i	$-0.217002\pi$
$773$	43.1769	1.55297	0.776483	+	0.630138i	$0.217002\pi$
$774$	−5.26795	−0.189353
$775$	−16.5885	−0.595875
$776$	3.80385	0.136550
$777$	−3.26795	−0.117237
$778$	−14.5359	−0.521137
$779$	9.92820	0.355715
$780$	0	0
$781$	−55.7654	−1.99544
$782$	3.07180	0.109847
$783$	−10.4641	−0.373956
$784$	1.00000	0.0357143
$785$	12.3923	0.442300
$786$	−1.07180	−0.0382297
$787$	−18.8564	−0.672158	−0.336079	−	0.941834i	$-0.609101\pi$
$787$	−18.8564	−0.672158	−0.336079	+	0.941834i	$0.609101\pi$
$788$	3.73205	0.132949
$789$	−21.1244	−0.752047
$790$	−24.5885	−0.874818
$791$	−9.66025	−0.343479
$792$	5.19615	0.184637
$793$	0	0
$794$	−0.607695	−0.0215663
$795$	−10.7321	−0.380627
$796$	−6.58846	−0.233522
$797$	−37.3731	−1.32382	−0.661911	−	0.749582i	$-0.730254\pi$
$797$	−37.3731	−1.32382	−0.661911	+	0.749582i	$0.730254\pi$
$798$	−6.46410	−0.228827
$799$	−56.9090	−2.01329
$800$	2.46410	0.0871191
$801$	−10.8564	−0.383592
$802$	24.9282	0.880245
$803$	−28.3923	−1.00194
$804$	10.0000	0.352673
$805$	1.46410	0.0516028
$806$	0	0
$807$	−4.00000	−0.140807
$808$	−8.92820	−0.314093
$809$	−12.7321	−0.447635	−0.223818	−	0.974631i	$-0.571852\pi$
$809$	−12.7321	−0.447635	−0.223818	+	0.974631i	$0.571852\pi$
$810$	−2.73205	−0.0959945
$811$	54.1051	1.89989	0.949944	−	0.312421i	$-0.101140\pi$
$811$	54.1051	1.89989	0.949944	+	0.312421i	$0.101140\pi$
$812$	−10.4641	−0.367218
$813$	9.66025	0.338800
$814$	−16.9808	−0.595175
$815$	−46.7846	−1.63879
$816$	−5.73205	−0.200662
$817$	34.0526	1.19135
$818$	−14.5885	−0.510073
$819$	0	0
$820$	4.19615	0.146536
$821$	−29.1962	−1.01895	−0.509476	−	0.860485i	$-0.670161\pi$
$821$	−29.1962	−1.01895	−0.509476	+	0.860485i	$0.670161\pi$
$822$	−12.5359	−0.437240
$823$	−33.7128	−1.17515	−0.587577	−	0.809168i	$-0.699918\pi$
$823$	−33.7128	−1.17515	−0.587577	+	0.809168i	$0.699918\pi$
$824$	−5.80385	−0.202187
$825$	12.8038	0.445773
$826$	−4.92820	−0.171474
$827$	−16.3923	−0.570016	−0.285008	−	0.958525i	$-0.591996\pi$
$827$	−16.3923	−0.570016	−0.285008	+	0.958525i	$0.591996\pi$
$828$	−0.535898	−0.0186238
$829$	46.5167	1.61559	0.807795	−	0.589463i	$-0.200661\pi$
$829$	46.5167	1.61559	0.807795	+	0.589463i	$0.200661\pi$
$830$	−34.7846	−1.20739
$831$	6.39230	0.221747
$832$	0	0
$833$	−5.73205	−0.198604
$834$	−21.0526	−0.728990
$835$	−51.7128	−1.78960
$836$	−33.5885	−1.16168
$837$	−6.73205	−0.232694
$838$	16.5885	0.573039
$839$	−2.67949	−0.0925063	−0.0462532	−	0.998930i	$-0.514728\pi$
