LMFDB - Embedded newform 7098.2.a.cm.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$56.6778153547$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.24698$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.554958 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.554958 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.554958 q^{10} -1.64310 q^{11} +1.00000 q^{12} -1.00000 q^{14} -0.554958 q^{15} +1.00000 q^{16} +2.91185 q^{17} +1.00000 q^{18} -6.85086 q^{19} -0.554958 q^{20} -1.00000 q^{21} -1.64310 q^{22} +2.93900 q^{23} +1.00000 q^{24} -4.69202 q^{25} +1.00000 q^{27} -1.00000 q^{28} -3.69202 q^{29} -0.554958 q^{30} +1.13706 q^{31} +1.00000 q^{32} -1.64310 q^{33} +2.91185 q^{34} +0.554958 q^{35} +1.00000 q^{36} -7.93900 q^{37} -6.85086 q^{38} -0.554958 q^{40} -2.55496 q^{41} -1.00000 q^{42} -10.1468 q^{43} -1.64310 q^{44} -0.554958 q^{45} +2.93900 q^{46} -11.5918 q^{47} +1.00000 q^{48} +1.00000 q^{49} -4.69202 q^{50} +2.91185 q^{51} +5.13706 q^{53} +1.00000 q^{54} +0.911854 q^{55} -1.00000 q^{56} -6.85086 q^{57} -3.69202 q^{58} +0.158834 q^{59} -0.554958 q^{60} -1.00000 q^{61} +1.13706 q^{62} -1.00000 q^{63} +1.00000 q^{64} -1.64310 q^{66} +1.69202 q^{67} +2.91185 q^{68} +2.93900 q^{69} +0.554958 q^{70} -1.01208 q^{71} +1.00000 q^{72} -5.97823 q^{73} -7.93900 q^{74} -4.69202 q^{75} -6.85086 q^{76} +1.64310 q^{77} +8.92692 q^{79} -0.554958 q^{80} +1.00000 q^{81} -2.55496 q^{82} +15.2664 q^{83} -1.00000 q^{84} -1.61596 q^{85} -10.1468 q^{86} -3.69202 q^{87} -1.64310 q^{88} -3.59419 q^{89} -0.554958 q^{90} +2.93900 q^{92} +1.13706 q^{93} -11.5918 q^{94} +3.80194 q^{95} +1.00000 q^{96} +16.1347 q^{97} +1.00000 q^{98} -1.64310 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 2 q^{5} + 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 2 * q^5 + 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 2 q^{5} + 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 2 q^{10} - 9 q^{11} + 3 q^{12} - 3 q^{14} - 2 q^{15} + 3 q^{16} + 5 q^{17} + 3 q^{18} - 7 q^{19} - 2 q^{20} - 3 q^{21} - 9 q^{22} - q^{23} + 3 q^{24} - 9 q^{25} + 3 q^{27} - 3 q^{28} - 6 q^{29} - 2 q^{30} - 2 q^{31} + 3 q^{32} - 9 q^{33} + 5 q^{34} + 2 q^{35} + 3 q^{36} - 14 q^{37} - 7 q^{38} - 2 q^{40} - 8 q^{41} - 3 q^{42} - 3 q^{43} - 9 q^{44} - 2 q^{45} - q^{46} - 7 q^{47} + 3 q^{48} + 3 q^{49} - 9 q^{50} + 5 q^{51} + 10 q^{53} + 3 q^{54} - q^{55} - 3 q^{56} - 7 q^{57} - 6 q^{58} - 8 q^{59} - 2 q^{60} - 3 q^{61} - 2 q^{62} - 3 q^{63} + 3 q^{64} - 9 q^{66} + 5 q^{68} - q^{69} + 2 q^{70} - 22 q^{71} + 3 q^{72} - 21 q^{73} - 14 q^{74} - 9 q^{75} - 7 q^{76} + 9 q^{77} - 2 q^{79} - 2 q^{80} + 3 q^{81} - 8 q^{82} - 3 q^{83} - 3 q^{84} - 15 q^{85} - 3 q^{86} - 6 q^{87} - 9 q^{88} - 24 q^{89} - 2 q^{90} - q^{92} - 2 q^{93} - 7 q^{94} + 7 q^{95} + 3 q^{96} + 2 q^{97} + 3 q^{98} - 9 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 2 * q^5 + 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 - 2 * q^10 - 9 * q^11 + 3 * q^12 - 3 * q^14 - 2 * q^15 + 3 * q^16 + 5 * q^17 + 3 * q^18 - 7 * q^19 - 2 * q^20 - 3 * q^21 - 9 * q^22 - q^23 + 3 * q^24 - 9 * q^25 + 3 * q^27 - 3 * q^28 - 6 * q^29 - 2 * q^30 - 2 * q^31 + 3 * q^32 - 9 * q^33 + 5 * q^34 + 2 * q^35 + 3 * q^36 - 14 * q^37 - 7 * q^38 - 2 * q^40 - 8 * q^41 - 3 * q^42 - 3 * q^43 - 9 * q^44 - 2 * q^45 - q^46 - 7 * q^47 + 3 * q^48 + 3 * q^49 - 9 * q^50 + 5 * q^51 + 10 * q^53 + 3 * q^54 - q^55 - 3 * q^56 - 7 * q^57 - 6 * q^58 - 8 * q^59 - 2 * q^60 - 3 * q^61 - 2 * q^62 - 3 * q^63 + 3 * q^64 - 9 * q^66 + 5 * q^68 - q^69 + 2 * q^70 - 22 * q^71 + 3 * q^72 - 21 * q^73 - 14 * q^74 - 9 * q^75 - 7 * q^76 + 9 * q^77 - 2 * q^79 - 2 * q^80 + 3 * q^81 - 8 * q^82 - 3 * q^83 - 3 * q^84 - 15 * q^85 - 3 * q^86 - 6 * q^87 - 9 * q^88 - 24 * q^89 - 2 * q^90 - q^92 - 2 * q^93 - 7 * q^94 + 7 * q^95 + 3 * q^96 + 2 * q^97 + 3 * q^98 - 9 * 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
$5$	−0.554958	−0.248185	−0.124092	−	0.992271i	$-0.539602\pi$
$5$	−0.554958	−0.248185	−0.124092	+	0.992271i	$0.539602\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.554958	−0.175493
$11$	−1.64310	−0.495415	−0.247707	−	0.968835i	$-0.579677\pi$
$11$	−1.64310	−0.495415	−0.247707	+	0.968835i	$0.579677\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	−0.554958	−0.143290
$16$	1.00000	0.250000
$17$	2.91185	0.706228	0.353114	−	0.935580i	$-0.385123\pi$
$17$	2.91185	0.706228	0.353114	+	0.935580i	$0.385123\pi$
$18$	1.00000	0.235702
$19$	−6.85086	−1.57169	−0.785847	−	0.618421i	$-0.787773\pi$
$19$	−6.85086	−1.57169	−0.785847	+	0.618421i	$0.787773\pi$
$20$	−0.554958	−0.124092
$21$	−1.00000	−0.218218
$22$	−1.64310	−0.350311
$23$	2.93900	0.612824	0.306412	−	0.951899i	$-0.400871\pi$
$23$	2.93900	0.612824	0.306412	+	0.951899i	$0.400871\pi$
$24$	1.00000	0.204124
$25$	−4.69202	−0.938404
$26$	0	0
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	−3.69202	−0.685591	−0.342796	−	0.939410i	$-0.611374\pi$
$29$	−3.69202	−0.685591	−0.342796	+	0.939410i	$0.611374\pi$
$30$	−0.554958	−0.101321
$31$	1.13706	0.204223	0.102111	−	0.994773i	$-0.467440\pi$
$31$	1.13706	0.204223	0.102111	+	0.994773i	$0.467440\pi$
$32$	1.00000	0.176777
$33$	−1.64310	−0.286028
$34$	2.91185	0.499379
$35$	0.554958	0.0938050
$36$	1.00000	0.166667
$37$	−7.93900	−1.30516	−0.652582	−	0.757718i	$-0.726314\pi$
$37$	−7.93900	−1.30516	−0.652582	+	0.757718i	$0.726314\pi$
$38$	−6.85086	−1.11136
$39$	0	0
$40$	−0.554958	−0.0877466
$41$	−2.55496	−0.399017	−0.199509	−	0.979896i	$-0.563935\pi$
$41$	−2.55496	−0.399017	−0.199509	+	0.979896i	$0.563935\pi$
$42$	−1.00000	−0.154303
$43$	−10.1468	−1.54737	−0.773683	−	0.633573i	$-0.781587\pi$
$43$	−10.1468	−1.54737	−0.773683	+	0.633573i	$0.781587\pi$
$44$	−1.64310	−0.247707
$45$	−0.554958	−0.0827283
$46$	2.93900	0.433332
$47$	−11.5918	−1.69084	−0.845418	−	0.534105i	$-0.820649\pi$
