LMFDB - Embedded newform 7098.2.a.cp.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$56.6778153547$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.8569169.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 12x^{4} + 11x^{3} + 44x^{2} - 9x - 41 $ x^6 - 2x^5 - 12x^4 + 11x^3 + 44x^2 - 9*x - 41
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.13488$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.41517 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.41517 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.41517 q^{10} +4.07170 q^{11} -1.00000 q^{12} +1.00000 q^{14} +1.41517 q^{15} +1.00000 q^{16} +0.175278 q^{17} -1.00000 q^{18} -3.70986 q^{19} -1.41517 q^{20} +1.00000 q^{21} -4.07170 q^{22} -7.64886 q^{23} +1.00000 q^{24} -2.99728 q^{25} -1.00000 q^{27} -1.00000 q^{28} +8.67727 q^{29} -1.41517 q^{30} +10.8238 q^{31} -1.00000 q^{32} -4.07170 q^{33} -0.175278 q^{34} +1.41517 q^{35} +1.00000 q^{36} -10.3422 q^{37} +3.70986 q^{38} +1.41517 q^{40} +0.0778681 q^{41} -1.00000 q^{42} +11.1379 q^{43} +4.07170 q^{44} -1.41517 q^{45} +7.64886 q^{46} -6.10157 q^{47} -1.00000 q^{48} +1.00000 q^{49} +2.99728 q^{50} -0.175278 q^{51} +1.46549 q^{53} +1.00000 q^{54} -5.76217 q^{55} +1.00000 q^{56} +3.70986 q^{57} -8.67727 q^{58} -2.37793 q^{59} +1.41517 q^{60} +11.7701 q^{61} -10.8238 q^{62} -1.00000 q^{63} +1.00000 q^{64} +4.07170 q^{66} -10.1245 q^{67} +0.175278 q^{68} +7.64886 q^{69} -1.41517 q^{70} -0.967422 q^{71} -1.00000 q^{72} -13.4323 q^{73} +10.3422 q^{74} +2.99728 q^{75} -3.70986 q^{76} -4.07170 q^{77} -12.8122 q^{79} -1.41517 q^{80} +1.00000 q^{81} -0.0778681 q^{82} +6.50855 q^{83} +1.00000 q^{84} -0.248048 q^{85} -11.1379 q^{86} -8.67727 q^{87} -4.07170 q^{88} -10.8545 q^{89} +1.41517 q^{90} -7.64886 q^{92} -10.8238 q^{93} +6.10157 q^{94} +5.25010 q^{95} +1.00000 q^{96} +13.1116 q^{97} -1.00000 q^{98} +4.07170 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} - 6 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 - 6 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} - 6 q^{7} - 6 q^{8} + 6 q^{9} - 3 q^{10} + 6 q^{11} - 6 q^{12} + 6 q^{14} - 3 q^{15} + 6 q^{16} + 10 q^{17} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 6 q^{21} - 6 q^{22} - 12 q^{23} + 6 q^{24} + 5 q^{25} - 6 q^{27} - 6 q^{28} + 4 q^{29} + 3 q^{30} - 7 q^{31} - 6 q^{32} - 6 q^{33} - 10 q^{34} - 3 q^{35} + 6 q^{36} - 3 q^{37} + 8 q^{38} - 3 q^{40} - 3 q^{41} - 6 q^{42} - 3 q^{43} + 6 q^{44} + 3 q^{45} + 12 q^{46} - 29 q^{47} - 6 q^{48} + 6 q^{49} - 5 q^{50} - 10 q^{51} - 12 q^{53} + 6 q^{54} + 29 q^{55} + 6 q^{56} + 8 q^{57} - 4 q^{58} - 2 q^{59} - 3 q^{60} + 13 q^{61} + 7 q^{62} - 6 q^{63} + 6 q^{64} + 6 q^{66} - 22 q^{67} + 10 q^{68} + 12 q^{69} + 3 q^{70} - q^{71} - 6 q^{72} - 29 q^{73} + 3 q^{74} - 5 q^{75} - 8 q^{76} - 6 q^{77} - 24 q^{79} + 3 q^{80} + 6 q^{81} + 3 q^{82} - 7 q^{83} + 6 q^{84} - 21 q^{85} + 3 q^{86} - 4 q^{87} - 6 q^{88} + 11 q^{89} - 3 q^{90} - 12 q^{92} + 7 q^{93} + 29 q^{94} + 8 q^{95} + 6 q^{96} + 4 q^{97} - 6 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 - 6 * q^7 - 6 * q^8 + 6 * q^9 - 3 * q^10 + 6 * q^11 - 6 * q^12 + 6 * q^14 - 3 * q^15 + 6 * q^16 + 10 * q^17 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 6 * q^21 - 6 * q^22 - 12 * q^23 + 6 * q^24 + 5 * q^25 - 6 * q^27 - 6 * q^28 + 4 * q^29 + 3 * q^30 - 7 * q^31 - 6 * q^32 - 6 * q^33 - 10 * q^34 - 3 * q^35 + 6 * q^36 - 3 * q^37 + 8 * q^38 - 3 * q^40 - 3 * q^41 - 6 * q^42 - 3 * q^43 + 6 * q^44 + 3 * q^45 + 12 * q^46 - 29 * q^47 - 6 * q^48 + 6 * q^49 - 5 * q^50 - 10 * q^51 - 12 * q^53 + 6 * q^54 + 29 * q^55 + 6 * q^56 + 8 * q^57 - 4 * q^58 - 2 * q^59 - 3 * q^60 + 13 * q^61 + 7 * q^62 - 6 * q^63 + 6 * q^64 + 6 * q^66 - 22 * q^67 + 10 * q^68 + 12 * q^69 + 3 * q^70 - q^71 - 6 * q^72 - 29 * q^73 + 3 * q^74 - 5 * q^75 - 8 * q^76 - 6 * q^77 - 24 * q^79 + 3 * q^80 + 6 * q^81 + 3 * q^82 - 7 * q^83 + 6 * q^84 - 21 * q^85 + 3 * q^86 - 4 * q^87 - 6 * q^88 + 11 * q^89 - 3 * q^90 - 12 * q^92 + 7 * q^93 + 29 * q^94 + 8 * q^95 + 6 * q^96 + 4 * q^97 - 6 * q^98 + 6 * 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
$5$	−1.41517	−0.632885	−0.316443	−	0.948612i	$-0.602489\pi$
$5$	−1.41517	−0.632885	−0.316443	+	0.948612i	$0.602489\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.41517	0.447518
$11$	4.07170	1.22766	0.613832	−	0.789437i	$-0.289627\pi$
$11$	4.07170	1.22766	0.613832	+	0.789437i	$0.289627\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	1.41517	0.365397
$16$	1.00000	0.250000
$17$	0.175278	0.0425111	0.0212555	−	0.999774i	$-0.493234\pi$
$17$	0.175278	0.0425111	0.0212555	+	0.999774i	$0.493234\pi$
$18$	−1.00000	−0.235702
$19$	−3.70986	−0.851101	−0.425550	−	0.904935i	$-0.639919\pi$
$19$	−3.70986	−0.851101	−0.425550	+	0.904935i	$0.639919\pi$
$20$	−1.41517	−0.316443
$21$	1.00000	0.218218
$22$	−4.07170	−0.868090
$23$	−7.64886	−1.59490	−0.797449	−	0.603386i	$-0.793818\pi$
$23$	−7.64886	−1.59490	−0.797449	+	0.603386i	$0.793818\pi$
$24$	1.00000	0.204124
$25$	−2.99728	−0.599456
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	8.67727	1.61133	0.805665	−	0.592372i	$-0.201808\pi$
$29$	8.67727	1.61133	0.805665	+	0.592372i	$0.201808\pi$
$30$	−1.41517	−0.258374
$31$	10.8238	1.94402	0.972009	−	0.234945i	$-0.0754910\pi$
$31$	10.8238	1.94402	0.972009	+	0.234945i	$0.0754910\pi$
$32$	−1.00000	−0.176777
$33$	−4.07170	−0.708792
$34$	−0.175278	−0.0300599
$35$	1.41517	0.239208
$36$	1.00000	0.166667
$37$	−10.3422	−1.70025	−0.850123	−	0.526584i	$-0.823472\pi$
$37$	−10.3422	−1.70025	−0.850123	+	0.526584i	$0.823472\pi$
$38$	3.70986	0.601819
$39$	0	0
$40$	1.41517	0.223759
$41$	0.0778681	0.0121609	0.00608047	−	0.999982i	$-0.498065\pi$
$41$	0.0778681	0.0121609	0.00608047	+	0.999982i	$0.498065\pi$
$42$	−1.00000	−0.154303
$43$	11.1379	1.69852	0.849258	−	0.527977i	$-0.177049\pi$
$43$	11.1379	1.69852	0.849258	+	0.527977i	$0.177049\pi$