$839$	−2.67949	−0.0925063	−0.0462532	+	0.998930i	$0.514728\pi$
$840$	−2.73205	−0.0942647
$841$	80.4974	2.77577
$842$	−9.32051	−0.321206
$843$	−9.26795	−0.319205
$844$	11.0718	0.381107
$845$	0	0
$846$	9.92820	0.341339
$847$	16.0000	0.549767
$848$	3.92820	0.134895
$849$	9.85641	0.338271
$850$	−14.1244	−0.484461
$851$	1.75129	0.0600334
$852$	−10.7321	−0.367674
$853$	−23.2487	−0.796021	−0.398010	−	0.917381i	$-0.630299\pi$
$853$	−23.2487	−0.796021	−0.398010	+	0.917381i	$0.630299\pi$
$854$	0.267949	0.00916903
$855$	17.6603	0.603968
$856$	−19.9282	−0.681132
$857$	12.5359	0.428218	0.214109	−	0.976810i	$-0.431315\pi$
$857$	12.5359	0.428218	0.214109	+	0.976810i	$0.431315\pi$
$858$	0	0
$859$	27.1962	0.927921	0.463960	−	0.885856i	$-0.346428\pi$
$859$	27.1962	0.927921	0.463960	+	0.885856i	$0.346428\pi$
$860$	14.3923	0.490774
$861$	−1.53590	−0.0523433
$862$	−11.1244	−0.378897
$863$	11.8564	0.403597	0.201798	−	0.979427i	$-0.435321\pi$
$863$	11.8564	0.403597	0.201798	+	0.979427i	$0.435321\pi$
$864$	1.00000	0.0340207
$865$	22.3923	0.761361
$866$	39.8564	1.35438
$867$	15.8564	0.538512
$868$	−6.73205	−0.228501
$869$	46.7654	1.58641
$870$	28.5885	0.969239
$871$	0	0
$872$	14.7321	0.498890
$873$	3.80385	0.128741
$874$	3.46410	0.117175
$875$	6.92820	0.234216
$876$	−5.46410	−0.184615
$877$	19.4115	0.655481	0.327741	−	0.944768i	$-0.393713\pi$
$877$	19.4115	0.655481	0.327741	+	0.944768i	$0.393713\pi$
$878$	−11.3205	−0.382049
$879$	14.9282	0.503516
$880$	−14.1962	−0.478552
$881$	15.7128	0.529378	0.264689	−	0.964334i	$-0.414731\pi$
$881$	15.7128	0.529378	0.264689	+	0.964334i	$0.414731\pi$
$882$	1.00000	0.0336718
$883$	−19.5167	−0.656788	−0.328394	−	0.944541i	$-0.606507\pi$
$883$	−19.5167	−0.656788	−0.328394	+	0.944541i	$0.606507\pi$
$884$	0	0
$885$	13.4641	0.452591
$886$	−25.0000	−0.839891
$887$	−3.33975	−0.112138	−0.0560688	−	0.998427i	$-0.517857\pi$
$887$	−3.33975	−0.112138	−0.0560688	+	0.998427i	$0.517857\pi$
$888$	−3.26795	−0.109665
$889$	−6.39230	−0.214391
$890$	29.6603	0.994214
$891$	5.19615	0.174078
$892$	1.46410	0.0490217
$893$	−64.1769	−2.14760
$894$	8.00000	0.267560
$895$	−9.46410	−0.316350
$896$	1.00000	0.0334077
$897$	0	0
$898$	−22.9808	−0.766878
$899$	70.4449	2.34947
$900$	2.46410	0.0821367
$901$	−22.5167	−0.750139
$902$	−7.98076	−0.265730
$903$	−5.26795	−0.175306
$904$	−9.66025	−0.321295
$905$	48.4449	1.61036
$906$	−9.19615	−0.305522
$907$	9.60770	0.319018	0.159509	−	0.987196i	$-0.449009\pi$