$47$	−11.5918	−1.69084	−0.845418	+	0.534105i	$0.820649\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−4.69202	−0.663552
$51$	2.91185	0.407741
$52$	0	0
$53$	5.13706	0.705630	0.352815	−	0.935693i	$-0.385225\pi$
$53$	5.13706	0.705630	0.352815	+	0.935693i	$0.385225\pi$
$54$	1.00000	0.136083
$55$	0.911854	0.122954
$56$	−1.00000	−0.133631
$57$	−6.85086	−0.907418
$58$	−3.69202	−0.484786
$59$	0.158834	0.0206784	0.0103392	−	0.999947i	$-0.496709\pi$
$59$	0.158834	0.0206784	0.0103392	+	0.999947i	$0.496709\pi$
$60$	−0.554958	−0.0716448
$61$	−1.00000	−0.128037	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	−1.00000	−0.128037	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	1.13706	0.144407
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−1.64310	−0.202252
$67$	1.69202	0.206713	0.103357	−	0.994644i	$-0.467042\pi$
$67$	1.69202	0.206713	0.103357	+	0.994644i	$0.467042\pi$
$68$	2.91185	0.353114
$69$	2.93900	0.353814
$70$	0.554958	0.0663302
$71$	−1.01208	−0.120112	−0.0600560	−	0.998195i	$-0.519128\pi$
$71$	−1.01208	−0.120112	−0.0600560	+	0.998195i	$0.519128\pi$
$72$	1.00000	0.117851
$73$	−5.97823	−0.699699	−0.349849	−	0.936806i	$-0.613767\pi$
$73$	−5.97823	−0.699699	−0.349849	+	0.936806i	$0.613767\pi$
$74$	−7.93900	−0.922890
$75$	−4.69202	−0.541788
$76$	−6.85086	−0.785847
$77$	1.64310	0.187249
$78$	0	0
$79$	8.92692	1.00436	0.502178	−	0.864764i	$-0.332532\pi$
$79$	8.92692	1.00436	0.502178	+	0.864764i	$0.332532\pi$
$80$	−0.554958	−0.0620462
$81$	1.00000	0.111111
$82$	−2.55496	−0.282148
$83$	15.2664	1.67570	0.837850	−	0.545900i	$-0.183812\pi$
$83$	15.2664	1.67570	0.837850	+	0.545900i	$0.183812\pi$
$84$	−1.00000	−0.109109
$85$	−1.61596	−0.175275
$86$	−10.1468	−1.09415
$87$	−3.69202	−0.395826
$88$	−1.64310	−0.175155
$89$	−3.59419	−0.380983	−0.190492	−	0.981689i	$-0.561008\pi$
$89$	−3.59419	−0.380983	−0.190492	+	0.981689i	$0.561008\pi$
$90$	−0.554958	−0.0584977
$91$	0	0
$92$	2.93900	0.306412
$93$	1.13706	0.117908
$94$	−11.5918	−1.19560
$95$	3.80194	0.390071
$96$	1.00000	0.102062
$97$	16.1347	1.63823	0.819114	−	0.573631i	$-0.194466\pi$
$97$	16.1347	1.63823	0.819114	+	0.573631i	$0.194466\pi$
$98$	1.00000	0.101015
$99$	−1.64310	−0.165138
$100$	−4.69202	−0.469202
$101$	−3.92394	−0.390446	−0.195223	−	0.980759i	$-0.562543\pi$
$101$	−3.92394	−0.390446	−0.195223	+	0.980759i	$0.562543\pi$
$102$	2.91185	0.288317
$103$	−11.3448	−1.11784	−0.558919	−	0.829222i	$-0.688784\pi$
$103$	−11.3448	−1.11784	−0.558919	+	0.829222i	$0.688784\pi$
$104$	0	0
$105$	0.554958	0.0541584
$106$	5.13706	0.498956
$107$	7.93362	0.766972	0.383486	−	0.923547i	$-0.374723\pi$
$107$	7.93362	0.766972	0.383486	+	0.923547i	$0.374723\pi$
$108$	1.00000	0.0962250
$109$	−8.86054	−0.848686	−0.424343	−	0.905501i	$-0.639495\pi$
$109$	−8.86054	−0.848686	−0.424343	+	0.905501i	$0.639495\pi$
$110$	0.911854	0.0869419
$111$	−7.93900	−0.753537
$112$	−1.00000	−0.0944911
$113$	−1.55496	−0.146278	−0.0731391	−	0.997322i	$-0.523302\pi$
$113$	−1.55496	−0.146278	−0.0731391	+	0.997322i	$0.523302\pi$
$114$	−6.85086	−0.641641
$115$	−1.63102	−0.152094
$116$	−3.69202	−0.342796
$117$	0	0
$118$	0.158834	0.0146218
$119$	−2.91185	−0.266929
$120$	−0.554958	−0.0506605
$121$	−8.30021	−0.754564
$122$	−1.00000	−0.0905357
$123$	−2.55496	−0.230373
$124$	1.13706	0.102111
$125$	5.37867	0.481083
$126$	−1.00000	−0.0890871
$127$	6.33944	0.562534	0.281267	−	0.959630i	$-0.409245\pi$
$127$	6.33944	0.562534	0.281267	+	0.959630i	$0.409245\pi$
$128$	1.00000	0.0883883
$129$	−10.1468	−0.893372
$130$	0	0
$131$	6.78986	0.593232	0.296616	−	0.954997i	$-0.404142\pi$
$131$	6.78986	0.593232	0.296616	+	0.954997i	$0.404142\pi$
$132$	−1.64310	−0.143014
$133$	6.85086	0.594044
$134$	1.69202	0.146168
$135$	−0.554958	−0.0477632
$136$	2.91185	0.249689
$137$	−11.0804	−0.946660	−0.473330	−	0.880885i	$-0.656948\pi$
$137$	−11.0804	−0.946660	−0.473330	+	0.880885i	$0.656948\pi$
$138$	2.93900	0.250184
$139$	−19.4306	−1.64808	−0.824040	−	0.566532i	$-0.808285\pi$
$139$	−19.4306	−1.64808	−0.824040	+	0.566532i	$0.808285\pi$
$140$	0.554958	0.0469025
$141$	−11.5918	−0.976205
$142$	−1.01208	−0.0849320
$143$	0	0
$144$	1.00000	0.0833333
$145$	2.04892	0.170153
$146$	−5.97823	−0.494762
$147$	1.00000	0.0824786
$148$	−7.93900	−0.652582
$149$	−14.5767	−1.19417	−0.597086	−	0.802177i	$-0.703675\pi$
$149$	−14.5767	−1.19417	−0.597086	+	0.802177i	$0.703675\pi$
$150$	−4.69202	−0.383102
$151$	13.6310	1.10928	0.554638	−	0.832091i	$-0.312857\pi$
$151$	13.6310	1.10928	0.554638	+	0.832091i	$0.312857\pi$
$152$	−6.85086	−0.555678
$153$	2.91185	0.235409
$154$	1.64310	0.132405
$155$	−0.631023	−0.0506850
$156$	0	0
$157$	5.52542	0.440976	0.220488	−	0.975390i	$-0.429235\pi$
$157$	5.52542	0.440976	0.220488	+	0.975390i	$0.429235\pi$
$158$	8.92692	0.710188
$159$	5.13706	0.407396
$160$	−0.554958	−0.0438733
$161$	−2.93900	−0.231626
$162$	1.00000	0.0785674
$163$	−7.57673	−0.593455	−0.296728	−	0.954962i	$-0.595895\pi$
$163$	−7.57673	−0.593455	−0.296728	+	0.954962i	$0.595895\pi$
$164$	−2.55496	−0.199509
$165$	0.911854	0.0709877
$166$	15.2664	1.18490
$167$	−20.2717	−1.56867	−0.784337	−	0.620335i	$-0.786997\pi$
$167$	−20.2717	−1.56867	−0.784337	+	0.620335i	$0.786997\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	−1.61596	−0.123938
$171$	−6.85086	−0.523898
$172$	−10.1468	−0.773683
$173$	−5.03146	−0.382535	−0.191267	−	0.981538i	$-0.561260\pi$
$173$	−5.03146	−0.382535	−0.191267	+	0.981538i	$0.561260\pi$
$174$	−3.69202	−0.279891
$175$	4.69202	0.354683
$176$	−1.64310	−0.123854
$177$	0.158834	0.0119387
$178$	−3.59419	−0.269396
$179$	4.52542	0.338246	0.169123	−	0.985595i	$-0.445907\pi$
$179$	4.52542	0.338246	0.169123	+	0.985595i	$0.445907\pi$
$180$	−0.554958	−0.0413641
$181$	7.59717	0.564693	0.282347	−	0.959312i	$-0.408887\pi$
$181$	7.59717	0.564693	0.282347	+	0.959312i	$0.408887\pi$
$182$	0	0
$183$	−1.00000	−0.0739221
$184$	2.93900	0.216666
$185$	4.40581	0.323922
$186$	1.13706	0.0833735