$44$	4.07170	0.613832
$45$	−1.41517	−0.210962
$46$	7.64886	1.12776
$47$	−6.10157	−0.890005	−0.445003	−	0.895529i	$-0.646797\pi$
$47$	−6.10157	−0.890005	−0.445003	+	0.895529i	$0.646797\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	2.99728	0.423879
$51$	−0.175278	−0.0245438
$52$	0	0
$53$	1.46549	0.201301	0.100651	−	0.994922i	$-0.467908\pi$
$53$	1.46549	0.201301	0.100651	+	0.994922i	$0.467908\pi$
$54$	1.00000	0.136083
$55$	−5.76217	−0.776971
$56$	1.00000	0.133631
$57$	3.70986	0.491383
$58$	−8.67727	−1.13938
$59$	−2.37793	−0.309580	−0.154790	−	0.987947i	$-0.549470\pi$
$59$	−2.37793	−0.309580	−0.154790	+	0.987947i	$0.549470\pi$
$60$	1.41517	0.182698
$61$	11.7701	1.50701	0.753505	−	0.657442i	$-0.228361\pi$
$61$	11.7701	1.50701	0.753505	+	0.657442i	$0.228361\pi$
$62$	−10.8238	−1.37463
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	4.07170	0.501192
$67$	−10.1245	−1.23691	−0.618455	−	0.785820i	$-0.712241\pi$
$67$	−10.1245	−1.23691	−0.618455	+	0.785820i	$0.712241\pi$
$68$	0.175278	0.0212555
$69$	7.64886	0.920815
$70$	−1.41517	−0.169146
$71$	−0.967422	−0.114812	−0.0574059	−	0.998351i	$-0.518283\pi$
$71$	−0.967422	−0.114812	−0.0574059	+	0.998351i	$0.518283\pi$
$72$	−1.00000	−0.117851
$73$	−13.4323	−1.57213	−0.786067	−	0.618142i	$-0.787886\pi$
$73$	−13.4323	−1.57213	−0.786067	+	0.618142i	$0.787886\pi$
$74$	10.3422	1.20226
$75$	2.99728	0.346096
$76$	−3.70986	−0.425550
$77$	−4.07170	−0.464014
$78$	0	0
$79$	−12.8122	−1.44148	−0.720740	−	0.693205i	$-0.756198\pi$
$79$	−12.8122	−1.44148	−0.720740	+	0.693205i	$0.756198\pi$
$80$	−1.41517	−0.158221
$81$	1.00000	0.111111
$82$	−0.0778681	−0.00859909
$83$	6.50855	0.714406	0.357203	−	0.934027i	$-0.383730\pi$
$83$	6.50855	0.714406	0.357203	+	0.934027i	$0.383730\pi$
$84$	1.00000	0.109109
$85$	−0.248048	−0.0269046
$86$	−11.1379	−1.20103
$87$	−8.67727	−0.930301
$88$	−4.07170	−0.434045
$89$	−10.8545	−1.15057	−0.575286	−	0.817952i	$-0.695109\pi$
$89$	−10.8545	−1.15057	−0.575286	+	0.817952i	$0.695109\pi$
$90$	1.41517	0.149173
$91$	0	0
$92$	−7.64886	−0.797449
$93$	−10.8238	−1.12238
$94$	6.10157	0.629329
$95$	5.25010	0.538649
$96$	1.00000	0.102062
$97$	13.1116	1.33128	0.665639	−	0.746274i	$-0.268159\pi$
$97$	13.1116	1.33128	0.665639	+	0.746274i	$0.268159\pi$
$98$	−1.00000	−0.101015
$99$	4.07170	0.409221
$100$	−2.99728	−0.299728
$101$	15.8582	1.57795	0.788973	−	0.614428i	$-0.210613\pi$
$101$	15.8582	1.57795	0.788973	+	0.614428i	$0.210613\pi$
$102$	0.175278	0.0173551
$103$	−1.44026	−0.141913	−0.0709564	−	0.997479i	$-0.522605\pi$
$103$	−1.44026	−0.141913	−0.0709564	+	0.997479i	$0.522605\pi$
$104$	0	0
$105$	−1.41517	−0.138107
$106$	−1.46549	−0.142341
$107$	3.86939	0.374068	0.187034	−	0.982353i	$-0.440113\pi$
$107$	3.86939	0.374068	0.187034	+	0.982353i	$0.440113\pi$
$108$	−1.00000	−0.0962250
$109$	−11.9795	−1.14742	−0.573712	−	0.819057i	$-0.694497\pi$
$109$	−11.9795	−1.14742	−0.573712	+	0.819057i	$0.694497\pi$
$110$	5.76217	0.549401
$111$	10.3422	0.981637
$112$	−1.00000	−0.0944911
$113$	−6.75363	−0.635328	−0.317664	−	0.948203i	$-0.602898\pi$
$113$	−6.75363	−0.635328	−0.317664	+	0.948203i	$0.602898\pi$
$114$	−3.70986	−0.347460
$115$	10.8245	1.00939
$116$	8.67727	0.805665
$117$	0	0
$118$	2.37793	0.218906
$119$	−0.175278	−0.0160677
$120$	−1.41517	−0.129187
$121$	5.57876	0.507160
$122$	−11.7701	−1.06562
$123$	−0.0778681	−0.00702113
$124$	10.8238	0.972009
$125$	11.3175	1.01227
$126$	1.00000	0.0890871
$127$	5.62686	0.499303	0.249651	−	0.968336i	$-0.419684\pi$
$127$	5.62686	0.499303	0.249651	+	0.968336i	$0.419684\pi$
$128$	−1.00000	−0.0883883
$129$	−11.1379	−0.980639
$130$	0	0
$131$	9.39480	0.820828	0.410414	−	0.911899i	$-0.365384\pi$
$131$	9.39480	0.820828	0.410414	+	0.911899i	$0.365384\pi$
$132$	−4.07170	−0.354396
$133$	3.70986	0.321686
$134$	10.1245	0.874628
$135$	1.41517	0.121799
$136$	−0.175278	−0.0150299
$137$	4.39642	0.375611	0.187806	−	0.982206i	$-0.439862\pi$
$137$	4.39642	0.375611	0.187806	+	0.982206i	$0.439862\pi$
$138$	−7.64886	−0.651114
$139$	16.0957	1.36522	0.682609	−	0.730784i	$-0.260845\pi$
$139$	16.0957	1.36522	0.682609	+	0.730784i	$0.260845\pi$
$140$	1.41517	0.119604
$141$	6.10157	0.513845
$142$	0.967422	0.0811842
$143$	0	0
$144$	1.00000	0.0833333
$145$	−12.2799	−1.01979
$146$	13.4323	1.11167
$147$	−1.00000	−0.0824786
$148$	−10.3422	−0.850123
$149$	10.4552	0.856524	0.428262	−	0.903655i	$-0.359126\pi$
$149$	10.4552	0.856524	0.428262	+	0.903655i	$0.359126\pi$
$150$	−2.99728	−0.244727
$151$	−8.81299	−0.717191	−0.358596	−	0.933493i	$-0.616744\pi$
$151$	−8.81299	−0.717191	−0.358596	+	0.933493i	$0.616744\pi$
$152$	3.70986	0.300909
$153$	0.175278	0.0141704
$154$	4.07170	0.328107
$155$	−15.3176	−1.23034
$156$	0	0
$157$	4.99142	0.398358	0.199179	−	0.979963i	$-0.436172\pi$
$157$	4.99142	0.398358	0.199179	+	0.979963i	$0.436172\pi$
$158$	12.8122	1.01928
$159$	−1.46549	−0.116221
$160$	1.41517	0.111879
$161$	7.64886	0.602815
$162$	−1.00000	−0.0785674
$163$	−8.84081	−0.692466	−0.346233	−	0.938149i	$-0.612539\pi$
$163$	−8.84081	−0.692466	−0.346233	+	0.938149i	$0.612539\pi$
$164$	0.0778681	0.00608047
$165$	5.76217	0.448584
$166$	−6.50855	−0.505161
$167$	14.6797	1.13595	0.567973	−	0.823047i	$-0.307728\pi$
$167$	14.6797	1.13595	0.567973	+	0.823047i	$0.307728\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	0.248048	0.0190244
$171$	−3.70986	−0.283700
$172$	11.1379	0.849258
$173$	−4.77122	−0.362749	−0.181375	−	0.983414i	$-0.558055\pi$
$173$	−4.77122	−0.362749	−0.181375	+	0.983414i	$0.558055\pi$
$174$	8.67727	0.657822
$175$	2.99728	0.226573
$176$	4.07170	0.306916
$177$	2.37793	0.178736
$178$	10.8545	0.813577
$179$	−22.9637	−1.71639	−0.858194	−	0.513325i	$-0.828414\pi$
$179$	−22.9637	−1.71639	−0.858194	+	0.513325i	$0.828414\pi$
$180$	−1.41517	−0.105481
$181$	−5.73189	−0.426048	−0.213024	−	0.977047i	$-0.568331\pi$
$181$	−5.73189	−0.426048	−0.213024	+	0.977047i	$0.568331\pi$
$182$	0	0