$907$	9.60770	0.319018	0.159509	+	0.987196i	$0.449009\pi$
$908$	−21.3205	−0.707546
$909$	−8.92820	−0.296130
$910$	0	0
$911$	14.8756	0.492852	0.246426	−	0.969162i	$-0.420744\pi$
$911$	14.8756	0.492852	0.246426	+	0.969162i	$0.420744\pi$
$912$	−6.46410	−0.214048
$913$	66.1577	2.18950
$914$	25.7128	0.850504
$915$	−0.732051	−0.0242009
$916$	3.39230	0.112085
$917$	−1.07180	−0.0353938
$918$	−5.73205	−0.189186
$919$	42.7128	1.40897	0.704483	−	0.709721i	$-0.251179\pi$
$919$	42.7128	1.40897	0.704483	+	0.709721i	$0.251179\pi$
$920$	1.46410	0.0482700
$921$	5.00000	0.164756
$922$	6.92820	0.228168
$923$	0	0
$924$	5.19615	0.170941
$925$	−8.05256	−0.264767
$926$	−32.6603	−1.07328
$927$	−5.80385	−0.190623
$928$	−10.4641	−0.343501
$929$	9.92820	0.325734	0.162867	−	0.986648i	$-0.447926\pi$
$929$	9.92820	0.325734	0.162867	+	0.986648i	$0.447926\pi$
$930$	18.3923	0.603107
$931$	−6.46410	−0.211852
$932$	12.5885	0.412349
$933$	−25.1962	−0.824885
$934$	−5.07180	−0.165954
$935$	81.3731	2.66118
$936$	0	0
$937$	−11.7128	−0.382641	−0.191320	−	0.981528i	$-0.561277\pi$
$937$	−11.7128	−0.382641	−0.191320	+	0.981528i	$0.561277\pi$
$938$	10.0000	0.326512
$939$	31.1244	1.01570
$940$	−27.1244	−0.884699
$941$	7.32051	0.238642	0.119321	−	0.992856i	$-0.461928\pi$
$941$	7.32051	0.238642	0.119321	+	0.992856i	$0.461928\pi$
$942$	−4.53590	−0.147788
$943$	0.823085	0.0268034
$944$	−4.92820	−0.160399
$945$	−2.73205	−0.0888736
$946$	−27.3731	−0.889975
$947$	−22.9090	−0.744441	−0.372221	−	0.928144i	$-0.621404\pi$
$947$	−22.9090	−0.744441	−0.372221	+	0.928144i	$0.621404\pi$
$948$	9.00000	0.292306
$949$	0	0
$950$	−15.9282	−0.516779
$951$	−26.7846	−0.868550
$952$	−5.73205	−0.185777
$953$	−17.6603	−0.572072	−0.286036	−	0.958219i	$-0.592338\pi$
$953$	−17.6603	−0.572072	−0.286036	+	0.958219i	$0.592338\pi$
$954$	3.92820	0.127180
$955$	−6.00000	−0.194155
$956$	−4.58846	−0.148401
$957$	−54.3731	−1.75763
$958$	22.8564	0.738457
$959$	−12.5359	−0.404805
$960$	−2.73205	−0.0881766
$961$	14.3205	0.461952
$962$	0	0
$963$	−19.9282	−0.642177
$964$	−2.92820	−0.0943111
$965$	−64.4449	−2.07455
$966$	−0.535898	−0.0172422
$967$	28.7846	0.925651	0.462825	−	0.886450i	$-0.346836\pi$
$967$	28.7846	0.925651	0.462825	+	0.886450i	$0.346836\pi$
$968$	16.0000	0.514259
$969$	37.0526	1.19030
$970$	−10.3923	−0.333677
$971$	−38.1051	−1.22285	−0.611426	−	0.791302i	$-0.709404\pi$
$971$	−38.1051	−1.22285	−0.611426	+	0.791302i	$0.709404\pi$
$972$	1.00000	0.0320750