$187$	−4.78448	−0.349876
$188$	−11.5918	−0.845418
$189$	−1.00000	−0.0727393
$190$	3.80194	0.275822
$191$	−20.6136	−1.49155	−0.745773	−	0.666201i	$-0.767919\pi$
$191$	−20.6136	−1.49155	−0.745773	+	0.666201i	$0.767919\pi$
$192$	1.00000	0.0721688
$193$	−5.88338	−0.423495	−0.211747	−	0.977324i	$-0.567915\pi$
$193$	−5.88338	−0.423495	−0.211747	+	0.977324i	$0.567915\pi$
$194$	16.1347	1.15840
$195$	0	0
$196$	1.00000	0.0714286
$197$	−19.1317	−1.36308	−0.681538	−	0.731783i	$-0.738689\pi$
$197$	−19.1317	−1.36308	−0.681538	+	0.731783i	$0.738689\pi$
$198$	−1.64310	−0.116770
$199$	−7.22282	−0.512012	−0.256006	−	0.966675i	$-0.582407\pi$
$199$	−7.22282	−0.512012	−0.256006	+	0.966675i	$0.582407\pi$
$200$	−4.69202	−0.331776
$201$	1.69202	0.119346
$202$	−3.92394	−0.276087
$203$	3.69202	0.259129
$204$	2.91185	0.203871
$205$	1.41789	0.0990301
$206$	−11.3448	−0.790431
$207$	2.93900	0.204275
$208$	0	0
$209$	11.2567	0.778640
$210$	0.554958	0.0382957
$211$	18.5894	1.27975	0.639874	−	0.768480i	$-0.278987\pi$
$211$	18.5894	1.27975	0.639874	+	0.768480i	$0.278987\pi$
$212$	5.13706	0.352815
$213$	−1.01208	−0.0693467
$214$	7.93362	0.542331
$215$	5.63102	0.384033
$216$	1.00000	0.0680414
$217$	−1.13706	−0.0771889
$218$	−8.86054	−0.600112
$219$	−5.97823	−0.403971
$220$	0.911854	0.0614772
$221$	0	0
$222$	−7.93900	−0.532831
$223$	20.3230	1.36093	0.680466	−	0.732780i	$-0.261777\pi$
$223$	20.3230	1.36093	0.680466	+	0.732780i	$0.261777\pi$
$224$	−1.00000	−0.0668153
$225$	−4.69202	−0.312801
$226$	−1.55496	−0.103434
$227$	14.8756	0.987329	0.493664	−	0.869652i	$-0.335657\pi$
$227$	14.8756	0.987329	0.493664	+	0.869652i	$0.335657\pi$
$228$	−6.85086	−0.453709
$229$	−4.42221	−0.292228	−0.146114	−	0.989268i	$-0.546677\pi$
$229$	−4.42221	−0.292228	−0.146114	+	0.989268i	$0.546677\pi$
$230$	−1.63102	−0.107546
$231$	1.64310	0.108108
$232$	−3.69202	−0.242393
$233$	−14.0030	−0.917366	−0.458683	−	0.888600i	$-0.651679\pi$
$233$	−14.0030	−0.917366	−0.458683	+	0.888600i	$0.651679\pi$
$234$	0	0
$235$	6.43296	0.419640
$236$	0.158834	0.0103392
$237$	8.92692	0.579866
$238$	−2.91185	−0.188747
$239$	−18.2741	−1.18205	−0.591027	−	0.806651i	$-0.701278\pi$
$239$	−18.2741	−1.18205	−0.591027	+	0.806651i	$0.701278\pi$
$240$	−0.554958	−0.0358224
$241$	−16.5972	−1.06912	−0.534559	−	0.845131i	$-0.679522\pi$
$241$	−16.5972	−1.06912	−0.534559	+	0.845131i	$0.679522\pi$
$242$	−8.30021	−0.533558
$243$	1.00000	0.0641500
$244$	−1.00000	−0.0640184
$245$	−0.554958	−0.0354550
$246$	−2.55496	−0.162898
$247$	0	0
$248$	1.13706	0.0722036
$249$	15.2664	0.967466
$250$	5.37867	0.340177
$251$	−8.93123	−0.563734	−0.281867	−	0.959453i	$-0.590954\pi$
$251$	−8.93123	−0.563734	−0.281867	+	0.959453i	$0.590954\pi$
$252$	−1.00000	−0.0629941
$253$	−4.82908	−0.303602
$254$	6.33944	0.397772
$255$	−1.61596	−0.101195
$256$	1.00000	0.0625000
$257$	3.21552	0.200579	0.100289	−	0.994958i	$-0.468023\pi$
$257$	3.21552	0.200579	0.100289	+	0.994958i	$0.468023\pi$
$258$	−10.1468	−0.631709
$259$	7.93900	0.493306
$260$	0	0
$261$	−3.69202	−0.228530
$262$	6.78986	0.419479
$263$	6.08815	0.375411	0.187706	−	0.982225i	$-0.439895\pi$
$263$	6.08815	0.375411	0.187706	+	0.982225i	$0.439895\pi$
$264$	−1.64310	−0.101126
$265$	−2.85086	−0.175127
$266$	6.85086	0.420053
$267$	−3.59419	−0.219961
$268$	1.69202	0.103357
$269$	3.47219	0.211703	0.105852	−	0.994382i	$-0.466243\pi$
$269$	3.47219	0.211703	0.105852	+	0.994382i	$0.466243\pi$
$270$	−0.554958	−0.0337737
$271$	23.5254	1.42907	0.714534	−	0.699601i	$-0.246639\pi$
$271$	23.5254	1.42907	0.714534	+	0.699601i	$0.246639\pi$
$272$	2.91185	0.176557
$273$	0	0
$274$	−11.0804	−0.669390
$275$	7.70948	0.464899
$276$	2.93900	0.176907
$277$	8.71917	0.523884	0.261942	−	0.965084i	$-0.415637\pi$
$277$	8.71917	0.523884	0.261942	+	0.965084i	$0.415637\pi$
$278$	−19.4306	−1.16537
$279$	1.13706	0.0680742
$280$	0.554958	0.0331651
$281$	−14.5453	−0.867698	−0.433849	−	0.900986i	$-0.642845\pi$
$281$	−14.5453	−0.867698	−0.433849	+	0.900986i	$0.642845\pi$
$282$	−11.5918	−0.690281
$283$	14.2567	0.847471	0.423735	−	0.905786i	$-0.360719\pi$
$283$	14.2567	0.847471	0.423735	+	0.905786i	$0.360719\pi$
$284$	−1.01208	−0.0600560
$285$	3.80194	0.225207
$286$	0	0
$287$	2.55496	0.150814
$288$	1.00000	0.0589256
$289$	−8.52111	−0.501242
$290$	2.04892	0.120317
$291$	16.1347	0.945831
$292$	−5.97823	−0.349849
$293$	−9.23059	−0.539257	−0.269628	−	0.962964i	$-0.586901\pi$
$293$	−9.23059	−0.539257	−0.269628	+	0.962964i	$0.586901\pi$
$294$	1.00000	0.0583212
$295$	−0.0881460	−0.00513206
$296$	−7.93900	−0.461445
$297$	−1.64310	−0.0953426
$298$	−14.5767	−0.844407
$299$	0	0
$300$	−4.69202	−0.270894
$301$	10.1468	0.584849
$302$	13.6310	0.784377
$303$	−3.92394	−0.225424
$304$	−6.85086	−0.392923
$305$	0.554958	0.0317768
$306$	2.91185	0.166460
$307$	−22.3086	−1.27322	−0.636609	−	0.771187i	$-0.719663\pi$
$307$	−22.3086	−1.27322	−0.636609	+	0.771187i	$0.719663\pi$
$308$	1.64310	0.0936245
$309$	−11.3448	−0.645384
$310$	−0.631023	−0.0358397
$311$	−4.97716	−0.282229	−0.141115	−	0.989993i	$-0.545069\pi$
$311$	−4.97716	−0.282229	−0.141115	+	0.989993i	$0.545069\pi$
$312$	0	0
$313$	8.58748	0.485393	0.242697	−	0.970102i	$-0.421968\pi$
$313$	8.58748	0.485393	0.242697	+	0.970102i	$0.421968\pi$
$314$	5.52542	0.311817
$315$	0.554958	0.0312683
$316$	8.92692	0.502178
$317$	29.7657	1.67181	0.835904	−	0.548876i	$-0.184944\pi$
$317$	29.7657	1.67181	0.835904	+	0.548876i	$0.184944\pi$
$318$	5.13706	0.288072
$319$	6.06638	0.339652
$320$	−0.554958	−0.0310231
$321$	7.93362	0.442812
$322$	−2.93900	−0.163784
$323$	−19.9487	−1.10997
$324$	1.00000	0.0555556
$325$	0	0
$326$	−7.57673	−0.419636
$327$	−8.86054	−0.489989
$328$	−2.55496	−0.141074
$329$	11.5918	0.639076
$330$	0.911854	0.0501959
$331$	7.87369	0.432777	0.216389	−	0.976307i	$-0.430572\pi$
$331$	7.87369	0.432777	0.216389	+	0.976307i	$0.430572\pi$
$332$	15.2664	0.837850
$333$	−7.93900	−0.435055
$334$	−20.2717	−1.10922
