LMFDB - Embedded newform 3549.2.a.bh.1.15

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			1.15
Root			$2.80363$ 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)

$f(q)$	$=$	$q+2.80363 q^{2} +1.00000 q^{3} +5.86034 q^{4} -3.14248 q^{5} +2.80363 q^{6} -1.00000 q^{7} +10.8230 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.80363 q^{2} +1.00000 q^{3} +5.86034 q^{4} -3.14248 q^{5} +2.80363 q^{6} -1.00000 q^{7} +10.8230 q^{8} +1.00000 q^{9} -8.81036 q^{10} +3.00418 q^{11} +5.86034 q^{12} -2.80363 q^{14} -3.14248 q^{15} +18.6229 q^{16} +3.41447 q^{17} +2.80363 q^{18} -4.86056 q^{19} -18.4160 q^{20} -1.00000 q^{21} +8.42260 q^{22} +5.37767 q^{23} +10.8230 q^{24} +4.87520 q^{25} +1.00000 q^{27} -5.86034 q^{28} +0.848910 q^{29} -8.81036 q^{30} +0.451052 q^{31} +30.5658 q^{32} +3.00418 q^{33} +9.57292 q^{34} +3.14248 q^{35} +5.86034 q^{36} -3.88581 q^{37} -13.6272 q^{38} -34.0110 q^{40} +10.5244 q^{41} -2.80363 q^{42} +7.20767 q^{43} +17.6055 q^{44} -3.14248 q^{45} +15.0770 q^{46} -9.33384 q^{47} +18.6229 q^{48} +1.00000 q^{49} +13.6683 q^{50} +3.41447 q^{51} -13.1147 q^{53} +2.80363 q^{54} -9.44058 q^{55} -10.8230 q^{56} -4.86056 q^{57} +2.38003 q^{58} +1.45785 q^{59} -18.4160 q^{60} +4.95821 q^{61} +1.26458 q^{62} -1.00000 q^{63} +48.4493 q^{64} +8.42260 q^{66} +4.57857 q^{67} +20.0100 q^{68} +5.37767 q^{69} +8.81036 q^{70} -2.36205 q^{71} +10.8230 q^{72} +1.24210 q^{73} -10.8944 q^{74} +4.87520 q^{75} -28.4845 q^{76} -3.00418 q^{77} -7.10832 q^{79} -58.5222 q^{80} +1.00000 q^{81} +29.5065 q^{82} +5.04895 q^{83} -5.86034 q^{84} -10.7299 q^{85} +20.2076 q^{86} +0.848910 q^{87} +32.5141 q^{88} -12.6846 q^{89} -8.81036 q^{90} +31.5150 q^{92} +0.451052 q^{93} -26.1686 q^{94} +15.2742 q^{95} +30.5658 q^{96} -4.29846 q^{97} +2.80363 q^{98} +3.00418 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.80363	1.98247	0.991233	−	0.132127i	$-0.0421807\pi$
$2$	2.80363	1.98247	0.991233	+	0.132127i	$0.0421807\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.86034	2.93017
$5$	−3.14248	−1.40536	−0.702681	−	0.711505i	$-0.748014\pi$
$5$	−3.14248	−1.40536	−0.702681	+	0.711505i	$0.748014\pi$
$6$	2.80363	1.14458
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	10.8230	3.82649
$9$	1.00000	0.333333
$10$	−8.81036	−2.78608
$11$	3.00418	0.905793	0.452897	−	0.891563i	$-0.350391\pi$
$11$	3.00418	0.905793	0.452897	+	0.891563i	$0.350391\pi$
$12$	5.86034	1.69173
$13$	0	0
$13$	0	0
$14$	−2.80363	−0.749302
$15$	−3.14248	−0.811386
$16$	18.6229	4.65572
$17$	3.41447	0.828132	0.414066	−	0.910247i	$-0.364108\pi$
$17$	3.41447	0.828132	0.414066	+	0.910247i	$0.364108\pi$
$18$	2.80363	0.660822
$19$	−4.86056	−1.11509	−0.557544	−	0.830147i	$-0.688256\pi$
$19$	−4.86056	−1.11509	−0.557544	+	0.830147i	$0.688256\pi$
$20$	−18.4160	−4.11795
$21$	−1.00000	−0.218218
$22$	8.42260	1.79570
$23$	5.37767	1.12132	0.560661	−	0.828045i	$-0.310547\pi$
$23$	5.37767	1.12132	0.560661	+	0.828045i	$0.310547\pi$
$24$	10.8230	2.20923
$25$	4.87520	0.975041
$26$	0	0
$27$	1.00000	0.192450
$28$	−5.86034	−1.10750
$29$	0.848910	0.157639	0.0788193	−	0.996889i	$-0.474885\pi$
$29$	0.848910	0.157639	0.0788193	+	0.996889i	$0.474885\pi$
$30$	−8.81036	−1.60854
$31$	0.451052	0.0810113	0.0405057	−	0.999179i	$-0.487103\pi$
$31$	0.451052	0.0810113	0.0405057	+	0.999179i	$0.487103\pi$
$32$	30.5658	5.40332
$33$	3.00418	0.522960
$34$	9.57292	1.64174
$35$	3.14248	0.531177
$36$	5.86034	0.976723
$37$	−3.88581	−0.638824	−0.319412	−	0.947616i	$-0.603485\pi$
$37$	−3.88581	−0.638824	−0.319412	+	0.947616i	$0.603485\pi$
$38$	−13.6272	−2.21063
$39$	0	0
$40$	−34.0110	−5.37761
$41$	10.5244	1.64363	0.821817	−	0.569752i	$-0.192961\pi$
$41$	10.5244	1.64363	0.821817	+	0.569752i	$0.192961\pi$
$42$	−2.80363	−0.432609
$43$	7.20767	1.09916	0.549579	−	0.835441i	$-0.314788\pi$
$43$	7.20767	1.09916	0.549579	+	0.835441i	$0.314788\pi$
$44$	17.6055	2.65413
$45$	−3.14248	−0.468454
$46$	15.0770	2.22298
$47$	−9.33384	−1.36148	−0.680741	−	0.732525i	$-0.738342\pi$
$47$	−9.33384	−1.36148	−0.680741	+	0.732525i	$0.738342\pi$
$48$	18.6229	2.68798
$49$	1.00000	0.142857
$50$	13.6683	1.93298
$51$	3.41447	0.478122
$52$	0	0
$53$	−13.1147	−1.80144	−0.900722	−	0.434395i	$-0.856962\pi$
$53$	−13.1147	−1.80144	−0.900722	+	0.434395i	$0.856962\pi$
$54$	2.80363	0.381526
$55$	−9.44058	−1.27297
$56$	−10.8230	−1.44628
$57$	−4.86056	−0.643797
$58$	2.38003	0.312513
$59$	1.45785	0.189797	0.0948983	−	0.995487i	$-0.469747\pi$
$59$	1.45785	0.189797	0.0948983	+	0.995487i	$0.469747\pi$
$60$	−18.4160	−2.37750
$61$	4.95821	0.634833	0.317417	−	0.948286i	$-0.397185\pi$
$61$	4.95821	0.634833	0.317417	+	0.948286i	$0.397185\pi$
$62$	1.26458	0.160602
$63$	−1.00000	−0.125988
$64$	48.4493	6.05617
$65$	0	0
$66$	8.42260	1.03675
$67$	4.57857	0.559361	0.279680	−	0.960093i	$-0.409771\pi$
$67$	4.57857	0.559361	0.279680	+	0.960093i	$0.409771\pi$
$68$	20.0100	2.42657
$69$	5.37767	0.647396
$70$	8.81036	1.05304
$71$	−2.36205	−0.280324	−0.140162	−	0.990129i	$-0.544762\pi$
$71$	−2.36205	−0.280324	−0.140162	+	0.990129i	$0.544762\pi$
$72$	10.8230	1.27550
$73$	1.24210	0.145377	0.0726887	−	0.997355i	$-0.476842\pi$
$73$	1.24210	0.145377	0.0726887	+	0.997355i	$0.476842\pi$
$74$	−10.8944	−1.26645
$75$	4.87520	0.562940
$76$	−28.4845	−3.26740
$77$	−3.00418	−0.342358
$78$	0	0
$79$	−7.10832	−0.799748	−0.399874	−	0.916570i	$-0.630946\pi$
