LMFDB - Embedded newform 3549.2.a.bg.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, 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("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.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:	$28.3389076774$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 27 x^{13} + 51 x^{12} + 290 x^{11} - 510 x^{10} - 1575 x^{9} + 2522 x^{8} + \cdots + 281 $ x^15 - 2x^14 - 27x^13 + 51x^12 + 290x^11 - 510x^10 - 1575x^9 + 2522x^8 + 4553x^7 - 6393x^6 - 6785x^5 + 7806x^4 + 4632x^3 - 3811x^2 - 1041x + 281
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$0.182130$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.182130 q^{2} +1.00000 q^{3} -1.96683 q^{4} -1.12886 q^{5} -0.182130 q^{6} +1.00000 q^{7} +0.722479 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.182130 q^{2} +1.00000 q^{3} -1.96683 q^{4} -1.12886 q^{5} -0.182130 q^{6} +1.00000 q^{7} +0.722479 q^{8} +1.00000 q^{9} +0.205599 q^{10} -4.01616 q^{11} -1.96683 q^{12} -0.182130 q^{14} -1.12886 q^{15} +3.80207 q^{16} +3.02631 q^{17} -0.182130 q^{18} -5.30303 q^{19} +2.22027 q^{20} +1.00000 q^{21} +0.731463 q^{22} -2.17379 q^{23} +0.722479 q^{24} -3.72568 q^{25} +1.00000 q^{27} -1.96683 q^{28} +3.53344 q^{29} +0.205599 q^{30} +4.85911 q^{31} -2.13743 q^{32} -4.01616 q^{33} -0.551182 q^{34} -1.12886 q^{35} -1.96683 q^{36} +6.38019 q^{37} +0.965841 q^{38} -0.815576 q^{40} -4.76127 q^{41} -0.182130 q^{42} -2.34151 q^{43} +7.89910 q^{44} -1.12886 q^{45} +0.395913 q^{46} +9.81123 q^{47} +3.80207 q^{48} +1.00000 q^{49} +0.678558 q^{50} +3.02631 q^{51} +2.98129 q^{53} -0.182130 q^{54} +4.53367 q^{55} +0.722479 q^{56} -5.30303 q^{57} -0.643546 q^{58} -11.4726 q^{59} +2.22027 q^{60} +4.70310 q^{61} -0.884989 q^{62} +1.00000 q^{63} -7.21485 q^{64} +0.731463 q^{66} +1.77088 q^{67} -5.95223 q^{68} -2.17379 q^{69} +0.205599 q^{70} -3.24776 q^{71} +0.722479 q^{72} +7.80784 q^{73} -1.16202 q^{74} -3.72568 q^{75} +10.4302 q^{76} -4.01616 q^{77} +17.4983 q^{79} -4.29200 q^{80} +1.00000 q^{81} +0.867171 q^{82} +0.705610 q^{83} -1.96683 q^{84} -3.41627 q^{85} +0.426459 q^{86} +3.53344 q^{87} -2.90159 q^{88} -13.0567 q^{89} +0.205599 q^{90} +4.27548 q^{92} +4.85911 q^{93} -1.78692 q^{94} +5.98637 q^{95} -2.13743 q^{96} -1.76727 q^{97} -0.182130 q^{98} -4.01616 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 2 q^{2} + 15 q^{3} + 28 q^{4} + 9 q^{5} - 2 q^{6} + 15 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) $ 15 * q - 2 * q^2 + 15 * q^3 + 28 * q^4 + 9 * q^5 - 2 * q^6 + 15 * q^7 - 9 * q^8 + 15 * q^9	\( 15 q - 2 q^{2} + 15 q^{3} + 28 q^{4} + 9 q^{5} - 2 q^{6} + 15 q^{7} - 9 q^{8} + 15 q^{9} + 21 q^{10} - 5 q^{11} + 28 q^{12} - 2 q^{14} + 9 q^{15} + 50 q^{16} - q^{17} - 2 q^{18} - 3 q^{19} + 23 q^{20} + 15 q^{21} + 21 q^{22} + 4 q^{23} - 9 q^{24} + 50 q^{25} + 15 q^{27} + 28 q^{28} + 9 q^{29} + 21 q^{30} - 7 q^{31} - 35 q^{32} - 5 q^{33} + 2 q^{34} + 9 q^{35} + 28 q^{36} - 17 q^{37} - 12 q^{38} + 46 q^{40} + 22 q^{41} - 2 q^{42} + 36 q^{43} - 29 q^{44} + 9 q^{45} + q^{46} + 12 q^{47} + 50 q^{48} + 15 q^{49} - 53 q^{50} - q^{51} - 5 q^{53} - 2 q^{54} + 43 q^{55} - 9 q^{56} - 3 q^{57} - 29 q^{58} + 29 q^{59} + 23 q^{60} + 12 q^{61} + 14 q^{62} + 15 q^{63} + 95 q^{64} + 21 q^{66} + 12 q^{67} - 16 q^{68} + 4 q^{69} + 21 q^{70} - 36 q^{71} - 9 q^{72} + 29 q^{73} - 5 q^{74} + 50 q^{75} - 25 q^{76} - 5 q^{77} + 35 q^{79} + 89 q^{80} + 15 q^{81} + 51 q^{82} + 10 q^{83} + 28 q^{84} - 23 q^{85} - 19 q^{86} + 9 q^{87} + 73 q^{88} - 25 q^{89} + 21 q^{90} - 31 q^{92} - 7 q^{93} - 19 q^{94} - 7 q^{95} - 35 q^{96} + 26 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) 15 * q - 2 * q^2 + 15 * q^3 + 28 * q^4 + 9 * q^5 - 2 * q^6 + 15 * q^7 - 9 * q^8 + 15 * q^9 + 21 * q^10 - 5 * q^11 + 28 * q^12 - 2 * q^14 + 9 * q^15 + 50 * q^16 - q^17 - 2 * q^18 - 3 * q^19 + 23 * q^20 + 15 * q^21 + 21 * q^22 + 4 * q^23 - 9 * q^24 + 50 * q^25 + 15 * q^27 + 28 * q^28 + 9 * q^29 + 21 * q^30 - 7 * q^31 - 35 * q^32 - 5 * q^33 + 2 * q^34 + 9 * q^35 + 28 * q^36 - 17 * q^37 - 12 * q^38 + 46 * q^40 + 22 * q^41 - 2 * q^42 + 36 * q^43 - 29 * q^44 + 9 * q^45 + q^46 + 12 * q^47 + 50 * q^48 + 15 * q^49 - 53 * q^50 - q^51 - 5 * q^53 - 2 * q^54 + 43 * q^55 - 9 * q^56 - 3 * q^57 - 29 * q^58 + 29 * q^59 + 23 * q^60 + 12 * q^61 + 14 * q^62 + 15 * q^63 + 95 * q^64 + 21 * q^66 + 12 * q^67 - 16 * q^68 + 4 * q^69 + 21 * q^70 - 36 * q^71 - 9 * q^72 + 29 * q^73 - 5 * q^74 + 50 * q^75 - 25 * q^76 - 5 * q^77 + 35 * q^79 + 89 * q^80 + 15 * q^81 + 51 * q^82 + 10 * q^83 + 28 * q^84 - 23 * q^85 - 19 * q^86 + 9 * q^87 + 73 * q^88 - 25 * q^89 + 21 * q^90 - 31 * q^92 - 7 * q^93 - 19 * q^94 - 7 * q^95 - 35 * q^96 + 26 * q^97 - 2 * q^98 - 5 * 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 $

$2$	−0.182130	−0.128785	−0.0643927	−	0.997925i	$-0.520511\pi$
$2$	−0.182130	−0.128785	−0.0643927	+	0.997925i	$0.520511\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.96683	−0.983414
$5$	−1.12886	−0.504841	−0.252420	−	0.967618i	$-0.581227\pi$
$5$	−1.12886	−0.504841	−0.252420	+	0.967618i	$0.581227\pi$
$6$	−0.182130	−0.0743543
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.722479	0.255435
$9$	1.00000	0.333333
$10$	0.205599	0.0650161
$11$	−4.01616	−1.21092	−0.605459	−	0.795877i	$-0.707010\pi$
$11$	−4.01616	−1.21092	−0.605459	+	0.795877i	$0.707010\pi$
$12$	−1.96683	−0.567775
$13$	0	0
$13$	0	0
$14$	−0.182130	−0.0486763
$15$	−1.12886	−0.291470
$16$	3.80207	0.950518
$17$	3.02631	0.733988	0.366994	−	0.930223i	$-0.380387\pi$
$17$	3.02631	0.733988	0.366994	+	0.930223i	$0.380387\pi$
$18$	−0.182130	−0.0429285
$19$	−5.30303	−1.21660	−0.608300	−	0.793708i	$-0.708148\pi$
$19$	−5.30303	−1.21660	−0.608300	+	0.793708i	$0.708148\pi$
$20$	2.22027	0.496468
$21$	1.00000	0.218218
$22$	0.731463	0.155948
$23$	−2.17379	−0.453267	−0.226634	−	0.973980i	$-0.572772\pi$
$23$	−2.17379	−0.453267	−0.226634	+	0.973980i	$0.572772\pi$
$24$	0.722479	0.147475
$25$	−3.72568	−0.745136
$26$	0	0
$27$	1.00000	0.192450
$28$	−1.96683	−0.371696
$29$	3.53344	0.656143	0.328072	−	0.944653i	$-0.393601\pi$