$335$	−0.939001	−0.0513031
$336$	−1.00000	−0.0545545
$337$	−30.8920	−1.68279	−0.841397	−	0.540417i	$-0.818266\pi$
$337$	−30.8920	−1.68279	−0.841397	+	0.540417i	$0.818266\pi$
$338$	0	0
$339$	−1.55496	−0.0844537
$340$	−1.61596	−0.0876376
$341$	−1.86831	−0.101175
$342$	−6.85086	−0.370452
$343$	−1.00000	−0.0539949
$344$	−10.1468	−0.547076
$345$	−1.63102	−0.0878113
$346$	−5.03146	−0.270493
$347$	−25.0713	−1.34590	−0.672948	−	0.739689i	$-0.734972\pi$
$347$	−25.0713	−1.34590	−0.672948	+	0.739689i	$0.734972\pi$
$348$	−3.69202	−0.197913
$349$	13.9597	0.747246	0.373623	−	0.927581i	$-0.378115\pi$
$349$	13.9597	0.747246	0.373623	+	0.927581i	$0.378115\pi$
$350$	4.69202	0.250799
$351$	0	0
$352$	−1.64310	−0.0875777
$353$	−20.0629	−1.06784	−0.533921	−	0.845535i	$-0.679282\pi$
$353$	−20.0629	−1.06784	−0.533921	+	0.845535i	$0.679282\pi$
$354$	0.158834	0.00844191
$355$	0.561663	0.0298100
$356$	−3.59419	−0.190492
$357$	−2.91185	−0.154112
$358$	4.52542	0.239176
$359$	−18.3642	−0.969225	−0.484612	−	0.874729i	$-0.661039\pi$
$359$	−18.3642	−0.969225	−0.484612	+	0.874729i	$0.661039\pi$
$360$	−0.554958	−0.0292489
$361$	27.9342	1.47022
$362$	7.59717	0.399298
$363$	−8.30021	−0.435648
$364$	0	0
$365$	3.31767	0.173655
$366$	−1.00000	−0.0522708
$367$	8.29829	0.433167	0.216584	−	0.976264i	$-0.430509\pi$
$367$	8.29829	0.433167	0.216584	+	0.976264i	$0.430509\pi$
$368$	2.93900	0.153206
$369$	−2.55496	−0.133006
$370$	4.40581	0.229047
$371$	−5.13706	−0.266703
$372$	1.13706	0.0589540
$373$	−10.2101	−0.528661	−0.264331	−	0.964432i	$-0.585151\pi$
$373$	−10.2101	−0.528661	−0.264331	+	0.964432i	$0.585151\pi$
$374$	−4.78448	−0.247400
$375$	5.37867	0.277753
$376$	−11.5918	−0.597801
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	7.15883	0.367725	0.183862	−	0.982952i	$-0.441140\pi$
$379$	7.15883	0.367725	0.183862	+	0.982952i	$0.441140\pi$
$380$	3.80194	0.195035
$381$	6.33944	0.324779
$382$	−20.6136	−1.05468
$383$	20.4403	1.04445	0.522224	−	0.852808i	$-0.325102\pi$
$383$	20.4403	1.04445	0.522224	+	0.852808i	$0.325102\pi$
$384$	1.00000	0.0510310
$385$	−0.911854	−0.0464724
$386$	−5.88338	−0.299456
$387$	−10.1468	−0.515788
$388$	16.1347	0.819114
$389$	12.9226	0.655202	0.327601	−	0.944816i	$-0.393760\pi$
$389$	12.9226	0.655202	0.327601	+	0.944816i	$0.393760\pi$
$390$	0	0
$391$	8.55794	0.432794
$392$	1.00000	0.0505076
$393$	6.78986	0.342503
$394$	−19.1317	−0.963840
$395$	−4.95407	−0.249266
$396$	−1.64310	−0.0825691
$397$	−9.34780	−0.469153	−0.234576	−	0.972098i	$-0.575370\pi$
$397$	−9.34780	−0.469153	−0.234576	+	0.972098i	$0.575370\pi$
$398$	−7.22282	−0.362047
$399$	6.85086	0.342972
$400$	−4.69202	−0.234601
$401$	−8.84415	−0.441656	−0.220828	−	0.975313i	$-0.570876\pi$
$401$	−8.84415	−0.441656	−0.220828	+	0.975313i	$0.570876\pi$
$402$	1.69202	0.0843904
$403$	0	0
$404$	−3.92394	−0.195223
$405$	−0.554958	−0.0275761
$406$	3.69202	0.183232
$407$	13.0446	0.646597
$408$	2.91185	0.144158
$409$	25.5176	1.26177	0.630883	−	0.775878i	$-0.282693\pi$
$409$	25.5176	1.26177	0.630883	+	0.775878i	$0.282693\pi$
$410$	1.41789	0.0700248
$411$	−11.0804	−0.546555
$412$	−11.3448	−0.558919
$413$	−0.158834	−0.00781569
$414$	2.93900	0.144444
$415$	−8.47219	−0.415883
$416$	0	0
$417$	−19.4306	−0.951519
$418$	11.2567	0.550582
$419$	34.6233	1.69146	0.845728	−	0.533614i	$-0.179166\pi$
$419$	34.6233	1.69146	0.845728	+	0.533614i	$0.179166\pi$
$420$	0.554958	0.0270792
$421$	5.02715	0.245008	0.122504	−	0.992468i	$-0.460908\pi$
$421$	5.02715	0.245008	0.122504	+	0.992468i	$0.460908\pi$
$422$	18.5894	0.904918
$423$	−11.5918	−0.563612
$424$	5.13706	0.249478
$425$	−13.6625	−0.662728
$426$	−1.01208	−0.0490355
$427$	1.00000	0.0483934
$428$	7.93362	0.383486
$429$	0	0
$430$	5.63102	0.271552
$431$	−22.0320	−1.06125	−0.530623	−	0.847608i	$-0.678042\pi$
$431$	−22.0320	−1.06125	−0.530623	+	0.847608i	$0.678042\pi$
$432$	1.00000	0.0481125
$433$	−23.5948	−1.13389	−0.566946	−	0.823755i	$-0.691875\pi$
$433$	−23.5948	−1.13389	−0.566946	+	0.823755i	$0.691875\pi$
$434$	−1.13706	−0.0545808
$435$	2.04892	0.0982381
$436$	−8.86054	−0.424343
$437$	−20.1347	−0.963172
$438$	−5.97823	−0.285651
$439$	6.50066	0.310260	0.155130	−	0.987894i	$-0.450420\pi$
$439$	6.50066	0.310260	0.155130	+	0.987894i	$0.450420\pi$
$440$	0.911854	0.0434709
$441$	1.00000	0.0476190
$442$	0	0
$443$	33.9221	1.61169	0.805845	−	0.592127i	$-0.201712\pi$
$443$	33.9221	1.61169	0.805845	+	0.592127i	$0.201712\pi$
$444$	−7.93900	−0.376768
$445$	1.99462	0.0945542
$446$	20.3230	0.962324
$447$	−14.5767	−0.689456
$448$	−1.00000	−0.0472456
$449$	−36.5133	−1.72317	−0.861585	−	0.507613i	$-0.830528\pi$
$449$	−36.5133	−1.72317	−0.861585	+	0.507613i	$0.830528\pi$
$450$	−4.69202	−0.221184
$451$	4.19806	0.197679
$452$	−1.55496	−0.0731391
$453$	13.6310	0.640441
$454$	14.8756	0.698147
$455$	0	0
$456$	−6.85086	−0.320821
$457$	25.6286	1.19886	0.599428	−	0.800428i	$-0.295395\pi$
$457$	25.6286	1.19886	0.599428	+	0.800428i	$0.295395\pi$
$458$	−4.42221	−0.206636
$459$	2.91185	0.135914
$460$	−1.63102	−0.0760468
$461$	20.0084	0.931882	0.465941	−	0.884816i	$-0.345716\pi$
$461$	20.0084	0.931882	0.465941	+	0.884816i	$0.345716\pi$
$462$	1.64310	0.0764441
$463$	29.2965	1.36152	0.680762	−	0.732505i	$-0.261649\pi$
$463$	29.2965	1.36152	0.680762	+	0.732505i	$0.261649\pi$
$464$	−3.69202	−0.171398
$465$	−0.631023	−0.0292630
$466$	−14.0030	−0.648676
$467$	20.7711	0.961170	0.480585	−	0.876948i	$-0.340424\pi$
$467$	20.7711	0.961170	0.480585	+	0.876948i	$0.340424\pi$
$468$	0	0
$469$	−1.69202	−0.0781303
$470$	6.43296	0.296730
$471$	5.52542	0.254598
$472$	0.158834	0.00731091
$473$	16.6722	0.766587
$474$	8.92692	0.410027
$475$	32.1444	1.47488
$476$	−2.91185	−0.133465
$477$	5.13706	0.235210
$478$	−18.2741	−0.835839
$479$	4.86831	0.222439	0.111219	−	0.993796i	$-0.464524\pi$
$479$	4.86831	0.222439	0.111219	+	0.993796i	$0.464524\pi$
$480$	−0.554958	−0.0253303
$481$	0	0
