LMFDB - Embedded newform 7098.2.a.cj.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			$0.445042$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.554958 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.554958 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.554958 q^{10} -0.356896 q^{11} -1.00000 q^{12} -1.00000 q^{14} -0.554958 q^{15} +1.00000 q^{16} -3.80194 q^{17} +1.00000 q^{18} +5.74094 q^{19} +0.554958 q^{20} +1.00000 q^{21} -0.356896 q^{22} -2.44504 q^{23} -1.00000 q^{24} -4.69202 q^{25} -1.00000 q^{27} -1.00000 q^{28} +0.405813 q^{29} -0.554958 q^{30} -4.74094 q^{31} +1.00000 q^{32} +0.356896 q^{33} -3.80194 q^{34} -0.554958 q^{35} +1.00000 q^{36} +3.54288 q^{37} +5.74094 q^{38} +0.554958 q^{40} -3.26875 q^{41} +1.00000 q^{42} -6.04892 q^{43} -0.356896 q^{44} +0.554958 q^{45} -2.44504 q^{46} +0.603875 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.69202 q^{50} +3.80194 q^{51} -1.35690 q^{53} -1.00000 q^{54} -0.198062 q^{55} -1.00000 q^{56} -5.74094 q^{57} +0.405813 q^{58} +5.54288 q^{59} -0.554958 q^{60} +4.38404 q^{61} -4.74094 q^{62} -1.00000 q^{63} +1.00000 q^{64} +0.356896 q^{66} -15.2959 q^{67} -3.80194 q^{68} +2.44504 q^{69} -0.554958 q^{70} +7.42758 q^{71} +1.00000 q^{72} -11.2295 q^{73} +3.54288 q^{74} +4.69202 q^{75} +5.74094 q^{76} +0.356896 q^{77} -1.76271 q^{79} +0.554958 q^{80} +1.00000 q^{81} -3.26875 q^{82} -11.4426 q^{83} +1.00000 q^{84} -2.10992 q^{85} -6.04892 q^{86} -0.405813 q^{87} -0.356896 q^{88} +4.80194 q^{89} +0.554958 q^{90} -2.44504 q^{92} +4.74094 q^{93} +0.603875 q^{94} +3.18598 q^{95} -1.00000 q^{96} +2.65279 q^{97} +1.00000 q^{98} -0.356896 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 3 q^{11} - 3 q^{12} - 3 q^{14} - 2 q^{15} + 3 q^{16} - 7 q^{17} + 3 q^{18} + 3 q^{19} + 2 q^{20} + 3 q^{21} + 3 q^{22} - 7 q^{23} - 3 q^{24} - 9 q^{25} - 3 q^{27} - 3 q^{28} - 12 q^{29} - 2 q^{30} + 3 q^{32} - 3 q^{33} - 7 q^{34} - 2 q^{35} + 3 q^{36} - 8 q^{37} + 3 q^{38} + 2 q^{40} - 2 q^{41} + 3 q^{42} - 9 q^{43} + 3 q^{44} + 2 q^{45} - 7 q^{46} - 7 q^{47} - 3 q^{48} + 3 q^{49} - 9 q^{50} + 7 q^{51} - 3 q^{54} - 5 q^{55} - 3 q^{56} - 3 q^{57} - 12 q^{58} - 2 q^{59} - 2 q^{60} + 3 q^{61} - 3 q^{63} + 3 q^{64} - 3 q^{66} - 32 q^{67} - 7 q^{68} + 7 q^{69} - 2 q^{70} + 6 q^{71} + 3 q^{72} - 13 q^{73} - 8 q^{74} + 9 q^{75} + 3 q^{76} - 3 q^{77} + 12 q^{79} + 2 q^{80} + 3 q^{81} - 2 q^{82} + 7 q^{83} + 3 q^{84} - 7 q^{85} - 9 q^{86} + 12 q^{87} + 3 q^{88} + 10 q^{89} + 2 q^{90} - 7 q^{92} - 7 q^{94} - 5 q^{95} - 3 q^{96} - 10 q^{97} + 3 q^{98} + 3 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 + 3 * q^11 - 3 * q^12 - 3 * q^14 - 2 * q^15 + 3 * q^16 - 7 * q^17 + 3 * q^18 + 3 * q^19 + 2 * q^20 + 3 * q^21 + 3 * q^22 - 7 * q^23 - 3 * q^24 - 9 * q^25 - 3 * q^27 - 3 * q^28 - 12 * q^29 - 2 * q^30 + 3 * q^32 - 3 * q^33 - 7 * q^34 - 2 * q^35 + 3 * q^36 - 8 * q^37 + 3 * q^38 + 2 * q^40 - 2 * q^41 + 3 * q^42 - 9 * q^43 + 3 * q^44 + 2 * q^45 - 7 * q^46 - 7 * q^47 - 3 * q^48 + 3 * q^49 - 9 * q^50 + 7 * q^51 - 3 * q^54 - 5 * q^55 - 3 * q^56 - 3 * q^57 - 12 * q^58 - 2 * q^59 - 2 * q^60 + 3 * q^61 - 3 * q^63 + 3 * q^64 - 3 * q^66 - 32 * q^67 - 7 * q^68 + 7 * q^69 - 2 * q^70 + 6 * q^71 + 3 * q^72 - 13 * q^73 - 8 * q^74 + 9 * q^75 + 3 * q^76 - 3 * q^77 + 12 * q^79 + 2 * q^80 + 3 * q^81 - 2 * q^82 + 7 * q^83 + 3 * q^84 - 7 * q^85 - 9 * q^86 + 12 * q^87 + 3 * q^88 + 10 * q^89 + 2 * q^90 - 7 * q^92 - 7 * q^94 - 5 * q^95 - 3 * q^96 - 10 * q^97 + 3 * q^98 + 3 * 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	$-0.460398\pi$
$5$	0.554958	0.248185	0.124092	+	0.992271i	$0.460398\pi$
$6$	−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
$11$	−0.356896	−0.107608	−0.0538041	−	0.998552i	$-0.517135\pi$
$11$	−0.356896	−0.107608	−0.0538041	+	0.998552i	$0.517135\pi$
$12$	−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
$17$	−3.80194	−0.922105	−0.461053	−	0.887373i	$-0.652528\pi$
$17$	−3.80194	−0.922105	−0.461053	+	0.887373i	$0.652528\pi$
$18$	1.00000	0.235702
$19$	5.74094	1.31706	0.658531	−	0.752554i	$-0.271178\pi$
$19$	5.74094	1.31706	0.658531	+	0.752554i	$0.271178\pi$
$20$	0.554958	0.124092
$21$	1.00000	0.218218
$22$	−0.356896	−0.0760905
$23$	−2.44504	−0.509826	−0.254913	−	0.966964i	$-0.582047\pi$
$23$	−2.44504	−0.509826	−0.254913	+	0.966964i	$0.582047\pi$
$24$	−1.00000	−0.204124
$25$	−4.69202	−0.938404
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	0.405813	0.0753576	0.0376788	−	0.999290i	$-0.488004\pi$
$29$	0.405813	0.0753576	0.0376788	+	0.999290i	$0.488004\pi$
$30$	−0.554958	−0.101321
$31$	−4.74094	−0.851498	−0.425749	−	0.904841i	$-0.639989\pi$
$31$	−4.74094	−0.851498	−0.425749	+	0.904841i	$0.639989\pi$
$32$	1.00000	0.176777
$33$	0.356896	0.0621276
$34$	−3.80194	−0.652027
$35$	−0.554958	−0.0938050
$36$	1.00000	0.166667
$37$	3.54288	0.582445	0.291223	−	0.956655i	$-0.405938\pi$
$37$	3.54288	0.582445	0.291223	+	0.956655i	$0.405938\pi$
$38$	5.74094	0.931303
$39$	0	0
$40$	0.554958	0.0877466
$41$	−3.26875	−0.510493	−0.255246	−	0.966876i	$-0.582157\pi$
$41$	−3.26875	−0.510493	−0.255246	+	0.966876i	$0.582157\pi$
$42$	1.00000	0.154303
$43$	−6.04892	−0.922451	−0.461226	−	0.887283i	$-0.652590\pi$
$43$	−6.04892	−0.922451	−0.461226	+	0.887283i	$0.652590\pi$
$44$	−0.356896	−0.0538041
$45$	0.554958	0.0827283
$46$	−2.44504	−0.360502
$47$	0.603875	0.0880843	0.0440421	−	0.999030i	$-0.485976\pi$
$47$	0.603875	0.0880843	0.0440421	+	0.999030i	$0.485976\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−4.69202	−0.663552
$51$	3.80194	0.532378
$52$	0	0
$53$	−1.35690	−0.186384	−0.0931920	−	0.995648i	$-0.529707\pi$
$53$	−1.35690	−0.186384	−0.0931920	+	0.995648i	$0.529707\pi$
$54$	−1.00000	−0.136083
$55$	−0.198062	−0.0267067
$56$	−1.00000	−0.133631
$57$	−5.74094	−0.760406