$29$	3.53344	0.656143	0.328072	+	0.944653i	$0.393601\pi$
$30$	0.205599	0.0375371
$31$	4.85911	0.872721	0.436361	−	0.899772i	$-0.356267\pi$
$31$	4.85911	0.872721	0.436361	+	0.899772i	$0.356267\pi$
$32$	−2.13743	−0.377848
$33$	−4.01616	−0.699123
$34$	−0.551182	−0.0945269
$35$	−1.12886	−0.190812
$36$	−1.96683	−0.327805
$37$	6.38019	1.04890	0.524448	−	0.851442i	$-0.324272\pi$
$37$	6.38019	1.04890	0.524448	+	0.851442i	$0.324272\pi$
$38$	0.965841	0.156680
$39$	0	0
$40$	−0.815576	−0.128954
$41$	−4.76127	−0.743586	−0.371793	−	0.928316i	$-0.621257\pi$
$41$	−4.76127	−0.743586	−0.371793	+	0.928316i	$0.621257\pi$
$42$	−0.182130	−0.0281033
$43$	−2.34151	−0.357077	−0.178538	−	0.983933i	$-0.557137\pi$
$43$	−2.34151	−0.357077	−0.178538	+	0.983933i	$0.557137\pi$
$44$	7.89910	1.19083
$45$	−1.12886	−0.168280
$46$	0.395913	0.0583742
$47$	9.81123	1.43111	0.715557	−	0.698554i	$-0.246173\pi$
$47$	9.81123	1.43111	0.715557	+	0.698554i	$0.246173\pi$
$48$	3.80207	0.548782
$49$	1.00000	0.142857
$50$	0.678558	0.0959626
$51$	3.02631	0.423768
$52$	0	0
$53$	2.98129	0.409512	0.204756	−	0.978813i	$-0.434360\pi$
$53$	2.98129	0.409512	0.204756	+	0.978813i	$0.434360\pi$
$54$	−0.182130	−0.0247848
$55$	4.53367	0.611321
$56$	0.722479	0.0965453
$57$	−5.30303	−0.702404
$58$	−0.643546	−0.0845017
$59$	−11.4726	−1.49361	−0.746803	−	0.665046i	$-0.768412\pi$
$59$	−11.4726	−1.49361	−0.746803	+	0.665046i	$0.768412\pi$
$60$	2.22027	0.286636
$61$	4.70310	0.602170	0.301085	−	0.953597i	$-0.402651\pi$
$61$	4.70310	0.602170	0.301085	+	0.953597i	$0.402651\pi$
$62$	−0.884989	−0.112394
$63$	1.00000	0.125988
$64$	−7.21485	−0.901857
$65$	0	0
$66$	0.731463	0.0900369
$67$	1.77088	0.216347	0.108174	−	0.994132i	$-0.465500\pi$
$67$	1.77088	0.216347	0.108174	+	0.994132i	$0.465500\pi$
$68$	−5.95223	−0.721814
$69$	−2.17379	−0.261694
$70$	0.205599	0.0245738
$71$	−3.24776	−0.385438	−0.192719	−	0.981254i	$-0.561731\pi$
$71$	−3.24776	−0.385438	−0.192719	+	0.981254i	$0.561731\pi$
$72$	0.722479	0.0851449
$73$	7.80784	0.913838	0.456919	−	0.889508i	$-0.348953\pi$
$73$	7.80784	0.913838	0.456919	+	0.889508i	$0.348953\pi$
$74$	−1.16202	−0.135083
$75$	−3.72568	−0.430204
$76$	10.4302	1.19642
$77$	−4.01616	−0.457684
$78$	0	0
$79$	17.4983	1.96871	0.984354	−	0.176200i	$-0.0563805\pi$
$79$	17.4983	1.96871	0.984354	+	0.176200i	$0.0563805\pi$
$80$	−4.29200	−0.479860
$81$	1.00000	0.111111
$82$	0.867171	0.0957630
$83$	0.705610	0.0774508	0.0387254	−	0.999250i	$-0.487670\pi$
$83$	0.705610	0.0774508	0.0387254	+	0.999250i	$0.487670\pi$
$84$	−1.96683	−0.214599
$85$	−3.41627	−0.370547
$86$	0.426459	0.0459863
$87$	3.53344	0.378825
$88$	−2.90159	−0.309310
$89$	−13.0567	−1.38401	−0.692004	−	0.721894i	$-0.743272\pi$
$89$	−13.0567	−1.38401	−0.692004	+	0.721894i	$0.743272\pi$
$90$	0.205599	0.0216720
$91$	0	0
$92$	4.27548	0.445750
$93$	4.85911	0.503866
$94$	−1.78692	−0.184307
$95$	5.98637	0.614189
$96$	−2.13743	−0.218150
$97$	−1.76727	−0.179439	−0.0897195	−	0.995967i	$-0.528597\pi$
$97$	−1.76727	−0.179439	−0.0897195	+	0.995967i	$0.528597\pi$
$98$	−0.182130	−0.0183979
$99$	−4.01616	−0.403639
$100$	7.32777	0.732777
$101$	15.3230	1.52469	0.762347	−	0.647169i	$-0.224047\pi$
$101$	15.3230	1.52469	0.762347	+	0.647169i	$0.224047\pi$
$102$	−0.551182	−0.0545751
$103$	8.19962	0.807933	0.403966	−	0.914774i	$-0.367631\pi$
$103$	8.19962	0.807933	0.403966	+	0.914774i	$0.367631\pi$
$104$	0	0
$105$	−1.12886	−0.110165
$106$	−0.542982	−0.0527391
$107$	16.8953	1.63333	0.816664	−	0.577114i	$-0.195821\pi$
$107$	16.8953	1.63333	0.816664	+	0.577114i	$0.195821\pi$
$108$	−1.96683	−0.189258
$109$	−5.62135	−0.538427	−0.269214	−	0.963080i	$-0.586764\pi$
$109$	−5.62135	−0.538427	−0.269214	+	0.963080i	$0.586764\pi$
$110$	−0.825718	−0.0787291
$111$	6.38019	0.605581
$112$	3.80207	0.359262
$113$	−2.71753	−0.255644	−0.127822	−	0.991797i	$-0.540799\pi$
$113$	−2.71753	−0.255644	−0.127822	+	0.991797i	$0.540799\pi$
$114$	0.965841	0.0904593
$115$	2.45391	0.228828
$116$	−6.94967	−0.645261
$117$	0	0
$118$	2.08950	0.192354
$119$	3.02631	0.277421
$120$	−0.815576	−0.0744516
$121$	5.12953	0.466321
$122$	−0.856575	−0.0775507
$123$	−4.76127	−0.429310
$124$	−9.55703	−0.858247
$125$	9.85006	0.881016
$126$	−0.182130	−0.0162254
$127$	11.6456	1.03338	0.516691	−	0.856172i	$-0.327164\pi$
$127$	11.6456	1.03338	0.516691	+	0.856172i	$0.327164\pi$
$128$	5.58890	0.493994
$129$	−2.34151	−0.206158
$130$	0	0
$131$	14.7907	1.29227	0.646133	−	0.763225i	$-0.276385\pi$
$131$	14.7907	1.29227	0.646133	+	0.763225i	$0.276385\pi$
$132$	7.89910	0.687528
$133$	−5.30303	−0.459831
$134$	−0.322530	−0.0278623
$135$	−1.12886	−0.0971567
$136$	2.18644	0.187486
$137$	−15.4499	−1.31998	−0.659989	−	0.751276i	$-0.729439\pi$
$137$	−15.4499	−1.31998	−0.659989	+	0.751276i	$0.729439\pi$
$138$	0.395913	0.0337024
$139$	−11.4715	−0.973001	−0.486501	−	0.873680i	$-0.661727\pi$
$139$	−11.4715	−0.973001	−0.486501	+	0.873680i	$0.661727\pi$
$140$	2.22027	0.187647
$141$	9.81123	0.826254
$142$	0.591514	0.0496388
$143$	0	0
$144$	3.80207	0.316839
$145$	−3.98875	−0.331248
$146$	−1.42204	−0.117689
$147$	1.00000	0.0824786
$148$	−12.5487	−1.03150
$149$	2.99238	0.245146	0.122573	−	0.992460i	$-0.460886\pi$
$149$	2.99238	0.245146	0.122573	+	0.992460i	$0.460886\pi$
$150$	0.678558	0.0554040
$151$	−0.860674	−0.0700407	−0.0350203	−	0.999387i	$-0.511150\pi$
$151$	−0.860674	−0.0700407	−0.0350203	+	0.999387i	$0.511150\pi$
$152$	−3.83133	−0.310762
$153$	3.02631	0.244663
$154$	0.731463	0.0589430
$155$	−5.48525	−0.440585
$156$	0	0
$157$	−4.62432	−0.369061	−0.184530	−	0.982827i	$-0.559076\pi$
$157$	−4.62432	−0.369061	−0.184530	+	0.982827i	$0.559076\pi$
$158$	−3.18696	−0.253541
$159$	2.98129	0.236432
$160$	2.41285	0.190753
$161$	−2.17379	−0.171319
$162$	−0.182130	−0.0143095
$163$	23.0446	1.80499	0.902496	−	0.430698i	$-0.141733\pi$
$163$	23.0446	1.80499	0.902496	+	0.430698i	$0.141733\pi$
$164$	9.36461	0.731253
$165$	4.53367	0.352946
$166$	−0.128513	−0.00997453
$167$	−3.47296	−0.268745	−0.134373	−	0.990931i	$-0.542902\pi$
$167$	−3.47296	−0.268745	−0.134373	+	0.990931i	$0.542902\pi$
$168$	0.722479	0.0557404