$482$	−16.5972	−0.755980
$483$	−2.93900	−0.133729
$484$	−8.30021	−0.377282
$485$	−8.95407	−0.406583
$486$	1.00000	0.0453609
$487$	−21.2336	−0.962185	−0.481092	−	0.876670i	$-0.659760\pi$
$487$	−21.2336	−0.962185	−0.481092	+	0.876670i	$0.659760\pi$
$488$	−1.00000	−0.0452679
$489$	−7.57673	−0.342632
$490$	−0.554958	−0.0250705
$491$	40.8829	1.84502	0.922510	−	0.385974i	$-0.126134\pi$
$491$	40.8829	1.84502	0.922510	+	0.385974i	$0.126134\pi$
$492$	−2.55496	−0.115186
$493$	−10.7506	−0.484184
$494$	0	0
$495$	0.911854	0.0409848
$496$	1.13706	0.0510557
$497$	1.01208	0.0453981
$498$	15.2664	0.684102
$499$	−8.41311	−0.376622	−0.188311	−	0.982109i	$-0.560301\pi$
$499$	−8.41311	−0.376622	−0.188311	+	0.982109i	$0.560301\pi$
$500$	5.37867	0.240541
$501$	−20.2717	−0.905674
$502$	−8.93123	−0.398620
$503$	−12.2543	−0.546391	−0.273196	−	0.961959i	$-0.588081\pi$
$503$	−12.2543	−0.546391	−0.273196	+	0.961959i	$0.588081\pi$
$504$	−1.00000	−0.0445435
$505$	2.17762	0.0969028
$506$	−4.82908	−0.214679
$507$	0	0
$508$	6.33944	0.281267
$509$	8.55688	0.379277	0.189638	−	0.981854i	$-0.439268\pi$
$509$	8.55688	0.379277	0.189638	+	0.981854i	$0.439268\pi$
$510$	−1.61596	−0.0715558
$511$	5.97823	0.264461
$512$	1.00000	0.0441942
$513$	−6.85086	−0.302473
$514$	3.21552	0.141831
$515$	6.29590	0.277430
$516$	−10.1468	−0.446686
$517$	19.0465	0.837665
$518$	7.93900	0.348820
$519$	−5.03146	−0.220857
$520$	0	0
$521$	11.1263	0.487452	0.243726	−	0.969844i	$-0.421630\pi$
$521$	11.1263	0.487452	0.243726	+	0.969844i	$0.421630\pi$
$522$	−3.69202	−0.161595
$523$	4.56166	0.199468	0.0997338	−	0.995014i	$-0.468201\pi$
$523$	4.56166	0.199468	0.0997338	+	0.995014i	$0.468201\pi$
$524$	6.78986	0.296616
$525$	4.69202	0.204777
$526$	6.08815	0.265456
$527$	3.31096	0.144228
$528$	−1.64310	−0.0715069
$529$	−14.3623	−0.624447
$530$	−2.85086	−0.123833
$531$	0.158834	0.00689279
$532$	6.85086	0.297022
$533$	0	0
$534$	−3.59419	−0.155536
$535$	−4.40283	−0.190351
$536$	1.69202	0.0730842
$537$	4.52542	0.195286
$538$	3.47219	0.149697
$539$	−1.64310	−0.0707735
$540$	−0.554958	−0.0238816
$541$	28.5623	1.22799	0.613994	−	0.789311i	$-0.289562\pi$
$541$	28.5623	1.22799	0.613994	+	0.789311i	$0.289562\pi$
$542$	23.5254	1.01050
$543$	7.59717	0.326026
$544$	2.91185	0.124845
$545$	4.91723	0.210631
$546$	0	0
$547$	30.9866	1.32489	0.662445	−	0.749110i	$-0.269519\pi$
$547$	30.9866	1.32489	0.662445	+	0.749110i	$0.269519\pi$
$548$	−11.0804	−0.473330
$549$	−1.00000	−0.0426790
$550$	7.70948	0.328733
$551$	25.2935	1.07754
$552$	2.93900	0.125092
$553$	−8.92692	−0.379611
$554$	8.71917	0.370442
$555$	4.40581	0.187016
$556$	−19.4306	−0.824040
$557$	36.7493	1.55712	0.778559	−	0.627572i	$-0.215951\pi$
$557$	36.7493	1.55712	0.778559	+	0.627572i	$0.215951\pi$
$558$	1.13706	0.0481357
$559$	0	0
$560$	0.554958	0.0234513
$561$	−4.78448	−0.202001
$562$	−14.5453	−0.613555
$563$	27.4711	1.15777	0.578885	−	0.815409i	$-0.303488\pi$
$563$	27.4711	1.15777	0.578885	+	0.815409i	$0.303488\pi$
$564$	−11.5918	−0.488103
$565$	0.862937	0.0363040
$566$	14.2567	0.599252
$567$	−1.00000	−0.0419961
$568$	−1.01208	−0.0424660
$569$	−9.84117	−0.412563	−0.206282	−	0.978493i	$-0.566136\pi$
$569$	−9.84117	−0.412563	−0.206282	+	0.978493i	$0.566136\pi$
$570$	3.80194	0.159246
$571$	−34.0767	−1.42606	−0.713032	−	0.701132i	$-0.752679\pi$
$571$	−34.0767	−1.42606	−0.713032	+	0.701132i	$0.752679\pi$
$572$	0	0
$573$	−20.6136	−0.861144
$574$	2.55496	0.106642
$575$	−13.7899	−0.575077
$576$	1.00000	0.0416667
$577$	−23.1420	−0.963413	−0.481706	−	0.876333i	$-0.659983\pi$
$577$	−23.1420	−0.963413	−0.481706	+	0.876333i	$0.659983\pi$
$578$	−8.52111	−0.354431
$579$	−5.88338	−0.244505
$580$	2.04892	0.0850767
$581$	−15.2664	−0.633355
$582$	16.1347	0.668804
$583$	−8.44073	−0.349579
$584$	−5.97823	−0.247381
$585$	0	0
$586$	−9.23059	−0.381312
$587$	−14.0911	−0.581603	−0.290802	−	0.956783i	$-0.593922\pi$
$587$	−14.0911	−0.581603	−0.290802	+	0.956783i	$0.593922\pi$
$588$	1.00000	0.0412393
$589$	−7.78986	−0.320975
$590$	−0.0881460	−0.00362891
$591$	−19.1317	−0.786972
$592$	−7.93900	−0.326291
$593$	−37.8388	−1.55385	−0.776926	−	0.629592i	$-0.783222\pi$
$593$	−37.8388	−1.55385	−0.776926	+	0.629592i	$0.783222\pi$
$594$	−1.64310	−0.0674174
$595$	1.61596	0.0662478
$596$	−14.5767	−0.597086
$597$	−7.22282	−0.295610
$598$	0	0
$599$	−44.8635	−1.83307	−0.916537	−	0.399950i	$-0.869028\pi$
$599$	−44.8635	−1.83307	−0.916537	+	0.399950i	$0.869028\pi$
$600$	−4.69202	−0.191551
$601$	44.9312	1.83278	0.916392	−	0.400283i	$-0.131088\pi$
$601$	44.9312	1.83278	0.916392	+	0.400283i	$0.131088\pi$
$602$	10.1468	0.413551
$603$	1.69202	0.0689044
$604$	13.6310	0.554638
$605$	4.60627	0.187271
$606$	−3.92394	−0.159399
$607$	19.6568	0.797847	0.398923	−	0.916984i	$-0.369384\pi$
$607$	19.6568	0.797847	0.398923	+	0.916984i	$0.369384\pi$
$608$	−6.85086	−0.277839
$609$	3.69202	0.149608
$610$	0.554958	0.0224696
$611$	0	0
$612$	2.91185	0.117705
$613$	4.22414	0.170612	0.0853058	−	0.996355i	$-0.472813\pi$
$613$	4.22414	0.170612	0.0853058	+	0.996355i	$0.472813\pi$
$614$	−22.3086	−0.900301
$615$	1.41789	0.0571750
$616$	1.64310	0.0662026
$617$	−3.31575	−0.133487	−0.0667435	−	0.997770i	$-0.521261\pi$
$617$	−3.31575	−0.133487	−0.0667435	+	0.997770i	$0.521261\pi$
$618$	−11.3448	−0.456355
$619$	−14.3230	−0.575692	−0.287846	−	0.957677i	$-0.592939\pi$
$619$	−14.3230	−0.575692	−0.287846	+	0.957677i	$0.592939\pi$
$620$	−0.631023	−0.0253425
$621$	2.93900	0.117938
$622$	−4.97716	−0.199566
$623$	3.59419	0.143998
$624$	0	0
$625$	20.4752	0.819007
$626$	8.58748	0.343225
$627$	11.2567	0.449548
$628$	5.52542	0.220488
$629$	−23.1172	−0.921744
$630$	0.554958	0.0221101
$631$	−12.4386	−0.495173	−0.247586	−	0.968866i	$-0.579637\pi$
$631$	−12.4386	−0.495173	−0.247586	+	0.968866i	$0.579637\pi$
$632$	8.92692	0.355094
$633$	18.5894	0.738862
$634$	29.7657	1.18215
$635$	−3.51812	−0.139612
$636$	5.13706	0.203698
$637$	0	0