$79$	−7.10832	−0.799748	−0.399874	+	0.916570i	$0.630946\pi$
$80$	−58.5222	−6.54298
$81$	1.00000	0.111111
$82$	29.5065	3.25845
$83$	5.04895	0.554195	0.277097	−	0.960842i	$-0.410628\pi$
$83$	5.04895	0.554195	0.277097	+	0.960842i	$0.410628\pi$
$84$	−5.86034	−0.639415
$85$	−10.7299	−1.16382
$86$	20.2076	2.17904
$87$	0.848910	0.0910127
$88$	32.5141	3.46601
$89$	−12.6846	−1.34456	−0.672282	−	0.740295i	$-0.734686\pi$
$89$	−12.6846	−1.34456	−0.672282	+	0.740295i	$0.734686\pi$
$90$	−8.81036	−0.928694
$91$	0	0
$92$	31.5150	3.28567
$93$	0.451052	0.0467719
$94$	−26.1686	−2.69909
$95$	15.2742	1.56710
$96$	30.5658	3.11961
$97$	−4.29846	−0.436442	−0.218221	−	0.975899i	$-0.570025\pi$
$97$	−4.29846	−0.436442	−0.218221	+	0.975899i	$0.570025\pi$
$98$	2.80363	0.283209
$99$	3.00418	0.301931
$100$	28.5703	2.85703
$101$	12.0756	1.20157	0.600784	−	0.799411i	$-0.294855\pi$
$101$	12.0756	1.20157	0.600784	+	0.799411i	$0.294855\pi$
$102$	9.57292	0.947861
$103$	−1.57289	−0.154981	−0.0774907	−	0.996993i	$-0.524691\pi$
$103$	−1.57289	−0.154981	−0.0774907	+	0.996993i	$0.524691\pi$
$104$	0	0
$105$	3.14248	0.306675
$106$	−36.7688	−3.57130
$107$	−12.2770	−1.18687	−0.593433	−	0.804884i	$-0.702228\pi$
$107$	−12.2770	−1.18687	−0.593433	+	0.804884i	$0.702228\pi$
$108$	5.86034	0.563911
$109$	−17.7042	−1.69576	−0.847879	−	0.530190i	$-0.822120\pi$
$109$	−17.7042	−1.69576	−0.847879	+	0.530190i	$0.822120\pi$
$110$	−26.4679	−2.52361
$111$	−3.88581	−0.368825
$112$	−18.6229	−1.75970
$113$	−7.67290	−0.721806	−0.360903	−	0.932603i	$-0.617531\pi$
$113$	−7.67290	−0.721806	−0.360903	+	0.932603i	$0.617531\pi$
$114$	−13.6272	−1.27631
$115$	−16.8993	−1.57586
$116$	4.97490	0.461908
$117$	0	0
$118$	4.08728	0.376265
$119$	−3.41447	−0.313004
$120$	−34.0110	−3.10476
$121$	−1.97492	−0.179538
$122$	13.9010	1.25854
$123$	10.5244	0.948952
$124$	2.64332	0.237377
$125$	0.392171	0.0350768
$126$	−2.80363	−0.249767
$127$	−15.0680	−1.33707	−0.668534	−	0.743682i	$-0.733078\pi$
$127$	−15.0680	−1.33707	−0.668534	+	0.743682i	$0.733078\pi$
$128$	74.7024	6.60283
$129$	7.20767	0.634600
$130$	0	0
$131$	−7.00728	−0.612229	−0.306114	−	0.951995i	$-0.599029\pi$
$131$	−7.00728	−0.612229	−0.306114	+	0.951995i	$0.599029\pi$
$132$	17.6055	1.53236
$133$	4.86056	0.421464
$134$	12.8366	1.10891
$135$	−3.14248	−0.270462
$136$	36.9547	3.16884
$137$	−12.3949	−1.05897	−0.529486	−	0.848319i	$-0.677615\pi$
$137$	−12.3949	−1.05897	−0.529486	+	0.848319i	$0.677615\pi$
$138$	15.0770	1.28344
$139$	−2.68693	−0.227903	−0.113951	−	0.993486i	$-0.536351\pi$
$139$	−2.68693	−0.227903	−0.113951	+	0.993486i	$0.536351\pi$
$140$	18.4160	1.55644
$141$	−9.33384	−0.786051
$142$	−6.62231	−0.555732
$143$	0	0
$144$	18.6229	1.55191
$145$	−2.66769	−0.221539
$146$	3.48240	0.288206
$147$	1.00000	0.0824786
$148$	−22.7722	−1.87186
$149$	2.60806	0.213660	0.106830	−	0.994277i	$-0.465930\pi$
$149$	2.60806	0.213660	0.106830	+	0.994277i	$0.465930\pi$
$150$	13.6683	1.11601
$151$	−5.13680	−0.418027	−0.209013	−	0.977913i	$-0.567025\pi$
$151$	−5.13680	−0.418027	−0.209013	+	0.977913i	$0.567025\pi$
$152$	−52.6056	−4.26688
$153$	3.41447	0.276044
$154$	−8.42260	−0.678712
$155$	−1.41742	−0.113850
$156$	0	0
$157$	10.8870	0.868874	0.434437	−	0.900702i	$-0.356947\pi$
$157$	10.8870	0.868874	0.434437	+	0.900702i	$0.356947\pi$
$158$	−19.9291	−1.58547
$159$	−13.1147	−1.04006
$160$	−96.0525	−7.59362
$161$	−5.37767	−0.423820
$162$	2.80363	0.220274
$163$	−2.53323	−0.198418	−0.0992088	−	0.995067i	$-0.531631\pi$
$163$	−2.53323	−0.198418	−0.0992088	+	0.995067i	$0.531631\pi$
$164$	61.6765	4.81612
$165$	−9.44058	−0.734948
$166$	14.1554	1.09867
$167$	1.10194	0.0852703	0.0426352	−	0.999091i	$-0.486425\pi$
$167$	1.10194	0.0852703	0.0426352	+	0.999091i	$0.486425\pi$
$168$	−10.8230	−0.835010
$169$	0	0
$170$	−30.0828	−2.30724
$171$	−4.86056	−0.371696
$172$	42.2394	3.22072
$173$	−22.0711	−1.67803	−0.839016	−	0.544107i	$-0.816868\pi$
$173$	−22.0711	−1.67803	−0.839016	+	0.544107i	$0.816868\pi$
$174$	2.38003	0.180430
$175$	−4.87520	−0.368531
$176$	55.9465	4.21712
$177$	1.45785	0.109579
$178$	−35.5629	−2.66555
$179$	7.20834	0.538777	0.269388	−	0.963032i	$-0.413178\pi$
$179$	7.20834	0.538777	0.269388	+	0.963032i	$0.413178\pi$
$180$	−18.4160	−1.37265
$181$	13.0966	0.973466	0.486733	−	0.873551i	$-0.338188\pi$
$181$	13.0966	0.973466	0.486733	+	0.873551i	$0.338188\pi$
$182$	0	0
$183$	4.95821	0.366521
$184$	58.2024	4.29073
$185$	12.2111	0.897778
$186$	1.26458	0.0927237
$187$	10.2577	0.750116
$188$	−54.6995	−3.98937
$189$	−1.00000	−0.0727393
$190$	42.8233	3.10673
$191$	24.5517	1.77650	0.888249	−	0.459363i	$-0.151922\pi$
$191$	24.5517	1.77650	0.888249	+	0.459363i	$0.151922\pi$
$192$	48.4493	3.49653
$193$	5.78789	0.416621	0.208311	−	0.978063i	$-0.433203\pi$
$193$	5.78789	0.416621	0.208311	+	0.978063i	$0.433203\pi$
$194$	−12.0513	−0.865232
$195$	0	0
$196$	5.86034	0.418596
$197$	0.0857381	0.00610859	0.00305429	−	0.999995i	$-0.499028\pi$
$197$	0.0857381	0.00610859	0.00305429	+	0.999995i	$0.499028\pi$
$198$	8.42260	0.598568
$199$	5.62060	0.398434	0.199217	−	0.979955i	$-0.436160\pi$
$199$	5.62060	0.398434	0.199217	+	0.979955i	$0.436160\pi$
$200$	52.7641	3.73099
$201$	4.57857	0.322947
$202$	33.8555	2.38207
$203$	−0.848910	−0.0595818
$204$	20.0100	1.40098
$205$	−33.0727	−2.30990
$206$	−4.40980	−0.307245
$207$	5.37767	0.373774
$208$	0	0
$209$	−14.6020	−1.01004