$169$	0	0
$170$	0.622206	0.0477210
$171$	−5.30303	−0.405533
$172$	4.60535	0.351154
$173$	19.7442	1.50112	0.750560	−	0.660802i	$-0.229784\pi$
$173$	19.7442	1.50112	0.750560	+	0.660802i	$0.229784\pi$
$174$	−0.643546	−0.0487871
$175$	−3.72568	−0.281635
$176$	−15.2697	−1.15100
$177$	−11.4726	−0.862333
$178$	2.37802	0.178240
$179$	19.0553	1.42426	0.712129	−	0.702049i	$-0.247731\pi$
$179$	19.0553	1.42426	0.712129	+	0.702049i	$0.247731\pi$
$180$	2.22027	0.165489
$181$	−3.45717	−0.256969	−0.128485	−	0.991712i	$-0.541011\pi$
$181$	−3.45717	−0.256969	−0.128485	+	0.991712i	$0.541011\pi$
$182$	0	0
$183$	4.70310	0.347663
$184$	−1.57052	−0.115780
$185$	−7.20233	−0.529526
$186$	−0.884989	−0.0648906
$187$	−12.1541	−0.888798
$188$	−19.2970	−1.40738
$189$	1.00000	0.0727393
$190$	−1.09030	−0.0790986
$191$	−21.0189	−1.52087	−0.760437	−	0.649411i	$-0.775015\pi$
$191$	−21.0189	−1.52087	−0.760437	+	0.649411i	$0.775015\pi$
$192$	−7.21485	−0.520687
$193$	18.9411	1.36341	0.681704	−	0.731628i	$-0.261239\pi$
$193$	18.9411	1.36341	0.681704	+	0.731628i	$0.261239\pi$
$194$	0.321873	0.0231091
$195$	0	0
$196$	−1.96683	−0.140488
$197$	8.43497	0.600966	0.300483	−	0.953787i	$-0.402852\pi$
$197$	8.43497	0.600966	0.300483	+	0.953787i	$0.402852\pi$
$198$	0.731463	0.0519828
$199$	20.3783	1.44458	0.722291	−	0.691590i	$-0.243089\pi$
$199$	20.3783	1.44458	0.722291	+	0.691590i	$0.243089\pi$
$200$	−2.69172	−0.190334
$201$	1.77088	0.124908
$202$	−2.79077	−0.196358
$203$	3.53344	0.247999
$204$	−5.95223	−0.416740
$205$	5.37481	0.375393
$206$	−1.49340	−0.104050
$207$	−2.17379	−0.151089
$208$	0	0
$209$	21.2978	1.47320
$210$	0.205599	0.0141877
$211$	24.7518	1.70398	0.851992	−	0.523555i	$-0.175394\pi$
$211$	24.7518	1.70398	0.851992	+	0.523555i	$0.175394\pi$
$212$	−5.86369	−0.402720
$213$	−3.24776	−0.222533
$214$	−3.07714	−0.210349
$215$	2.64323	0.180267
$216$	0.722479	0.0491584
$217$	4.85911	0.329858
$218$	1.02382	0.0693416
$219$	7.80784	0.527605
$220$	−8.91696	−0.601181
$221$	0	0
$222$	−1.16202	−0.0779899
$223$	24.1397	1.61652	0.808258	−	0.588829i	$-0.200411\pi$
$223$	24.1397	1.61652	0.808258	+	0.588829i	$0.200411\pi$
$224$	−2.13743	−0.142813
$225$	−3.72568	−0.248379
$226$	0.494944	0.0329232
$227$	20.6751	1.37226	0.686128	−	0.727480i	$-0.259309\pi$
$227$	20.6751	1.37226	0.686128	+	0.727480i	$0.259309\pi$
$228$	10.4302	0.690754
$229$	7.17578	0.474189	0.237094	−	0.971487i	$-0.423805\pi$
$229$	7.17578	0.474189	0.237094	+	0.971487i	$0.423805\pi$
$230$	−0.446930	−0.0294697
$231$	−4.01616	−0.264244
$232$	2.55284	0.167602
$233$	−15.9753	−1.04658	−0.523288	−	0.852156i	$-0.675295\pi$
$233$	−15.9753	−1.04658	−0.523288	+	0.852156i	$0.675295\pi$
$234$	0	0
$235$	−11.0755	−0.722485
$236$	22.5646	1.46883
$237$	17.4983	1.13663
$238$	−0.551182	−0.0357278
$239$	16.2796	1.05304	0.526519	−	0.850164i	$-0.323497\pi$
$239$	16.2796	1.05304	0.526519	+	0.850164i	$0.323497\pi$
$240$	−4.29200	−0.277048
$241$	−23.2533	−1.49788	−0.748939	−	0.662639i	$-0.769437\pi$
$241$	−23.2533	−1.49788	−0.748939	+	0.662639i	$0.769437\pi$
$242$	−0.934241	−0.0600553
$243$	1.00000	0.0641500
$244$	−9.25018	−0.592182
$245$	−1.12886	−0.0721201
$246$	0.867171	0.0552888
$247$	0	0
$248$	3.51060	0.222923
$249$	0.705610	0.0447162
$250$	−1.79399	−0.113462
$251$	3.48547	0.220001	0.110000	−	0.993932i	$-0.464915\pi$
$251$	3.48547	0.220001	0.110000	+	0.993932i	$0.464915\pi$
$252$	−1.96683	−0.123899
$253$	8.73030	0.548869
$254$	−2.12102	−0.133084
$255$	−3.41627	−0.213935
$256$	13.4118	0.838238
$257$	−12.3642	−0.771260	−0.385630	−	0.922654i	$-0.626016\pi$
$257$	−12.3642	−0.771260	−0.385630	+	0.922654i	$0.626016\pi$
$258$	0.426459	0.0265502
$259$	6.38019	0.396446
$260$	0	0
$261$	3.53344	0.218714
$262$	−2.69382	−0.166425
$263$	−24.7086	−1.52360	−0.761800	−	0.647813i	$-0.775684\pi$
$263$	−24.7086	−1.52360	−0.761800	+	0.647813i	$0.775684\pi$
$264$	−2.90159	−0.178580
$265$	−3.36545	−0.206738
$266$	0.965841	0.0592195
$267$	−13.0567	−0.799057
$268$	−3.48301	−0.212759
$269$	−12.5615	−0.765887	−0.382944	−	0.923772i	$-0.625090\pi$
$269$	−12.5615	−0.765887	−0.382944	+	0.923772i	$0.625090\pi$
$270$	0.205599	0.0125124
$271$	−3.82063	−0.232087	−0.116044	−	0.993244i	$-0.537021\pi$
$271$	−3.82063	−0.232087	−0.116044	+	0.993244i	$0.537021\pi$
$272$	11.5062	0.697669
$273$	0	0
$274$	2.81390	0.169994
$275$	14.9629	0.902298
$276$	4.27548	0.257354
$277$	20.1591	1.21124	0.605620	−	0.795754i	$-0.292925\pi$
$277$	20.1591	1.21124	0.605620	+	0.795754i	$0.292925\pi$
$278$	2.08931	0.125308
$279$	4.85911	0.290907
$280$	−0.815576	−0.0487400
$281$	−7.17004	−0.427729	−0.213864	−	0.976863i	$-0.568605\pi$
$281$	−7.17004	−0.427729	−0.213864	+	0.976863i	$0.568605\pi$
$282$	−1.78692	−0.106409
$283$	−9.74389	−0.579214	−0.289607	−	0.957146i	$-0.593525\pi$
$283$	−9.74389	−0.579214	−0.289607	+	0.957146i	$0.593525\pi$
$284$	6.38778	0.379045
$285$	5.98637	0.354602
$286$	0	0
$287$	−4.76127	−0.281049
$288$	−2.13743	−0.125949
$289$	−7.84145	−0.461262
$290$	0.726472	0.0426599
$291$	−1.76727	−0.103599
$292$	−15.3567	−0.898681
$293$	−0.348391	−0.0203532	−0.0101766	−	0.999948i	$-0.503239\pi$
$293$	−0.348391	−0.0203532	−0.0101766	+	0.999948i	$0.503239\pi$
$294$	−0.182130	−0.0106220
$295$	12.9509	0.754033
$296$	4.60955	0.267925
$297$	−4.01616	−0.233041
$298$	−0.545003	−0.0315712
$299$	0	0
$300$	7.32777	0.423069
$301$	−2.34151	−0.134962
$302$	0.156755	0.00902021
$303$	15.3230	0.880282
$304$	−20.1625	−1.15640
$305$	−5.30913	−0.304000
$306$	−0.551182	−0.0315090
$307$	−5.97146	−0.340809	−0.170405	−	0.985374i	$-0.554507\pi$
$307$	−5.97146	−0.340809	−0.170405	+	0.985374i	$0.554507\pi$
$308$	7.89910	0.450093
$309$	8.19962	0.466460
$310$	0.999028	0.0567410
$311$	−6.16012	−0.349308	−0.174654	−	0.984630i	$-0.555881\pi$
$311$	−6.16012	−0.349308	−0.174654	+	0.984630i	$0.555881\pi$
$312$	0	0
$313$	22.5210	1.27296	0.636482	−	0.771291i	$-0.280389\pi$
$313$	22.5210	1.27296	0.636482	+	0.771291i	$0.280389\pi$
$314$	0.842228	0.0475296
$315$	−1.12886	−0.0636040
$316$	−34.4161	−1.93606
$317$	30.4700	1.71136	0.855682	−	0.517501i	$-0.173138\pi$
$317$	30.4700	1.71136	0.855682	+	0.517501i	$0.173138\pi$