$183$	−11.7701	−0.870073
$184$	7.64886	0.563882
$185$	14.6360	1.07606
$186$	10.8238	0.793642
$187$	0.713678	0.0521893
$188$	−6.10157	−0.445003
$189$	1.00000	0.0727393
$190$	−5.25010	−0.380882
$191$	26.4125	1.91114	0.955571	−	0.294761i	$-0.0952402\pi$
$191$	26.4125	1.91114	0.955571	+	0.294761i	$0.0952402\pi$
$192$	−1.00000	−0.0721688
$193$	−0.968652	−0.0697251	−0.0348625	−	0.999392i	$-0.511099\pi$
$193$	−0.968652	−0.0697251	−0.0348625	+	0.999392i	$0.511099\pi$
$194$	−13.1116	−0.941356
$195$	0	0
$196$	1.00000	0.0714286
$197$	2.11498	0.150686	0.0753432	−	0.997158i	$-0.475995\pi$
$197$	2.11498	0.150686	0.0753432	+	0.997158i	$0.475995\pi$
$198$	−4.07170	−0.289363
$199$	−12.1033	−0.857978	−0.428989	−	0.903310i	$-0.641130\pi$
$199$	−12.1033	−0.857978	−0.428989	+	0.903310i	$0.641130\pi$
$200$	2.99728	0.211940
$201$	10.1245	0.714131
$202$	−15.8582	−1.11578
$203$	−8.67727	−0.609025
$204$	−0.175278	−0.0122719
$205$	−0.110197	−0.00769649
$206$	1.44026	0.100348
$207$	−7.64886	−0.531633
$208$	0	0
$209$	−15.1054	−1.04487
$210$	1.41517	0.0976563
$211$	−1.58439	−0.109074	−0.0545371	−	0.998512i	$-0.517368\pi$
$211$	−1.58439	−0.109074	−0.0545371	+	0.998512i	$0.517368\pi$
$212$	1.46549	0.100651
$213$	0.967422	0.0662866
$214$	−3.86939	−0.264506
$215$	−15.7621	−1.07497
$216$	1.00000	0.0680414
$217$	−10.8238	−0.734769
$218$	11.9795	0.811351
$219$	13.4323	0.907672
$220$	−5.76217	−0.388485
$221$	0	0
$222$	−10.3422	−0.694123
$223$	−23.9339	−1.60273	−0.801367	−	0.598173i	$-0.795893\pi$
$223$	−23.9339	−1.60273	−0.801367	+	0.598173i	$0.795893\pi$
$224$	1.00000	0.0668153
$225$	−2.99728	−0.199819
$226$	6.75363	0.449245
$227$	15.4010	1.02220	0.511099	−	0.859522i	$-0.329239\pi$
$227$	15.4010	1.02220	0.511099	+	0.859522i	$0.329239\pi$
$228$	3.70986	0.245692
$229$	−14.4179	−0.952759	−0.476380	−	0.879240i	$-0.658051\pi$
$229$	−14.4179	−0.952759	−0.476380	+	0.879240i	$0.658051\pi$
$230$	−10.8245	−0.713745
$231$	4.07170	0.267898
$232$	−8.67727	−0.569691
$233$	8.98072	0.588346	0.294173	−	0.955752i	$-0.404956\pi$
$233$	8.98072	0.588346	0.294173	+	0.955752i	$0.404956\pi$
$234$	0	0
$235$	8.63479	0.563271
$236$	−2.37793	−0.154790
$237$	12.8122	0.832239
$238$	0.175278	0.0113616
$239$	17.0044	1.09992	0.549960	−	0.835191i	$-0.314643\pi$
$239$	17.0044	1.09992	0.549960	+	0.835191i	$0.314643\pi$
$240$	1.41517	0.0913491
$241$	14.2446	0.917575	0.458788	−	0.888546i	$-0.348284\pi$
$241$	14.2446	0.917575	0.458788	+	0.888546i	$0.348284\pi$
$242$	−5.57876	−0.358616
$243$	−1.00000	−0.0641500
$244$	11.7701	0.753505
$245$	−1.41517	−0.0904122
$246$	0.0778681	0.00496469
$247$	0	0
$248$	−10.8238	−0.687314
$249$	−6.50855	−0.412463
$250$	−11.3175	−0.715785
$251$	9.64122	0.608548	0.304274	−	0.952585i	$-0.401586\pi$
$251$	9.64122	0.608548	0.304274	+	0.952585i	$0.401586\pi$
$252$	−1.00000	−0.0629941
$253$	−31.1439	−1.95800
$254$	−5.62686	−0.353060
$255$	0.248048	0.0155334
$256$	1.00000	0.0625000
$257$	4.36305	0.272159	0.136080	−	0.990698i	$-0.456550\pi$
$257$	4.36305	0.272159	0.136080	+	0.990698i	$0.456550\pi$
$258$	11.1379	0.693417
$259$	10.3422	0.642633
$260$	0	0
$261$	8.67727	0.537110
$262$	−9.39480	−0.580413
$263$	−1.84080	−0.113509	−0.0567544	−	0.998388i	$-0.518075\pi$
$263$	−1.84080	−0.113509	−0.0567544	+	0.998388i	$0.518075\pi$
$264$	4.07170	0.250596
$265$	−2.07393	−0.127401
$266$	−3.70986	−0.227466
$267$	10.8545	0.664283
$268$	−10.1245	−0.618455
$269$	31.6360	1.92888	0.964441	−	0.264298i	$-0.0851402\pi$
$269$	31.6360	1.92888	0.964441	+	0.264298i	$0.0851402\pi$
$270$	−1.41517	−0.0861248
$271$	−15.3780	−0.934147	−0.467073	−	0.884219i	$-0.654692\pi$
$271$	−15.3780	−0.934147	−0.467073	+	0.884219i	$0.654692\pi$
$272$	0.175278	0.0106278
$273$	0	0
$274$	−4.39642	−0.265597
$275$	−12.2040	−0.735931
$276$	7.64886	0.460407
$277$	−25.7574	−1.54761	−0.773806	−	0.633422i	$-0.781650\pi$
$277$	−25.7574	−1.54761	−0.773806	+	0.633422i	$0.781650\pi$
$278$	−16.0957	−0.965355
$279$	10.8238	0.648006
$280$	−1.41517	−0.0845729
$281$	−14.5313	−0.866862	−0.433431	−	0.901187i	$-0.642697\pi$
$281$	−14.5313	−0.866862	−0.433431	+	0.901187i	$0.642697\pi$
$282$	−6.10157	−0.363343
$283$	−10.7148	−0.636927	−0.318463	−	0.947935i	$-0.603167\pi$
$283$	−10.7148	−0.636927	−0.318463	+	0.947935i	$0.603167\pi$
$284$	−0.967422	−0.0574059
$285$	−5.25010	−0.310989
$286$	0	0
$287$	−0.0778681	−0.00459641
$288$	−1.00000	−0.0589256
$289$	−16.9693	−0.998193
$290$	12.2799	0.721098
$291$	−13.1116	−0.768614
$292$	−13.4323	−0.786067
$293$	−26.4961	−1.54792	−0.773959	−	0.633236i	$-0.781726\pi$
$293$	−26.4961	−1.54792	−0.773959	+	0.633236i	$0.781726\pi$
$294$	1.00000	0.0583212
$295$	3.36519	0.195929
$296$	10.3422	0.601128
$297$	−4.07170	−0.236264
$298$	−10.4552	−0.605654
$299$	0	0
$300$	2.99728	0.173048
$301$	−11.1379	−0.641979
$302$	8.81299	0.507131
$303$	−15.8582	−0.911027
$304$	−3.70986	−0.212775
$305$	−16.6568	−0.953765
$306$	−0.175278	−0.0100200
$307$	−15.3336	−0.875136	−0.437568	−	0.899185i	$-0.644160\pi$
$307$	−15.3336	−0.875136	−0.437568	+	0.899185i	$0.644160\pi$
$308$	−4.07170	−0.232007
$309$	1.44026	0.0819334
$310$	15.3176	0.869982
$311$	−27.2896	−1.54745	−0.773727	−	0.633520i	$-0.781610\pi$
$311$	−27.2896	−1.54745	−0.773727	+	0.633520i	$0.781610\pi$
$312$	0	0
$313$	−13.2437	−0.748577	−0.374289	−	0.927312i	$-0.622113\pi$
$313$	−13.2437	−0.748577	−0.374289	+	0.927312i	$0.622113\pi$
$314$	−4.99142	−0.281682
$315$	1.41517	0.0797361
$316$	−12.8122	−0.720740
$317$	5.54960	0.311697	0.155848	−	0.987781i	$-0.450189\pi$
$317$	5.54960	0.311697	0.155848	+	0.987781i	$0.450189\pi$
$318$	1.46549	0.0821809
$319$	35.3313	1.97817
$320$	−1.41517	−0.0791107
$321$	−3.86939	−0.215968
$322$	−7.64886	−0.426254
$323$	−0.650256	−0.0361812
$324$	1.00000	0.0555556
$325$	0	0
$326$	8.84081	0.489647
$327$	11.9795	0.662465
$328$	−0.0778681	−0.00429954
$329$	6.10157	0.336390
$330$	−5.76217	−0.317197
$331$	−31.5741	−1.73547	−0.867735	−	0.497027i	$-0.834425\pi$