$638$	6.06638	0.240170
$639$	−1.01208	−0.0400373
$640$	−0.554958	−0.0219366
$641$	14.6396	0.578231	0.289116	−	0.957294i	$-0.406639\pi$
$641$	14.6396	0.578231	0.289116	+	0.957294i	$0.406639\pi$
$642$	7.93362	0.313115
$643$	−27.3575	−1.07887	−0.539437	−	0.842026i	$-0.681363\pi$
$643$	−27.3575	−1.07887	−0.539437	+	0.842026i	$0.681363\pi$
$644$	−2.93900	−0.115813
$645$	5.63102	0.221721
$646$	−19.9487	−0.784871
$647$	41.8786	1.64642	0.823209	−	0.567739i	$-0.192182\pi$
$647$	41.8786	1.64642	0.823209	+	0.567739i	$0.192182\pi$
$648$	1.00000	0.0392837
$649$	−0.260980	−0.0102444
$650$	0	0
$651$	−1.13706	−0.0445650
$652$	−7.57673	−0.296728
$653$	16.0237	0.627055	0.313528	−	0.949579i	$-0.398489\pi$
$653$	16.0237	0.627055	0.313528	+	0.949579i	$0.398489\pi$
$654$	−8.86054	−0.346475
$655$	−3.76809	−0.147231
$656$	−2.55496	−0.0997544
$657$	−5.97823	−0.233233
$658$	11.5918	0.451895
$659$	0.572417	0.0222982	0.0111491	−	0.999938i	$-0.496451\pi$
$659$	0.572417	0.0222982	0.0111491	+	0.999938i	$0.496451\pi$
$660$	0.911854	0.0354939
$661$	44.4596	1.72928	0.864640	−	0.502393i	$-0.167547\pi$
$661$	44.4596	1.72928	0.864640	+	0.502393i	$0.167547\pi$
$662$	7.87369	0.306020
$663$	0	0
$664$	15.2664	0.592450
$665$	−3.80194	−0.147433
$666$	−7.93900	−0.307630
$667$	−10.8509	−0.420147
$668$	−20.2717	−0.784337
$669$	20.3230	0.785734
$670$	−0.939001	−0.0362768
$671$	1.64310	0.0634313
$672$	−1.00000	−0.0385758
$673$	16.9748	0.654329	0.327165	−	0.944967i	$-0.393907\pi$
$673$	16.9748	0.654329	0.327165	+	0.944967i	$0.393907\pi$
$674$	−30.8920	−1.18992
$675$	−4.69202	−0.180596
$676$	0	0
$677$	−36.7372	−1.41193	−0.705963	−	0.708249i	$-0.749486\pi$
$677$	−36.7372	−1.41193	−0.705963	+	0.708249i	$0.749486\pi$
$678$	−1.55496	−0.0597178
$679$	−16.1347	−0.619192
$680$	−1.61596	−0.0619691
$681$	14.8756	0.570035
$682$	−1.86831	−0.0715414
$683$	43.2083	1.65332	0.826661	−	0.562701i	$-0.190238\pi$
$683$	43.2083	1.65332	0.826661	+	0.562701i	$0.190238\pi$
$684$	−6.85086	−0.261949
$685$	6.14914	0.234947
$686$	−1.00000	−0.0381802
$687$	−4.42221	−0.168718
$688$	−10.1468	−0.386841
$689$	0	0
$690$	−1.63102	−0.0620920
$691$	−6.82132	−0.259495	−0.129748	−	0.991547i	$-0.541417\pi$
$691$	−6.82132	−0.259495	−0.129748	+	0.991547i	$0.541417\pi$
$692$	−5.03146	−0.191267
$693$	1.64310	0.0624164
$694$	−25.0713	−0.951693
$695$	10.7832	0.409028
$696$	−3.69202	−0.139946
$697$	−7.43967	−0.281797
$698$	13.9597	0.528383
$699$	−14.0030	−0.529641
$700$	4.69202	0.177342
$701$	−18.8931	−0.713581	−0.356791	−	0.934184i	$-0.616129\pi$
$701$	−18.8931	−0.713581	−0.356791	+	0.934184i	$0.616129\pi$
$702$	0	0
$703$	54.3889	2.05132
$704$	−1.64310	−0.0619268
$705$	6.43296	0.242279
$706$	−20.0629	−0.755078
$707$	3.92394	0.147575
$708$	0.158834	0.00596933
$709$	8.39804	0.315395	0.157698	−	0.987487i	$-0.449593\pi$
$709$	8.39804	0.315395	0.157698	+	0.987487i	$0.449593\pi$
$710$	0.561663	0.0210788
$711$	8.92692	0.334786
$712$	−3.59419	−0.134698
$713$	3.34183	0.125153
$714$	−2.91185	−0.108973
$715$	0	0
$716$	4.52542	0.169123
$717$	−18.2741	−0.682460
$718$	−18.3642	−0.685346
$719$	−7.10023	−0.264794	−0.132397	−	0.991197i	$-0.542267\pi$
$719$	−7.10023	−0.264794	−0.132397	+	0.991197i	$0.542267\pi$
$720$	−0.554958	−0.0206821
$721$	11.3448	0.422503
$722$	27.9342	1.03960
$723$	−16.5972	−0.617255
$724$	7.59717	0.282347
$725$	17.3230	0.643362
$726$	−8.30021	−0.308050
$727$	3.00431	0.111424	0.0557119	−	0.998447i	$-0.482257\pi$
$727$	3.00431	0.111424	0.0557119	+	0.998447i	$0.482257\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	3.31767	0.122792
$731$	−29.5459	−1.09279
$732$	−1.00000	−0.0369611
$733$	−4.32198	−0.159636	−0.0798180	−	0.996809i	$-0.525434\pi$
$733$	−4.32198	−0.159636	−0.0798180	+	0.996809i	$0.525434\pi$
$734$	8.29829	0.306295
$735$	−0.554958	−0.0204699
$736$	2.93900	0.108333
$737$	−2.78017	−0.102409
$738$	−2.55496	−0.0940493
$739$	32.7372	1.20426	0.602129	−	0.798399i	$-0.294319\pi$
$739$	32.7372	1.20426	0.602129	+	0.798399i	$0.294319\pi$
$740$	4.40581	0.161961
$741$	0	0
$742$	−5.13706	−0.188588
$743$	−42.9028	−1.57395	−0.786975	−	0.616985i	$-0.788354\pi$
$743$	−42.9028	−1.57395	−0.786975	+	0.616985i	$0.788354\pi$
$744$	1.13706	0.0416868
$745$	8.08947	0.296375
$746$	−10.2101	−0.373820
$747$	15.2664	0.558567
$748$	−4.78448	−0.174938
$749$	−7.93362	−0.289888
$750$	5.37867	0.196401
$751$	−53.3793	−1.94784	−0.973918	−	0.226899i	$-0.927141\pi$
$751$	−53.3793	−1.94784	−0.973918	+	0.226899i	$0.927141\pi$
$752$	−11.5918	−0.422709
$753$	−8.93123	−0.325472
$754$	0	0
$755$	−7.56465	−0.275306
$756$	−1.00000	−0.0363696
$757$	−7.80923	−0.283831	−0.141916	−	0.989879i	$-0.545326\pi$
$757$	−7.80923	−0.283831	−0.141916	+	0.989879i	$0.545326\pi$
$758$	7.15883	0.260021
$759$	−4.82908	−0.175285
$760$	3.80194	0.137911
$761$	−27.3303	−0.990724	−0.495362	−	0.868687i	$-0.664965\pi$
$761$	−27.3303	−0.990724	−0.495362	+	0.868687i	$0.664965\pi$
$762$	6.33944	0.229654
$763$	8.86054	0.320773
$764$	−20.6136	−0.745773
$765$	−1.61596	−0.0584251
$766$	20.4403	0.738536
$767$	0	0
$768$	1.00000	0.0360844
$769$	5.21014	0.187883	0.0939413	−	0.995578i	$-0.470053\pi$
$769$	5.21014	0.187883	0.0939413	+	0.995578i	$0.470053\pi$
$770$	−0.911854	−0.0328609
$771$	3.21552	0.115804
$772$	−5.88338	−0.211747
$773$	45.7689	1.64619	0.823097	−	0.567901i	$-0.192244\pi$
$773$	45.7689	1.64619	0.823097	+	0.567901i	$0.192244\pi$
$774$	−10.1468	−0.364717
$775$	−5.33513	−0.191643
$776$	16.1347	0.579201
$777$	7.93900	0.284810
$778$	12.9226	0.463298
$779$	17.5036	0.627133
$780$	0	0
$781$	1.66296	0.0595052
$782$	8.55794	0.306031
$783$	−3.69202	−0.131942
$784$	1.00000	0.0357143
$785$	−3.06638	−0.109444
$786$	6.78986	0.242186
$787$	34.6732	1.23597	0.617984	−	0.786191i	$-0.287950\pi$
$787$	34.6732	1.23597	0.617984	+	0.786191i	$0.287950\pi$
$788$	−19.1317	−0.681538
$789$	6.08815	0.216744
$790$	−4.95407	−0.176258
$791$	1.55496	0.0552879
$792$	−1.64310	−0.0583852