$210$	8.81036	0.607973
$211$	18.1162	1.24717	0.623587	−	0.781754i	$-0.285675\pi$
$211$	18.1162	1.24717	0.623587	+	0.781754i	$0.285675\pi$
$212$	−76.8567	−5.27854
$213$	−2.36205	−0.161845
$214$	−34.4203	−2.35292
$215$	−22.6500	−1.54472
$216$	10.8230	0.736409
$217$	−0.451052	−0.0306194
$218$	−49.6361	−3.36178
$219$	1.24210	0.0839336
$220$	−55.3250	−3.73001
$221$	0	0
$222$	−10.8944	−0.731183
$223$	5.32513	0.356597	0.178298	−	0.983976i	$-0.442941\pi$
$223$	5.32513	0.356597	0.178298	+	0.983976i	$0.442941\pi$
$224$	−30.5658	−2.04226
$225$	4.87520	0.325014
$226$	−21.5120	−1.43096
$227$	−22.2569	−1.47725	−0.738623	−	0.674119i	$-0.764523\pi$
$227$	−22.2569	−1.47725	−0.738623	+	0.674119i	$0.764523\pi$
$228$	−28.4845	−1.88643
$229$	−8.26095	−0.545899	−0.272949	−	0.962028i	$-0.587999\pi$
$229$	−8.26095	−0.545899	−0.272949	+	0.962028i	$0.587999\pi$
$230$	−47.3792	−3.12409
$231$	−3.00418	−0.197660
$232$	9.18772	0.603203
$233$	1.14151	0.0747825	0.0373913	−	0.999301i	$-0.488095\pi$
$233$	1.14151	0.0747825	0.0373913	+	0.999301i	$0.488095\pi$
$234$	0	0
$235$	29.3315	1.91337
$236$	8.54352	0.556136
$237$	−7.10832	−0.461735
$238$	−9.57292	−0.620520
$239$	−11.3967	−0.737190	−0.368595	−	0.929590i	$-0.620161\pi$
$239$	−11.3967	−0.737190	−0.368595	+	0.929590i	$0.620161\pi$
$240$	−58.5222	−3.77759
$241$	14.7693	0.951374	0.475687	−	0.879615i	$-0.342200\pi$
$241$	14.7693	0.951374	0.475687	+	0.879615i	$0.342200\pi$
$242$	−5.53695	−0.355929
$243$	1.00000	0.0641500
$244$	29.0568	1.86017
$245$	−3.14248	−0.200766
$246$	29.5065	1.88126
$247$	0	0
$248$	4.88172	0.309989
$249$	5.04895	0.319964
$250$	1.09950	0.0695386
$251$	13.8604	0.874858	0.437429	−	0.899253i	$-0.355889\pi$
$251$	13.8604	0.874858	0.437429	+	0.899253i	$0.355889\pi$
$252$	−5.86034	−0.369167
$253$	16.1555	1.01569
$254$	−42.2451	−2.65069
$255$	−10.7299	−0.671934
$256$	112.539	7.03371
$257$	−13.1717	−0.821630	−0.410815	−	0.911719i	$-0.634756\pi$
$257$	−13.1717	−0.821630	−0.410815	+	0.911719i	$0.634756\pi$
$258$	20.2076	1.25807
$259$	3.88581	0.241453
$260$	0	0
$261$	0.848910	0.0525462
$262$	−19.6458	−1.21372
$263$	−30.2616	−1.86601	−0.933006	−	0.359860i	$-0.882824\pi$
$263$	−30.2616	−1.86601	−0.933006	+	0.359860i	$0.882824\pi$
$264$	32.5141	2.00110
$265$	41.2128	2.53168
$266$	13.6272	0.835538
$267$	−12.6846	−0.776284
$268$	26.8320	1.63902
$269$	−24.4467	−1.49054	−0.745272	−	0.666760i	$-0.767680\pi$
$269$	−24.4467	−1.49054	−0.745272	+	0.666760i	$0.767680\pi$
$270$	−8.81036	−0.536181
$271$	−19.0695	−1.15839	−0.579193	−	0.815190i	$-0.696632\pi$
$271$	−19.0695	−1.15839	−0.579193	+	0.815190i	$0.696632\pi$
$272$	63.5874	3.85555
$273$	0	0
$274$	−34.7508	−2.09938
$275$	14.6460	0.883185
$276$	31.5150	1.89698
$277$	3.66058	0.219943	0.109971	−	0.993935i	$-0.464924\pi$
$277$	3.66058	0.219943	0.109971	+	0.993935i	$0.464924\pi$
$278$	−7.53316	−0.451809
$279$	0.451052	0.0270038
$280$	34.0110	2.03254
$281$	−8.89390	−0.530565	−0.265283	−	0.964171i	$-0.585465\pi$
$281$	−8.89390	−0.530565	−0.265283	+	0.964171i	$0.585465\pi$
$282$	−26.1686	−1.55832
$283$	−12.7960	−0.760646	−0.380323	−	0.924854i	$-0.624187\pi$
$283$	−12.7960	−0.760646	−0.380323	+	0.924854i	$0.624187\pi$
$284$	−13.8424	−0.821396
$285$	15.2742	0.904767
$286$	0	0
$287$	−10.5244	−0.621235
$288$	30.5658	1.80111
$289$	−5.34136	−0.314198
$290$	−7.47920	−0.439194
$291$	−4.29846	−0.251980
$292$	7.27915	0.425980
$293$	7.11839	0.415861	0.207930	−	0.978144i	$-0.433327\pi$
$293$	7.11839	0.415861	0.207930	+	0.978144i	$0.433327\pi$
$294$	2.80363	0.163511
$295$	−4.58128	−0.266733
$296$	−42.0560	−2.44446
$297$	3.00418	0.174320
$298$	7.31203	0.423574
$299$	0	0
$300$	28.5703	1.64951
$301$	−7.20767	−0.415443
$302$	−14.4017	−0.828724
$303$	12.0756	0.693726
$304$	−90.5177	−5.19155
$305$	−15.5811	−0.892170
$306$	9.57292	0.547248
$307$	26.1182	1.49065	0.745323	−	0.666704i	$-0.232295\pi$
$307$	26.1182	1.49065	0.745323	+	0.666704i	$0.232295\pi$
$308$	−17.6055	−1.00317
$309$	−1.57289	−0.0894786
$310$	−3.97393	−0.225704
$311$	23.4754	1.33117	0.665584	−	0.746323i	$-0.268183\pi$
$311$	23.4754	1.33117	0.665584	+	0.746323i	$0.268183\pi$
$312$	0	0
$313$	−17.0234	−0.962220	−0.481110	−	0.876660i	$-0.659766\pi$
$313$	−17.0234	−0.962220	−0.481110	+	0.876660i	$0.659766\pi$
$314$	30.5230	1.72251
$315$	3.14248	0.177059
$316$	−41.6572	−2.34340
$317$	−9.59342	−0.538820	−0.269410	−	0.963026i	$-0.586829\pi$
$317$	−9.59342	−0.538820	−0.269410	+	0.963026i	$0.586829\pi$
$318$	−36.7688	−2.06189
$319$	2.55028	0.142788
$320$	−152.251	−8.51110
$321$	−12.2770	−0.685237
$322$	−15.0770	−0.840209
$323$	−16.5963	−0.923440
$324$	5.86034	0.325574
$325$	0	0
$326$	−7.10223	−0.393356
$327$	−17.7042	−0.979046
$328$	113.905	6.28935
$329$	9.33384	0.514591
$330$	−26.4679	−1.45701
$331$	1.52112	0.0836084	0.0418042	−	0.999126i	$-0.486689\pi$
$331$	1.52112	0.0836084	0.0418042	+	0.999126i	$0.486689\pi$
$332$	29.5886	1.62388
$333$	−3.88581	−0.212941
$334$	3.08942	0.169045
$335$	−14.3881	−0.786104
$336$	−18.6229	−1.01596
$337$	28.2047	1.53641	0.768204	−	0.640206i	$-0.221151\pi$
$337$	28.2047	1.53641	0.768204	+	0.640206i	$0.221151\pi$
$338$	0	0
$339$	−7.67290	−0.416735
$340$	−62.8810	−3.41020
$341$	1.35504	0.0733795
$342$	−13.6272	−0.736875
$343$	−1.00000	−0.0539949
$344$	78.0083	4.20593
$345$	−16.8993	−0.909825
$346$	−61.8791	−3.32664
$347$	7.59551	0.407748	0.203874	−	0.978997i	$-0.434647\pi$