$331$	−31.5741	−1.73547	−0.867735	+	0.497027i	$0.834425\pi$
$332$	6.50855	0.357203
$333$	−10.3422	−0.566749
$334$	−14.6797	−0.803235
$335$	14.3280	0.782823
$336$	1.00000	0.0545545
$337$	−12.7574	−0.694940	−0.347470	−	0.937691i	$-0.612959\pi$
$337$	−12.7574	−0.694940	−0.347470	+	0.937691i	$0.612959\pi$
$338$	0	0
$339$	6.75363	0.366807
$340$	−0.248048	−0.0134523
$341$	44.0714	2.38660
$342$	3.70986	0.200606
$343$	−1.00000	−0.0539949
$344$	−11.1379	−0.600516
$345$	−10.8245	−0.582770
$346$	4.77122	0.256503
$347$	−18.6609	−1.00177	−0.500885	−	0.865514i	$-0.666992\pi$
$347$	−18.6609	−1.00177	−0.500885	+	0.865514i	$0.666992\pi$
$348$	−8.67727	−0.465151
$349$	11.9865	0.641624	0.320812	−	0.947143i	$-0.396044\pi$
$349$	11.9865	0.641624	0.320812	+	0.947143i	$0.396044\pi$
$350$	−2.99728	−0.160211
$351$	0	0
$352$	−4.07170	−0.217022
$353$	−15.2312	−0.810677	−0.405339	−	0.914167i	$-0.632846\pi$
$353$	−15.2312	−0.810677	−0.405339	+	0.914167i	$0.632846\pi$
$354$	−2.37793	−0.126386
$355$	1.36907	0.0726627
$356$	−10.8545	−0.575286
$357$	0.175278	0.00927667
$358$	22.9637	1.21367
$359$	0.360573	0.0190303	0.00951516	−	0.999955i	$-0.496971\pi$
$359$	0.360573	0.0190303	0.00951516	+	0.999955i	$0.496971\pi$
$360$	1.41517	0.0745863
$361$	−5.23693	−0.275628
$362$	5.73189	0.301262
$363$	−5.57876	−0.292809
$364$	0	0
$365$	19.0091	0.994980
$366$	11.7701	0.615235
$367$	−14.8854	−0.777013	−0.388506	−	0.921446i	$-0.627009\pi$
$367$	−14.8854	−0.777013	−0.388506	+	0.921446i	$0.627009\pi$
$368$	−7.64886	−0.398725
$369$	0.0778681	0.00405365
$370$	−14.6360	−0.760890
$371$	−1.46549	−0.0760847
$372$	−10.8238	−0.561189
$373$	2.87141	0.148676	0.0743379	−	0.997233i	$-0.476316\pi$
$373$	2.87141	0.148676	0.0743379	+	0.997233i	$0.476316\pi$
$374$	−0.713678	−0.0369034
$375$	−11.3175	−0.584436
$376$	6.10157	0.314664
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	−19.1351	−0.982905	−0.491452	−	0.870904i	$-0.663534\pi$
$379$	−19.1351	−0.982905	−0.491452	+	0.870904i	$0.663534\pi$
$380$	5.25010	0.269325
$381$	−5.62686	−0.288273
$382$	−26.4125	−1.35138
$383$	−5.56171	−0.284190	−0.142095	−	0.989853i	$-0.545384\pi$
$383$	−5.56171	−0.284190	−0.142095	+	0.989853i	$0.545384\pi$
$384$	1.00000	0.0510310
$385$	5.76217	0.293667
$386$	0.968652	0.0493031
$387$	11.1379	0.566172
$388$	13.1116	0.665639
$389$	−30.8945	−1.56641	−0.783207	−	0.621762i	$-0.786417\pi$
$389$	−30.8945	−1.56641	−0.783207	+	0.621762i	$0.786417\pi$
$390$	0	0
$391$	−1.34067	−0.0678008
$392$	−1.00000	−0.0505076
$393$	−9.39480	−0.473905
$394$	−2.11498	−0.106551
$395$	18.1314	0.912292
$396$	4.07170	0.204611
$397$	−1.97922	−0.0993343	−0.0496672	−	0.998766i	$-0.515816\pi$
$397$	−1.97922	−0.0993343	−0.0496672	+	0.998766i	$0.515816\pi$
$398$	12.1033	0.606682
$399$	−3.70986	−0.185725
$400$	−2.99728	−0.149864
$401$	29.0395	1.45016	0.725081	−	0.688664i	$-0.241802\pi$
$401$	29.0395	1.45016	0.725081	+	0.688664i	$0.241802\pi$
$402$	−10.1245	−0.504967
$403$	0	0
$404$	15.8582	0.788973
$405$	−1.41517	−0.0703206
$406$	8.67727	0.430646
$407$	−42.1103	−2.08733
$408$	0.175278	0.00867753
$409$	11.8742	0.587141	0.293571	−	0.955937i	$-0.405156\pi$
$409$	11.8742	0.587141	0.293571	+	0.955937i	$0.405156\pi$
$410$	0.110197	0.00544224
$411$	−4.39642	−0.216859
$412$	−1.44026	−0.0709564
$413$	2.37793	0.117010
$414$	7.64886	0.375921
$415$	−9.21074	−0.452137
$416$	0	0
$417$	−16.0957	−0.788209
$418$	15.1054	0.738832
$419$	−19.6870	−0.961775	−0.480888	−	0.876782i	$-0.659685\pi$
$419$	−19.6870	−0.961775	−0.480888	+	0.876782i	$0.659685\pi$
$420$	−1.41517	−0.0690535
$421$	15.0848	0.735190	0.367595	−	0.929986i	$-0.380181\pi$
$421$	15.0848	0.735190	0.367595	+	0.929986i	$0.380181\pi$
$422$	1.58439	0.0771270
$423$	−6.10157	−0.296668
$424$	−1.46549	−0.0711707
$425$	−0.525356	−0.0254835
$426$	−0.967422	−0.0468717
$427$	−11.7701	−0.569596
$428$	3.86939	0.187034
$429$	0	0
$430$	15.7621	0.760116
$431$	−30.6633	−1.47700	−0.738500	−	0.674253i	$-0.764466\pi$
$431$	−30.6633	−1.47700	−0.738500	+	0.674253i	$0.764466\pi$
$432$	−1.00000	−0.0481125
$433$	23.9630	1.15159	0.575793	−	0.817595i	$-0.304693\pi$
$433$	23.9630	1.15159	0.575793	+	0.817595i	$0.304693\pi$
$434$	10.8238	0.519560
$435$	12.2799	0.588774
$436$	−11.9795	−0.573712
$437$	28.3762	1.35742
$438$	−13.4323	−0.641821
$439$	−4.35519	−0.207862	−0.103931	−	0.994585i	$-0.533142\pi$
$439$	−4.35519	−0.207862	−0.103931	+	0.994585i	$0.533142\pi$
$440$	5.76217	0.274701
$441$	1.00000	0.0476190
$442$	0	0
$443$	−21.8068	−1.03607	−0.518036	−	0.855359i	$-0.673337\pi$
$443$	−21.8068	−1.03607	−0.518036	+	0.855359i	$0.673337\pi$
$444$	10.3422	0.490819
$445$	15.3610	0.728180
$446$	23.9339	1.13330
$447$	−10.4552	−0.494514
$448$	−1.00000	−0.0472456
$449$	−19.7899	−0.933945	−0.466972	−	0.884272i	$-0.654655\pi$
$449$	−19.7899	−0.933945	−0.466972	+	0.884272i	$0.654655\pi$
$450$	2.99728	0.141293
$451$	0.317056	0.0149296
$452$	−6.75363	−0.317664
$453$	8.81299	0.414071
$454$	−15.4010	−0.722803
$455$	0	0
$456$	−3.70986	−0.173730
$457$	6.88576	0.322102	0.161051	−	0.986946i	$-0.448512\pi$
$457$	6.88576	0.322102	0.161051	+	0.986946i	$0.448512\pi$
$458$	14.4179	0.673703
$459$	−0.175278	−0.00818126
$460$	10.8245	0.504694
$461$	−8.23466	−0.383527	−0.191763	−	0.981441i	$-0.561421\pi$
$461$	−8.23466	−0.383527	−0.191763	+	0.981441i	$0.561421\pi$
$462$	−4.07170	−0.189433
$463$	16.4527	0.764622	0.382311	−	0.924034i	$-0.375128\pi$
$463$	16.4527	0.764622	0.382311	+	0.924034i	$0.375128\pi$
$464$	8.67727	0.402832
$465$	15.3176	0.710337
$466$	−8.98072	−0.416024
$467$	10.0180	0.463579	0.231790	−	0.972766i	$-0.425542\pi$
$467$	10.0180	0.463579	0.231790	+	0.972766i	$0.425542\pi$
$468$	0	0
$469$	10.1245	0.467508
$470$	−8.63479	−0.398293
$471$	−4.99142	−0.229992
$472$	2.37793	0.109453
$473$	45.3503	2.08521
$474$	−12.8122	−0.588482
$475$	11.1195	0.510197
$476$	−0.175278	−0.00803384
$477$	1.46549	0.0671004