$58$	0.405813	0.0532859
$59$	5.54288	0.721621	0.360811	−	0.932639i	$-0.382500\pi$
$59$	5.54288	0.721621	0.360811	+	0.932639i	$0.382500\pi$
$60$	−0.554958	−0.0716448
$61$	4.38404	0.561319	0.280660	−	0.959807i	$-0.409447\pi$
$61$	4.38404	0.561319	0.280660	+	0.959807i	$0.409447\pi$
$62$	−4.74094	−0.602100
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	0.356896	0.0439308
$67$	−15.2959	−1.86869	−0.934346	−	0.356368i	$-0.884015\pi$
$67$	−15.2959	−1.86869	−0.934346	+	0.356368i	$0.884015\pi$
$68$	−3.80194	−0.461053
$69$	2.44504	0.294348
$70$	−0.554958	−0.0663302
$71$	7.42758	0.881492	0.440746	−	0.897632i	$-0.354714\pi$
$71$	7.42758	0.881492	0.440746	+	0.897632i	$0.354714\pi$
$72$	1.00000	0.117851
$73$	−11.2295	−1.31432	−0.657158	−	0.753753i	$-0.728242\pi$
$73$	−11.2295	−1.31432	−0.657158	+	0.753753i	$0.728242\pi$
$74$	3.54288	0.411851
$75$	4.69202	0.541788
$76$	5.74094	0.658531
$77$	0.356896	0.0406721
$78$	0	0
$79$	−1.76271	−0.198320	−0.0991601	−	0.995071i	$-0.531616\pi$
$79$	−1.76271	−0.198320	−0.0991601	+	0.995071i	$0.531616\pi$
$80$	0.554958	0.0620462
$81$	1.00000	0.111111
$82$	−3.26875	−0.360973
$83$	−11.4426	−1.25599	−0.627997	−	0.778216i	$-0.716125\pi$
$83$	−11.4426	−1.25599	−0.627997	+	0.778216i	$0.716125\pi$
$84$	1.00000	0.109109
$85$	−2.10992	−0.228853
$86$	−6.04892	−0.652272
$87$	−0.405813	−0.0435077
$88$	−0.356896	−0.0380452
$89$	4.80194	0.509004	0.254502	−	0.967072i	$-0.418088\pi$
$89$	4.80194	0.509004	0.254502	+	0.967072i	$0.418088\pi$
$90$	0.554958	0.0584977
$91$	0	0
$92$	−2.44504	−0.254913
$93$	4.74094	0.491612
$94$	0.603875	0.0622850
$95$	3.18598	0.326875
$96$	−1.00000	−0.102062
$97$	2.65279	0.269350	0.134675	−	0.990890i	$-0.457001\pi$
$97$	2.65279	0.269350	0.134675	+	0.990890i	$0.457001\pi$
$98$	1.00000	0.101015
$99$	−0.356896	−0.0358694
$100$	−4.69202	−0.469202
$101$	−9.10752	−0.906232	−0.453116	−	0.891451i	$-0.649688\pi$
$101$	−9.10752	−0.906232	−0.453116	+	0.891451i	$0.649688\pi$
$102$	3.80194	0.376448
$103$	12.2784	1.20983	0.604915	−	0.796290i	$-0.293207\pi$
$103$	12.2784	1.20983	0.604915	+	0.796290i	$0.293207\pi$
$104$	0	0
$105$	0.554958	0.0541584
$106$	−1.35690	−0.131793
$107$	6.08575	0.588332	0.294166	−	0.955754i	$-0.404958\pi$
$107$	6.08575	0.588332	0.294166	+	0.955754i	$0.404958\pi$
$108$	−1.00000	−0.0962250
$109$	−20.2010	−1.93491	−0.967455	−	0.253044i	$-0.918568\pi$
$109$	−20.2010	−1.93491	−0.967455	+	0.253044i	$0.918568\pi$
$110$	−0.198062	−0.0188845
$111$	−3.54288	−0.336275
$112$	−1.00000	−0.0944911
$113$	2.81700	0.265001	0.132501	−	0.991183i	$-0.457699\pi$
$113$	2.81700	0.265001	0.132501	+	0.991183i	$0.457699\pi$
$114$	−5.74094	−0.537688
$115$	−1.35690	−0.126531
$116$	0.405813	0.0376788
$117$	0	0
$118$	5.54288	0.510263
$119$	3.80194	0.348523
$120$	−0.554958	−0.0506605
$121$	−10.8726	−0.988420
$122$	4.38404	0.396913
$123$	3.26875	0.294733
$124$	−4.74094	−0.425749
$125$	−5.37867	−0.481083
$126$	−1.00000	−0.0890871
$127$	−1.40581	−0.124746	−0.0623729	−	0.998053i	$-0.519867\pi$
$127$	−1.40581	−0.124746	−0.0623729	+	0.998053i	$0.519867\pi$
$128$	1.00000	0.0883883
$129$	6.04892	0.532577
$130$	0	0
$131$	−9.50365	−0.830338	−0.415169	−	0.909744i	$-0.636277\pi$
$131$	−9.50365	−0.830338	−0.415169	+	0.909744i	$0.636277\pi$
$132$	0.356896	0.0310638
$133$	−5.74094	−0.497803
$134$	−15.2959	−1.32136
$135$	−0.554958	−0.0477632
$136$	−3.80194	−0.326013
$137$	1.03684	0.0885829	0.0442914	−	0.999019i	$-0.485897\pi$
$137$	1.03684	0.0885829	0.0442914	+	0.999019i	$0.485897\pi$
$138$	2.44504	0.208136
$139$	8.74094	0.741397	0.370698	−	0.928753i	$-0.379118\pi$
$139$	8.74094	0.741397	0.370698	+	0.928753i	$0.379118\pi$
$140$	−0.554958	−0.0469025
$141$	−0.603875	−0.0508555
$142$	7.42758	0.623309
$143$	0	0
$144$	1.00000	0.0833333
$145$	0.225209	0.0187026
$146$	−11.2295	−0.929362
$147$	−1.00000	−0.0824786
$148$	3.54288	0.291223
$149$	9.38835	0.769124	0.384562	−	0.923099i	$-0.374352\pi$
$149$	9.38835	0.769124	0.384562	+	0.923099i	$0.374352\pi$
$150$	4.69202	0.383102
$151$	8.66248	0.704943	0.352471	−	0.935823i	$-0.385341\pi$
$151$	8.66248	0.704943	0.352471	+	0.935823i	$0.385341\pi$
$152$	5.74094	0.465652
$153$	−3.80194	−0.307368
$154$	0.356896	0.0287595
$155$	−2.63102	−0.211329
$156$	0	0
$157$	7.10992	0.567433	0.283717	−	0.958908i	$-0.408433\pi$
$157$	7.10992	0.567433	0.283717	+	0.958908i	$0.408433\pi$
$158$	−1.76271	−0.140234
$159$	1.35690	0.107609
$160$	0.554958	0.0438733
$161$	2.44504	0.192696
$162$	1.00000	0.0785674
$163$	−18.8931	−1.47982	−0.739910	−	0.672706i	$-0.765132\pi$
$163$	−18.8931	−1.47982	−0.739910	+	0.672706i	$0.765132\pi$
$164$	−3.26875	−0.255246
$165$	0.198062	0.0154191
$166$	−11.4426	−0.888122
$167$	3.13169	0.242337	0.121169	−	0.992632i	$-0.461336\pi$
$167$	3.13169	0.242337	0.121169	+	0.992632i	$0.461336\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	−2.10992	−0.161823
$171$	5.74094	0.439021
$172$	−6.04892	−0.461226
$173$	−4.39612	−0.334231	−0.167116	−	0.985937i	$-0.553445\pi$
$173$	−4.39612	−0.334231	−0.167116	+	0.985937i	$0.553445\pi$
$174$	−0.405813	−0.0307646
$175$	4.69202	0.354683
$176$	−0.356896	−0.0269020
$177$	−5.54288	−0.416628
$178$	4.80194	0.359920
$179$	−16.9215	−1.26478	−0.632388	−	0.774652i	$-0.717925\pi$
$179$	−16.9215	−1.26478	−0.632388	+	0.774652i	$0.717925\pi$
$180$	0.554958	0.0413641
$181$	−9.71917	−0.722420	−0.361210	−	0.932484i	$-0.617636\pi$
$181$	−9.71917	−0.722420	−0.361210	+	0.932484i	$0.617636\pi$
$182$	0	0
$183$	−4.38404	−0.324078
$184$	−2.44504	−0.180251
$185$	1.96615	0.144554
$186$	4.74094	0.347622
$187$	1.35690	0.0992261
$188$	0.603875	0.0440421
$189$	1.00000	0.0727393
$190$	3.18598	0.231135
$191$	3.40581	0.246436	0.123218	−	0.992380i	$-0.460679\pi$
$191$	3.40581	0.246436	0.123218	+	0.992380i	$0.460679\pi$
$192$	−1.00000	−0.0721688
$193$	−17.0804	−1.22947	−0.614736	−	0.788733i	$-0.710738\pi$