$347$	7.59551	0.407748	0.203874	+	0.978997i	$0.434647\pi$
$348$	4.97490	0.266683
$349$	33.9613	1.81791	0.908954	−	0.416896i	$-0.136882\pi$
$349$	33.9613	1.81791	0.908954	+	0.416896i	$0.136882\pi$
$350$	−13.6683	−0.730600
$351$	0	0
$352$	91.8250	4.89429
$353$	14.4675	0.770027	0.385013	−	0.922911i	$-0.374197\pi$
$353$	14.4675	0.770027	0.385013	+	0.922911i	$0.374197\pi$
$354$	4.08728	0.217237
$355$	7.42270	0.393956
$356$	−74.3360	−3.93980
$357$	−3.41447	−0.180713
$358$	20.2095	1.06811
$359$	−9.99212	−0.527364	−0.263682	−	0.964610i	$-0.584937\pi$
$359$	−9.99212	−0.527364	−0.263682	+	0.964610i	$0.584937\pi$
$360$	−34.0110	−1.79254
$361$	4.62504	0.243423
$362$	36.7181	1.92986
$363$	−1.97492	−0.103657
$364$	0	0
$365$	−3.90329	−0.204308
$366$	13.9010	0.726616
$367$	−19.5834	−1.02224	−0.511122	−	0.859508i	$-0.670770\pi$
$367$	−19.5834	−1.02224	−0.511122	+	0.859508i	$0.670770\pi$
$368$	100.148	5.22057
$369$	10.5244	0.547878
$370$	34.2354	1.77981
$371$	13.1147	0.680882
$372$	2.64332	0.137050
$373$	−3.57778	−0.185250	−0.0926252	−	0.995701i	$-0.529526\pi$
$373$	−3.57778	−0.185250	−0.0926252	+	0.995701i	$0.529526\pi$
$374$	28.7587	1.48708
$375$	0.392171	0.0202516
$376$	−101.020	−5.20970
$377$	0	0
$378$	−2.80363	−0.144203
$379$	−9.43289	−0.484535	−0.242268	−	0.970209i	$-0.577891\pi$
$379$	−9.43289	−0.484535	−0.242268	+	0.970209i	$0.577891\pi$
$380$	89.5122	4.59188
$381$	−15.0680	−0.771956
$382$	68.8338	3.52184
$383$	−18.2451	−0.932281	−0.466141	−	0.884711i	$-0.654356\pi$
$383$	−18.2451	−0.932281	−0.466141	+	0.884711i	$0.654356\pi$
$384$	74.7024	3.81214
$385$	9.44058	0.481136
$386$	16.2271	0.825938
$387$	7.20767	0.366386
$388$	−25.1904	−1.27885
$389$	7.06982	0.358454	0.179227	−	0.983808i	$-0.442640\pi$
$389$	7.06982	0.358454	0.179227	+	0.983808i	$0.442640\pi$
$390$	0	0
$391$	18.3619	0.928603
$392$	10.8230	0.546642
$393$	−7.00728	−0.353470
$394$	0.240378	0.0121101
$395$	22.3378	1.12394
$396$	17.6055	0.884709
$397$	−4.76261	−0.239029	−0.119514	−	0.992832i	$-0.538134\pi$
$397$	−4.76261	−0.239029	−0.119514	+	0.992832i	$0.538134\pi$
$398$	15.7581	0.789881
$399$	4.86056	0.243332
$400$	90.7904	4.53952
$401$	−32.3631	−1.61614	−0.808068	−	0.589090i	$-0.799487\pi$
$401$	−32.3631	−1.61614	−0.808068	+	0.589090i	$0.799487\pi$
$402$	12.8366	0.640232
$403$	0	0
$404$	70.7672	3.52080
$405$	−3.14248	−0.156151
$406$	−2.38003	−0.118119
$407$	−11.6737	−0.578642
$408$	36.9547	1.82953
$409$	−2.00033	−0.0989101	−0.0494550	−	0.998776i	$-0.515748\pi$
$409$	−2.00033	−0.0989101	−0.0494550	+	0.998776i	$0.515748\pi$
$410$	−92.7236	−4.57929
$411$	−12.3949	−0.611398
$412$	−9.21767	−0.454122
$413$	−1.45785	−0.0717363
$414$	15.0770	0.740994
$415$	−15.8662	−0.778844
$416$	0	0
$417$	−2.68693	−0.131580
$418$	−40.9385	−2.00237
$419$	−32.9805	−1.61120	−0.805601	−	0.592458i	$-0.798158\pi$
$419$	−32.9805	−1.61120	−0.805601	+	0.592458i	$0.798158\pi$
$420$	18.4160	0.898610
$421$	14.2283	0.693445	0.346723	−	0.937968i	$-0.387295\pi$
$421$	14.2283	0.693445	0.346723	+	0.937968i	$0.387295\pi$
$422$	50.7912	2.47248
$423$	−9.33384	−0.453827
$424$	−141.940	−6.89322
$425$	16.6463	0.807462
$426$	−6.62231	−0.320852
$427$	−4.95821	−0.239945
$428$	−71.9476	−3.47772
$429$	0	0
$430$	−63.5021	−3.06235
$431$	−23.9213	−1.15225	−0.576124	−	0.817362i	$-0.695436\pi$
$431$	−23.9213	−1.15225	−0.576124	+	0.817362i	$0.695436\pi$
$432$	18.6229	0.895995
$433$	30.3234	1.45725	0.728624	−	0.684914i	$-0.240160\pi$
$433$	30.3234	1.45725	0.728624	+	0.684914i	$0.240160\pi$
$434$	−1.26458	−0.0607019
$435$	−2.66769	−0.127906
$436$	−103.753	−4.96886
$437$	−26.1385	−1.25037
$438$	3.48240	0.166396
$439$	−11.7009	−0.558452	−0.279226	−	0.960225i	$-0.590078\pi$
$439$	−11.7009	−0.558452	−0.279226	+	0.960225i	$0.590078\pi$
$440$	−102.175	−4.87100
$441$	1.00000	0.0476190
$442$	0	0
$443$	5.05620	0.240227	0.120114	−	0.992760i	$-0.461674\pi$
$443$	5.05620	0.240227	0.120114	+	0.992760i	$0.461674\pi$
$444$	−22.7722	−1.08072
$445$	39.8611	1.88960
$446$	14.9297	0.706941
$447$	2.60806	0.123357
$448$	−48.4493	−2.28902
$449$	17.3705	0.819763	0.409882	−	0.912139i	$-0.365570\pi$
$449$	17.3705	0.819763	0.409882	+	0.912139i	$0.365570\pi$
$450$	13.6683	0.644328
$451$	31.6171	1.48879
$452$	−44.9658	−2.11501
$453$	−5.13680	−0.241348
$454$	−62.4002	−2.92859
$455$	0	0
$456$	−52.6056	−2.46349
$457$	34.5376	1.61560	0.807800	−	0.589456i	$-0.200658\pi$
$457$	34.5376	1.61560	0.807800	+	0.589456i	$0.200658\pi$
$458$	−23.1606	−1.08223
$459$	3.41447	0.159374
$460$	−99.0354	−4.61755
$461$	−11.1375	−0.518723	−0.259361	−	0.965780i	$-0.583512\pi$
$461$	−11.1375	−0.518723	−0.259361	+	0.965780i	$0.583512\pi$
$462$	−8.42260	−0.391855
$463$	−8.14843	−0.378690	−0.189345	−	0.981911i	$-0.560636\pi$
$463$	−8.14843	−0.378690	−0.189345	+	0.981911i	$0.560636\pi$
$464$	15.8092	0.733922
$465$	−1.41742	−0.0657314
$466$	3.20036	0.148254
$467$	14.8950	0.689258	0.344629	−	0.938739i	$-0.388005\pi$
$467$	14.8950	0.689258	0.344629	+	0.938739i	$0.388005\pi$
$468$	0	0
$469$	−4.57857	−0.211419
$470$	82.2345	3.79320
$471$	10.8870	0.501645
$472$	15.7783	0.726255
$473$	21.6531	0.995611
$474$	−19.9291	−0.915374
$475$	−23.6962	−1.08726
$476$	−20.0100	−0.917156
$477$	−13.1147	−0.600482
$478$	−31.9521	−1.46145
$479$	−13.3435	−0.609679	−0.304840	−	0.952404i	$-0.598603\pi$
$479$	−13.3435	−0.609679	−0.304840	+	0.952404i	$0.598603\pi$