$318$	−0.542982	−0.0304489
$319$	−14.1909	−0.794535
$320$	8.14455	0.455294
$321$	16.8953	0.943002
$322$	0.395913	0.0220634
$323$	−16.0486	−0.892969
$324$	−1.96683	−0.109268
$325$	0	0
$326$	−4.19711	−0.232457
$327$	−5.62135	−0.310861
$328$	−3.43992	−0.189938
$329$	9.81123	0.540910
$330$	−0.825718	−0.0454543
$331$	1.62675	0.0894142	0.0447071	−	0.999000i	$-0.485765\pi$
$331$	1.62675	0.0894142	0.0447071	+	0.999000i	$0.485765\pi$
$332$	−1.38781	−0.0761662
$333$	6.38019	0.349632
$334$	0.632530	0.0346105
$335$	−1.99907	−0.109221
$336$	3.80207	0.207420
$337$	3.76808	0.205261	0.102630	−	0.994720i	$-0.467274\pi$
$337$	3.76808	0.205261	0.102630	+	0.994720i	$0.467274\pi$
$338$	0	0
$339$	−2.71753	−0.147596
$340$	6.71923	0.364401
$341$	−19.5149	−1.05679
$342$	0.965841	0.0522267
$343$	1.00000	0.0539949
$344$	−1.69169	−0.0912098
$345$	2.45391	0.132114
$346$	−3.59600	−0.193322
$347$	11.2926	0.606216	0.303108	−	0.952956i	$-0.401976\pi$
$347$	11.2926	0.606216	0.303108	+	0.952956i	$0.401976\pi$
$348$	−6.94967	−0.372542
$349$	−2.74933	−0.147168	−0.0735840	−	0.997289i	$-0.523444\pi$
$349$	−2.74933	−0.147168	−0.0735840	+	0.997289i	$0.523444\pi$
$350$	0.678558	0.0362704
$351$	0	0
$352$	8.58425	0.457542
$353$	−21.6903	−1.15446	−0.577229	−	0.816582i	$-0.695866\pi$
$353$	−21.6903	−1.15446	−0.577229	+	0.816582i	$0.695866\pi$
$354$	2.08950	0.111056
$355$	3.66626	0.194585
$356$	25.6803	1.36105
$357$	3.02631	0.160169
$358$	−3.47054	−0.183424
$359$	25.2837	1.33442	0.667212	−	0.744868i	$-0.267488\pi$
$359$	25.2837	1.33442	0.667212	+	0.744868i	$0.267488\pi$
$360$	−0.815576	−0.0429846
$361$	9.12216	0.480114
$362$	0.629654	0.0330939
$363$	5.12953	0.269230
$364$	0	0
$365$	−8.81394	−0.461343
$366$	−0.856575	−0.0447739
$367$	38.1307	1.99041	0.995203	−	0.0978339i	$-0.0311914\pi$
$367$	38.1307	1.99041	0.995203	+	0.0978339i	$0.0311914\pi$
$368$	−8.26492	−0.430839
$369$	−4.76127	−0.247862
$370$	1.31176	0.0681952
$371$	2.98129	0.154781
$372$	−9.55703	−0.495509
$373$	−26.6379	−1.37926	−0.689630	−	0.724162i	$-0.742227\pi$
$373$	−26.6379	−1.37926	−0.689630	+	0.724162i	$0.742227\pi$
$374$	2.21363	0.114464
$375$	9.85006	0.508655
$376$	7.08840	0.365556
$377$	0	0
$378$	−0.182130	−0.00936776
$379$	−6.72882	−0.345636	−0.172818	−	0.984954i	$-0.555287\pi$
$379$	−6.72882	−0.345636	−0.172818	+	0.984954i	$0.555287\pi$
$380$	−11.7742	−0.604002
$381$	11.6456	0.596623
$382$	3.82817	0.195866
$383$	−1.17016	−0.0597924	−0.0298962	−	0.999553i	$-0.509518\pi$
$383$	−1.17016	−0.0597924	−0.0298962	+	0.999553i	$0.509518\pi$
$384$	5.58890	0.285207
$385$	4.53367	0.231057
$386$	−3.44974	−0.175587
$387$	−2.34151	−0.119026
$388$	3.47592	0.176463
$389$	−21.3343	−1.08169	−0.540847	−	0.841121i	$-0.681896\pi$
$389$	−21.3343	−1.08169	−0.540847	+	0.841121i	$0.681896\pi$
$390$	0	0
$391$	−6.57857	−0.332693
$392$	0.722479	0.0364907
$393$	14.7907	0.746090
$394$	−1.53626	−0.0773957
$395$	−19.7531	−0.993885
$396$	7.89910	0.396944
$397$	26.3909	1.32452	0.662262	−	0.749273i	$-0.269597\pi$
$397$	26.3909	1.32452	0.662262	+	0.749273i	$0.269597\pi$
$398$	−3.71151	−0.186041
$399$	−5.30303	−0.265484
$400$	−14.1653	−0.708265
$401$	−11.6178	−0.580165	−0.290082	−	0.957002i	$-0.593683\pi$
$401$	−11.6178	−0.580165	−0.290082	+	0.957002i	$0.593683\pi$
$402$	−0.322530	−0.0160863
$403$	0	0
$404$	−30.1377	−1.49941
$405$	−1.12886	−0.0560934
$406$	−0.643546	−0.0319386
$407$	−25.6239	−1.27013
$408$	2.18644	0.108245
$409$	−10.8356	−0.535785	−0.267893	−	0.963449i	$-0.586327\pi$
$409$	−10.8356	−0.535785	−0.267893	+	0.963449i	$0.586327\pi$
$410$	−0.978913	−0.0483451
$411$	−15.4499	−0.762089
$412$	−16.1273	−0.794533
$413$	−11.4726	−0.564530
$414$	0.395913	0.0194581
$415$	−0.796534	−0.0391003
$416$	0	0
$417$	−11.4715	−0.561763
$418$	−3.87897	−0.189727
$419$	−37.6639	−1.84000	−0.920001	−	0.391917i	$-0.871812\pi$
$419$	−37.6639	−1.84000	−0.920001	+	0.391917i	$0.871812\pi$
$420$	2.22027	0.108338
$421$	2.59040	0.126249	0.0631243	−	0.998006i	$-0.479894\pi$
$421$	2.59040	0.126249	0.0631243	+	0.998006i	$0.479894\pi$
$422$	−4.50805	−0.219448
$423$	9.81123	0.477038
$424$	2.15392	0.104603
$425$	−11.2751	−0.546920
$426$	0.591514	0.0286590
$427$	4.70310	0.227599
$428$	−33.2301	−1.60624
$429$	0	0
$430$	−0.481412	−0.0232157
$431$	−39.9546	−1.92455	−0.962273	−	0.272086i	$-0.912287\pi$
$431$	−39.9546	−1.92455	−0.962273	+	0.272086i	$0.912287\pi$
$432$	3.80207	0.182927
$433$	6.08994	0.292664	0.146332	−	0.989236i	$-0.453253\pi$
$433$	6.08994	0.292664	0.146332	+	0.989236i	$0.453253\pi$
$434$	−0.884989	−0.0424808
$435$	−3.98875	−0.191246
$436$	11.0562	0.529497
$437$	11.5277	0.551445
$438$	−1.42204	−0.0679478
$439$	−20.6796	−0.986984	−0.493492	−	0.869750i	$-0.664280\pi$
$439$	−20.6796	−0.986984	−0.493492	+	0.869750i	$0.664280\pi$
$440$	3.27548	0.156153
$441$	1.00000	0.0476190
$442$	0	0
$443$	−9.26524	−0.440205	−0.220102	−	0.975477i	$-0.570639\pi$
$443$	−9.26524	−0.440205	−0.220102	+	0.975477i	$0.570639\pi$
$444$	−12.5487	−0.595537
$445$	14.7392	0.698704
$446$	−4.39657	−0.208184
$447$	2.99238	0.141535
$448$	−7.21485	−0.340870
$449$	−36.2207	−1.70936	−0.854681	−	0.519154i	$-0.826247\pi$
$449$	−36.2207	−1.70936	−0.854681	+	0.519154i	$0.826247\pi$
$450$	0.678558	0.0319875
$451$	19.1220	0.900421
$452$	5.34492	0.251404
$453$	−0.860674	−0.0404380
$454$	−3.76556	−0.176727
$455$	0	0
$456$	−3.83133	−0.179418
$457$	−16.7049	−0.781422	−0.390711	−	0.920513i	$-0.627771\pi$
$457$	−16.7049	−0.781422	−0.390711	+	0.920513i	$0.627771\pi$
$458$	−1.30693	−0.0610686
$459$	3.02631	0.141256
$460$	−4.82641	−0.225033
$461$	−24.5420	−1.14303	−0.571517	−	0.820590i	$-0.693645\pi$
$461$	−24.5420	−1.14303	−0.571517	+	0.820590i	$0.693645\pi$
$462$	0.731463	0.0340307
$463$	−18.5726	−0.863143	−0.431572	−	0.902079i	$-0.642041\pi$
$463$	−18.5726	−0.863143	−0.431572	+	0.902079i	$0.642041\pi$
$464$	13.4344	0.623676
$465$	−5.48525	−0.254372
$466$	2.90958	0.134784
$467$	11.8882	0.550119	0.275059	−	0.961427i	$-0.411302\pi$
$467$	11.8882	0.550119	0.275059	+	0.961427i	$0.411302\pi$
$468$	0	0
$469$	1.77088	0.0817715
$470$	2.01718	0.0930455