$193$	−17.0804	−1.22947	−0.614736	+	0.788733i	$0.710738\pi$
$194$	2.65279	0.190459
$195$	0	0
$196$	1.00000	0.0714286
$197$	3.89977	0.277847	0.138924	−	0.990303i	$-0.455636\pi$
$197$	3.89977	0.277847	0.138924	+	0.990303i	$0.455636\pi$
$198$	−0.356896	−0.0253635
$199$	3.52111	0.249605	0.124802	−	0.992182i	$-0.460170\pi$
$199$	3.52111	0.249605	0.124802	+	0.992182i	$0.460170\pi$
$200$	−4.69202	−0.331776
$201$	15.2959	1.07889
$202$	−9.10752	−0.640803
$203$	−0.405813	−0.0284825
$204$	3.80194	0.266189
$205$	−1.81402	−0.126697
$206$	12.2784	0.855479
$207$	−2.44504	−0.169942
$208$	0	0
$209$	−2.04892	−0.141727
$210$	0.554958	0.0382957
$211$	−3.18598	−0.219332	−0.109666	−	0.993968i	$-0.534978\pi$
$211$	−3.18598	−0.219332	−0.109666	+	0.993968i	$0.534978\pi$
$212$	−1.35690	−0.0931920
$213$	−7.42758	−0.508930
$214$	6.08575	0.416014
$215$	−3.35690	−0.228938
$216$	−1.00000	−0.0680414
$217$	4.74094	0.321836
$218$	−20.2010	−1.36819
$219$	11.2295	0.758821
$220$	−0.198062	−0.0133534
$221$	0	0
$222$	−3.54288	−0.237782
$223$	3.35450	0.224634	0.112317	−	0.993672i	$-0.464173\pi$
$223$	3.35450	0.224634	0.112317	+	0.993672i	$0.464173\pi$
$224$	−1.00000	−0.0668153
$225$	−4.69202	−0.312801
$226$	2.81700	0.187384
$227$	−10.8804	−0.722157	−0.361079	−	0.932535i	$-0.617591\pi$
$227$	−10.8804	−0.722157	−0.361079	+	0.932535i	$0.617591\pi$
$228$	−5.74094	−0.380203
$229$	−12.0804	−0.798294	−0.399147	−	0.916887i	$-0.630694\pi$
$229$	−12.0804	−0.798294	−0.399147	+	0.916887i	$0.630694\pi$
$230$	−1.35690	−0.0894711
$231$	−0.356896	−0.0234820
$232$	0.405813	0.0266429
$233$	−23.8810	−1.56450	−0.782248	−	0.622968i	$-0.785927\pi$
$233$	−23.8810	−1.56450	−0.782248	+	0.622968i	$0.785927\pi$
$234$	0	0
$235$	0.335126	0.0218612
$236$	5.54288	0.360811
$237$	1.76271	0.114500
$238$	3.80194	0.246443
$239$	−17.4819	−1.13081	−0.565404	−	0.824814i	$-0.691280\pi$
$239$	−17.4819	−1.13081	−0.565404	+	0.824814i	$0.691280\pi$
$240$	−0.554958	−0.0358224
$241$	−2.22521	−0.143338	−0.0716692	−	0.997428i	$-0.522833\pi$
$241$	−2.22521	−0.143338	−0.0716692	+	0.997428i	$0.522833\pi$
$242$	−10.8726	−0.698919
$243$	−1.00000	−0.0641500
$244$	4.38404	0.280660
$245$	0.554958	0.0354550
$246$	3.26875	0.208408
$247$	0	0
$248$	−4.74094	−0.301050
$249$	11.4426	0.725148
$250$	−5.37867	−0.340177
$251$	−8.30665	−0.524311	−0.262156	−	0.965026i	$-0.584433\pi$
$251$	−8.30665	−0.524311	−0.262156	+	0.965026i	$0.584433\pi$
$252$	−1.00000	−0.0629941
$253$	0.872625	0.0548615
$254$	−1.40581	−0.0882086
$255$	2.10992	0.132128
$256$	1.00000	0.0625000
$257$	4.66248	0.290838	0.145419	−	0.989370i	$-0.453547\pi$
$257$	4.66248	0.290838	0.145419	+	0.989370i	$0.453547\pi$
$258$	6.04892	0.376589
$259$	−3.54288	−0.220144
$260$	0	0
$261$	0.405813	0.0251192
$262$	−9.50365	−0.587137
$263$	−20.6015	−1.27034	−0.635171	−	0.772372i	$-0.719070\pi$
$263$	−20.6015	−1.27034	−0.635171	+	0.772372i	$0.719070\pi$
$264$	0.356896	0.0219654
$265$	−0.753020	−0.0462577
$266$	−5.74094	−0.352000
$267$	−4.80194	−0.293874
$268$	−15.2959	−0.934346
$269$	32.3032	1.96956	0.984780	−	0.173804i	$-0.0556060\pi$
$269$	32.3032	1.96956	0.984780	+	0.173804i	$0.0556060\pi$
$270$	−0.554958	−0.0337737
$271$	−5.21850	−0.317002	−0.158501	−	0.987359i	$-0.550666\pi$
$271$	−5.21850	−0.317002	−0.158501	+	0.987359i	$0.550666\pi$
$272$	−3.80194	−0.230526
$273$	0	0
$274$	1.03684	0.0626375
$275$	1.67456	0.100980
$276$	2.44504	0.147174
$277$	−6.27950	−0.377299	−0.188649	−	0.982045i	$-0.560411\pi$
$277$	−6.27950	−0.377299	−0.188649	+	0.982045i	$0.560411\pi$
$278$	8.74094	0.524247
$279$	−4.74094	−0.283833
$280$	−0.554958	−0.0331651
$281$	0.423272	0.0252503	0.0126251	−	0.999920i	$-0.495981\pi$
$281$	0.423272	0.0252503	0.0126251	+	0.999920i	$0.495981\pi$
$282$	−0.603875	−0.0359603
$283$	10.9946	0.653563	0.326781	−	0.945100i	$-0.394036\pi$
$283$	10.9946	0.653563	0.326781	+	0.945100i	$0.394036\pi$
$284$	7.42758	0.440746
$285$	−3.18598	−0.188721
$286$	0	0
$287$	3.26875	0.192948
$288$	1.00000	0.0589256
$289$	−2.54527	−0.149722
$290$	0.225209	0.0132247
$291$	−2.65279	−0.155509
$292$	−11.2295	−0.657158
$293$	−15.3177	−0.894868	−0.447434	−	0.894317i	$-0.647662\pi$
$293$	−15.3177	−0.894868	−0.447434	+	0.894317i	$0.647662\pi$
$294$	−1.00000	−0.0583212
$295$	3.07606	0.179095
$296$	3.54288	0.205926
$297$	0.356896	0.0207092
$298$	9.38835	0.543853
$299$	0	0
$300$	4.69202	0.270894
$301$	6.04892	0.348654
$302$	8.66248	0.498470
$303$	9.10752	0.523214
$304$	5.74094	0.329265
$305$	2.43296	0.139311
$306$	−3.80194	−0.217342
$307$	−19.8280	−1.13164	−0.565822	−	0.824527i	$-0.691441\pi$
$307$	−19.8280	−1.13164	−0.565822	+	0.824527i	$0.691441\pi$
$308$	0.356896	0.0203360
$309$	−12.2784	−0.698496
$310$	−2.63102	−0.149432
$311$	24.6461	1.39755	0.698776	−	0.715341i	$-0.253729\pi$
$311$	24.6461	1.39755	0.698776	+	0.715341i	$0.253729\pi$
$312$	0	0
$313$	11.2034	0.633256	0.316628	−	0.948550i	$-0.397449\pi$
$313$	11.2034	0.633256	0.316628	+	0.948550i	$0.397449\pi$
$314$	7.10992	0.401236
$315$	−0.554958	−0.0312683
$316$	−1.76271	−0.0991601
$317$	−24.8756	−1.39715	−0.698577	−	0.715535i	$-0.746183\pi$
$317$	−24.8756	−1.39715	−0.698577	+	0.715535i	$0.746183\pi$
$318$	1.35690	0.0760909
$319$	−0.144833	−0.00810909
$320$	0.554958	0.0310231
$321$	−6.08575	−0.339674
$322$	2.44504	0.136257
$323$	−21.8267	−1.21447
$324$	1.00000	0.0555556
$325$	0	0
$326$	−18.8931	−1.04639
$327$	20.2010	1.11712
$328$	−3.26875	−0.180487
$329$	−0.603875	−0.0332927
$330$	0.198062	0.0109030
$331$	22.7289	1.24929	0.624645	−	0.780908i	$-0.285243\pi$
$331$	22.7289	1.24929	0.624645	+	0.780908i	$0.285243\pi$
$332$	−11.4426	−0.627997
$333$	3.54288	0.194148
$334$	3.13169	0.171358
$335$	−8.48858	−0.463781
$336$	1.00000	0.0545545
$337$	10.5743	0.576021	0.288010	−	0.957627i	$-0.407006\pi$