$480$	−96.0525	−4.38418
$481$	0	0
$482$	41.4076	1.88607
$483$	−5.37767	−0.244693
$484$	−11.5737	−0.526078
$485$	13.5078	0.613359
$486$	2.80363	0.127175
$487$	−15.0870	−0.683657	−0.341828	−	0.939762i	$-0.611046\pi$
$487$	−15.0870	−0.683657	−0.341828	+	0.939762i	$0.611046\pi$
$488$	53.6625	2.42919
$489$	−2.53323	−0.114556
$490$	−8.81036	−0.398012
$491$	−18.6136	−0.840022	−0.420011	−	0.907519i	$-0.637974\pi$
$491$	−18.6136	−0.840022	−0.420011	+	0.907519i	$0.637974\pi$
$492$	61.6765	2.78059
$493$	2.89858	0.130546
$494$	0	0
$495$	−9.44058	−0.424322
$496$	8.39990	0.377166
$497$	2.36205	0.105952
$498$	14.1554	0.634318
$499$	−18.3295	−0.820543	−0.410272	−	0.911963i	$-0.634566\pi$
$499$	−18.3295	−0.820543	−0.410272	+	0.911963i	$0.634566\pi$
$500$	2.29825	0.102781
$501$	1.10194	0.0492308
$502$	38.8593	1.73438
$503$	−13.0416	−0.581495	−0.290748	−	0.956800i	$-0.593904\pi$
$503$	−13.0416	−0.581495	−0.290748	+	0.956800i	$0.593904\pi$
$504$	−10.8230	−0.482093
$505$	−37.9474	−1.68864
$506$	45.2940	2.01356
$507$	0	0
$508$	−88.3035	−3.91783
$509$	−17.0920	−0.757590	−0.378795	−	0.925481i	$-0.623661\pi$
$509$	−17.0920	−0.757590	−0.378795	+	0.925481i	$0.623661\pi$
$510$	−30.0828	−1.33209
$511$	−1.24210	−0.0549475
$512$	166.114	7.34126
$513$	−4.86056	−0.214599
$514$	−36.9287	−1.62885
$515$	4.94278	0.217805
$516$	42.2394	1.85948
$517$	−28.0405	−1.23322
$518$	10.8944	0.478672
$519$	−22.0711	−0.968812
$520$	0	0
$521$	−33.7225	−1.47741	−0.738705	−	0.674029i	$-0.764562\pi$
$521$	−33.7225	−1.47741	−0.738705	+	0.674029i	$0.764562\pi$
$522$	2.38003	0.104171
$523$	35.8559	1.56787	0.783934	−	0.620844i	$-0.213210\pi$
$523$	35.8559	1.56787	0.783934	+	0.620844i	$0.213210\pi$
$524$	−41.0650	−1.79393
$525$	−4.87520	−0.212771
$526$	−84.8424	−3.69930
$527$	1.54011	0.0670881
$528$	55.9465	2.43476
$529$	5.91938	0.257364
$530$	115.545	5.01897
$531$	1.45785	0.0632655
$532$	28.4845	1.23496
$533$	0	0
$534$	−35.5629	−1.53896
$535$	38.5804	1.66797
$536$	49.5537	2.14039
$537$	7.20834	0.311063
$538$	−68.5396	−2.95495
$539$	3.00418	0.129399
$540$	−18.4160	−0.792499
$541$	17.9589	0.772113	0.386056	−	0.922475i	$-0.373837\pi$
$541$	17.9589	0.772113	0.386056	+	0.922475i	$0.373837\pi$
$542$	−53.4637	−2.29646
$543$	13.0966	0.562031
$544$	104.366	4.47466
$545$	55.6352	2.38315
$546$	0	0
$547$	30.1484	1.28905	0.644526	−	0.764583i	$-0.277055\pi$
$547$	30.1484	1.28905	0.644526	+	0.764583i	$0.277055\pi$
$548$	−72.6386	−3.10297
$549$	4.95821	0.211611
$550$	41.0619	1.75088
$551$	−4.12618	−0.175781
$552$	58.2024	2.47726
$553$	7.10832	0.302276
$554$	10.2629	0.436029
$555$	12.2111	0.518333
$556$	−15.7463	−0.667793
$557$	13.5998	0.576243	0.288122	−	0.957594i	$-0.406969\pi$
$557$	13.5998	0.576243	0.288122	+	0.957594i	$0.406969\pi$
$558$	1.26458	0.0535341
$559$	0	0
$560$	58.5222	2.47301
$561$	10.2577	0.433080
$562$	−24.9352	−1.05183
$563$	11.4717	0.483475	0.241737	−	0.970342i	$-0.422283\pi$
$563$	11.4717	0.483475	0.241737	+	0.970342i	$0.422283\pi$
$564$	−54.6995	−2.30326
$565$	24.1120	1.01440
$566$	−35.8754	−1.50795
$567$	−1.00000	−0.0419961
$568$	−25.5644	−1.07266
$569$	10.7718	0.451578	0.225789	−	0.974176i	$-0.427504\pi$
$569$	10.7718	0.451578	0.225789	+	0.974176i	$0.427504\pi$
$570$	42.8233	1.79367
$571$	13.6895	0.572887	0.286443	−	0.958097i	$-0.407527\pi$
$571$	13.6895	0.572887	0.286443	+	0.958097i	$0.407527\pi$
$572$	0	0
$573$	24.5517	1.02566
$574$	−29.5065	−1.23158
$575$	26.2173	1.09334
$576$	48.4493	2.01872
$577$	31.9864	1.33161	0.665805	−	0.746126i	$-0.268088\pi$
$577$	31.9864	1.33161	0.665805	+	0.746126i	$0.268088\pi$
$578$	−14.9752	−0.622886
$579$	5.78789	0.240536
$580$	−15.6335	−0.649148
$581$	−5.04895	−0.209466
$582$	−12.0513	−0.499542
$583$	−39.3989	−1.63174
$584$	13.4432	0.556286
$585$	0	0
$586$	19.9573	0.824429
$587$	36.5126	1.50704	0.753519	−	0.657427i	$-0.228355\pi$
$587$	36.5126	1.50704	0.753519	+	0.657427i	$0.228355\pi$
$588$	5.86034	0.241676
$589$	−2.19237	−0.0903348
$590$	−12.8442	−0.528788
$591$	0.0857381	0.00352679
$592$	−72.3651	−2.97419
$593$	7.28387	0.299112	0.149556	−	0.988753i	$-0.452215\pi$
$593$	7.28387	0.299112	0.149556	+	0.988753i	$0.452215\pi$
$594$	8.42260	0.345583
$595$	10.7299	0.439884
$596$	15.2841	0.626061
$597$	5.62060	0.230036
$598$	0	0
$599$	46.1528	1.88575	0.942876	−	0.333144i	$-0.108110\pi$
$599$	46.1528	1.88575	0.942876	+	0.333144i	$0.108110\pi$
$600$	52.7641	2.15409
$601$	−24.4355	−0.996746	−0.498373	−	0.866963i	$-0.666069\pi$
$601$	−24.4355	−0.996746	−0.498373	+	0.866963i	$0.666069\pi$
$602$	−20.2076	−0.823602
$603$	4.57857	0.186454
$604$	−30.1034	−1.22489
$605$	6.20616	0.252316
$606$	33.8555	1.37529
$607$	−26.2738	−1.06642	−0.533210	−	0.845983i	$-0.679014\pi$
$607$	−26.2738	−1.06642	−0.533210	+	0.845983i	$0.679014\pi$
$608$	−148.567	−6.02518
$609$	−0.848910	−0.0343996
$610$	−43.6836	−1.76870
$611$	0	0
$612$	20.0100	0.808855
$613$	39.0382	1.57674	0.788370	−	0.615202i	$-0.210926\pi$
$613$	39.0382	1.57674	0.788370	+	0.615202i	$0.210926\pi$
$614$	73.2258	2.95515
$615$	−33.0727	−1.33362
$616$	−32.5141	−1.31003
$617$	−9.26856	−0.373138	−0.186569	−	0.982442i	$-0.559737\pi$
$617$	−9.26856	−0.373138	−0.186569	+	0.982442i	$0.559737\pi$
$618$	−4.40980	−0.177388
$619$	45.4890	1.82836	0.914179	−	0.405310i	$-0.132836\pi$
$619$	45.4890	1.82836	0.914179	+	0.405310i	$0.132836\pi$
$620$	−8.30658	−0.333600