$973$	−21.0526	−0.674914
$974$	−29.4449	−0.943474
$975$	0	0
$976$	0.267949	0.00857684
$977$	−19.6077	−0.627306	−0.313653	−	0.949538i	$-0.601553\pi$
$977$	−19.6077	−0.627306	−0.313653	+	0.949538i	$0.601553\pi$
$978$	17.1244	0.547577
$979$	−56.4115	−1.80292
$980$	−2.73205	−0.0872722
$981$	14.7321	0.470358
$982$	14.3923	0.459277
$983$	−18.0000	−0.574111	−0.287055	−	0.957914i	$-0.592676\pi$
$983$	−18.0000	−0.574111	−0.287055	+	0.957914i	$0.592676\pi$
$984$	−1.53590	−0.0489627
$985$	−10.1962	−0.324876
$986$	59.9808	1.91018
$987$	9.92820	0.316018
$988$	0	0
$989$	2.82309	0.0897689
$990$	−14.1962	−0.451183
$991$	−11.2487	−0.357327	−0.178664	−	0.983910i	$-0.557177\pi$
$991$	−11.2487	−0.357327	−0.178664	+	0.983910i	$0.557177\pi$
$992$	−6.73205	−0.213743
$993$	34.7846	1.10386
$994$	−10.7321	−0.340400
$995$	18.0000	0.570638
$996$	12.7321	0.403430
$997$	−8.90897	−0.282150	−0.141075	−	0.989999i	$-0.545056\pi$
$997$	−8.90897	−0.282150	−0.141075	+	0.989999i	$0.545056\pi$
$998$	−10.5885	−0.335172
$999$	−3.26795	−0.103393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.by.1.1		2
13.6	odd	12		546.2.s.b.127.1	yes	4
13.11	odd	12		546.2.s.b.43.1	✓	4
13.12	even	2		7098.2.a.bo.1.2		2
39.11	even	12		1638.2.bj.a.1135.2		4
39.32	even	12		1638.2.bj.a.127.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.b.43.1	✓	4	13.11	odd	12
546.2.s.b.127.1	yes	4	13.6	odd	12
1638.2.bj.a.127.2		4	39.32	even	12
1638.2.bj.a.1135.2		4	39.11	even	12
7098.2.a.bo.1.2		2	13.12	even	2
7098.2.a.by.1.1		2	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.73205 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.73205 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.73205 q^{10} +5.19615 q^{11} +1.00000 q^{12} +1.00000 q^{14} -2.73205 q^{15} +1.00000 q^{16} -5.73205 q^{17} +1.00000 q^{18} -6.46410 q^{19} -2.73205 q^{20} +1.00000 q^{21} +5.19615 q^{22} -0.535898 q^{23} +1.00000 q^{24} +2.46410 q^{25} +1.00000 q^{27} +1.00000 q^{28} -10.4641 q^{29} -2.73205 q^{30} -6.73205 q^{31} +1.00000 q^{32} +5.19615 q^{33} -5.73205 q^{34} -2.73205 q^{35} +1.00000 q^{36} -3.26795 q^{37} -6.46410 q^{38} -2.73205 q^{40} -1.53590 q^{41} +1.00000 q^{42} -5.26795 q^{43} +5.19615 q^{44} -2.73205 q^{45} -0.535898 q^{46} +9.92820 q^{47} +1.00000 q^{48} +1.00000 q^{49} +2.46410 q^{50} -5.73205 q^{51} +3.92820 q^{53} +1.00000 q^{54} -14.1962 q^{55} +1.00000 q^{56} -6.46410 q^{57} -10.4641 q^{58} -4.92820 q^{59} -2.73205 q^{60} +0.267949 