$337$	10.5743	0.576021	0.288010	+	0.957627i	$0.407006\pi$
$338$	0	0
$339$	−2.81700	−0.152999
$340$	−2.10992	−0.114426
$341$	1.69202	0.0916281
$342$	5.74094	0.310434
$343$	−1.00000	−0.0539949
$344$	−6.04892	−0.326136
$345$	1.35690	0.0730528
$346$	−4.39612	−0.236337
$347$	7.57002	0.406380	0.203190	−	0.979139i	$-0.434869\pi$
$347$	7.57002	0.406380	0.203190	+	0.979139i	$0.434869\pi$
$348$	−0.405813	−0.0217539
$349$	−5.50066	−0.294444	−0.147222	−	0.989103i	$-0.547033\pi$
$349$	−5.50066	−0.294444	−0.147222	+	0.989103i	$0.547033\pi$
$350$	4.69202	0.250799
$351$	0	0
$352$	−0.356896	−0.0190226
$353$	−33.0508	−1.75912	−0.879559	−	0.475789i	$-0.842162\pi$
$353$	−33.0508	−1.75912	−0.879559	+	0.475789i	$0.842162\pi$
$354$	−5.54288	−0.294601
$355$	4.12200	0.218773
$356$	4.80194	0.254502
$357$	−3.80194	−0.201220
$358$	−16.9215	−0.894331
$359$	−11.8702	−0.626487	−0.313243	−	0.949673i	$-0.601416\pi$
$359$	−11.8702	−0.626487	−0.313243	+	0.949673i	$0.601416\pi$
$360$	0.554958	0.0292489
$361$	13.9584	0.734651
$362$	−9.71917	−0.510828
$363$	10.8726	0.570665
$364$	0	0
$365$	−6.23191	−0.326193
$366$	−4.38404	−0.229158
$367$	−2.46980	−0.128922	−0.0644612	−	0.997920i	$-0.520533\pi$
$367$	−2.46980	−0.128922	−0.0644612	+	0.997920i	$0.520533\pi$
$368$	−2.44504	−0.127457
$369$	−3.26875	−0.170164
$370$	1.96615	0.102215
$371$	1.35690	0.0704465
$372$	4.74094	0.245806
$373$	−9.28514	−0.480766	−0.240383	−	0.970678i	$-0.577273\pi$
$373$	−9.28514	−0.480766	−0.240383	+	0.970678i	$0.577273\pi$
$374$	1.35690	0.0701634
$375$	5.37867	0.277753
$376$	0.603875	0.0311425
$377$	0	0
$378$	1.00000	0.0514344
$379$	−0.292913	−0.0150459	−0.00752297	−	0.999972i	$-0.502395\pi$
$379$	−0.292913	−0.0150459	−0.00752297	+	0.999972i	$0.502395\pi$
$380$	3.18598	0.163437
$381$	1.40581	0.0720220
$382$	3.40581	0.174257
$383$	28.2446	1.44323	0.721615	−	0.692294i	$-0.243400\pi$
$383$	28.2446	1.44323	0.721615	+	0.692294i	$0.243400\pi$
$384$	−1.00000	−0.0510310
$385$	0.198062	0.0100942
$386$	−17.0804	−0.869368
$387$	−6.04892	−0.307484
$388$	2.65279	0.134675
$389$	−23.1618	−1.17435	−0.587175	−	0.809460i	$-0.699760\pi$
$389$	−23.1618	−1.17435	−0.587175	+	0.809460i	$0.699760\pi$
$390$	0	0
$391$	9.29590	0.470114
$392$	1.00000	0.0505076
$393$	9.50365	0.479396
$394$	3.89977	0.196468
$395$	−0.978230	−0.0492201
$396$	−0.356896	−0.0179347
$397$	−21.8767	−1.09796	−0.548979	−	0.835836i	$-0.684983\pi$
$397$	−21.8767	−1.09796	−0.548979	+	0.835836i	$0.684983\pi$
$398$	3.52111	0.176497
$399$	5.74094	0.287406
$400$	−4.69202	−0.234601
$401$	15.3381	0.765949	0.382974	−	0.923759i	$-0.374900\pi$
$401$	15.3381	0.765949	0.382974	+	0.923759i	$0.374900\pi$
$402$	15.2959	0.762890
$403$	0	0
$404$	−9.10752	−0.453116
$405$	0.554958	0.0275761
$406$	−0.405813	−0.0201402
$407$	−1.26444	−0.0626759
$408$	3.80194	0.188224
$409$	18.6383	0.921606	0.460803	−	0.887503i	$-0.347562\pi$
$409$	18.6383	0.921606	0.460803	+	0.887503i	$0.347562\pi$
$410$	−1.81402	−0.0895880
$411$	−1.03684	−0.0511433
$412$	12.2784	0.604915
$413$	−5.54288	−0.272747
$414$	−2.44504	−0.120167
$415$	−6.35019	−0.311719
$416$	0	0
$417$	−8.74094	−0.428046
$418$	−2.04892	−0.100216
$419$	39.2258	1.91631	0.958153	−	0.286257i	$-0.0924111\pi$
$419$	39.2258	1.91631	0.958153	+	0.286257i	$0.0924111\pi$
$420$	0.554958	0.0270792
$421$	−7.94139	−0.387040	−0.193520	−	0.981096i	$-0.561990\pi$
$421$	−7.94139	−0.387040	−0.193520	+	0.981096i	$0.561990\pi$
$422$	−3.18598	−0.155091
$423$	0.603875	0.0293614
$424$	−1.35690	−0.0658967
$425$	17.8388	0.865308
$426$	−7.42758	−0.359868
$427$	−4.38404	−0.212159
$428$	6.08575	0.294166
$429$	0	0
$430$	−3.35690	−0.161884
$431$	24.2674	1.16892	0.584460	−	0.811422i	$-0.301306\pi$
$431$	24.2674	1.16892	0.584460	+	0.811422i	$0.301306\pi$
$432$	−1.00000	−0.0481125
$433$	−20.7832	−0.998775	−0.499387	−	0.866379i	$-0.666441\pi$
$433$	−20.7832	−0.998775	−0.499387	+	0.866379i	$0.666441\pi$
$434$	4.74094	0.227572
$435$	−0.225209	−0.0107980
$436$	−20.2010	−0.967455
$437$	−14.0368	−0.671473
$438$	11.2295	0.536567
$439$	38.5502	1.83990	0.919950	−	0.392036i	$-0.128229\pi$
$439$	38.5502	1.83990	0.919950	+	0.392036i	$0.128229\pi$
$440$	−0.198062	−0.00944225
$441$	1.00000	0.0476190
$442$	0	0
$443$	−1.59850	−0.0759470	−0.0379735	−	0.999279i	$-0.512090\pi$
$443$	−1.59850	−0.0759470	−0.0379735	+	0.999279i	$0.512090\pi$
$444$	−3.54288	−0.168137
$445$	2.66487	0.126327
$446$	3.35450	0.158840
$447$	−9.38835	−0.444054
$448$	−1.00000	−0.0472456
$449$	26.2064	1.23676	0.618379	−	0.785880i	$-0.287790\pi$
$449$	26.2064	1.23676	0.618379	+	0.785880i	$0.287790\pi$
$450$	−4.69202	−0.221184
$451$	1.16660	0.0549332
$452$	2.81700	0.132501
$453$	−8.66248	−0.406999
$454$	−10.8804	−0.510642
$455$	0	0
$456$	−5.74094	−0.268844
$457$	11.1540	0.521764	0.260882	−	0.965371i	$-0.415987\pi$
$457$	11.1540	0.521764	0.260882	+	0.965371i	$0.415987\pi$
$458$	−12.0804	−0.564479
$459$	3.80194	0.177459
$460$	−1.35690	−0.0632656
$461$	17.9191	0.834578	0.417289	−	0.908774i	$-0.362980\pi$
$461$	17.9191	0.834578	0.417289	+	0.908774i	$0.362980\pi$
$462$	−0.356896	−0.0166043
$463$	−11.5453	−0.536554	−0.268277	−	0.963342i	$-0.586454\pi$
$463$	−11.5453	−0.536554	−0.268277	+	0.963342i	$0.586454\pi$
$464$	0.405813	0.0188394
$465$	2.63102	0.122011
$466$	−23.8810	−1.10627
$467$	−18.4620	−0.854321	−0.427160	−	0.904176i	$-0.640486\pi$
$467$	−18.4620	−0.854321	−0.427160	+	0.904176i	$0.640486\pi$
$468$	0	0
$469$	15.2959	0.706299
$470$	0.335126	0.0154582
$471$	−7.10992	−0.327608
$472$	5.54288	0.255132
$473$	2.15883	0.0992633
$474$	1.76271	0.0809639
$475$	−26.9366	−1.23594
$476$	3.80194	0.174262
$477$	−1.35690	−0.0621280
$478$	−17.4819	−0.799602
$479$	−35.8756	−1.63920	−0.819599	−	0.572937i	$-0.805804\pi$
$479$	−35.8756	−1.63920	−0.819599	+	0.572937i	$0.805804\pi$
$480$	−0.554958	−0.0253303
$481$	0	0
$482$	−2.22521	−0.101356