$621$	5.37767	0.215799
$622$	65.8163	2.63899
$623$	12.6846	0.508197
$624$	0	0
$625$	−25.6084	−1.02434
$626$	−47.7273	−1.90757
$627$	−14.6020	−0.583147
$628$	63.8013	2.54595
$629$	−13.2680	−0.529030
$630$	8.81036	0.351013
$631$	20.9773	0.835092	0.417546	−	0.908656i	$-0.362890\pi$
$631$	20.9773	0.835092	0.417546	+	0.908656i	$0.362890\pi$
$632$	−76.9331	−3.06023
$633$	18.1162	0.720056
$634$	−26.8964	−1.06819
$635$	47.3509	1.87906
$636$	−76.8567	−3.04757
$637$	0	0
$638$	7.15003	0.283072
$639$	−2.36205	−0.0934412
$640$	−234.751	−9.27936
$641$	−11.4475	−0.452148	−0.226074	−	0.974110i	$-0.572589\pi$
$641$	−11.4475	−0.452148	−0.226074	+	0.974110i	$0.572589\pi$
$642$	−34.4203	−1.35846
$643$	−27.7242	−1.09334	−0.546668	−	0.837350i	$-0.684104\pi$
$643$	−27.7242	−1.09334	−0.546668	+	0.837350i	$0.684104\pi$
$644$	−31.5150	−1.24186
$645$	−22.6500	−0.891842
$646$	−46.5298	−1.83069
$647$	24.7236	0.971984	0.485992	−	0.873963i	$-0.338458\pi$
$647$	24.7236	0.971984	0.485992	+	0.873963i	$0.338458\pi$
$648$	10.8230	0.425166
$649$	4.37965	0.171916
$650$	0	0
$651$	−0.451052	−0.0176781
$652$	−14.8456	−0.581397
$653$	−12.2921	−0.481027	−0.240513	−	0.970646i	$-0.577316\pi$
$653$	−12.2921	−0.481027	−0.240513	+	0.970646i	$0.577316\pi$
$654$	−49.6361	−1.94092
$655$	22.0203	0.860402
$656$	195.995	7.65230
$657$	1.24210	0.0484591
$658$	26.1686	1.02016
$659$	43.4003	1.69063	0.845317	−	0.534265i	$-0.179411\pi$
$659$	43.4003	1.69063	0.845317	+	0.534265i	$0.179411\pi$
$660$	−55.3250	−2.15352
$661$	0.585779	0.0227841	0.0113921	−	0.999935i	$-0.496374\pi$
$661$	0.585779	0.0227841	0.0113921	+	0.999935i	$0.496374\pi$
$662$	4.26466	0.165751
$663$	0	0
$664$	54.6446	2.12062
$665$	−15.2742	−0.592309
$666$	−10.8944	−0.422149
$667$	4.56516	0.176764
$668$	6.45772	0.249857
$669$	5.32513	0.205881
$670$	−40.3388	−1.55842
$671$	14.8953	0.575028
$672$	−30.5658	−1.17910
$673$	−11.6662	−0.449698	−0.224849	−	0.974394i	$-0.572189\pi$
$673$	−11.6662	−0.449698	−0.224849	+	0.974394i	$0.572189\pi$
$674$	79.0755	3.04587
$675$	4.87520	0.187647
$676$	0	0
$677$	9.21779	0.354268	0.177134	−	0.984187i	$-0.443317\pi$
$677$	9.21779	0.354268	0.177134	+	0.984187i	$0.443317\pi$
$678$	−21.5120	−0.826163
$679$	4.29846	0.164960
$680$	−116.130	−4.45337
$681$	−22.2569	−0.852888
$682$	3.79903	0.145472
$683$	23.5144	0.899753	0.449876	−	0.893091i	$-0.351468\pi$
$683$	23.5144	0.899753	0.449876	+	0.893091i	$0.351468\pi$
$684$	−28.4845	−1.08913
$685$	38.9509	1.48824
$686$	−2.80363	−0.107043
$687$	−8.26095	−0.315175
$688$	134.228	5.11738
$689$	0	0
$690$	−47.3792	−1.80370
$691$	−6.30097	−0.239700	−0.119850	−	0.992792i	$-0.538241\pi$
$691$	−6.30097	−0.239700	−0.119850	+	0.992792i	$0.538241\pi$
$692$	−129.344	−4.91692
$693$	−3.00418	−0.114119
$694$	21.2950	0.808347
$695$	8.44364	0.320286
$696$	9.18772	0.348260
$697$	35.9353	1.36114
$698$	95.2150	3.60394
$699$	1.14151	0.0431757
$700$	−28.5703	−1.07986
$701$	25.9334	0.979492	0.489746	−	0.871865i	$-0.337090\pi$
$701$	25.9334	0.979492	0.489746	+	0.871865i	$0.337090\pi$
$702$	0	0
$703$	18.8872	0.712345
$704$	145.550	5.48564
$705$	29.3315	1.10469
$706$	40.5615	1.52655
$707$	−12.0756	−0.454150
$708$	8.54352	0.321085
$709$	44.7279	1.67979	0.839895	−	0.542748i	$-0.182616\pi$
$709$	44.7279	1.67979	0.839895	+	0.542748i	$0.182616\pi$
$710$	20.8105	0.781004
$711$	−7.10832	−0.266583
$712$	−137.285	−5.14496
$713$	2.42561	0.0908398
$714$	−9.57292	−0.358258
$715$	0	0
$716$	42.2433	1.57871
$717$	−11.3967	−0.425617
$718$	−28.0142	−1.04548
$719$	1.13604	0.0423672	0.0211836	−	0.999776i	$-0.493257\pi$
$719$	1.13604	0.0423672	0.0211836	+	0.999776i	$0.493257\pi$
$720$	−58.5222	−2.18099
$721$	1.57289	0.0585775
$722$	12.9669	0.482578
$723$	14.7693	0.549276
$724$	76.7508	2.85242
$725$	4.13861	0.153704
$726$	−5.53695	−0.205496
$727$	−41.7837	−1.54967	−0.774836	−	0.632162i	$-0.782168\pi$
$727$	−41.7837	−1.54967	−0.774836	+	0.632162i	$0.782168\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−10.9434	−0.405033
$731$	24.6104	0.910248
$732$	29.0568	1.07397
$733$	46.4593	1.71601	0.858006	−	0.513639i	$-0.171703\pi$
$733$	46.4593	1.71601	0.858006	+	0.513639i	$0.171703\pi$
$734$	−54.9046	−2.02656
$735$	−3.14248	−0.115912
$736$	164.373	6.05886
$737$	13.7548	0.506665
$738$	29.5065	1.08615
$739$	−5.69151	−0.209365	−0.104683	−	0.994506i	$-0.533383\pi$
$739$	−5.69151	−0.209365	−0.104683	+	0.994506i	$0.533383\pi$
$740$	71.5612	2.63064
$741$	0	0
$742$	36.7688	1.34983
$743$	3.88256	0.142437	0.0712186	−	0.997461i	$-0.477311\pi$
$743$	3.88256	0.142437	0.0712186	+	0.997461i	$0.477311\pi$
$744$	4.88172	0.178972
$745$	−8.19578	−0.300270
$746$	−10.0308	−0.367253
$747$	5.04895	0.184732
$748$	60.1135	2.19797
$749$	12.2770	0.448593
$750$	1.09950	0.0401481
$751$	−40.3197	−1.47129	−0.735644	−	0.677368i	$-0.763120\pi$
$751$	−40.3197	−1.47129	−0.735644	+	0.677368i	$0.763120\pi$
$752$	−173.823	−6.33868
$753$	13.8604	0.505100
$754$	0	0
$755$	16.1423	0.587479
$756$	−5.86034	−0.213138
$757$	9.61102	0.349319	0.174659	−	0.984629i	$-0.444118\pi$
$757$	9.61102	0.349319	0.174659	+	0.984629i	$0.444118\pi$
$758$	−26.4463	−0.960574
$759$	16.1555	0.586407
$760$	165.312	5.99651
$761$	30.1840	1.09417	0.547085	−	0.837077i	$-0.315738\pi$
$761$	30.1840	1.09417	0.547085	+	0.837077i	$0.315738\pi$
$762$	−42.2451	−1.53038
$763$	17.7042	0.640936
$764$	143.881	5.20544
$765$	−10.7299	−0.387941