$471$	−4.62432	−0.213077
$472$	−8.28871	−0.381519
$473$	9.40387	0.432390
$474$	−3.18696	−0.146382
$475$	19.7574	0.906531
$476$	−5.95223	−0.272820
$477$	2.98129	0.136504
$478$	−2.96500	−0.135616
$479$	−11.8285	−0.540460	−0.270230	−	0.962796i	$-0.587100\pi$
$479$	−11.8285	−0.540460	−0.270230	+	0.962796i	$0.587100\pi$
$480$	2.41285	0.110131
$481$	0	0
$482$	4.23513	0.192905
$483$	−2.17379	−0.0989110
$484$	−10.0889	−0.458586
$485$	1.99500	0.0905882
$486$	−0.182130	−0.00826158
$487$	30.3027	1.37315	0.686573	−	0.727061i	$-0.259114\pi$
$487$	30.3027	1.37315	0.686573	+	0.727061i	$0.259114\pi$
$488$	3.39789	0.153815
$489$	23.0446	1.04211
$490$	0.205599	0.00928802
$491$	−5.28571	−0.238541	−0.119270	−	0.992862i	$-0.538056\pi$
$491$	−5.28571	−0.238541	−0.119270	+	0.992862i	$0.538056\pi$
$492$	9.36461	0.422189
$493$	10.6933	0.481601
$494$	0	0
$495$	4.53367	0.203774
$496$	18.4747	0.829538
$497$	−3.24776	−0.145682
$498$	−0.128513	−0.00575880
$499$	34.7232	1.55442	0.777211	−	0.629240i	$-0.216634\pi$
$499$	34.7232	1.55442	0.777211	+	0.629240i	$0.216634\pi$
$500$	−19.3734	−0.866404
$501$	−3.47296	−0.155160
$502$	−0.634809	−0.0283329
$503$	−25.8848	−1.15414	−0.577072	−	0.816693i	$-0.695805\pi$
$503$	−25.8848	−1.15414	−0.577072	+	0.816693i	$0.695805\pi$
$504$	0.722479	0.0321818
$505$	−17.2975	−0.769728
$506$	−1.59005	−0.0706863
$507$	0	0
$508$	−22.9049	−1.01624
$509$	21.4431	0.950449	0.475224	−	0.879865i	$-0.342367\pi$
$509$	21.4431	0.950449	0.475224	+	0.879865i	$0.342367\pi$
$510$	0.622206	0.0275518
$511$	7.80784	0.345398
$512$	−13.6205	−0.601946
$513$	−5.30303	−0.234135
$514$	2.25190	0.0993270
$515$	−9.25622	−0.407878
$516$	4.60535	0.202739
$517$	−39.4034	−1.73296
$518$	−1.16202	−0.0510564
$519$	19.7442	0.866672
$520$	0	0
$521$	−25.1058	−1.09990	−0.549951	−	0.835197i	$-0.685354\pi$
$521$	−25.1058	−1.09990	−0.549951	+	0.835197i	$0.685354\pi$
$522$	−0.643546	−0.0281672
$523$	11.4300	0.499797	0.249898	−	0.968272i	$-0.419603\pi$
$523$	11.4300	0.499797	0.249898	+	0.968272i	$0.419603\pi$
$524$	−29.0907	−1.27083
$525$	−3.72568	−0.162602
$526$	4.50018	0.196217
$527$	14.7052	0.640567
$528$	−15.2697	−0.664529
$529$	−18.2746	−0.794549
$530$	0.612950	0.0266249
$531$	−11.4726	−0.497868
$532$	10.4302	0.452205
$533$	0	0
$534$	2.37802	0.102907
$535$	−19.0724	−0.824571
$536$	1.27942	0.0552626
$537$	19.0553	0.822295
$538$	2.28782	0.0986351
$539$	−4.01616	−0.172988
$540$	2.22027	0.0955453
$541$	−1.47534	−0.0634297	−0.0317148	−	0.999497i	$-0.510097\pi$
$541$	−1.47534	−0.0634297	−0.0317148	+	0.999497i	$0.510097\pi$
$542$	0.695852	0.0298894
$543$	−3.45717	−0.148361
$544$	−6.46852	−0.277335
$545$	6.34571	0.271820
$546$	0	0
$547$	9.19462	0.393134	0.196567	−	0.980490i	$-0.437021\pi$
$547$	9.19462	0.393134	0.196567	+	0.980490i	$0.437021\pi$
$548$	30.3874	1.29808
$549$	4.70310	0.200723
$550$	−2.72520	−0.116203
$551$	−18.7380	−0.798264
$552$	−1.57052	−0.0668457
$553$	17.4983	0.744102
$554$	−3.67157	−0.155990
$555$	−7.20233	−0.305722
$556$	22.5625	0.956863
$557$	−7.14740	−0.302845	−0.151423	−	0.988469i	$-0.548385\pi$
$557$	−7.14740	−0.302845	−0.151423	+	0.988469i	$0.548385\pi$
$558$	−0.884989	−0.0374646
$559$	0	0
$560$	−4.29200	−0.181370
$561$	−12.1541	−0.513148
$562$	1.30588	0.0550852
$563$	−39.3042	−1.65648	−0.828238	−	0.560376i	$-0.810657\pi$
$563$	−39.3042	−1.65648	−0.828238	+	0.560376i	$0.810657\pi$
$564$	−19.2970	−0.812550
$565$	3.06771	0.129059
$566$	1.77465	0.0745943
$567$	1.00000	0.0419961
$568$	−2.34644	−0.0984542
$569$	29.9610	1.25603	0.628015	−	0.778201i	$-0.283868\pi$
$569$	29.9610	1.25603	0.628015	+	0.778201i	$0.283868\pi$
$570$	−1.09030	−0.0456676
$571$	39.1397	1.63795	0.818973	−	0.573833i	$-0.194544\pi$
$571$	39.1397	1.63795	0.818973	+	0.573833i	$0.194544\pi$
$572$	0	0
$573$	−21.0189	−0.878078
$574$	0.867171	0.0361950
$575$	8.09886	0.337746
$576$	−7.21485	−0.300619
$577$	23.2869	0.969445	0.484723	−	0.874668i	$-0.338921\pi$
$577$	23.2869	0.969445	0.484723	+	0.874668i	$0.338921\pi$
$578$	1.42816	0.0594038
$579$	18.9411	0.787164
$580$	7.84520	0.325754
$581$	0.705610	0.0292736
$582$	0.321873	0.0133421
$583$	−11.9733	−0.495885
$584$	5.64099	0.233426
$585$	0	0
$586$	0.0634524	0.00262120
$587$	−14.6189	−0.603387	−0.301694	−	0.953405i	$-0.597552\pi$
$587$	−14.6189	−0.603387	−0.301694	+	0.953405i	$0.597552\pi$
$588$	−1.96683	−0.0811106
$589$	−25.7680	−1.06175
$590$	−2.35875	−0.0971084
$591$	8.43497	0.346968
$592$	24.2579	0.996995
$593$	28.8553	1.18495	0.592473	−	0.805590i	$-0.298152\pi$
$593$	28.8553	1.18495	0.592473	+	0.805590i	$0.298152\pi$
$594$	0.731463	0.0300123
$595$	−3.41627	−0.140054
$596$	−5.88550	−0.241080
$597$	20.3783	0.834029
$598$	0	0
$599$	18.1056	0.739773	0.369887	−	0.929077i	$-0.379397\pi$
$599$	18.1056	0.739773	0.369887	+	0.929077i	$0.379397\pi$
$600$	−2.69172	−0.109889
$601$	0.149746	0.00610829	0.00305414	−	0.999995i	$-0.499028\pi$
$601$	0.149746	0.00610829	0.00305414	+	0.999995i	$0.499028\pi$
$602$	0.426459	0.0173812
$603$	1.77088	0.0721157
$604$	1.69280	0.0688790
$605$	−5.79051	−0.235418
$606$	−2.79077	−0.113367
$607$	14.2380	0.577904	0.288952	−	0.957344i	$-0.406693\pi$
$607$	14.2380	0.577904	0.288952	+	0.957344i	$0.406693\pi$
$608$	11.3349	0.459689
$609$	3.53344	0.143182
$610$	0.966952	0.0391507
$611$	0	0
$612$	−5.95223	−0.240605
$613$	−1.87784	−0.0758451	−0.0379226	−	0.999281i	$-0.512074\pi$
$613$	−1.87784	−0.0758451	−0.0379226	+	0.999281i	$0.512074\pi$
$614$	1.08758	0.0438912
$615$	5.37481	0.216733
$616$	−2.90159	−0.116908
$617$	38.8688	1.56480	0.782400	−	0.622776i	$-0.213995\pi$
$617$	38.8688	1.56480	0.782400	+	0.622776i	$0.213995\pi$
$618$	−1.49340	−0.0600733
$619$	−41.6563	−1.67431	−0.837153	−	0.546969i	$-0.815782\pi$
$619$	−41.6563	−1.67431	−0.837153	+	0.546969i	$0.815782\pi$
$620$	10.7885	0.433278
$621$	−2.17379	−0.0872313
$622$	1.12194	0.0449858
$623$	−13.0567	−0.523106
$624$	0	0
$625$	7.50907	0.300363
$626$	−4.10176	−0.163939
$627$	21.2978	0.850553
$628$	9.09525	0.362940
$629$	19.3084	0.769877
$630$	0.205599	0.00819126
$631$	−28.6876	−1.14203	−0.571017	−	0.820938i	$-0.693451\pi$