$478$	−17.0044	−0.777761
$479$	6.92045	0.316203	0.158102	−	0.987423i	$-0.449463\pi$
$479$	6.92045	0.316203	0.158102	+	0.987423i	$0.449463\pi$
$480$	−1.41517	−0.0645936
$481$	0	0
$482$	−14.2446	−0.648824
$483$	−7.64886	−0.348035
$484$	5.57876	0.253580
$485$	−18.5552	−0.842547
$486$	1.00000	0.0453609
$487$	−18.3787	−0.832818	−0.416409	−	0.909177i	$-0.636712\pi$
$487$	−18.3787	−0.832818	−0.416409	+	0.909177i	$0.636712\pi$
$488$	−11.7701	−0.532809
$489$	8.84081	0.399795
$490$	1.41517	0.0639311
$491$	6.56572	0.296307	0.148153	−	0.988964i	$-0.452667\pi$
$491$	6.56572	0.296307	0.148153	+	0.988964i	$0.452667\pi$
$492$	−0.0778681	−0.00351056
$493$	1.52093	0.0684993
$494$	0	0
$495$	−5.76217	−0.258990
$496$	10.8238	0.486004
$497$	0.967422	0.0433948
$498$	6.50855	0.291655
$499$	−30.2325	−1.35339	−0.676697	−	0.736261i	$-0.736589\pi$
$499$	−30.2325	−1.35339	−0.676697	+	0.736261i	$0.736589\pi$
$500$	11.3175	0.506136
$501$	−14.6797	−0.655839
$502$	−9.64122	−0.430309
$503$	25.1720	1.12236	0.561182	−	0.827693i	$-0.310347\pi$
$503$	25.1720	1.12236	0.561182	+	0.827693i	$0.310347\pi$
$504$	1.00000	0.0445435
$505$	−22.4421	−0.998659
$506$	31.1439	1.38451
$507$	0	0
$508$	5.62686	0.249651
$509$	−35.7620	−1.58512	−0.792562	−	0.609791i	$-0.791253\pi$
$509$	−35.7620	−1.58512	−0.792562	+	0.609791i	$0.791253\pi$
$510$	−0.248048	−0.0109838
$511$	13.4323	0.594211
$512$	−1.00000	−0.0441942
$513$	3.70986	0.163794
$514$	−4.36305	−0.192446
$515$	2.03822	0.0898146
$516$	−11.1379	−0.490320
$517$	−24.8438	−1.09263
$518$	−10.3422	−0.454410
$519$	4.77122	0.209433
$520$	0	0
$521$	14.1087	0.618114	0.309057	−	0.951044i	$-0.399987\pi$
$521$	14.1087	0.618114	0.309057	+	0.951044i	$0.399987\pi$
$522$	−8.67727	−0.379794
$523$	7.89153	0.345072	0.172536	−	0.985003i	$-0.444804\pi$
$523$	7.89153	0.345072	0.172536	+	0.985003i	$0.444804\pi$
$524$	9.39480	0.410414
$525$	−2.99728	−0.130812
$526$	1.84080	0.0802629
$527$	1.89718	0.0826422
$528$	−4.07170	−0.177198
$529$	35.5051	1.54370
$530$	2.07393	0.0900858
$531$	−2.37793	−0.103193
$532$	3.70986	0.160843
$533$	0	0
$534$	−10.8545	−0.469719
$535$	−5.47586	−0.236742
$536$	10.1245	0.437314
$537$	22.9637	0.990957
$538$	−31.6360	−1.36393
$539$	4.07170	0.175381
$540$	1.41517	0.0608994
$541$	−16.5196	−0.710234	−0.355117	−	0.934822i	$-0.615559\pi$
$541$	−16.5196	−0.710234	−0.355117	+	0.934822i	$0.615559\pi$
$542$	15.3780	0.660542
$543$	5.73189	0.245979
$544$	−0.175278	−0.00751497
$545$	16.9530	0.726188
$546$	0	0
$547$	−33.4659	−1.43090	−0.715450	−	0.698664i	$-0.753778\pi$
$547$	−33.4659	−1.43090	−0.715450	+	0.698664i	$0.753778\pi$
$548$	4.39642	0.187806
$549$	11.7701	0.502337
$550$	12.2040	0.520382
$551$	−32.1915	−1.37140
$552$	−7.64886	−0.325557
$553$	12.8122	0.544828
$554$	25.7574	1.09433
$555$	−14.6360	−0.621264
$556$	16.0957	0.682609
$557$	−3.60699	−0.152833	−0.0764166	−	0.997076i	$-0.524348\pi$
$557$	−3.60699	−0.152833	−0.0764166	+	0.997076i	$0.524348\pi$
$558$	−10.8238	−0.458209
$559$	0	0
$560$	1.41517	0.0598021
$561$	−0.713678	−0.0301315
$562$	14.5313	0.612964
$563$	6.38110	0.268931	0.134466	−	0.990918i	$-0.457068\pi$
$563$	6.38110	0.268931	0.134466	+	0.990918i	$0.457068\pi$
$564$	6.10157	0.256922
$565$	9.55756	0.402090
$566$	10.7148	0.450375
$567$	−1.00000	−0.0419961
$568$	0.967422	0.0405921
$569$	−14.7973	−0.620336	−0.310168	−	0.950682i	$-0.600385\pi$
$569$	−14.7973	−0.620336	−0.310168	+	0.950682i	$0.600385\pi$
$570$	5.25010	0.219903
$571$	−9.25991	−0.387515	−0.193758	−	0.981049i	$-0.562068\pi$
$571$	−9.25991	−0.387515	−0.193758	+	0.981049i	$0.562068\pi$
$572$	0	0
$573$	−26.4125	−1.10340
$574$	0.0778681	0.00325015
$575$	22.9258	0.956071
$576$	1.00000	0.0416667
$577$	−33.4037	−1.39061	−0.695307	−	0.718712i	$-0.744732\pi$
$577$	−33.4037	−1.39061	−0.695307	+	0.718712i	$0.744732\pi$
$578$	16.9693	0.705829
$579$	0.968652	0.0402558
$580$	−12.2799	−0.509893
$581$	−6.50855	−0.270020
$582$	13.1116	0.543492
$583$	5.96706	0.247130
$584$	13.4323	0.555833
$585$	0	0
$586$	26.4961	1.09454
$587$	18.7274	0.772962	0.386481	−	0.922297i	$-0.373690\pi$
$587$	18.7274	0.772962	0.386481	+	0.922297i	$0.373690\pi$
$588$	−1.00000	−0.0412393
$589$	−40.1549	−1.65455
$590$	−3.36519	−0.138543
$591$	−2.11498	−0.0869988
$592$	−10.3422	−0.425061
$593$	5.14931	0.211457	0.105728	−	0.994395i	$-0.466283\pi$
$593$	5.14931	0.211457	0.105728	+	0.994395i	$0.466283\pi$
$594$	4.07170	0.167064
$595$	0.248048	0.0101690
$596$	10.4552	0.428262
$597$	12.1033	0.495354
$598$	0	0
$599$	−45.6132	−1.86371	−0.931853	−	0.362835i	$-0.881809\pi$
$599$	−45.6132	−1.86371	−0.931853	+	0.362835i	$0.881809\pi$
$600$	−2.99728	−0.122363
$601$	−31.5141	−1.28549	−0.642743	−	0.766082i	$-0.722204\pi$
$601$	−31.5141	−1.28549	−0.642743	+	0.766082i	$0.722204\pi$
$602$	11.1379	0.453948
$603$	−10.1245	−0.412304
$604$	−8.81299	−0.358596
$605$	−7.89492	−0.320974
$606$	15.8582	0.644194
$607$	42.2168	1.71353	0.856763	−	0.515711i	$-0.172472\pi$
$607$	42.2168	1.71353	0.856763	+	0.515711i	$0.172472\pi$
$608$	3.70986	0.150455
$609$	8.67727	0.351621
$610$	16.6568	0.674414
$611$	0	0
$612$	0.175278	0.00708518
$613$	30.4135	1.22839	0.614196	−	0.789154i	$-0.289480\pi$
$613$	30.4135	1.22839	0.614196	+	0.789154i	$0.289480\pi$
$614$	15.3336	0.618815
$615$	0.110197	0.00444357
$616$	4.07170	0.164054
$617$	−21.6796	−0.872788	−0.436394	−	0.899756i	$-0.643745\pi$
$617$	−21.6796	−0.872788	−0.436394	+	0.899756i	$0.643745\pi$
$618$	−1.44026	−0.0579357
$619$	−17.6083	−0.707739	−0.353870	−	0.935295i	$-0.615134\pi$
$619$	−17.6083	−0.707739	−0.353870	+	0.935295i	$0.615134\pi$
$620$	−15.3176	−0.615170
$621$	7.64886	0.306938
$622$	27.2896	1.09421
$623$	10.8545	0.434875
$624$	0	0
$625$	−1.02991	−0.0411965
$626$	13.2437	0.529324
$627$	15.1054	0.603254
$628$	4.99142	0.199179
$629$	−1.81275	−0.0722793
$630$	−1.41517	−0.0563819
$631$	16.8392	0.670358	0.335179	−	0.942154i	$-0.391203\pi$
$631$	16.8392	0.670358	0.335179	+	0.942154i	$0.391203\pi$