$766$	−51.1525	−1.84822
$767$	0	0
$768$	112.539	4.06091
$769$	−10.8144	−0.389976	−0.194988	−	0.980806i	$-0.562467\pi$
$769$	−10.8144	−0.389976	−0.194988	+	0.980806i	$0.562467\pi$
$770$	26.4679	0.953836
$771$	−13.1717	−0.474368
$772$	33.9190	1.22077
$773$	−45.5987	−1.64007	−0.820036	−	0.572311i	$-0.806047\pi$
$773$	−45.5987	−1.64007	−0.820036	+	0.572311i	$0.806047\pi$
$774$	20.2076	0.726348
$775$	2.19897	0.0789894
$776$	−46.5220	−1.67004
$777$	3.88581	0.139403
$778$	19.8212	0.710623
$779$	−51.1544	−1.83280
$780$	0	0
$781$	−7.09601	−0.253915
$782$	51.4801	1.84092
$783$	0.848910	0.0303376
$784$	18.6229	0.665103
$785$	−34.2121	−1.22108
$786$	−19.6458	−0.700743
$787$	−32.4330	−1.15611	−0.578055	−	0.815997i	$-0.696188\pi$
$787$	−32.4330	−1.15611	−0.578055	+	0.815997i	$0.696188\pi$
$788$	0.502454	0.0178992
$789$	−30.2616	−1.07734
$790$	62.6268	2.22816
$791$	7.67290	0.272817
$792$	32.5141	1.15534
$793$	0	0
$794$	−13.3526	−0.473866
$795$	41.2128	1.46167
$796$	32.9386	1.16748
$797$	41.0287	1.45331	0.726656	−	0.687001i	$-0.241073\pi$
$797$	41.0287	1.45331	0.726656	+	0.687001i	$0.241073\pi$
$798$	13.6272	0.482398
$799$	−31.8702	−1.12749
$800$	149.014	5.26846
$801$	−12.6846	−0.448188
$802$	−90.7341	−3.20393
$803$	3.73150	0.131682
$804$	26.8320	0.946290
$805$	16.8993	0.595620
$806$	0	0
$807$	−24.4467	−0.860566
$808$	130.694	4.59779
$809$	−10.6632	−0.374898	−0.187449	−	0.982274i	$-0.560022\pi$
$809$	−10.6632	−0.374898	−0.187449	+	0.982274i	$0.560022\pi$
$810$	−8.81036	−0.309565
$811$	−5.60921	−0.196966	−0.0984831	−	0.995139i	$-0.531399\pi$
$811$	−5.60921	−0.196966	−0.0984831	+	0.995139i	$0.531399\pi$
$812$	−4.97490	−0.174585
$813$	−19.0695	−0.668795
$814$	−32.7286	−1.14714
$815$	7.96062	0.278848
$816$	63.5874	2.22600
$817$	−35.0333	−1.22566
$818$	−5.60819	−0.196086
$819$	0	0
$820$	−193.817	−6.76840
$821$	12.4008	0.432790	0.216395	−	0.976306i	$-0.430570\pi$
$821$	12.4008	0.432790	0.216395	+	0.976306i	$0.430570\pi$
$822$	−34.7508	−1.21207
$823$	23.9208	0.833827	0.416913	−	0.908946i	$-0.363112\pi$
$823$	23.9208	0.833827	0.416913	+	0.908946i	$0.363112\pi$
$824$	−17.0233	−0.593036
$825$	14.6460	0.509907
$826$	−4.08728	−0.142215
$827$	−2.10966	−0.0733600	−0.0366800	−	0.999327i	$-0.511678\pi$
$827$	−2.10966	−0.0733600	−0.0366800	+	0.999327i	$0.511678\pi$
$828$	31.5150	1.09522
$829$	47.4770	1.64895	0.824473	−	0.565901i	$-0.191472\pi$
$829$	47.4770	1.64895	0.824473	+	0.565901i	$0.191472\pi$
$830$	−44.4831	−1.54403
$831$	3.66058	0.126984
$832$	0	0
$833$	3.41447	0.118305
$834$	−7.53316	−0.260852
$835$	−3.46281	−0.119836
$836$	−85.5726	−2.95959
$837$	0.451052	0.0155906
$838$	−92.4651	−3.19415
$839$	−8.30337	−0.286664	−0.143332	−	0.989675i	$-0.545782\pi$
$839$	−8.30337	−0.286664	−0.143332	+	0.989675i	$0.545782\pi$
$840$	34.0110	1.17349
$841$	−28.2794	−0.975150
$842$	39.8909	1.37473
$843$	−8.89390	−0.306322
$844$	106.167	3.65443
$845$	0	0
$846$	−26.1686	−0.899696
$847$	1.97492	0.0678592
$848$	−244.234	−8.38703
$849$	−12.7960	−0.439159
$850$	46.6699	1.60077
$851$	−20.8966	−0.716327
$852$	−13.8424	−0.474233
$853$	5.14634	0.176207	0.0881036	−	0.996111i	$-0.471919\pi$
$853$	5.14634	0.176207	0.0881036	+	0.996111i	$0.471919\pi$
$854$	−13.9010	−0.475682
$855$	15.2742	0.522368
$856$	−132.874	−4.54153
$857$	6.25760	0.213756	0.106878	−	0.994272i	$-0.465915\pi$
$857$	6.25760	0.213756	0.106878	+	0.994272i	$0.465915\pi$
$858$	0	0
$859$	−4.10387	−0.140022	−0.0700112	−	0.997546i	$-0.522304\pi$
$859$	−4.10387	−0.140022	−0.0700112	+	0.997546i	$0.522304\pi$
$860$	−132.737	−4.52628
$861$	−10.5244	−0.358670
$862$	−67.0665	−2.28429
$863$	−37.8902	−1.28980	−0.644899	−	0.764268i	$-0.723101\pi$
$863$	−37.8902	−1.28980	−0.644899	+	0.764268i	$0.723101\pi$
$864$	30.5658	1.03987
$865$	69.3579	2.35824
$866$	85.0155	2.88895
$867$	−5.34136	−0.181402
$868$	−2.64332	−0.0897201
$869$	−21.3546	−0.724407
$870$	−7.47920	−0.253569
$871$	0	0
$872$	−191.612	−6.48881
$873$	−4.29846	−0.145481
$874$	−73.2827	−2.47882
$875$	−0.392171	−0.0132578
$876$	7.27915	0.245940
$877$	55.7199	1.88153	0.940764	−	0.339063i	$-0.110110\pi$
$877$	55.7199	1.88153	0.940764	+	0.339063i	$0.110110\pi$
$878$	−32.8049	−1.10711
$879$	7.11839	0.240097
$880$	−175.811	−5.92658
$881$	−34.4048	−1.15913	−0.579564	−	0.814927i	$-0.696777\pi$
$881$	−34.4048	−1.15913	−0.579564	+	0.814927i	$0.696777\pi$
$882$	2.80363	0.0944031
$883$	−36.9973	−1.24506	−0.622529	−	0.782597i	$-0.713895\pi$
$883$	−36.9973	−1.24506	−0.622529	+	0.782597i	$0.713895\pi$
$884$	0	0
$885$	−4.58128	−0.153998
$886$	14.1757	0.476242
$887$	−55.3301	−1.85780	−0.928902	−	0.370325i	$-0.879246\pi$
$887$	−55.3301	−1.85780	−0.928902	+	0.370325i	$0.879246\pi$
$888$	−42.0560	−1.41131
$889$	15.0680	0.505364
$890$	111.756	3.74606
$891$	3.00418	0.100644
$892$	31.2070	1.04489
$893$	45.3677	1.51817
$894$	7.31203	0.244551
$895$	−22.6521	−0.757176
$896$	−74.7024	−2.49563
$897$	0	0
$898$	48.7004	1.62515
$899$	0.382903	0.0127705
$900$	28.5703	0.952345
$901$	−44.7799	−1.49183
$902$	88.6427	2.95148
$903$	−7.20767	−0.239856
$904$	−83.0435	−2.76199
$905$	−41.1560	−1.36807
$906$	−14.4017	−0.478464
$907$	12.5397	0.416375	0.208188	−	0.978089i	$-0.433243\pi$
$907$	12.5397	0.416375	0.208188	+	0.978089i	$0.433243\pi$
$908$	−130.433	−4.32858
$909$	12.0756	0.400523
$910$	0	0
$911$	−11.4861	−0.380552	−0.190276	−	0.981731i	$-0.560938\pi$