q^{61} -6.73205 q^{62} +1.00000 q^{63} +1.00000 q^{64} +5.19615 q^{66} +10.0000 q^{67} -5.73205 q^{68} -0.535898 q^{69} -2.73205 q^{70} -10.7321 q^{71} +1.00000 q^{72} -5.46410 q^{73} -3.26795 q^{74} +2.46410 q^{75} -6.46410 q^{76} +5.19615 q^{77} +9.00000 q^{79} -2.73205 q^{80} +1.00000 q^{81} -1.53590 q^{82} +12.7321 q^{83} +1.00000 q^{84} +15.6603 q^{85} -5.26795 q^{86} -10.4641 q^{87} +5.19615 q^{88} -10.8564 q^{89} -2.73205 q^{90} -0.535898 q^{92} -6.73205 q^{93} +9.92820 q^{94} +17.6603 q^{95} +1.00000 q^{96} +3.80385 q^{97} +1.00000 q^{98} +5.19615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{12} + 2 q^{14} - 2 q^{15} + 2 q^{16} - 8 q^{17} + 2 q^{18} - 6 q^{19} - 2 q^{20} + 2 q^{21} - 8 q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{27} + 2 q^{28} - 14 q^{29} - 2 q^{30} - 10 q^{31} + 2 q^{32} - 8 q^{34} - 2 q^{35} + 2 q^{36} - 10 q^{37} - 6 q^{38} - 2 q^{40} - 10 q^{41} + 2 q^{42} - 14 q^{43} - 2 q^{45} - 8 q^{46} + 6 q^{47} + 2 q^{48} + 2 q^{49} - 2 q^{50} - 8 q^{51} - 6 q^{53} + 2 q^{54} - 18 q^{55} + 2 q^{56} - 6 q^{57} - 14 q^{58} + 4 q^{59} - 2 q^{60} + 4 q^{61} - 10 q^{62} + 2 q^{63} + 2 q^{64} + 20 q^{67} - 8 q^{68} - 8 q^{69} - 2 q^{70} - 18 q^{71} + 2 q^{72} - 4 q^{73} - 10 q^{74} - 2 q^{75} - 6 q^{76} + 18 q^{79} - 2 q^{80} + 2 q^{81} - 10 q^{82} + 22 q^{83} + 2 q^{84} + 14 q^{85} - 14 q^{86} - 14 q^{87} + 6 q^{89} - 2 q^{90} - 8 q^{92} - 10 q^{93} + 6 q^{94} + 18 q^{95} + 2 q^{96} + 18 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^12 + 2 * q^14 - 2 * q^15 + 2 * q^16 - 8 * q^17 + 2 * q^18 - 6 * q^19 - 2 * q^20 + 2 * q^21 - 8 * q^23 + 2 * q^24 - 2 * q^25 + 2 * q^27 + 2 * q^28 - 14 * q^29 - 2 * q^30 - 10 * q^31 + 2 * q^32 - 8 * q^34 - 2 * q^35 + 2 * q^36 - 10 * q^37 - 6 * q^38 - 2 * q^40 - 10 * q^41 + 2 * q^42 - 14 * q^43 - 2 * q^45 - 8 * q^46 + 6 * q^47 + 2 * q^48 + 2 * q^49 - 2 * q^50 - 8 * q^51 - 6 * q^53 + 2 * q^54 - 18 * q^55 + 2 * q^56 - 6 * q^57 - 14 * q^58 + 4 * q^59 - 2 * q^60 + 4 * q^61 - 10 * q^62 + 2 * q^63 + 2 * q^64 + 20 * q^67 - 8 * q^68 - 8 * q^69 - 2 * q^70 - 18 * q^71 + 2 * q^72 - 4 * q^73 - 10 * q^74 - 2 * q^75 - 6 * q^76 + 18 * q^79 - 2 * q^80 + 2 * q^81 - 10 * q^82 + 22 * q^83 + 2 * q^84 + 14 * q^85 - 14 * q^86 - 14 * q^87 + 6 * q^89 - 2 * q^90 - 8 * q^92 - 10 * q^93 + 6 * q^94 + 18 * q^95 + 2 * q^96 + 18 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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