$631$	−28.6876	−1.14203	−0.571017	+	0.820938i	$0.693451\pi$
$632$	12.6421	0.502877
$633$	24.7518	0.983796
$634$	−5.54950	−0.220399
$635$	−13.1463	−0.521693
$636$	−5.86369	−0.232510
$637$	0	0
$638$	2.58458	0.102325
$639$	−3.24776	−0.128479
$640$	−6.30908	−0.249388
$641$	−18.5217	−0.731564	−0.365782	−	0.930701i	$-0.619198\pi$
$641$	−18.5217	−0.731564	−0.365782	+	0.930701i	$0.619198\pi$
$642$	−3.07714	−0.121445
$643$	31.6909	1.24977	0.624884	−	0.780718i	$-0.285146\pi$
$643$	31.6909	1.24977	0.624884	+	0.780718i	$0.285146\pi$
$644$	4.27548	0.168477
$645$	2.64323	0.104077
$646$	2.92293	0.115001
$647$	22.6938	0.892184	0.446092	−	0.894987i	$-0.352815\pi$
$647$	22.6938	0.892184	0.446092	+	0.894987i	$0.352815\pi$
$648$	0.722479	0.0283816
$649$	46.0758	1.80863
$650$	0	0
$651$	4.85911	0.190443
$652$	−45.3248	−1.77505
$653$	−45.9806	−1.79936	−0.899680	−	0.436550i	$-0.856200\pi$
$653$	−45.9806	−1.79936	−0.899680	+	0.436550i	$0.856200\pi$
$654$	1.02382	0.0400344
$655$	−16.6966	−0.652389
$656$	−18.1027	−0.706792
$657$	7.80784	0.304613
$658$	−1.78692	−0.0696613
$659$	26.6785	1.03925	0.519623	−	0.854396i	$-0.326072\pi$
$659$	26.6785	1.03925	0.519623	+	0.854396i	$0.326072\pi$
$660$	−8.91696	−0.347092
$661$	−8.73868	−0.339895	−0.169948	−	0.985453i	$-0.554360\pi$
$661$	−8.73868	−0.339895	−0.169948	+	0.985453i	$0.554360\pi$
$662$	−0.296280	−0.0115152
$663$	0	0
$664$	0.509788	0.0197836
$665$	5.98637	0.232142
$666$	−1.16202	−0.0450275
$667$	−7.68097	−0.297408
$668$	6.83071	0.264288
$669$	24.1397	0.933296
$670$	0.364091	0.0140660
$671$	−18.8884	−0.729178
$672$	−2.13743	−0.0824531
$673$	45.5288	1.75501	0.877503	−	0.479570i	$-0.159207\pi$
$673$	45.5288	1.75501	0.877503	+	0.479570i	$0.159207\pi$
$674$	−0.686281	−0.0264346
$675$	−3.72568	−0.143401
$676$	0	0
$677$	0.826184	0.0317528	0.0158764	−	0.999874i	$-0.494946\pi$
$677$	0.826184	0.0317528	0.0158764	+	0.999874i	$0.494946\pi$
$678$	0.494944	0.0190082
$679$	−1.76727	−0.0678216
$680$	−2.46819	−0.0946506
$681$	20.6751	0.792273
$682$	3.55426	0.136100
$683$	24.3274	0.930860	0.465430	−	0.885085i	$-0.345900\pi$
$683$	24.3274	0.930860	0.465430	+	0.885085i	$0.345900\pi$
$684$	10.4302	0.398807
$685$	17.4408	0.666378
$686$	−0.182130	−0.00695376
$687$	7.17578	0.273773
$688$	−8.90259	−0.339408
$689$	0	0
$690$	−0.446930	−0.0170143
$691$	24.8245	0.944367	0.472184	−	0.881500i	$-0.343466\pi$
$691$	24.8245	0.944367	0.472184	+	0.881500i	$0.343466\pi$
$692$	−38.8334	−1.47622
$693$	−4.01616	−0.152561
$694$	−2.05671	−0.0780718
$695$	12.9497	0.491211
$696$	2.55284	0.0967650
$697$	−14.4091	−0.545783
$698$	0.500735	0.0189531
$699$	−15.9753	−0.604241
$700$	7.32777	0.276964
$701$	−51.0338	−1.92752	−0.963760	−	0.266770i	$-0.914044\pi$
$701$	−51.0338	−1.92752	−0.963760	+	0.266770i	$0.914044\pi$
$702$	0	0
$703$	−33.8344	−1.27609
$704$	28.9760	1.09207
$705$	−11.0755	−0.417127
$706$	3.95045	0.148677
$707$	15.3230	0.576280
$708$	22.5646	0.848031
$709$	12.6412	0.474752	0.237376	−	0.971418i	$-0.423713\pi$
$709$	12.6412	0.474752	0.237376	+	0.971418i	$0.423713\pi$
$710$	−0.667736	−0.0250597
$711$	17.4983	0.656236
$712$	−9.43319	−0.353524
$713$	−10.5627	−0.395576
$714$	−0.551182	−0.0206275
$715$	0	0
$716$	−37.4784	−1.40064
$717$	16.2796	0.607971
$718$	−4.60493	−0.171854
$719$	−7.25090	−0.270413	−0.135206	−	0.990817i	$-0.543170\pi$
$719$	−7.25090	−0.270413	−0.135206	+	0.990817i	$0.543170\pi$
$720$	−4.29200	−0.159953
$721$	8.19962	0.305370
$722$	−1.66142	−0.0618316
$723$	−23.2533	−0.864801
$724$	6.79966	0.252707
$725$	−13.1645	−0.488916
$726$	−0.934241	−0.0346729
$727$	18.1643	0.673677	0.336838	−	0.941563i	$-0.390642\pi$
$727$	18.1643	0.673677	0.336838	+	0.941563i	$0.390642\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	1.60528	0.0594142
$731$	−7.08613	−0.262090
$732$	−9.25018	−0.341897
$733$	13.6504	0.504189	0.252094	−	0.967703i	$-0.418881\pi$
$733$	13.6504	0.504189	0.252094	+	0.967703i	$0.418881\pi$
$734$	−6.94474	−0.256335
$735$	−1.12886	−0.0416386
$736$	4.64633	0.171266
$737$	−7.11212	−0.261978
$738$	0.867171	0.0319210
$739$	−24.7742	−0.911333	−0.455667	−	0.890150i	$-0.650599\pi$
$739$	−24.7742	−0.911333	−0.455667	+	0.890150i	$0.650599\pi$
$740$	14.1658	0.520743
$741$	0	0
$742$	−0.542982	−0.0199335
$743$	−29.4286	−1.07963	−0.539815	−	0.841783i	$-0.681506\pi$
$743$	−29.4286	−1.07963	−0.539815	+	0.841783i	$0.681506\pi$
$744$	3.51060	0.128705
$745$	−3.37798	−0.123760
$746$	4.85157	0.177629
$747$	0.705610	0.0258169
$748$	23.9051	0.874057
$749$	16.8953	0.617340
$750$	−1.79399	−0.0655073
$751$	−23.6648	−0.863543	−0.431771	−	0.901983i	$-0.642111\pi$
$751$	−23.6648	−0.863543	−0.431771	+	0.901983i	$0.642111\pi$
$752$	37.3030	1.36030
$753$	3.48547	0.127018
$754$	0	0
$755$	0.971579	0.0353594
$756$	−1.96683	−0.0715329
$757$	18.5355	0.673683	0.336841	−	0.941561i	$-0.390641\pi$
$757$	18.5355	0.673683	0.336841	+	0.941561i	$0.390641\pi$
$758$	1.22552	0.0445129
$759$	8.73030	0.316890
$760$	4.32503	0.156885
$761$	9.30977	0.337479	0.168739	−	0.985661i	$-0.446030\pi$
$761$	9.30977	0.337479	0.168739	+	0.985661i	$0.446030\pi$
$762$	−2.12102	−0.0768363
$763$	−5.62135	−0.203506
$764$	41.3406	1.49565
$765$	−3.41627	−0.123516
$766$	0.213121	0.00770039
$767$	0	0
$768$	13.4118	0.483957
$769$	−10.5730	−0.381272	−0.190636	−	0.981661i	$-0.561055\pi$
$769$	−10.5730	−0.381272	−0.190636	+	0.981661i	$0.561055\pi$
$770$	−0.825718	−0.0297568
$771$	−12.3642	−0.445287
$772$	−37.2539	−1.34080
$773$	35.7370	1.28537	0.642686	−	0.766130i	$-0.277820\pi$
$773$	35.7370	1.28537	0.642686	+	0.766130i	$0.277820\pi$
$774$	0.426459	0.0153288
$775$	−18.1035	−0.650296
$776$	−1.27681	−0.0458350
$777$	6.38019	0.228888
$778$	3.88562	0.139306
$779$	25.2492	0.904646
$780$	0	0
$781$	13.0435	0.466733
$782$	1.19816	0.0428459
$783$	3.53344	0.126275
$784$	3.80207	0.135788
$785$	5.22020	0.186317
$786$	−2.69382	−0.0960855
$787$	−15.8102	−0.563574	−0.281787	−	0.959477i	$-0.590927\pi$
$787$	−15.8102	−0.563574	−0.281787	+	0.959477i	$0.590927\pi$
$788$	−16.5901	−0.590999
$789$	−24.7086	−0.879650
$790$	3.59763	0.127998
$791$	−2.71753	−0.0966243
$792$	−2.90159	−0.103103
$793$	0	0
$794$	−4.80658	−0.170579