$911$	−11.4861	−0.380552	−0.190276	+	0.981731i	$0.560938\pi$
$912$	−90.5177	−2.99734
$913$	15.1679	0.501986
$914$	96.8306	3.20287
$915$	−15.5811	−0.515095
$916$	−48.4120	−1.59958
$917$	7.00728	0.231401
$918$	9.57292	0.315954
$919$	33.9296	1.11924	0.559618	−	0.828751i	$-0.310948\pi$
$919$	33.9296	1.11924	0.559618	+	0.828751i	$0.310948\pi$
$920$	−182.900	−6.03003
$921$	26.1182	0.860624
$922$	−31.2253	−1.02835
$923$	0	0
$924$	−17.6055	−0.579178
$925$	−18.9441	−0.622879
$926$	−22.8452	−0.750739
$927$	−1.57289	−0.0516605
$928$	25.9476	0.851772
$929$	50.4939	1.65665	0.828326	−	0.560247i	$-0.189294\pi$
$929$	50.4939	1.65665	0.828326	+	0.560247i	$0.189294\pi$
$930$	−3.97393	−0.130310
$931$	−4.86056	−0.159298
$932$	6.68961	0.219125
$933$	23.4754	0.768550
$934$	41.7601	1.36643
$935$	−32.2346	−1.05418
$936$	0	0
$937$	14.7689	0.482478	0.241239	−	0.970466i	$-0.422446\pi$
$937$	14.7689	0.482478	0.241239	+	0.970466i	$0.422446\pi$
$938$	−12.8366	−0.419130
$939$	−17.0234	−0.555538
$940$	171.892	5.60651
$941$	−30.1402	−0.982544	−0.491272	−	0.871006i	$-0.663468\pi$
$941$	−30.1402	−0.982544	−0.491272	+	0.871006i	$0.663468\pi$
$942$	30.5230	0.994493
$943$	56.5967	1.84304
$944$	27.1495	0.883640
$945$	3.14248	0.102225
$946$	60.7073	1.97376
$947$	27.1523	0.882331	0.441165	−	0.897426i	$-0.354565\pi$
$947$	27.1523	0.882331	0.441165	+	0.897426i	$0.354565\pi$
$948$	−41.6572	−1.35296
$949$	0	0
$950$	−66.4354	−2.15545
$951$	−9.59342	−0.311088
$952$	−36.9547	−1.19771
$953$	−19.0337	−0.616560	−0.308280	−	0.951296i	$-0.599753\pi$
$953$	−19.0337	−0.616560	−0.308280	+	0.951296i	$0.599753\pi$
$954$	−36.7688	−1.19043
$955$	−77.1533	−2.49662
$956$	−66.7884	−2.16009
$957$	2.55028	0.0824387
$958$	−37.4102	−1.20867
$959$	12.3949	0.400254
$960$	−152.251	−4.91389
$961$	−30.7966	−0.993437
$962$	0	0
$963$	−12.2770	−0.395622
$964$	86.5530	2.78769
$965$	−18.1883	−0.585504
$966$	−15.0770	−0.485095
$967$	2.60639	0.0838158	0.0419079	−	0.999121i	$-0.486656\pi$
$967$	2.60639	0.0838158	0.0419079	+	0.999121i	$0.486656\pi$
$968$	−21.3745	−0.687003
$969$	−16.5963	−0.533149
$970$	37.8710	1.21596
$971$	38.7695	1.24417	0.622086	−	0.782949i	$-0.286286\pi$
$971$	38.7695	1.24417	0.622086	+	0.782949i	$0.286286\pi$
$972$	5.86034	0.187970
$973$	2.68693	0.0861391
$974$	−42.2983	−1.35533
$975$	0	0
$976$	92.3362	2.95561
$977$	−41.1599	−1.31682	−0.658411	−	0.752658i	$-0.728771\pi$
$977$	−41.1599	−1.31682	−0.658411	+	0.752658i	$0.728771\pi$
$978$	−7.10223	−0.227104
$979$	−38.1067	−1.21790
$980$	−18.4160	−0.588278
$981$	−17.7042	−0.565252
$982$	−52.1857	−1.66531
$983$	−8.61935	−0.274914	−0.137457	−	0.990508i	$-0.543893\pi$
$983$	−8.61935	−0.274914	−0.137457	+	0.990508i	$0.543893\pi$
$984$	113.905	3.63116
$985$	−0.269431	−0.00858477
$986$	8.12655	0.258802
$987$	9.33384	0.297100
$988$	0	0
$989$	38.7605	1.23251
$990$	−26.4679	−0.841204
$991$	32.1624	1.02167	0.510835	−	0.859679i	$-0.329336\pi$
$991$	32.1624	1.02167	0.510835	+	0.859679i	$0.329336\pi$
$992$	13.7868	0.437730
$993$	1.52112	0.0482714
$994$	6.62231	0.210047
$995$	−17.6626	−0.559943
$996$	29.5886	0.937550
$997$	−28.8875	−0.914876	−0.457438	−	0.889242i	$-0.651233\pi$
$997$	−28.8875	−0.914876	−0.457438	+	0.889242i	$0.651233\pi$
$998$	−51.3893	−1.62670
$999$	−3.88581	−0.122942

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bh.1.15	yes	15
13.12	even	2		3549.2.a.bg.1.1	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.bg.1.1	✓	15	13.12	even	2
3549.2.a.bh.1.15	yes	15	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:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q+2.80363 q^{2} +1.00000 q^{3} +5.86034 q^{4} -3.14248 q^{5} +2.80363 q^{6} -1.00000 q^{7} +10.8230 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.80363 q^{2} +1.00000 q^{3} +5.86034 q^{4} -3.14248 q^{5} +2.80363 q^{6} -1.00000 q^{7} +10.8230 q^{8} +1.00000 q^{9} -8.81036 q^{10} +3.00418 q^{11} +5.86034 q^{12} -2.80363 q^{14} -3.14248 q^{15} +18.6229 q^{16} +3.41447 q^{17} +2.80363 q^{18} -4.86056 q^{19} -18.4160 q^{20} -1.00000 q^{21} +8.42260 q^{22} +5.37767 q^{23} +10.8230 q^{24} +4.87520 q^{25} +1.00000 q^{27} -5.86034 q^{28} +0.848910 q^{29} -8.81036 q^{30} +0.451052 q^{31} +30.5658 q^{32} +3.00418 q^{33} +9.57292 q^{34} +3.14248 q^{35} +5.86034 q^{36} -3.88581 q^{37} -13.6272 q^{38} -34.0110 q^{40} +10.5244 q^{41} -2.80363 q^{42} +7.20767 q^{43} +17.6055 q^{44} -3.14248 q^{45} +15.0770 q^{46} -9.33384 q^{47} +18.6229 q^{48} +1.00000 q^{49} +13.6683 q^{50} +3.41447 q^{51} -13.1147 q^{53} +2.80363 q^{54} -9.44058 q^{55} -10.8230 q^{56} -4.86056 q^{57} +2.38003 q^{58} +1.45785 q^{59} -18.4160 q^{60} +4.95821 q^{61} +1.26458 q^{62} -1.00000 q^{63} +48.4493 q^{64} +8.42260 q^{66} +4.57857 q^{67} +20.0100 q^{68} +5.37767 q^{69} +8.81036 q^{70} -2.36205 q^{71} +10.8230 q^{72} +1.24210 q^{73} -10.8944 q^{74} +4.87520 q^{75} -28.4845 q^{76} -3.00418 q^{77} -7.10832 q^{79} -58.5222 q^{80} +1.00000 q^{81} +29.5065 q^{82} +5.04895 q^{83} -5.86034 q^{84} -10.7299 q^{85} +20.2076 q^{86} +0.848910 q^{87} +32.5141 q^{88} -12.6846 q^{89} -8.81036 q^{90} +31.5150 q^{92} +0.451052 q^{93} -26.1686 q^{94} +15.2742 q^{95} +30.5658 q^{96} -4.29846 q^{97} +2.80363 q^{98} +3.00418 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) \) 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

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