$483$	−2.44504	−0.111253
$484$	−10.8726	−0.494210
$485$	1.47219	0.0668487
$486$	−1.00000	−0.0453609
$487$	−1.90648	−0.0863907	−0.0431954	−	0.999067i	$-0.513754\pi$
$487$	−1.90648	−0.0863907	−0.0431954	+	0.999067i	$0.513754\pi$
$488$	4.38404	0.198456
$489$	18.8931	0.854374
$490$	0.554958	0.0250705
$491$	−17.7536	−0.801209	−0.400605	−	0.916251i	$-0.631200\pi$
$491$	−17.7536	−0.801209	−0.400605	+	0.916251i	$0.631200\pi$
$492$	3.26875	0.147367
$493$	−1.54288	−0.0694877
$494$	0	0
$495$	−0.198062	−0.00890224
$496$	−4.74094	−0.212874
$497$	−7.42758	−0.333173
$498$	11.4426	0.512757
$499$	−24.8528	−1.11256	−0.556281	−	0.830994i	$-0.687772\pi$
$499$	−24.8528	−1.11256	−0.556281	+	0.830994i	$0.687772\pi$
$500$	−5.37867	−0.240541
$501$	−3.13169	−0.139913
$502$	−8.30665	−0.370744
$503$	42.3870	1.88994	0.944972	−	0.327151i	$-0.106089\pi$
$503$	42.3870	1.88994	0.944972	+	0.327151i	$0.106089\pi$
$504$	−1.00000	−0.0445435
$505$	−5.05429	−0.224913
$506$	0.872625	0.0387929
$507$	0	0
$508$	−1.40581	−0.0623729
$509$	2.93362	0.130031	0.0650153	−	0.997884i	$-0.479290\pi$
$509$	2.93362	0.130031	0.0650153	+	0.997884i	$0.479290\pi$
$510$	2.10992	0.0934287
$511$	11.2295	0.496765
$512$	1.00000	0.0441942
$513$	−5.74094	−0.253469
$514$	4.66248	0.205653
$515$	6.81402	0.300262
$516$	6.04892	0.266289
$517$	−0.215521	−0.00947859
$518$	−3.54288	−0.155665
$519$	4.39612	0.192968
$520$	0	0
$521$	−40.1396	−1.75855	−0.879273	−	0.476318i	$-0.841971\pi$
$521$	−40.1396	−1.75855	−0.879273	+	0.476318i	$0.841971\pi$
$522$	0.405813	0.0177620
$523$	−14.8418	−0.648985	−0.324492	−	0.945888i	$-0.605193\pi$
$523$	−14.8418	−0.648985	−0.324492	+	0.945888i	$0.605193\pi$
$524$	−9.50365	−0.415169
$525$	−4.69202	−0.204777
$526$	−20.6015	−0.898267
$527$	18.0248	0.785171
$528$	0.356896	0.0155319
$529$	−17.0218	−0.740077
$530$	−0.753020	−0.0327091
$531$	5.54288	0.240540
$532$	−5.74094	−0.248901
$533$	0	0
$534$	−4.80194	−0.207800
$535$	3.37734	0.146015
$536$	−15.2959	−0.660682
$537$	16.9215	0.730218
$538$	32.3032	1.39269
$539$	−0.356896	−0.0153726
$540$	−0.554958	−0.0238816
$541$	−39.0127	−1.67729	−0.838643	−	0.544682i	$-0.816650\pi$
$541$	−39.0127	−1.67729	−0.838643	+	0.544682i	$0.816650\pi$
$542$	−5.21850	−0.224154
$543$	9.71917	0.417089
$544$	−3.80194	−0.163007
$545$	−11.2107	−0.480215
$546$	0	0
$547$	27.0978	1.15862	0.579310	−	0.815107i	$-0.303322\pi$
$547$	27.0978	1.15862	0.579310	+	0.815107i	$0.303322\pi$
$548$	1.03684	0.0442914
$549$	4.38404	0.187106
$550$	1.67456	0.0714036
$551$	2.32975	0.0992506
$552$	2.44504	0.104068
$553$	1.76271	0.0749580
$554$	−6.27950	−0.266791
$555$	−1.96615	−0.0834583
$556$	8.74094	0.370698
$557$	−32.2338	−1.36579	−0.682896	−	0.730516i	$-0.739280\pi$
$557$	−32.2338	−1.36579	−0.682896	+	0.730516i	$0.739280\pi$
$558$	−4.74094	−0.200700
$559$	0	0
$560$	−0.554958	−0.0234513
$561$	−1.35690	−0.0572882
$562$	0.423272	0.0178546
$563$	15.8237	0.666890	0.333445	−	0.942770i	$-0.391789\pi$
$563$	15.8237	0.666890	0.333445	+	0.942770i	$0.391789\pi$
$564$	−0.603875	−0.0254277
$565$	1.56332	0.0657693
$566$	10.9946	0.462138
$567$	−1.00000	−0.0419961
$568$	7.42758	0.311654
$569$	−22.0127	−0.922819	−0.461410	−	0.887187i	$-0.652656\pi$
$569$	−22.0127	−0.922819	−0.461410	+	0.887187i	$0.652656\pi$
$570$	−3.18598	−0.133446
$571$	10.0379	0.420073	0.210037	−	0.977694i	$-0.432642\pi$
$571$	10.0379	0.420073	0.210037	+	0.977694i	$0.432642\pi$
$572$	0	0
$573$	−3.40581	−0.142280
$574$	3.26875	0.136435
$575$	11.4722	0.478423
$576$	1.00000	0.0416667
$577$	−2.85325	−0.118782	−0.0593911	−	0.998235i	$-0.518916\pi$
$577$	−2.85325	−0.118782	−0.0593911	+	0.998235i	$0.518916\pi$
$578$	−2.54527	−0.105869
$579$	17.0804	0.709836
$580$	0.225209	0.00935131
$581$	11.4426	0.474721
$582$	−2.65279	−0.109962
$583$	0.484271	0.0200564
$584$	−11.2295	−0.464681
$585$	0	0
$586$	−15.3177	−0.632767
$587$	42.0514	1.73565	0.867824	−	0.496872i	$-0.165518\pi$
$587$	42.0514	1.73565	0.867824	+	0.496872i	$0.165518\pi$
$588$	−1.00000	−0.0412393
$589$	−27.2174	−1.12148
$590$	3.07606	0.126640
$591$	−3.89977	−0.160415
$592$	3.54288	0.145611
$593$	0.00909768	0.000373597 0	0.000186798	−	1.00000i	$-0.499941\pi$
$593$	0.00909768	0.000373597 0	0.000186798		1.00000i	$0.499941\pi$
$594$	0.356896	0.0146436
$595$	2.10992	0.0864981
$596$	9.38835	0.384562
$597$	−3.52111	−0.144109
$598$	0	0
$599$	9.13169	0.373111	0.186555	−	0.982444i	$-0.440268\pi$
$599$	9.13169	0.373111	0.186555	+	0.982444i	$0.440268\pi$
$600$	4.69202	0.191551
$601$	−10.7791	−0.439689	−0.219844	−	0.975535i	$-0.570555\pi$
$601$	−10.7791	−0.439689	−0.219844	+	0.975535i	$0.570555\pi$
$602$	6.04892	0.246535
$603$	−15.2959	−0.622897
$604$	8.66248	0.352471
$605$	−6.03385	−0.245311
$606$	9.10752	0.369968
$607$	−3.04354	−0.123533	−0.0617667	−	0.998091i	$-0.519673\pi$
$607$	−3.04354	−0.123533	−0.0617667	+	0.998091i	$0.519673\pi$
$608$	5.74094	0.232826
$609$	0.405813	0.0164444
$610$	2.43296	0.0985077
$611$	0	0
$612$	−3.80194	−0.153684
$613$	−21.2228	−0.857181	−0.428591	−	0.903499i	$-0.640990\pi$
$613$	−21.2228	−0.857181	−0.428591	+	0.903499i	$0.640990\pi$
$614$	−19.8280	−0.800194
$615$	1.81402	0.0731483
$616$	0.356896	0.0143797
$617$	−19.1019	−0.769013	−0.384506	−	0.923122i	$-0.625628\pi$
$617$	−19.1019	−0.769013	−0.384506	+	0.923122i	$0.625628\pi$
$618$	−12.2784	−0.493911
$619$	−21.1454	−0.849906	−0.424953	−	0.905215i	$-0.639709\pi$
$619$	−21.1454	−0.849906	−0.424953	+	0.905215i	$0.639709\pi$
$620$	−2.63102	−0.105664
$621$	2.44504	0.0981162
$622$	24.6461	0.988218
$623$	−4.80194	−0.192386
$624$	0	0
$625$	20.4752	0.819007
$626$	11.2034	0.447779
$627$	2.04892	0.0818259
$628$	7.10992	0.283717
$629$	−13.4698	−0.537076
$630$	−0.554958	−0.0221101
$631$	−32.4359	−1.29125	−0.645627	−	0.763653i	$-0.723404\pi$
$631$	−32.4359	−1.29125	−0.645627	+	0.763653i	$0.723404\pi$