$795$	−3.36545	−0.119360
$796$	−40.0807	−1.42062
$797$	42.4880	1.50500	0.752502	−	0.658590i	$-0.228847\pi$
$797$	42.4880	1.50500	0.752502	+	0.658590i	$0.228847\pi$
$798$	0.965841	0.0341904
$799$	29.6918	1.05042
$800$	7.96337	0.281548
$801$	−13.0567	−0.461336
$802$	2.11595	0.0747167
$803$	−31.3575	−1.10658
$804$	−3.48301	−0.122836
$805$	2.45391	0.0864888
$806$	0	0
$807$	−12.5615	−0.442185
$808$	11.0705	0.389460
$809$	−18.9303	−0.665553	−0.332776	−	0.943006i	$-0.607985\pi$
$809$	−18.9303	−0.665553	−0.332776	+	0.943006i	$0.607985\pi$
$810$	0.205599	0.00722401
$811$	−18.5956	−0.652978	−0.326489	−	0.945201i	$-0.605866\pi$
$811$	−18.5956	−0.652978	−0.326489	+	0.945201i	$0.605866\pi$
$812$	−6.94967	−0.243886
$813$	−3.82063	−0.133996
$814$	4.66687	0.163574
$815$	−26.0141	−0.911234
$816$	11.5062	0.402799
$817$	12.4171	0.434419
$818$	1.97349	0.0690013
$819$	0	0
$820$	−10.5713	−0.369167
$821$	46.8163	1.63390	0.816951	−	0.576707i	$-0.195663\pi$
$821$	46.8163	1.63390	0.816951	+	0.576707i	$0.195663\pi$
$822$	2.81390	0.0981459
$823$	−36.5999	−1.27579	−0.637896	−	0.770123i	$-0.720195\pi$
$823$	−36.5999	−1.27579	−0.637896	+	0.770123i	$0.720195\pi$
$824$	5.92405	0.206374
$825$	14.9629	0.520942
$826$	2.08950	0.0727032
$827$	−37.5007	−1.30403	−0.652013	−	0.758208i	$-0.726075\pi$
$827$	−37.5007	−1.30403	−0.652013	+	0.758208i	$0.726075\pi$
$828$	4.27548	0.148583
$829$	3.74445	0.130050	0.0650250	−	0.997884i	$-0.479287\pi$
$829$	3.74445	0.130050	0.0650250	+	0.997884i	$0.479287\pi$
$830$	0.145073	0.00503555
$831$	20.1591	0.699310
$832$	0	0
$833$	3.02631	0.104855
$834$	2.08931	0.0723468
$835$	3.92048	0.135674
$836$	−41.8892	−1.44877
$837$	4.85911	0.167955
$838$	6.85972	0.236965
$839$	24.0282	0.829547	0.414773	−	0.909925i	$-0.363861\pi$
$839$	24.0282	0.829547	0.414773	+	0.909925i	$0.363861\pi$
$840$	−0.815576	−0.0281400
$841$	−16.5148	−0.569476
$842$	−0.471790	−0.0162590
$843$	−7.17004	−0.246949
$844$	−48.6825	−1.67572
$845$	0	0
$846$	−1.78692	−0.0614355
$847$	5.12953	0.176253
$848$	11.3351	0.389248
$849$	−9.74389	−0.334409
$850$	2.05353	0.0704353
$851$	−13.8692	−0.475431
$852$	6.38778	0.218842
$853$	42.2325	1.44601	0.723006	−	0.690841i	$-0.242760\pi$
$853$	42.2325	1.44601	0.723006	+	0.690841i	$0.242760\pi$
$854$	−0.856575	−0.0293114
$855$	5.98637	0.204730
$856$	12.2065	0.417209
$857$	16.7604	0.572524	0.286262	−	0.958151i	$-0.407587\pi$
$857$	16.7604	0.572524	0.286262	+	0.958151i	$0.407587\pi$
$858$	0	0
$859$	−37.9949	−1.29637	−0.648185	−	0.761483i	$-0.724472\pi$
$859$	−37.9949	−1.29637	−0.648185	+	0.761483i	$0.724472\pi$
$860$	−5.19879	−0.177277
$861$	−4.76127	−0.162264
$862$	7.27693	0.247853
$863$	−31.3316	−1.06654	−0.533269	−	0.845945i	$-0.679037\pi$
$863$	−31.3316	−1.06654	−0.533269	+	0.845945i	$0.679037\pi$
$864$	−2.13743	−0.0727168
$865$	−22.2884	−0.757827
$866$	−1.10916	−0.0376908
$867$	−7.84145	−0.266310
$868$	−9.55703	−0.324387
$869$	−70.2758	−2.38394
$870$	0.726472	0.0246297
$871$	0	0
$872$	−4.06130	−0.137533
$873$	−1.76727	−0.0598130
$874$	−2.09954	−0.0710180
$875$	9.85006	0.332993
$876$	−15.3567	−0.518854
$877$	−21.5909	−0.729075	−0.364537	−	0.931189i	$-0.618773\pi$
$877$	−21.5909	−0.729075	−0.364537	+	0.931189i	$0.618773\pi$
$878$	3.76638	0.127109
$879$	−0.348391	−0.0117509
$880$	17.2374	0.581071
$881$	−8.51629	−0.286921	−0.143461	−	0.989656i	$-0.545823\pi$
$881$	−8.51629	−0.286921	−0.143461	+	0.989656i	$0.545823\pi$
$882$	−0.182130	−0.00613264
$883$	7.62183	0.256495	0.128248	−	0.991742i	$-0.459065\pi$
$883$	7.62183	0.256495	0.128248	+	0.991742i	$0.459065\pi$
$884$	0	0
$885$	12.9509	0.435341
$886$	1.68748	0.0566919
$887$	−5.49147	−0.184385	−0.0921927	−	0.995741i	$-0.529388\pi$
$887$	−5.49147	−0.184385	−0.0921927	+	0.995741i	$0.529388\pi$
$888$	4.60955	0.154686
$889$	11.6456	0.390581
$890$	−2.68445	−0.0899828
$891$	−4.01616	−0.134546
$892$	−47.4787	−1.58970
$893$	−52.0293	−1.74109
$894$	−0.545003	−0.0182276
$895$	−21.5107	−0.719023
$896$	5.58890	0.186712
$897$	0	0
$898$	6.59688	0.220141
$899$	17.1694	0.572630
$900$	7.32777	0.244259
$901$	9.02230	0.300576
$902$	−3.48270	−0.115961
$903$	−2.34151	−0.0779205
$904$	−1.96336	−0.0653003
$905$	3.90265	0.129729
$906$	0.156755	0.00520782
$907$	52.3003	1.73660	0.868301	−	0.496038i	$-0.165212\pi$
$907$	52.3003	1.73660	0.868301	+	0.496038i	$0.165212\pi$
$908$	−40.6644	−1.34950
$909$	15.3230	0.508231
$910$	0	0
$911$	−53.1804	−1.76195	−0.880973	−	0.473167i	$-0.843111\pi$
$911$	−53.1804	−1.76195	−0.880973	+	0.473167i	$0.843111\pi$
$912$	−20.1625	−0.667648
$913$	−2.83384	−0.0937865
$914$	3.04246	0.100636
$915$	−5.30913	−0.175514
$916$	−14.1135	−0.466324
$917$	14.7907	0.488431
$918$	−0.551182	−0.0181917
$919$	9.23684	0.304695	0.152348	−	0.988327i	$-0.451317\pi$
$919$	9.23684	0.304695	0.152348	+	0.988327i	$0.451317\pi$
$920$	1.77289	0.0584506
$921$	−5.97146	−0.196766
$922$	4.46983	0.147206
$923$	0	0
$924$	7.89910	0.259861
$925$	−23.7705	−0.781570
$926$	3.38263	0.111160
$927$	8.19962	0.269311
$928$	−7.55248	−0.247922
$929$	25.2833	0.829517	0.414759	−	0.909931i	$-0.363866\pi$
$929$	25.2833	0.829517	0.414759	+	0.909931i	$0.363866\pi$
$930$	0.999028	0.0327594
$931$	−5.30303	−0.173800
$932$	31.4206	1.02922
$933$	−6.16012	−0.201673
$934$	−2.16519	−0.0708473
$935$	13.7203	0.448702
$936$	0	0
$937$	−42.6293	−1.39264	−0.696320	−	0.717732i	$-0.745180\pi$
$937$	−42.6293	−1.39264	−0.696320	+	0.717732i	$0.745180\pi$
$938$	−0.322530	−0.0105310
$939$	22.5210	0.734947
$940$	21.7836	0.710502
$941$	4.78825	0.156093	0.0780463	−	0.996950i	$-0.475132\pi$
$941$	4.78825	0.156093	0.0780463	+	0.996950i	$0.475132\pi$
$942$	0.842228	0.0274413
$943$	10.3500	0.337043
$944$	−43.6196	−1.41970
$945$	−1.12886	−0.0367218
$946$	−1.71273	−0.0556856
$947$	−9.40557	−0.305640	−0.152820	−	0.988254i	$-0.548835\pi$
$947$	−9.40557	−0.305640	−0.152820	+	0.988254i	$0.548835\pi$
$948$	−34.4161	−1.11778
$949$	0	0
$950$	−3.59841	−0.116748
$951$	30.4700	0.988057
$952$	2.18644	0.0708630
$953$	−11.7968	−0.382135	−0.191068	−	0.981577i	$-0.561195\pi$
$953$	−11.7968	−0.382135	−0.191068	+	0.981577i	$0.561195\pi$