$632$	12.8122	0.509640
$633$	1.58439	0.0629740
$634$	−5.54960	−0.220403
$635$	−7.96299	−0.316001
$636$	−1.46549	−0.0581107
$637$	0	0
$638$	−35.3313	−1.39878
$639$	−0.967422	−0.0382706
$640$	1.41517	0.0559397
$641$	15.1988	0.600318	0.300159	−	0.953889i	$-0.402960\pi$
$641$	15.1988	0.600318	0.300159	+	0.953889i	$0.402960\pi$
$642$	3.86939	0.152712
$643$	−30.5984	−1.20668	−0.603341	−	0.797483i	$-0.706164\pi$
$643$	−30.5984	−1.20668	−0.603341	+	0.797483i	$0.706164\pi$
$644$	7.64886	0.301407
$645$	15.7621	0.620632
$646$	0.650256	0.0255840
$647$	30.3598	1.19357	0.596784	−	0.802402i	$-0.296445\pi$
$647$	30.3598	1.19357	0.596784	+	0.802402i	$0.296445\pi$
$648$	−1.00000	−0.0392837
$649$	−9.68223	−0.380061
$650$	0	0
$651$	10.8238	0.424219
$652$	−8.84081	−0.346233
$653$	−18.1242	−0.709253	−0.354626	−	0.935008i	$-0.615392\pi$
$653$	−18.1242	−0.709253	−0.354626	+	0.935008i	$0.615392\pi$
$654$	−11.9795	−0.468434
$655$	−13.2953	−0.519490
$656$	0.0778681	0.00304024
$657$	−13.4323	−0.524044
$658$	−6.10157	−0.237864
$659$	−33.8305	−1.31785	−0.658925	−	0.752208i	$-0.728989\pi$
$659$	−33.8305	−1.31785	−0.658925	+	0.752208i	$0.728989\pi$
$660$	5.76217	0.224292
$661$	−22.9044	−0.890876	−0.445438	−	0.895313i	$-0.646952\pi$
$661$	−22.9044	−0.890876	−0.445438	+	0.895313i	$0.646952\pi$
$662$	31.5741	1.22716
$663$	0	0
$664$	−6.50855	−0.252581
$665$	−5.25010	−0.203590
$666$	10.3422	0.400752
$667$	−66.3713	−2.56991
$668$	14.6797	0.567973
$669$	23.9339	0.925339
$670$	−14.3280	−0.553539
$671$	47.9245	1.85010
$672$	−1.00000	−0.0385758
$673$	1.03772	0.0400011	0.0200006	−	0.999800i	$-0.493633\pi$
$673$	1.03772	0.0400011	0.0200006	+	0.999800i	$0.493633\pi$
$674$	12.7574	0.491397
$675$	2.99728	0.115365
$676$	0	0
$677$	7.17675	0.275825	0.137912	−	0.990444i	$-0.455961\pi$
$677$	7.17675	0.275825	0.137912	+	0.990444i	$0.455961\pi$
$678$	−6.75363	−0.259371
$679$	−13.1116	−0.503176
$680$	0.248048	0.00951222
$681$	−15.4010	−0.590166
$682$	−44.0714	−1.68758
$683$	−0.546636	−0.0209164	−0.0104582	−	0.999945i	$-0.503329\pi$
$683$	−0.546636	−0.0209164	−0.0104582	+	0.999945i	$0.503329\pi$
$684$	−3.70986	−0.141850
$685$	−6.22170	−0.237719
$686$	1.00000	0.0381802
$687$	14.4179	0.550076
$688$	11.1379	0.424629
$689$	0	0
$690$	10.8245	0.412081
$691$	−34.5370	−1.31385	−0.656925	−	0.753956i	$-0.728143\pi$
$691$	−34.5370	−1.31385	−0.656925	+	0.753956i	$0.728143\pi$
$692$	−4.77122	−0.181375
$693$	−4.07170	−0.154671
$694$	18.6609	0.708358
$695$	−22.7782	−0.864026
$696$	8.67727	0.328911
$697$	0.0136485	0.000516975 0
$698$	−11.9865	−0.453697
$699$	−8.98072	−0.339682
$700$	2.99728	0.113287
$701$	−37.9560	−1.43358	−0.716790	−	0.697289i	$-0.754389\pi$
$701$	−37.9560	−1.43358	−0.716790	+	0.697289i	$0.754389\pi$
$702$	0	0
$703$	38.3681	1.44708
$704$	4.07170	0.153458
$705$	−8.63479	−0.325205
$706$	15.2312	0.573235
$707$	−15.8582	−0.596407
$708$	2.37793	0.0893681
$709$	−25.4854	−0.957123	−0.478561	−	0.878054i	$-0.658842\pi$
$709$	−25.4854	−0.957123	−0.478561	+	0.878054i	$0.658842\pi$
$710$	−1.36907	−0.0513803
$711$	−12.8122	−0.480493
$712$	10.8545	0.406789
$713$	−82.7900	−3.10051
$714$	−0.175278	−0.00655960
$715$	0	0
$716$	−22.9637	−0.858194
$717$	−17.0044	−0.635039
$718$	−0.360573	−0.0134565
$719$	−18.3328	−0.683699	−0.341850	−	0.939755i	$-0.611053\pi$
$719$	−18.3328	−0.683699	−0.341850	+	0.939755i	$0.611053\pi$
$720$	−1.41517	−0.0527405
$721$	1.44026	0.0536380
$722$	5.23693	0.194898
$723$	−14.2446	−0.529762
$724$	−5.73189	−0.213024
$725$	−26.0082	−0.965921
$726$	5.57876	0.207047
$727$	8.32283	0.308677	0.154338	−	0.988018i	$-0.450675\pi$
$727$	8.32283	0.308677	0.154338	+	0.988018i	$0.450675\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−19.0091	−0.703557
$731$	1.95223	0.0722058
$732$	−11.7701	−0.435036
$733$	16.4886	0.609021	0.304511	−	0.952509i	$-0.401507\pi$
$733$	16.4886	0.609021	0.304511	+	0.952509i	$0.401507\pi$
$734$	14.8854	0.549431
$735$	1.41517	0.0521995
$736$	7.64886	0.281941
$737$	−41.2241	−1.51851
$738$	−0.0778681	−0.00286636
$739$	23.2044	0.853588	0.426794	−	0.904349i	$-0.359643\pi$
$739$	23.2044	0.853588	0.426794	+	0.904349i	$0.359643\pi$
$740$	14.6360	0.538030
$741$	0	0
$742$	1.46549	0.0538000
$743$	1.03785	0.0380749	0.0190375	−	0.999819i	$-0.493940\pi$
$743$	1.03785	0.0380749	0.0190375	+	0.999819i	$0.493940\pi$
$744$	10.8238	0.396821
$745$	−14.7959	−0.542081
$746$	−2.87141	−0.105130
$747$	6.50855	0.238135
$748$	0.713678	0.0260947
$749$	−3.86939	−0.141384
$750$	11.3175	0.413258
$751$	−41.2089	−1.50373	−0.751866	−	0.659316i	$-0.770846\pi$
$751$	−41.2089	−1.50373	−0.751866	+	0.659316i	$0.770846\pi$
$752$	−6.10157	−0.222501
$753$	−9.64122	−0.351345
$754$	0	0
$755$	12.4719	0.453900
$756$	1.00000	0.0363696
$757$	−25.4374	−0.924539	−0.462270	−	0.886739i	$-0.652965\pi$
$757$	−25.4374	−0.924539	−0.462270	+	0.886739i	$0.652965\pi$
$758$	19.1351	0.695019
$759$	31.1439	1.13045
$760$	−5.25010	−0.190441
$761$	−25.1935	−0.913264	−0.456632	−	0.889656i	$-0.650944\pi$
$761$	−25.1935	−0.913264	−0.456632	+	0.889656i	$0.650944\pi$
$762$	5.62686	0.203839
$763$	11.9795	0.433685
$764$	26.4125	0.955571
$765$	−0.248048	−0.00896821
$766$	5.56171	0.200953
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	−7.83552	−0.282556	−0.141278	−	0.989970i	$-0.545121\pi$
$769$	−7.83552	−0.282556	−0.141278	+	0.989970i	$0.545121\pi$
$770$	−5.76217	−0.207654
$771$	−4.36305	−0.157131
$772$	−0.968652	−0.0348625
$773$	10.2961	0.370324	0.185162	−	0.982708i	$-0.440719\pi$
$773$	10.2961	0.370324	0.185162	+	0.982708i	$0.440719\pi$
$774$	−11.1379	−0.400344
$775$	−32.4421	−1.16535
$776$	−13.1116	−0.470678
$777$	−10.3422	−0.371024
$778$	30.8945	1.10762
$779$	−0.288880	−0.0103502
$780$	0	0
$781$	−3.93905	−0.140950
$782$	1.34067	0.0479424
$783$	−8.67727	−0.310100
$784$	1.00000	0.0357143
$785$	−7.06373	−0.252115
$786$	9.39480	0.335101
$787$	−26.6177	−0.948820	−0.474410	−	0.880304i	$-0.657339\pi$