$632$	−1.76271	−0.0701168
$633$	3.18598	0.126631
$634$	−24.8756	−0.987937
$635$	−0.780167	−0.0309600
$636$	1.35690	0.0538044
$637$	0	0
$638$	−0.144833	−0.00573400
$639$	7.42758	0.293831
$640$	0.554958	0.0219366
$641$	18.4499	0.728729	0.364365	−	0.931256i	$-0.381286\pi$
$641$	18.4499	0.728729	0.364365	+	0.931256i	$0.381286\pi$
$642$	−6.08575	−0.240186
$643$	−18.8334	−0.742717	−0.371358	−	0.928490i	$-0.621108\pi$
$643$	−18.8334	−0.742717	−0.371358	+	0.928490i	$0.621108\pi$
$644$	2.44504	0.0963481
$645$	3.35690	0.132178
$646$	−21.8267	−0.858760
$647$	47.8049	1.87941	0.939703	−	0.341992i	$-0.111102\pi$
$647$	47.8049	1.87941	0.939703	+	0.341992i	$0.111102\pi$
$648$	1.00000	0.0392837
$649$	−1.97823	−0.0776523
$650$	0	0
$651$	−4.74094	−0.185812
$652$	−18.8931	−0.739910
$653$	41.1637	1.61086	0.805431	−	0.592690i	$-0.201934\pi$
$653$	41.1637	1.61086	0.805431	+	0.592690i	$0.201934\pi$
$654$	20.2010	0.789923
$655$	−5.27413	−0.206077
$656$	−3.26875	−0.127623
$657$	−11.2295	−0.438105
$658$	−0.603875	−0.0235415
$659$	31.9758	1.24560	0.622801	−	0.782380i	$-0.285995\pi$
$659$	31.9758	1.24560	0.622801	+	0.782380i	$0.285995\pi$
$660$	0.198062	0.00770956
$661$	−43.2567	−1.68249	−0.841245	−	0.540655i	$-0.818177\pi$
$661$	−43.2567	−1.68249	−0.841245	+	0.540655i	$0.818177\pi$
$662$	22.7289	0.883382
$663$	0	0
$664$	−11.4426	−0.444061
$665$	−3.18598	−0.123547
$666$	3.54288	0.137284
$667$	−0.992230	−0.0384193
$668$	3.13169	0.121169
$669$	−3.35450	−0.129693
$670$	−8.48858	−0.327943
$671$	−1.56465	−0.0604025
$672$	1.00000	0.0385758
$673$	−12.6872	−0.489057	−0.244528	−	0.969642i	$-0.578633\pi$
$673$	−12.6872	−0.489057	−0.244528	+	0.969642i	$0.578633\pi$
$674$	10.5743	0.407308
$675$	4.69202	0.180596
$676$	0	0
$677$	−7.39672	−0.284279	−0.142139	−	0.989847i	$-0.545398\pi$
$677$	−7.39672	−0.284279	−0.142139	+	0.989847i	$0.545398\pi$
$678$	−2.81700	−0.108186
$679$	−2.65279	−0.101805
$680$	−2.10992	−0.0809116
$681$	10.8804	0.416938
$682$	1.69202	0.0647909
$683$	5.76138	0.220453	0.110227	−	0.993906i	$-0.464842\pi$
$683$	5.76138	0.220453	0.110227	+	0.993906i	$0.464842\pi$
$684$	5.74094	0.219510
$685$	0.575400	0.0219849
$686$	−1.00000	−0.0381802
$687$	12.0804	0.460895
$688$	−6.04892	−0.230613
$689$	0	0
$690$	1.35690	0.0516561
$691$	3.84894	0.146420	0.0732102	−	0.997317i	$-0.476676\pi$
$691$	3.84894	0.146420	0.0732102	+	0.997317i	$0.476676\pi$
$692$	−4.39612	−0.167116
$693$	0.356896	0.0135574
$694$	7.57002	0.287354
$695$	4.85086	0.184003
$696$	−0.405813	−0.0153823
$697$	12.4276	0.470728
$698$	−5.50066	−0.208203
$699$	23.8810	0.903262
$700$	4.69202	0.177342
$701$	26.4776	1.00004	0.500022	−	0.866013i	$-0.333325\pi$
$701$	26.4776	1.00004	0.500022	+	0.866013i	$0.333325\pi$
$702$	0	0
$703$	20.3394	0.767116
$704$	−0.356896	−0.0134510
$705$	−0.335126	−0.0126216
$706$	−33.0508	−1.24388
$707$	9.10752	0.342524
$708$	−5.54288	−0.208314
$709$	19.4886	0.731909	0.365955	−	0.930633i	$-0.380743\pi$
$709$	19.4886	0.731909	0.365955	+	0.930633i	$0.380743\pi$
$710$	4.12200	0.154696
$711$	−1.76271	−0.0661068
$712$	4.80194	0.179960
$713$	11.5918	0.434116
$714$	−3.80194	−0.142284
$715$	0	0
$716$	−16.9215	−0.632388
$717$	17.4819	0.652873
$718$	−11.8702	−0.442993
$719$	48.2140	1.79808	0.899039	−	0.437868i	$-0.144266\pi$
$719$	48.2140	1.79808	0.899039	+	0.437868i	$0.144266\pi$
$720$	0.554958	0.0206821
$721$	−12.2784	−0.457273
$722$	13.9584	0.519477
$723$	2.22521	0.0827564
$724$	−9.71917	−0.361210
$725$	−1.90408	−0.0707159
$726$	10.8726	0.403521
$727$	−15.6987	−0.582234	−0.291117	−	0.956688i	$-0.594027\pi$
$727$	−15.6987	−0.582234	−0.291117	+	0.956688i	$0.594027\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−6.23191	−0.230653
$731$	22.9976	0.850597
$732$	−4.38404	−0.162039
$733$	34.5478	1.27605	0.638026	−	0.770015i	$-0.279751\pi$
$733$	34.5478	1.27605	0.638026	+	0.770015i	$0.279751\pi$
$734$	−2.46980	−0.0911618
$735$	−0.554958	−0.0204699
$736$	−2.44504	−0.0901254
$737$	5.45904	0.201086
$738$	−3.26875	−0.120324
$739$	−38.3739	−1.41161	−0.705803	−	0.708408i	$-0.749414\pi$
$739$	−38.3739	−1.41161	−0.705803	+	0.708408i	$0.749414\pi$
$740$	1.96615	0.0722770
$741$	0	0
$742$	1.35690	0.0498132
$743$	−20.3110	−0.745137	−0.372568	−	0.928005i	$-0.621523\pi$
$743$	−20.3110	−0.745137	−0.372568	+	0.928005i	$0.621523\pi$
$744$	4.74094	0.173811
$745$	5.21014	0.190885
$746$	−9.28514	−0.339953
$747$	−11.4426	−0.418665
$748$	1.35690	0.0496130
$749$	−6.08575	−0.222369
$750$	5.37867	0.196401
$751$	18.8552	0.688035	0.344017	−	0.938963i	$-0.388212\pi$
$751$	18.8552	0.688035	0.344017	+	0.938963i	$0.388212\pi$
$752$	0.603875	0.0220211
$753$	8.30665	0.302711
$754$	0	0
$755$	4.80731	0.174956
$756$	1.00000	0.0363696
$757$	3.10885	0.112993	0.0564966	−	0.998403i	$-0.482007\pi$
$757$	3.10885	0.112993	0.0564966	+	0.998403i	$0.482007\pi$
$758$	−0.292913	−0.0106391
$759$	−0.872625	−0.0316743
$760$	3.18598	0.115568
$761$	48.7928	1.76874	0.884370	−	0.466787i	$-0.154589\pi$
$761$	48.7928	1.76874	0.884370	+	0.466787i	$0.154589\pi$
$762$	1.40581	0.0509272
$763$	20.2010	0.731327
$764$	3.40581	0.123218
$765$	−2.10992	−0.0762842
$766$	28.2446	1.02052
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	9.82610	0.354338	0.177169	−	0.984180i	$-0.443306\pi$
$769$	9.82610	0.354338	0.177169	+	0.984180i	$0.443306\pi$
$770$	0.198062	0.00713767
$771$	−4.66248	−0.167915
$772$	−17.0804	−0.614736
$773$	−4.30260	−0.154754	−0.0773769	−	0.997002i	$-0.524654\pi$
$773$	−4.30260	−0.154754	−0.0773769	+	0.997002i	$0.524654\pi$
$774$	−6.04892	−0.217424
$775$	22.2446	0.799049
$776$	2.65279	0.0952297
$777$	3.54288	0.127100
$778$	−23.1618	−0.830391
$779$	−18.7657	−0.672351
$780$	0	0
$781$	−2.65087	−0.0948557
$782$	9.29590	0.332421
$783$	−0.405813	−0.0145026
$784$	1.00000	0.0357143
$785$	3.94571	0.140828
$786$	9.50365	0.338984