$954$	−0.542982	−0.0175797
$955$	23.7274	0.767800
$956$	−32.0191	−1.03557
$957$	−14.1909	−0.458725
$958$	2.15433	0.0696033
$959$	−15.4499	−0.498904
$960$	8.14455	0.262864
$961$	−7.38907	−0.238357
$962$	0	0
$963$	16.8953	0.544443
$964$	45.7353	1.47304
$965$	−21.3818	−0.688304
$966$	0.395913	0.0127383
$967$	−30.0746	−0.967135	−0.483568	−	0.875307i	$-0.660659\pi$
$967$	−30.0746	−0.967135	−0.483568	+	0.875307i	$0.660659\pi$
$968$	3.70597	0.119115
$969$	−16.0486	−0.515556
$970$	−0.363349	−0.0116664
$971$	−19.2259	−0.616987	−0.308494	−	0.951226i	$-0.599825\pi$
$971$	−19.2259	−0.616987	−0.308494	+	0.951226i	$0.599825\pi$
$972$	−1.96683	−0.0630861
$973$	−11.4715	−0.367760
$974$	−5.51903	−0.176841
$975$	0	0
$976$	17.8815	0.572373
$977$	−19.0860	−0.610615	−0.305308	−	0.952254i	$-0.598759\pi$
$977$	−19.0860	−0.610615	−0.305308	+	0.952254i	$0.598759\pi$
$978$	−4.19711	−0.134209
$979$	52.4378	1.67592
$980$	2.22027	0.0709240
$981$	−5.62135	−0.179476
$982$	0.962686	0.0307206
$983$	42.0109	1.33994	0.669970	−	0.742389i	$-0.266307\pi$
$983$	42.0109	1.33994	0.669970	+	0.742389i	$0.266307\pi$
$984$	−3.43992	−0.109661
$985$	−9.52188	−0.303392
$986$	−1.94757	−0.0620232
$987$	9.81123	0.312295
$988$	0	0
$989$	5.08996	0.161851
$990$	−0.825718	−0.0262430
$991$	−20.0564	−0.637112	−0.318556	−	0.947904i	$-0.603198\pi$
$991$	−20.0564	−0.637112	−0.318556	+	0.947904i	$0.603198\pi$
$992$	−10.3860	−0.329756
$993$	1.62675	0.0516233
$994$	0.591514	0.0187617
$995$	−23.0043	−0.729284
$996$	−1.38781	−0.0439746
$997$	31.9271	1.01114	0.505570	−	0.862785i	$-0.331282\pi$
$997$	31.9271	1.01114	0.505570	+	0.862785i	$0.331282\pi$
$998$	−6.32413	−0.200187
$999$	6.38019	0.201860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bg.1.8	✓	15
13.12	even	2		3549.2.a.bh.1.8	yes	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.bg.1.8	✓	15	1.1	even	1	trivial
3549.2.a.bh.1.8	yes	15	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:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q-0.182130 q^{2} +1.00000 q^{3} -1.96683 q^{4} -1.12886 q^{5} -0.182130 q^{6} +1.00000 q^{7} +0.722479 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.182130 q^{2} +1.00000 q^{3} -1.96683 q^{4} -1.12886 q^{5} -0.182130 q^{6} +1.00000 q^{7} +0.722479 q^{8} +1.00000 q^{9} +0.205599 q^{10} -4.01616 q^{11} -1.96683 q^{12} -0.182130 q^{14} -1.12886 q^{15} +3.80207 q^{16} +3.02631 q^{17} -0.182130 q^{18} -5.30303 q^{19} +2.22027 q^{20} +1.00000 q^{21} +0.731463 q^{22} -2.17379 q^{23} +0.722479 q^{24} -3.72568 q^{25} +1.00000 q^{27} -1.96683 q^{28} +3.53344 q^{29} +0.205599 q^{30} +4.85911 q^{31} -2.13743 q^{32} -4.01616 q^{33} -0.551182 q^{34} -1.12886 q^{35} -1.96683 q^{36} +6.38019 q^{37} +0.965841 q^{38} -0.815576 q^{40} -4.76127 q^{41} -0.182130 q^{42} -2.34151 q^{43} +7.89910 q^{44} -1.12886 q^{45} +0.395913 q^{46} +9.81123 q^{47} +3.80207 q^{48} +1.00000 q^{49} +0.678558 q^{50} +3.02631 q^{51} +2.98129 q^{53} -0.182130 q^{54} +4.53367 q^{55} +0.722479 q^{56} -5.30303 q^{57} -0.643546 q^{58} -11.4726 q^{59} +2.22027 q^{60} +4.70310 q^{61} -0.884989 q^{62} +1.00000 q^{63} -7.21485 q^{64} +0.731463 q^{66} +1.77088 q^{67} -5.95223 q^{68} -2.17379 q^{69} +0.205599 q^{70} -3.24776 q^{71} +0.722479 q^{72} +7.80784 q^{73} -1.16202 q^{74} -3.72568 q^{75} +10.4302 q^{76} -4.01616 q^{77} +17.4983 q^{79} -4.29200 q^{80} +1.00000 q^{81} +0.867171 q^{82} +0.705610 q^{83} -1.96683 q^{84} -3.41627 q^{85} +0.426459 q^{86} +3.53344 q^{87} -2.90159 q^{88} -13.0567 q^{89} +0.205599 q^{90} +4.27548 q^{92} +4.85911 q^{93} -1.78692 q^{94} +5.98637 q^{95} -2.13743 q^{96} -1.76727 q^{97} -0.182130 q^{98} -4.01616 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 2 q^{2} + 15 q^{3} + 28 q^{4} + 9 q^{5} - 2 q^{6} + 15 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) \) 15 * q - 2 * q^2 + 15 * q^3 + 28 * q^4 + 9 * q^5 - 2 * q^6 + 15 * q^7 - 9 * q^8 + 15 * q^9	\( 15 q - 2 q^{2} + 15 q^{3} + 28 q^{4} + 9 q^{5} - 2 q^{6} + 15 q^{7} - 9 q^{8} + 15 q^{9} + 21 q^{10} - 5 q^{11} + 28 q^{12} - 2 q^{14} + 9 q^{15} + 50 q^{16} - q^{17} - 2 q^{18} - 3 q^{19} + 23 q^{20} + 15 q^{21} + 21 q^{22} + 4 q^{23} - 9 q^{24} + 50 q^{25} + 15 q^{27} + 28 q^{28} + 9 q^{29} + 21 q^{30} - 7 q^{31} - 35 q^{32} - 5 q^{33} + 2 q^{34} + 9 q^{35} + 28 q^{36} - 17 q^{37} - 12 q^{38} + 46 q^{40} + 22 q^{41} - 2 q^{42} + 36 q^{43} - 29 q^{44} + 9 q^{45} + q^{46} + 12 q^{47} + 50 q^{48} + 15 q^{49} - 53 q^{50} - q^{51} - 5 q^{53} - 2 q^{54} + 43 q^{55} - 9 q^{56} - 3 q^{57} - 29 q^{58} + 29 q^{59} + 23 q^{60} + 12 q^{61} + 14 q^{62} + 15 q^{63} + 95 q^{64} + 21 q^{66} + 12 q^{67} - 16 q^{68} + 4 q^{69} + 21 q^{70} - 36 q^{71} - 9 q^{72} + 29 q^{73} - 5 q^{74} + 50 q^{75} - 25 q^{76} - 5 q^{77} + 35 q^{79} + 89 q^{80} + 15 q^{81} + 51 q^{82} + 10 q^{83} + 28 q^{84} - 23 q^{85} - 19 q^{86} + 9 q^{87} + 73 q^{88} - 25 q^{89} + 21 q^{90} - 31 q^{92} - 7 q^{93} - 19 q^{94} - 7 q^{95} - 35 q^{96} + 26 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) 15 * q - 2 * q^2 + 15 * q^3 + 28 * q^4 + 9 * q^5 - 2 * q^6 + 15 * q^7 - 9 * q^8 + 15 * q^9 + 21 * q^10 - 5 * q^11 + 28 * q^12 - 2 * q^14 + 9 * q^15 + 50 * q^16 - q^17 - 2 * q^18 - 3 * q^19 + 23 * q^20 + 15 * q^21 + 21 * q^22 + 4 * q^23 - 9 * q^24 + 50 * q^25 + 15 * q^27 + 28 * q^28 + 9 * q^29 + 21 * q^30 - 7 * q^31 - 35 * q^32 - 5 * q^33 + 2 * q^34 + 9 * q^35 + 28 * q^36 - 17 * q^37 - 12 * q^38 + 46 * q^40 + 22 * q^41 - 2 * q^42 + 36 * q^43 - 29 * q^44 + 9 * q^45 + q^46 + 12 * q^47 + 50 * q^48 + 15 * q^49 - 53 * q^50 - q^51 - 5 * q^53 - 2 * q^54 + 43 * q^55 - 9 * q^56 - 3 * q^57 - 29 * q^58 + 29 * q^59 + 23 * q^60 + 12 * q^61 + 14 * q^62 + 15 * q^63 + 95 * q^64 + 21 * q^66 + 12 * q^67 - 16 * q^68 + 4 * q^69 + 21 * q^70 - 36 * q^71 - 9 * q^72 + 29 * q^73 - 5 * q^74 + 50 * q^75 - 25 * q^76 - 5 * q^77 + 35 * q^79 + 89 * q^80 + 15 * q^81 + 51 * q^82 + 10 * q^83 + 28 * q^84 - 23 * q^85 - 19 * q^86 + 9 * q^87 + 73 * q^88 - 25 * q^89 + 21 * q^90 - 31 * q^92 - 7 * q^93 - 19 * q^94 - 7 * q^95 - 35 * q^96 + 26 * q^97 - 2 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more