$793$	0	0
$794$	−9.34780	−0.331741
$795$	−2.85086	−0.101109
$796$	−7.22282	−0.256006
$797$	−17.2034	−0.609377	−0.304689	−	0.952452i	$-0.598552\pi$
$797$	−17.2034	−0.609377	−0.304689	+	0.952452i	$0.598552\pi$
$798$	6.85086	0.242518
$799$	−33.7536	−1.19412
$800$	−4.69202	−0.165888
$801$	−3.59419	−0.126994
$802$	−8.84415	−0.312298
$803$	9.82285	0.346641
$804$	1.69202	0.0596730
$805$	1.63102	0.0574860
$806$	0	0
$807$	3.47219	0.122227
$808$	−3.92394	−0.138044
$809$	−10.7821	−0.379078	−0.189539	−	0.981873i	$-0.560699\pi$
$809$	−10.7821	−0.379078	−0.189539	+	0.981873i	$0.560699\pi$
$810$	−0.554958	−0.0194992
$811$	25.5864	0.898461	0.449230	−	0.893416i	$-0.351698\pi$
$811$	25.5864	0.898461	0.449230	+	0.893416i	$0.351698\pi$
$812$	3.69202	0.129565
$813$	23.5254	0.825072
$814$	13.0446	0.457213
$815$	4.20477	0.147287
$816$	2.91185	0.101935
$817$	69.5139	2.43198
$818$	25.5176	0.892204
$819$	0	0
$820$	1.41789	0.0495150
$821$	−18.1323	−0.632821	−0.316410	−	0.948622i	$-0.602478\pi$
$821$	−18.1323	−0.632821	−0.316410	+	0.948622i	$0.602478\pi$
$822$	−11.0804	−0.386473
$823$	29.7254	1.03616	0.518081	−	0.855331i	$-0.326647\pi$
$823$	29.7254	1.03616	0.518081	+	0.855331i	$0.326647\pi$
$824$	−11.3448	−0.395215
$825$	7.70948	0.268410
$826$	−0.158834	−0.00552653
$827$	41.5086	1.44339	0.721697	−	0.692209i	$-0.243362\pi$
$827$	41.5086	1.44339	0.721697	+	0.692209i	$0.243362\pi$
$828$	2.93900	0.102137
$829$	−1.03790	−0.0360478	−0.0180239	−	0.999838i	$-0.505737\pi$
$829$	−1.03790	−0.0360478	−0.0180239	+	0.999838i	$0.505737\pi$
$830$	−8.47219	−0.294074
$831$	8.71917	0.302465
$832$	0	0
$833$	2.91185	0.100890
$834$	−19.4306	−0.672826
$835$	11.2500	0.389321
$836$	11.2567	0.389320
$837$	1.13706	0.0393027
$838$	34.6233	1.19604
$839$	−8.78448	−0.303274	−0.151637	−	0.988436i	$-0.548454\pi$
$839$	−8.78448	−0.303274	−0.151637	+	0.988436i	$0.548454\pi$
$840$	0.554958	0.0191479
$841$	−15.3690	−0.529965
$842$	5.02715	0.173247
$843$	−14.5453	−0.500966
$844$	18.5894	0.639874
$845$	0	0
$846$	−11.5918	−0.398534
$847$	8.30021	0.285199
$848$	5.13706	0.176407
$849$	14.2567	0.489288
$850$	−13.6625	−0.468619
$851$	−23.3327	−0.799836
$852$	−1.01208	−0.0346733
$853$	10.9709	0.375638	0.187819	−	0.982204i	$-0.439858\pi$
$853$	10.9709	0.375638	0.187819	+	0.982204i	$0.439858\pi$
$854$	1.00000	0.0342193
$855$	3.80194	0.130024
$856$	7.93362	0.271166
$857$	−12.1293	−0.414329	−0.207164	−	0.978306i	$-0.566423\pi$
$857$	−12.1293	−0.414329	−0.207164	+	0.978306i	$0.566423\pi$
$858$	0	0
$859$	23.2010	0.791609	0.395805	−	0.918335i	$-0.370466\pi$
$859$	23.2010	0.791609	0.395805	+	0.918335i	$0.370466\pi$
$860$	5.63102	0.192016
$861$	2.55496	0.0870727
$862$	−22.0320	−0.750415
$863$	40.3172	1.37241	0.686207	−	0.727407i	$-0.259275\pi$
$863$	40.3172	1.37241	0.686207	+	0.727407i	$0.259275\pi$
$864$	1.00000	0.0340207
$865$	2.79225	0.0949393
$866$	−23.5948	−0.801783
$867$	−8.52111	−0.289392
$868$	−1.13706	−0.0385944
$869$	−14.6679	−0.497573
$870$	2.04892	0.0694648
$871$	0	0
$872$	−8.86054	−0.300056
$873$	16.1347	0.546076
$874$	−20.1347	−0.681065
$875$	−5.37867	−0.181832
$876$	−5.97823	−0.201986
$877$	−29.4674	−0.995044	−0.497522	−	0.867452i	$-0.665757\pi$
$877$	−29.4674	−0.995044	−0.497522	+	0.867452i	$0.665757\pi$
$878$	6.50066	0.219387
$879$	−9.23059	−0.311340
$880$	0.911854	0.0307386
$881$	−10.9022	−0.367303	−0.183652	−	0.982991i	$-0.558792\pi$
$881$	−10.9022	−0.367303	−0.183652	+	0.982991i	$0.558792\pi$
$882$	1.00000	0.0336718
$883$	2.76404	0.0930173	0.0465086	−	0.998918i	$-0.485191\pi$
$883$	2.76404	0.0930173	0.0465086	+	0.998918i	$0.485191\pi$
$884$	0	0
$885$	−0.0881460	−0.00296300
$886$	33.9221	1.13964
$887$	−19.0814	−0.640692	−0.320346	−	0.947301i	$-0.603799\pi$
$887$	−19.0814	−0.640692	−0.320346	+	0.947301i	$0.603799\pi$
$888$	−7.93900	−0.266415
$889$	−6.33944	−0.212618
$890$	1.99462	0.0668599
$891$	−1.64310	−0.0550461
$892$	20.3230	0.680466
$893$	79.4137	2.65748
$894$	−14.5767	−0.487519
$895$	−2.51142	−0.0839474
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	−36.5133	−1.21847
$899$	−4.19806	−0.140013
$900$	−4.69202	−0.156401
$901$	14.9584	0.498336
$902$	4.19806	0.139780
$903$	10.1468	0.337663
$904$	−1.55496	−0.0517171
$905$	−4.21611	−0.140148
$906$	13.6310	0.452860
$907$	4.29935	0.142758	0.0713789	−	0.997449i	$-0.477260\pi$
$907$	4.29935	0.142758	0.0713789	+	0.997449i	$0.477260\pi$
$908$	14.8756	0.493664
$909$	−3.92394	−0.130149
$910$	0	0
$911$	17.5520	0.581523	0.290761	−	0.956796i	$-0.406091\pi$
$911$	17.5520	0.581523	0.290761	+	0.956796i	$0.406091\pi$
$912$	−6.85086	−0.226854
$913$	−25.0842	−0.830166
$914$	25.6286	0.847720
$915$	0.554958	0.0183463
$916$	−4.42221	−0.146114
$917$	−6.78986	−0.224221
$918$	2.91185	0.0961055
$919$	−29.8498	−0.984654	−0.492327	−	0.870410i	$-0.663854\pi$
$919$	−29.8498	−0.984654	−0.492327	+	0.870410i	$0.663854\pi$
$920$	−1.63102	−0.0537732
$921$	−22.3086	−0.735092
$922$	20.0084	0.658940
$923$	0	0
$924$	1.64310	0.0540542
$925$	37.2500	1.22477
$926$	29.2965	0.962742
$927$	−11.3448	−0.372613
$928$	−3.69202	−0.121197
$929$	−45.7536	−1.50113	−0.750564	−	0.660798i	$-0.770218\pi$
$929$	−45.7536	−1.50113	−0.750564	+	0.660798i	$0.770218\pi$
$930$	−0.631023	−0.0206920
$931$	−6.85086	−0.224528
$932$	−14.0030	−0.458683
$933$	−4.97716	−0.162945
$934$	20.7711	0.679650
$935$	2.65519	0.0868339
$936$	0	0
$937$	45.0180	1.47068	0.735338	−	0.677701i	$-0.237024\pi$
$937$	45.0180	1.47068	0.735338	+	0.677701i	$0.237024\pi$
$938$	−1.69202	−0.0552465
$939$	8.58748	0.280242
$940$	6.43296	0.209820
$941$	11.0349	0.359728	0.179864	−	0.983691i	$-0.442434\pi$
$941$	11.0349	0.359728	0.179864	+	0.983691i	$0.442434\pi$
$942$	5.52542	0.180028
$943$	−7.50902	−0.244527
$944$	0.158834	0.00516959
$945$	0.554958	0.0180528
$946$	16.6722	0.542059
$947$	−31.5623	−1.02564	−0.512818	−	0.858498i	$-0.671398\pi$
$947$	−31.5623	−1.02564	−0.512818	+	0.858498i	$0.671398\pi$