$787$	−26.6177	−0.948820	−0.474410	+	0.880304i	$0.657339\pi$
$788$	2.11498	0.0753432
$789$	1.84080	0.0655344
$790$	−18.1314	−0.645088
$791$	6.75363	0.240131
$792$	−4.07170	−0.144682
$793$	0	0
$794$	1.97922	0.0702400
$795$	2.07393	0.0735548
$796$	−12.1033	−0.428989
$797$	0.187412	0.00663846	0.00331923	−	0.999994i	$-0.498943\pi$
$797$	0.187412	0.00663846	0.00331923	+	0.999994i	$0.498943\pi$
$798$	3.70986	0.131328
$799$	−1.06947	−0.0378351
$800$	2.99728	0.105970
$801$	−10.8545	−0.383524
$802$	−29.0395	−1.02542
$803$	−54.6924	−1.93005
$804$	10.1245	0.357065
$805$	−10.8245	−0.381513
$806$	0	0
$807$	−31.6360	−1.11364
$808$	−15.8582	−0.557888
$809$	39.0116	1.37157	0.685787	−	0.727802i	$-0.259458\pi$
$809$	39.0116	1.37157	0.685787	+	0.727802i	$0.259458\pi$
$810$	1.41517	0.0497242
$811$	−1.18549	−0.0416282	−0.0208141	−	0.999783i	$-0.506626\pi$
$811$	−1.18549	−0.0416282	−0.0208141	+	0.999783i	$0.506626\pi$
$812$	−8.67727	−0.304513
$813$	15.3780	0.539330
$814$	42.1103	1.47597
$815$	12.5113	0.438252
$816$	−0.175278	−0.00613594
$817$	−41.3201	−1.44561
$818$	−11.8742	−0.415172
$819$	0	0
$820$	−0.110197	−0.00384824
$821$	−12.9215	−0.450964	−0.225482	−	0.974247i	$-0.572396\pi$
$821$	−12.9215	−0.450964	−0.225482	+	0.974247i	$0.572396\pi$
$822$	4.39642	0.153343
$823$	32.2111	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$823$	32.2111	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$824$	1.44026	0.0501738
$825$	12.2040	0.424890
$826$	−2.37793	−0.0827388
$827$	34.4870	1.19923	0.599614	−	0.800289i	$-0.295321\pi$
$827$	34.4870	1.19923	0.599614	+	0.800289i	$0.295321\pi$
$828$	−7.64886	−0.265816
$829$	8.89981	0.309103	0.154552	−	0.987985i	$-0.450607\pi$
$829$	8.89981	0.309103	0.154552	+	0.987985i	$0.450607\pi$
$830$	9.21074	0.319709
$831$	25.7574	0.893515
$832$	0	0
$833$	0.175278	0.00607301
$834$	16.0957	0.557348
$835$	−20.7743	−0.718924
$836$	−15.1054	−0.522433
$837$	−10.8238	−0.374126
$838$	19.6870	0.680078
$839$	−48.9238	−1.68904	−0.844518	−	0.535527i	$-0.820113\pi$
$839$	−48.9238	−1.68904	−0.844518	+	0.535527i	$0.820113\pi$
$840$	1.41517	0.0488282
$841$	46.2951	1.59638
$842$	−15.0848	−0.519858
$843$	14.5313	0.500483
$844$	−1.58439	−0.0545371
$845$	0	0
$846$	6.10157	0.209776
$847$	−5.57876	−0.191688
$848$	1.46549	0.0503253
$849$	10.7148	0.367730
$850$	0.525356	0.0180196
$851$	79.1060	2.71172
$852$	0.967422	0.0331433
$853$	53.0982	1.81805	0.909024	−	0.416744i	$-0.136829\pi$
$853$	53.0982	1.81805	0.909024	+	0.416744i	$0.136829\pi$
$854$	11.7701	0.402766
$855$	5.25010	0.179550
$856$	−3.86939	−0.132253
$857$	−10.4137	−0.355725	−0.177862	−	0.984055i	$-0.556918\pi$
$857$	−10.4137	−0.355725	−0.177862	+	0.984055i	$0.556918\pi$
$858$	0	0
$859$	−13.4321	−0.458297	−0.229149	−	0.973391i	$-0.573594\pi$
$859$	−13.4321	−0.458297	−0.229149	+	0.973391i	$0.573594\pi$
$860$	−15.7621	−0.537483
$861$	0.0778681	0.00265374
$862$	30.6633	1.04440
$863$	18.5663	0.632003	0.316002	−	0.948759i	$-0.397660\pi$
$863$	18.5663	0.632003	0.316002	+	0.948759i	$0.397660\pi$
$864$	1.00000	0.0340207
$865$	6.75211	0.229579
$866$	−23.9630	−0.814295
$867$	16.9693	0.576307
$868$	−10.8238	−0.367385
$869$	−52.1673	−1.76965
$870$	−12.2799	−0.416326
$871$	0	0
$872$	11.9795	0.405675
$873$	13.1116	0.443759
$874$	−28.3762	−0.959840
$875$	−11.3175	−0.382603
$876$	13.4323	0.453836
$877$	−30.6148	−1.03379	−0.516894	−	0.856050i	$-0.672912\pi$
$877$	−30.6148	−1.03379	−0.516894	+	0.856050i	$0.672912\pi$
$878$	4.35519	0.146981
$879$	26.4961	0.893691
$880$	−5.76217	−0.194243
$881$	−48.1939	−1.62369	−0.811846	−	0.583871i	$-0.801537\pi$
$881$	−48.1939	−1.62369	−0.811846	+	0.583871i	$0.801537\pi$
$882$	−1.00000	−0.0336718
$883$	−18.0495	−0.607413	−0.303707	−	0.952766i	$-0.598224\pi$
$883$	−18.0495	−0.607413	−0.303707	+	0.952766i	$0.598224\pi$
$884$	0	0
$885$	−3.36519	−0.113120
$886$	21.8068	0.732613
$887$	−28.5032	−0.957044	−0.478522	−	0.878075i	$-0.658827\pi$
$887$	−28.5032	−0.957044	−0.478522	+	0.878075i	$0.658827\pi$
$888$	−10.3422	−0.347061
$889$	−5.62686	−0.188719
$890$	−15.3610	−0.514901
$891$	4.07170	0.136407
$892$	−23.9339	−0.801367
$893$	22.6360	0.757484
$894$	10.4552	0.349674
$895$	32.4977	1.08628
$896$	1.00000	0.0334077
$897$	0	0
$898$	19.7899	0.660399
$899$	93.9213	3.13245
$900$	−2.99728	−0.0999093
$901$	0.256868	0.00855753
$902$	−0.317056	−0.0105568
$903$	11.1379	0.370647
$904$	6.75363	0.224622
$905$	8.11163	0.269640
$906$	−8.81299	−0.292792
$907$	20.1709	0.669764	0.334882	−	0.942260i	$-0.391304\pi$
$907$	20.1709	0.669764	0.334882	+	0.942260i	$0.391304\pi$
$908$	15.4010	0.511099
$909$	15.8582	0.525982
$910$	0	0
$911$	−29.7185	−0.984616	−0.492308	−	0.870421i	$-0.663847\pi$
$911$	−29.7185	−0.984616	−0.492308	+	0.870421i	$0.663847\pi$
$912$	3.70986	0.122846
$913$	26.5009	0.877051
$914$	−6.88576	−0.227761
$915$	16.6568	0.550657
$916$	−14.4179	−0.476380
$917$	−9.39480	−0.310244
$918$	0.175278	0.00578502
$919$	−10.9671	−0.361772	−0.180886	−	0.983504i	$-0.557896\pi$
$919$	−10.9671	−0.361772	−0.180886	+	0.983504i	$0.557896\pi$
$920$	−10.8245	−0.356872
$921$	15.3336	0.505260
$922$	8.23466	0.271194
$923$	0	0
$924$	4.07170	0.133949
$925$	30.9984	1.01922
$926$	−16.4527	−0.540669
$927$	−1.44026	−0.0473043
$928$	−8.67727	−0.284845
$929$	36.1771	1.18693	0.593466	−	0.804859i	$-0.297759\pi$
$929$	36.1771	1.18693	0.593466	+	0.804859i	$0.297759\pi$
$930$	−15.3176	−0.502284
$931$	−3.70986	−0.121586
$932$	8.98072	0.294173
$933$	27.2896	0.893423
$934$	−10.0180	−0.327800
$935$	−1.00998	−0.0330299
$936$	0	0
$937$	−2.58075	−0.0843094	−0.0421547	−	0.999111i	$-0.513422\pi$
$937$	−2.58075	−0.0843094	−0.0421547	+	0.999111i	$0.513422\pi$
$938$	−10.1245	−0.330578
$939$	13.2437	0.432191
$940$	8.63479	0.281636
$941$	27.3758	0.892426	0.446213	−	0.894927i	$-0.352772\pi$
$941$	27.3758	0.892426	0.446213	+	0.894927i	$0.352772\pi$
$942$	4.99142	0.162629
$943$	−0.595602	−0.0193955