$787$	30.7904	1.09756	0.548780	−	0.835967i	$-0.315092\pi$
$787$	30.7904	1.09756	0.548780	+	0.835967i	$0.315092\pi$
$788$	3.89977	0.138924
$789$	20.6015	0.733432
$790$	−0.978230	−0.0348039
$791$	−2.81700	−0.100161
$792$	−0.356896	−0.0126817
$793$	0	0
$794$	−21.8767	−0.776374
$795$	0.753020	0.0267069
$796$	3.52111	0.124802
$797$	−9.83877	−0.348507	−0.174254	−	0.984701i	$-0.555751\pi$
$797$	−9.83877	−0.348507	−0.174254	+	0.984701i	$0.555751\pi$
$798$	5.74094	0.203227
$799$	−2.29590	−0.0812230
$800$	−4.69202	−0.165888
$801$	4.80194	0.169668
$802$	15.3381	0.541607
$803$	4.00777	0.141431
$804$	15.2959	0.539445
$805$	1.35690	0.0478243
$806$	0	0
$807$	−32.3032	−1.13713
$808$	−9.10752	−0.320402
$809$	32.8364	1.15447	0.577233	−	0.816580i	$-0.304133\pi$
$809$	32.8364	1.15447	0.577233	+	0.816580i	$0.304133\pi$
$810$	0.554958	0.0194992
$811$	27.1420	0.953083	0.476542	−	0.879152i	$-0.341890\pi$
$811$	27.1420	0.953083	0.476542	+	0.879152i	$0.341890\pi$
$812$	−0.405813	−0.0142413
$813$	5.21850	0.183021
$814$	−1.26444	−0.0443185
$815$	−10.4849	−0.367269
$816$	3.80194	0.133094
$817$	−34.7265	−1.21493
$818$	18.6383	0.651674
$819$	0	0
$820$	−1.81402	−0.0633483
$821$	−30.8896	−1.07805	−0.539027	−	0.842288i	$-0.681208\pi$
$821$	−30.8896	−1.07805	−0.539027	+	0.842288i	$0.681208\pi$
$822$	−1.03684	−0.0361638
$823$	−10.5284	−0.366997	−0.183499	−	0.983020i	$-0.558742\pi$
$823$	−10.5284	−0.366997	−0.183499	+	0.983020i	$0.558742\pi$
$824$	12.2784	0.427740
$825$	−1.67456	−0.0583008
$826$	−5.54288	−0.192861
$827$	46.2573	1.60852	0.804261	−	0.594276i	$-0.202561\pi$
$827$	46.2573	1.60852	0.804261	+	0.594276i	$0.202561\pi$
$828$	−2.44504	−0.0849711
$829$	14.8595	0.516091	0.258046	−	0.966133i	$-0.416922\pi$
$829$	14.8595	0.516091	0.258046	+	0.966133i	$0.416922\pi$
$830$	−6.35019	−0.220418
$831$	6.27950	0.217834
$832$	0	0
$833$	−3.80194	−0.131729
$834$	−8.74094	−0.302674
$835$	1.73795	0.0601444
$836$	−2.04892	−0.0708633
$837$	4.74094	0.163871
$838$	39.2258	1.35503
$839$	−25.5284	−0.881338	−0.440669	−	0.897670i	$-0.645259\pi$
$839$	−25.5284	−0.881338	−0.440669	+	0.897670i	$0.645259\pi$
$840$	0.554958	0.0191479
$841$	−28.8353	−0.994321
$842$	−7.94139	−0.273679
$843$	−0.423272	−0.0145782
$844$	−3.18598	−0.109666
$845$	0	0
$846$	0.603875	0.0207617
$847$	10.8726	0.373588
$848$	−1.35690	−0.0465960
$849$	−10.9946	−0.377334
$850$	17.8388	0.611865
$851$	−8.66248	−0.296946
$852$	−7.42758	−0.254465
$853$	−21.0640	−0.721217	−0.360609	−	0.932717i	$-0.617431\pi$
$853$	−21.0640	−0.721217	−0.360609	+	0.932717i	$0.617431\pi$
$854$	−4.38404	−0.150019
$855$	3.18598	0.108958
$856$	6.08575	0.208007
$857$	32.2922	1.10308	0.551540	−	0.834149i	$-0.314040\pi$
$857$	32.2922	1.10308	0.551540	+	0.834149i	$0.314040\pi$
$858$	0	0
$859$	24.7700	0.845142	0.422571	−	0.906330i	$-0.361128\pi$
$859$	24.7700	0.845142	0.422571	+	0.906330i	$0.361128\pi$
$860$	−3.35690	−0.114469
$861$	−3.26875	−0.111399
$862$	24.2674	0.826552
$863$	1.51514	0.0515759	0.0257880	−	0.999667i	$-0.491791\pi$
$863$	1.51514	0.0515759	0.0257880	+	0.999667i	$0.491791\pi$
$864$	−1.00000	−0.0340207
$865$	−2.43967	−0.0829511
$866$	−20.7832	−0.706240
$867$	2.54527	0.0864419
$868$	4.74094	0.160918
$869$	0.629104	0.0213409
$870$	−0.225209	−0.00763531
$871$	0	0
$872$	−20.2010	−0.684094
$873$	2.65279	0.0897834
$874$	−14.0368	−0.474803
$875$	5.37867	0.181832
$876$	11.2295	0.379410
$877$	16.0425	0.541716	0.270858	−	0.962619i	$-0.412693\pi$
$877$	16.0425	0.541716	0.270858	+	0.962619i	$0.412693\pi$
$878$	38.5502	1.30101
$879$	15.3177	0.516652
$880$	−0.198062	−0.00667668
$881$	−18.8452	−0.634911	−0.317456	−	0.948273i	$-0.602828\pi$
$881$	−18.8452	−0.634911	−0.317456	+	0.948273i	$0.602828\pi$
$882$	1.00000	0.0336718
$883$	41.0092	1.38007	0.690035	−	0.723776i	$-0.257595\pi$
$883$	41.0092	1.38007	0.690035	+	0.723776i	$0.257595\pi$
$884$	0	0
$885$	−3.07606	−0.103401
$886$	−1.59850	−0.0537026
$887$	−5.77107	−0.193774	−0.0968868	−	0.995295i	$-0.530888\pi$
$887$	−5.77107	−0.193774	−0.0968868	+	0.995295i	$0.530888\pi$
$888$	−3.54288	−0.118891
$889$	1.40581	0.0471495
$890$	2.66487	0.0893268
$891$	−0.356896	−0.0119565
$892$	3.35450	0.112317
$893$	3.46681	0.116012
$894$	−9.38835	−0.313994
$895$	−9.39075	−0.313898
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	26.2064	0.874520
$899$	−1.92394	−0.0641668
$900$	−4.69202	−0.156401
$901$	5.15883	0.171866
$902$	1.16660	0.0388436
$903$	−6.04892	−0.201295
$904$	2.81700	0.0936921
$905$	−5.39373	−0.179294
$906$	−8.66248	−0.287792
$907$	48.1618	1.59919	0.799593	−	0.600542i	$-0.205048\pi$
$907$	48.1618	1.59919	0.799593	+	0.600542i	$0.205048\pi$
$908$	−10.8804	−0.361079
$909$	−9.10752	−0.302077
$910$	0	0
$911$	9.32736	0.309029	0.154515	−	0.987991i	$-0.450619\pi$
$911$	9.32736	0.309029	0.154515	+	0.987991i	$0.450619\pi$
$912$	−5.74094	−0.190101
$913$	4.08383	0.135155
$914$	11.1540	0.368943
$915$	−2.43296	−0.0804312
$916$	−12.0804	−0.399147
$917$	9.50365	0.313838
$918$	3.80194	0.125483
$919$	−45.0877	−1.48731	−0.743653	−	0.668566i	$-0.766908\pi$
$919$	−45.0877	−1.48731	−0.743653	+	0.668566i	$0.766908\pi$
$920$	−1.35690	−0.0447355
$921$	19.8280	0.653355
$922$	17.9191	0.590136
$923$	0	0
$924$	−0.356896	−0.0117410
$925$	−16.6233	−0.546569
$926$	−11.5453	−0.379401
$927$	12.2784	0.403277
$928$	0.405813	0.0133215
$929$	−31.1704	−1.02267	−0.511335	−	0.859382i	$-0.670849\pi$
$929$	−31.1704	−1.02267	−0.511335	+	0.859382i	$0.670849\pi$
$930$	2.63102	0.0862746
$931$	5.74094	0.188152
$932$	−23.8810	−0.782248
$933$	−24.6461	−0.806877
$934$	−18.4620	−0.604096
$935$	0.753020	0.0246264
$936$	0	0
$937$	12.4698	0.407370	0.203685	−	0.979036i	$-0.434708\pi$
$937$	12.4698	0.407370	0.203685	+	0.979036i	$0.434708\pi$
$938$	15.2959	0.499429
$939$	−11.2034	−0.365610
$940$	0.335126	0.0109306