$948$	8.92692	0.289933
$949$	0	0
$950$	32.1444	1.04290
$951$	29.7657	0.965219
$952$	−2.91185	−0.0943737
$953$	56.4282	1.82789	0.913944	−	0.405840i	$-0.133021\pi$
$953$	56.4282	1.82789	0.913944	+	0.405840i	$0.133021\pi$
$954$	5.13706	0.166319
$955$	11.4397	0.370179
$956$	−18.2741	−0.591027
$957$	6.06638	0.196098
$958$	4.86831	0.157288
$959$	11.0804	0.357804
$960$	−0.554958	−0.0179112
$961$	−29.7071	−0.958293
$962$	0	0
$963$	7.93362	0.255657
$964$	−16.5972	−0.534559
$965$	3.26503	0.105105
$966$	−2.93900	−0.0945608
$967$	−30.7084	−0.987516	−0.493758	−	0.869599i	$-0.664377\pi$
$967$	−30.7084	−0.987516	−0.493758	+	0.869599i	$0.664377\pi$
$968$	−8.30021	−0.266779
$969$	−19.9487	−0.640844
$970$	−8.95407	−0.287498
$971$	13.0847	0.419908	0.209954	−	0.977711i	$-0.432669\pi$
$971$	13.0847	0.419908	0.209954	+	0.977711i	$0.432669\pi$
$972$	1.00000	0.0320750
$973$	19.4306	0.622915
$974$	−21.2336	−0.680367
$975$	0	0
$976$	−1.00000	−0.0320092
$977$	−23.3978	−0.748561	−0.374281	−	0.927315i	$-0.622110\pi$
$977$	−23.3978	−0.748561	−0.374281	+	0.927315i	$0.622110\pi$
$978$	−7.57673	−0.242277
$979$	5.90562	0.188745
$980$	−0.554958	−0.0177275
$981$	−8.86054	−0.282895
$982$	40.8829	1.30463
$983$	−30.3207	−0.967079	−0.483539	−	0.875323i	$-0.660649\pi$
$983$	−30.3207	−0.967079	−0.483539	+	0.875323i	$0.660649\pi$
$984$	−2.55496	−0.0814491
$985$	10.6173	0.338295
$986$	−10.7506	−0.342370
$987$	11.5918	0.368971
$988$	0	0
$989$	−29.8213	−0.948263
$990$	0.911854	0.0289806
$991$	−34.1745	−1.08559	−0.542794	−	0.839866i	$-0.682634\pi$
$991$	−34.1745	−1.08559	−0.542794	+	0.839866i	$0.682634\pi$
$992$	1.13706	0.0361018
$993$	7.87369	0.249864
$994$	1.01208	0.0321013
$995$	4.00836	0.127074
$996$	15.2664	0.483733
$997$	35.8146	1.13426	0.567130	−	0.823628i	$-0.308054\pi$
$997$	35.8146	1.13426	0.567130	+	0.823628i	$0.308054\pi$
$998$	−8.41311	−0.266312
$999$	−7.93900	−0.251179

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.cm.1.2	yes	3
13.12	even	2		7098.2.a.cf.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cf.1.2	✓	3	13.12	even	2
7098.2.a.cm.1.2	yes	3	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.554958 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.554958 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.554958 q^{10} -1.64310 q^{11} +1.00000 q^{12} -1.00000 q^{14} -0.554958 q^{15} +1.00000 q^{16} +2.91185 q^{17} +1.00000 q^{18} -6.85086 q^{19} -0.554958 q^{20} -1.00000 q^{21} -1.64310 q^{22} +2.93900 q^{23} +1.00000 q^{24} -4.69202 q^{25} +1.00000 q^{27} -1.00000 q^{28} -3.69202 q^{29} -0.554958 q^{30} +1.13706 q^{31} +1.00000 q^{32} -1.64310 q^{33} +2.91185 q^{34} +0.554958 q^{35} +1.00000 q^{36} -7.93900 q^{37} -6.85086 q^{38} -0.554958 q^{40} -2.55496 q^{41} -1.00000 q^{42} -10.1468 q^{43} -1.64310 q^{44} -0.554958 q^{45} +2.93900 q^{46} -11.5918 q^{47} +1.00000 q^{48} +1.00000 q^{49} -4.69202 q^{50} +2.91185 q^{51} +5.13706 q^{53} +1.00000 q^{54} +0.911854 q^{55} -1.00000 q^{56} -6.85086 q^{57} -3.69202 q^{58} +0.158834 q^{59} -0.554958 q^{60} -1.00000 q^{61} +1.13706 q^{62} -1.00000 q^{63} +1.00000 q^{64} -1.64310 q^{66} +1.69202 q^{67} +2.91185 q^{68} +2.93900 q^{69} +0.554958 q^{70} -1.01208 q^{71} +1.00000 q^{72} -5.97823 q^{73} -7.93900 q^{74} -4.69202 q^{75} -6.85086 q^{76} +1.64310 q^{77} +8.92692 q^{79} -0.554958 q^{80} +1.00000 q^{81} -2.55496 q^{82} +15.2664 q^{83} -1.00000 q^{84} -1.61596 q^{85} -10.1468 q^{86} -3.69202 q^{87} -1.64310 q^{88} -3.59419 q^{89} -0.554958 q^{90} +2.93900 q^{92} +1.13706 q^{93} -11.5918 q^{94} +3.80194 q^{95} +1.00000 q^{96} +16.1347 q^{97} +1.00000 q^{98} -1.64310 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 2 q^{5} + 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 2 * q^5 + 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 2 q^{5} + 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 2 q^{10} - 9 q^{11} + 3 q^{12} - 3 q^{14} - 2 q^{15} + 3 q^{16} + 5 q^{17} + 3 q^{18} - 7 q^{19} - 2 q^{20} - 3 q^{21} - 9 q^{22} - q^{23} + 3 q^{24} - 9 q^{25} + 3 q^{27} - 3 q^{28} - 6 q^{29} - 2 q^{30} - 2 q^{31} + 3 q^{32} - 9 q^{33} + 5 q^{34} + 2 q^{35} + 3 q^{36} - 14 q^{37} - 7 q^{38} - 2 q^{40} - 8 q^{41} - 3 q^{42} - 3 q^{43} - 9 q^{44} - 2 q^{45} - q^{46} - 7 q^{47} + 3 q^{48} + 3 q^{49} - 9 q^{50} + 5 q^{51} + 10 q^{53} + 3 q^{54} - q^{55} - 3 q^{56} - 7 q^{57} - 6 q^{58} - 8 q^{59} - 2 q^{60} - 3 q^{61} - 2 q^{62} - 3 q^{63} + 3 q^{64} - 9 q^{66} + 5 q^{68} - q^{69} + 2 q^{70} - 22 q^{71} + 3 q^{72} - 21 q^{73} - 14 q^{74} - 9 q^{75} - 7 q^{76} + 9 q^{77} - 2 q^{79} - 2 q^{80} + 3 q^{81} - 8 q^{82} - 3 q^{83} - 3 q^{84} - 15 q^{85} - 3 q^{86} - 6 q^{87} - 9 q^{88} - 24 q^{89} - 2 q^{90} - q^{92} - 2 q^{93} - 7 q^{94} + 7 q^{95} + 3 q^{96} + 2 q^{97} + 3 q^{98} - 9 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 2 * q^5 + 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 - 2 * q^10 - 9 * q^11 + 3 * q^12 - 3 * q^14 - 2 * q^15 + 3 * q^16 + 5 * q^17 + 3 * q^18 - 7 * q^19 - 2 * q^20 - 3 * q^21 - 9 * q^22 - q^23 + 3 * q^24 - 9 * q^25 + 3 * q^27 - 3 * q^28 - 6 * q^29 - 2 * q^30 - 2 * q^31 + 3 * q^32 - 9 * q^33 + 5 * q^34 + 2 * q^35 + 3 * q^36 - 14 * q^37 - 7 * q^38 - 2 * q^40 - 8 * q^41 - 3 * q^42 - 3 * q^43 - 9 * q^44 - 2 * q^45 - q^46 - 7 * q^47 + 3 * q^48 + 3 * q^49 - 9 * q^50 + 5 * q^51 + 10 * q^53 + 3 * q^54 - q^55 - 3 * q^56 - 7 * q^57 - 6 * q^58 - 8 * q^59 - 2 * q^60 - 3 * q^61 - 2 * q^62 - 3 * q^63 + 3 * q^64 - 9 * q^66 + 5 * q^68 - q^69 + 2 * q^70 - 22 * q^71 + 3 * q^72 - 21 * q^73 - 14 * q^74 - 9 * q^75 - 7 * q^76 + 9 * q^77 - 2 * q^79 - 2 * q^80 + 3 * q^81 - 8 * q^82 - 3 * q^83 - 3 * q^84 - 15 * q^85 - 3 * q^86 - 6 * q^87 - 9 * q^88 - 24 * q^89 - 2 * q^90 - q^92 - 2 * q^93 - 7 * q^94 + 7 * q^95 + 3 * q^96 + 2 * q^97 + 3 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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