$944$	−2.37793	−0.0773951
$945$	−1.41517	−0.0460356
$946$	−45.3503	−1.47447
$947$	36.2494	1.17795	0.588973	−	0.808153i	$-0.299533\pi$
$947$	36.2494	1.17795	0.588973	+	0.808153i	$0.299533\pi$
$948$	12.8122	0.416120
$949$	0	0
$950$	−11.1195	−0.360764
$951$	−5.54960	−0.179958
$952$	0.175278	0.00568078
$953$	21.5910	0.699401	0.349700	−	0.936862i	$-0.386283\pi$
$953$	21.5910	0.699401	0.349700	+	0.936862i	$0.386283\pi$
$954$	−1.46549	−0.0474472
$955$	−37.3783	−1.20953
$956$	17.0044	0.549960
$957$	−35.3313	−1.14210
$958$	−6.92045	−0.223589
$959$	−4.39642	−0.141968
$960$	1.41517	0.0456746
$961$	86.1553	2.77920
$962$	0	0
$963$	3.86939	0.124689
$964$	14.2446	0.458788
$965$	1.37081	0.0441280
$966$	7.64886	0.246098
$967$	12.0490	0.387470	0.193735	−	0.981054i	$-0.437940\pi$
$967$	12.0490	0.387470	0.193735	+	0.981054i	$0.437940\pi$
$968$	−5.57876	−0.179308
$969$	0.650256	0.0208892
$970$	18.5552	0.595771
$971$	−42.8673	−1.37568	−0.687838	−	0.725864i	$-0.741440\pi$
$971$	−42.8673	−1.37568	−0.687838	+	0.725864i	$0.741440\pi$
$972$	−1.00000	−0.0320750
$973$	−16.0957	−0.516004
$974$	18.3787	0.588891
$975$	0	0
$976$	11.7701	0.376753
$977$	26.5896	0.850676	0.425338	−	0.905035i	$-0.360155\pi$
$977$	26.5896	0.850676	0.425338	+	0.905035i	$0.360155\pi$
$978$	−8.84081	−0.282698
$979$	−44.1962	−1.41252
$980$	−1.41517	−0.0452061
$981$	−11.9795	−0.382475
$982$	−6.56572	−0.209521
$983$	−47.8792	−1.52711	−0.763554	−	0.645744i	$-0.776548\pi$
$983$	−47.8792	−1.52711	−0.763554	+	0.645744i	$0.776548\pi$
$984$	0.0778681	0.00248234
$985$	−2.99307	−0.0953672
$986$	−1.52093	−0.0484363
$987$	−6.10157	−0.194215
$988$	0	0
$989$	−85.1924	−2.70896
$990$	5.76217	0.183134
$991$	−46.0744	−1.46360	−0.731801	−	0.681519i	$-0.761320\pi$
$991$	−46.0744	−1.46360	−0.731801	+	0.681519i	$0.761320\pi$
$992$	−10.8238	−0.343657
$993$	31.5741	1.00197
$994$	−0.967422	−0.0306848
$995$	17.1282	0.543002
$996$	−6.50855	−0.206231
$997$	58.9967	1.86844	0.934222	−	0.356692i	$-0.116096\pi$
$997$	58.9967	1.86844	0.934222	+	0.356692i	$0.116096\pi$
$998$	30.2325	0.956994
$999$	10.3422	0.327212

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.41517 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.41517 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.41517 q^{10} +4.07170 q^{11} -1.00000 q^{12} +1.00000 q^{14} +1.41517 q^{15} +1.00000 q^{16} +0.175278 q^{17} -1.00000 q^{18} -3.70986 q^{19} -1.41517 q^{20} +1.00000 q^{21} -4.07170 q^{22} -7.64886 q^{23} +1.00000 q^{24} -2.99728 q^{25} -1.00000 q^{27} -1.00000 q^{28} +8.67727 q^{29} -1.41517 q^{30} +10.8238 q^{31} -1.00000 q^{32} -4.07170 q^{33} -0.175278 q^{34} +1.41517 q^{35} +1.00000 q^{36} -10.3422 q^{37} +3.70986 q^{38} +1.41517 q^{40} +0.0778681 q^{41} -1.00000 q^{42} +11.1379 q^{43} +4.07170 q^{44} -1.41517 q^{45} +7.64886 q^{46} -6.10157 q^{47} -1.00000 q^{48} +1.00000 q^{49} +2.99728 q^{50} -0.175278 q^{51} +1.46549 q^{53} +1.00000 q^{54} -5.76217 q^{55} +1.00000 q^{56} +3.70986 q^{57} -8.67727 q^{58} -2.37793 q^{59} +1.41517 q^{60} +11.7701 q^{61} -10.8238 q^{62} -1.00000 q^{63} +1.00000 q^{64} +4.07170 q^{66} -10.1245 q^{67} +0.175278 q^{68} +7.64886 q^{69} -1.41517 q^{70} -0.967422 q^{71} -1.00000 q^{72} -13.4323 q^{73} +10.3422 q^{74} +2.99728 q^{75} -3.70986 q^{76} -4.07170 q^{77} -12.8122 q^{79} -1.41517 q^{80} +1.00000 q^{81} -0.0778681 q^{82} +6.50855 q^{83} +1.00000 q^{84} -0.248048 q^{85} -11.1379 q^{86} -8.67727 q^{87} -4.07170 q^{88} -10.8545 q^{89} +1.41517 q^{90} -7.64886 q^{92} -10.8238 q^{93} +6.10157 q^{94} +5.25010 q^{95} +1.00000 q^{96} +13.1116 q^{97} -1.00000 q^{98} +4.07170 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} - 6 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 - 6 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} - 6 q^{7} - 6 q^{8} + 6 q^{9} - 3 q^{10} + 6 q^{11} - 6 q^{12} + 6 q^{14} - 3 q^{15} + 6 q^{16} + 10 q^{17} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 6 q^{21} - 6 q^{22} - 12 q^{23} + 6 q^{24} + 5 q^{25} - 6 q^{27} - 6 q^{28} + 4 q^{29} + 3 q^{30} - 7 q^{31} - 6 q^{32} - 6 q^{33} - 10 q^{34} - 3 q^{35} + 6 q^{36} - 3 q^{37} + 8 q^{38} - 3 q^{40} - 3 q^{41} - 6 q^{42} - 3 q^{43} + 6 q^{44} + 3 q^{45} + 12 q^{46} - 29 q^{47} - 6 q^{48} + 6 q^{49} - 5 q^{50} - 10 q^{51} - 12 q^{53} + 6 q^{54} + 29 q^{55} + 6 q^{56} + 8 q^{57} - 4 q^{58} - 2 q^{59} - 3 q^{60} + 13 q^{61} + 7 q^{62} - 6 q^{63} + 6 q^{64} + 6 q^{66} - 22 q^{67} + 10 q^{68} + 12 q^{69} + 3 q^{70} - q^{71} - 6 q^{72} - 29 q^{73} + 3 q^{74} - 5 q^{75} - 8 q^{76} - 6 q^{77} - 24 q^{79} + 3 q^{80} + 6 q^{81} + 3 q^{82} - 7 q^{83} + 6 q^{84} - 21 q^{85} + 3 q^{86} - 4 q^{87} - 6 q^{88} + 11 q^{89} - 3 q^{90} - 12 q^{92} + 7 q^{93} + 29 q^{94} + 8 q^{95} + 6 q^{96} + 4 q^{97} - 6 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 - 6 * q^7 - 6 * q^8 + 6 * q^9 - 3 * q^10 + 6 * q^11 - 6 * q^12 + 6 * q^14 - 3 * q^15 + 6 * q^16 + 10 * q^17 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 6 * q^21 - 6 * q^22 - 12 * q^23 + 6 * q^24 + 5 * q^25 - 6 * q^27 - 6 * q^28 + 4 * q^29 + 3 * q^30 - 7 * q^31 - 6 * q^32 - 6 * q^33 - 10 * q^34 - 3 * q^35 + 6 * q^36 - 3 * q^37 + 8 * q^38 - 3 * q^40 - 3 * q^41 - 6 * q^42 - 3 * q^43 + 6 * q^44 + 3 * q^45 + 12 * q^46 - 29 * q^47 - 6 * q^48 + 6 * q^49 - 5 * q^50 - 10 * q^51 - 12 * q^53 + 6 * q^54 + 29 * q^55 + 6 * q^56 + 8 * q^57 - 4 * q^58 - 2 * q^59 - 3 * q^60 + 13 * q^61 + 7 * q^62 - 6 * q^63 + 6 * q^64 + 6 * q^66 - 22 * q^67 + 10 * q^68 + 12 * q^69 + 3 * q^70 - q^71 - 6 * q^72 - 29 * q^73 + 3 * q^74 - 5 * q^75 - 8 * q^76 - 6 * q^77 - 24 * q^79 + 3 * q^80 + 6 * q^81 + 3 * q^82 - 7 * q^83 + 6 * q^84 - 21 * q^85 + 3 * q^86 - 4 * q^87 - 6 * q^88 + 11 * q^89 - 3 * q^90 - 12 * q^92 + 7 * q^93 + 29 * q^94 + 8 * q^95 + 6 * q^96 + 4 * q^97 - 6 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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