$941$	−10.9866	−0.358153	−0.179076	−	0.983835i	$-0.557311\pi$
$941$	−10.9866	−0.358153	−0.179076	+	0.983835i	$0.557311\pi$
$942$	−7.10992	−0.231654
$943$	7.99223	0.260263
$944$	5.54288	0.180405
$945$	0.554958	0.0180528
$946$	2.15883	0.0701897
$947$	57.7445	1.87644	0.938222	−	0.346033i	$-0.112472\pi$
$947$	57.7445	1.87644	0.938222	+	0.346033i	$0.112472\pi$
$948$	1.76271	0.0572501
$949$	0	0
$950$	−26.9366	−0.873939
$951$	24.8756	0.806647
$952$	3.80194	0.123222
$953$	−38.7942	−1.25667	−0.628333	−	0.777944i	$-0.716263\pi$
$953$	−38.7942	−1.25667	−0.628333	+	0.777944i	$0.716263\pi$
$954$	−1.35690	−0.0439311
$955$	1.89008	0.0611617
$956$	−17.4819	−0.565404
$957$	0.144833	0.00468179
$958$	−35.8756	−1.15909
$959$	−1.03684	−0.0334812
$960$	−0.554958	−0.0179112
$961$	−8.52350	−0.274952
$962$	0	0
$963$	6.08575	0.196111
$964$	−2.22521	−0.0716692
$965$	−9.47889	−0.305136
$966$	−2.44504	−0.0786679
$967$	−41.1588	−1.32358	−0.661789	−	0.749690i	$-0.730203\pi$
$967$	−41.1588	−1.32358	−0.661789	+	0.749690i	$0.730203\pi$
$968$	−10.8726	−0.349459
$969$	21.8267	0.701174
$970$	1.47219	0.0472691
$971$	30.9084	0.991898	0.495949	−	0.868352i	$-0.334820\pi$
$971$	30.9084	0.991898	0.495949	+	0.868352i	$0.334820\pi$
$972$	−1.00000	−0.0320750
$973$	−8.74094	−0.280222
$974$	−1.90648	−0.0610875
$975$	0	0
$976$	4.38404	0.140330
$977$	−40.6249	−1.29971	−0.649853	−	0.760060i	$-0.725170\pi$
$977$	−40.6249	−1.29971	−0.649853	+	0.760060i	$0.725170\pi$
$978$	18.8931	0.604134
$979$	−1.71379	−0.0547730
$980$	0.554958	0.0177275
$981$	−20.2010	−0.644970
$982$	−17.7536	−0.566541
$983$	36.6335	1.16843	0.584214	−	0.811600i	$-0.301403\pi$
$983$	36.6335	1.16843	0.584214	+	0.811600i	$0.301403\pi$
$984$	3.26875	0.104204
$985$	2.16421	0.0689575
$986$	−1.54288	−0.0491352
$987$	0.603875	0.0192216
$988$	0	0
$989$	14.7899	0.470290
$990$	−0.198062	−0.00629483
$991$	0.754348	0.0239627	0.0119813	−	0.999928i	$-0.496186\pi$
$991$	0.754348	0.0239627	0.0119813	+	0.999928i	$0.496186\pi$
$992$	−4.74094	−0.150525
$993$	−22.7289	−0.721278
$994$	−7.42758	−0.235589
$995$	1.95407	0.0619481
$996$	11.4426	0.362574
$997$	35.2336	1.11586	0.557929	−	0.829889i	$-0.311596\pi$
$997$	35.2336	1.11586	0.557929	+	0.829889i	$0.311596\pi$
$998$	−24.8528	−0.786701
$999$	−3.54288	−0.112092

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.554958 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.554958 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.554958 q^{10} -0.356896 q^{11} -1.00000 q^{12} -1.00000 q^{14} -0.554958 q^{15} +1.00000 q^{16} -3.80194 q^{17} +1.00000 q^{18} +5.74094 q^{19} +0.554958 q^{20} +1.00000 q^{21} -0.356896 q^{22} -2.44504 q^{23} -1.00000 q^{24} -4.69202 q^{25} -1.00000 q^{27} -1.00000 q^{28} +0.405813 q^{29} -0.554958 q^{30} -4.74094 q^{31} +1.00000 q^{32} +0.356896 q^{33} -3.80194 q^{34} -0.554958 q^{35} +1.00000 q^{36} +3.54288 q^{37} +5.74094 q^{38} +0.554958 q^{40} -3.26875 q^{41} +1.00000 q^{42} -6.04892 q^{43} -0.356896 q^{44} +0.554958 q^{45} -2.44504 q^{46} +0.603875 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.69202 q^{50} +3.80194 q^{51} -1.35690 q^{53} -1.00000 q^{54} -0.198062 q^{55} -1.00000 q^{56} -5.74094 q^{57} +0.405813 q^{58} +5.54288 q^{59} -0.554958 q^{60} +4.38404 q^{61} -4.74094 q^{62} -1.00000 q^{63} +1.00000 q^{64} +0.356896 q^{66} -15.2959 q^{67} -3.80194 q^{68} +2.44504 q^{69} -0.554958 q^{70} +7.42758 q^{71} +1.00000 q^{72} -11.2295 q^{73} +3.54288 q^{74} +4.69202 q^{75} +5.74094 q^{76} +0.356896 q^{77} -1.76271 q^{79} +0.554958 q^{80} +1.00000 q^{81} -3.26875 q^{82} -11.4426 q^{83} +1.00000 q^{84} -2.10992 q^{85} -6.04892 q^{86} -0.405813 q^{87} -0.356896 q^{88} +4.80194 q^{89} +0.554958 q^{90} -2.44504 q^{92} +4.74094 q^{93} +0.603875 q^{94} +3.18598 q^{95} -1.00000 q^{96} +2.65279 q^{97} +1.00000 q^{98} -0.356896 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} + 2 q^{10} + 3 q^{11} - 3 q^{12} - 3 q^{14} - 2 q^{15} + 3 q^{16} - 7 q^{17} + 3 q^{18} + 3 q^{19} + 2 q^{20} + 3 q^{21} + 3 q^{22} - 7 q^{23} - 3 q^{24} - 9 q^{25} - 3 q^{27} - 3 q^{28} - 12 q^{29} - 2 q^{30} + 3 q^{32} - 3 q^{33} - 7 q^{34} - 2 q^{35} + 3 q^{36} - 8 q^{37} + 3 q^{38} + 2 q^{40} - 2 q^{41} + 3 q^{42} - 9 q^{43} + 3 q^{44} + 2 q^{45} - 7 q^{46} - 7 q^{47} - 3 q^{48} + 3 q^{49} - 9 q^{50} + 7 q^{51} - 3 q^{54} - 5 q^{55} - 3 q^{56} - 3 q^{57} - 12 q^{58} - 2 q^{59} - 2 q^{60} + 3 q^{61} - 3 q^{63} + 3 q^{64} - 3 q^{66} - 32 q^{67} - 7 q^{68} + 7 q^{69} - 2 q^{70} + 6 q^{71} + 3 q^{72} - 13 q^{73} - 8 q^{74} + 9 q^{75} + 3 q^{76} - 3 q^{77} + 12 q^{79} + 2 q^{80} + 3 q^{81} - 2 q^{82} + 7 q^{83} + 3 q^{84} - 7 q^{85} - 9 q^{86} + 12 q^{87} + 3 q^{88} + 10 q^{89} + 2 q^{90} - 7 q^{92} - 7 q^{94} - 5 q^{95} - 3 q^{96} - 10 q^{97} + 3 q^{98} + 3 q^{99}+O(q^{100}) \) 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 + 3 * q^11 - 3 * q^12 - 3 * q^14 - 2 * q^15 + 3 * q^16 - 7 * q^17 + 3 * q^18 + 3 * q^19 + 2 * q^20 + 3 * q^21 + 3 * q^22 - 7 * q^23 - 3 * q^24 - 9 * q^25 - 3 * q^27 - 3 * q^28 - 12 * q^29 - 2 * q^30 + 3 * q^32 - 3 * q^33 - 7 * q^34 - 2 * q^35 + 3 * q^36 - 8 * q^37 + 3 * q^38 + 2 * q^40 - 2 * q^41 + 3 * q^42 - 9 * q^43 + 3 * q^44 + 2 * q^45 - 7 * q^46 - 7 * q^47 - 3 * q^48 + 3 * q^49 - 9 * q^50 + 7 * q^51 - 3 * q^54 - 5 * q^55 - 3 * q^56 - 3 * q^57 - 12 * q^58 - 2 * q^59 - 2 * q^60 + 3 * q^61 - 3 * q^63 + 3 * q^64 - 3 * q^66 - 32 * q^67 - 7 * q^68 + 7 * q^69 - 2 * q^70 + 6 * q^71 + 3 * q^72 - 13 * q^73 - 8 * q^74 + 9 * q^75 + 3 * q^76 - 3 * q^77 + 12 * q^79 + 2 * q^80 + 3 * q^81 - 2 * q^82 + 7 * q^83 + 3 * q^84 - 7 * q^85 - 9 * q^86 + 12 * q^87 + 3 * q^88 + 10 * q^89 + 2 * q^90 - 7 * q^92 - 7 * q^94 - 5 * q^95 - 3 * q^96 - 10 * q^97 + 3 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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