LMFDB - Embedded newform 935.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [935,2,Mod(1,935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(935, 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("935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 935 = 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	935.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:	$7.46601258899$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.321.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 1 $ x^3 - x^2 - 4*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.239123$ of defining polynomial
Character	$\chi$	$=$	935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.239123 q^{2} +0.239123 q^{3} -1.94282 q^{4} -1.00000 q^{5} +0.0571799 q^{6} -0.942820 q^{8} -2.94282 q^{9} +O(q^{10})$	\(q+0.239123 q^{2} +0.239123 q^{3} -1.94282 q^{4} -1.00000 q^{5} +0.0571799 q^{6} -0.942820 q^{8} -2.94282 q^{9} -0.239123 q^{10} -1.00000 q^{11} -0.464574 q^{12} +2.70370 q^{13} -0.239123 q^{15} +3.66019 q^{16} +1.00000 q^{17} -0.703697 q^{18} +6.84213 q^{19} +1.94282 q^{20} -0.239123 q^{22} +2.89931 q^{23} -0.225450 q^{24} +1.00000 q^{25} +0.646517 q^{26} -1.42107 q^{27} +1.94282 q^{29} -0.0571799 q^{30} +8.84213 q^{31} +2.76088 q^{32} -0.239123 q^{33} +0.239123 q^{34} +5.71737 q^{36} -3.66019 q^{37} +1.63611 q^{38} +0.646517 q^{39} +0.942820 q^{40} +3.64652 q^{41} +3.28263 q^{43} +1.94282 q^{44} +2.94282 q^{45} +0.693293 q^{46} -7.88564 q^{47} +0.875237 q^{48} -7.00000 q^{49} +0.239123 q^{50} +0.239123 q^{51} -5.25280 q^{52} +2.36389 q^{53} -0.339810 q^{54} +1.00000 q^{55} +1.63611 q^{57} +0.464574 q^{58} -8.70370 q^{59} +0.464574 q^{60} +10.2255 q^{61} +2.11436 q^{62} -6.66019 q^{64} -2.70370 q^{65} -0.0571799 q^{66} +13.8856 q^{67} -1.94282 q^{68} +0.693293 q^{69} -0.363887 q^{71} +2.77455 q^{72} +4.11436 q^{73} -0.875237 q^{74} +0.239123 q^{75} -13.2930 q^{76} +0.154597 q^{78} +5.28263 q^{79} -3.66019 q^{80} +8.48865 q^{81} +0.871967 q^{82} +15.5458 q^{83} -1.00000 q^{85} +0.784953 q^{86} +0.464574 q^{87} +0.942820 q^{88} +0.353483 q^{89} +0.703697 q^{90} -5.63284 q^{92} +2.11436 q^{93} -1.88564 q^{94} -6.84213 q^{95} +0.660190 q^{96} -15.1488 q^{97} -1.67386 q^{98} +2.94282 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + q^{3} + 3 q^{4} - 3 q^{5} + 9 q^{6} + 6 q^{8}+O(q^{10}) $ 3 * q + q^2 + q^3 + 3 * q^4 - 3 * q^5 + 9 * q^6 + 6 * q^8	$ 3 q + q^{2} + q^{3} + 3 q^{4} - 3 q^{5} + 9 q^{6} + 6 q^{8} - q^{10} - 3 q^{11} + 8 q^{12} - q^{13} - q^{15} + 3 q^{16} + 3 q^{17} + 7 q^{18} + 4 q^{19} - 3 q^{20} - q^{22} + q^{23} + 9 q^{24} + 3 q^{25} - 16 q^{26} + 4 q^{27} - 3 q^{29} - 9 q^{30} + 10 q^{31} + 8 q^{32} - q^{33} + q^{34} + 18 q^{36} - 3 q^{37} + 22 q^{38} - 16 q^{39} - 6 q^{40} - 7 q^{41} + 9 q^{43} - 3 q^{44} + 28 q^{46} - 6 q^{47} + 20 q^{48} - 21 q^{49} + q^{50} + q^{51} - 26 q^{52} - 10 q^{53} - 9 q^{54} + 3 q^{55} + 22 q^{57} - 8 q^{58} - 17 q^{59} - 8 q^{60} + 21 q^{61} + 24 q^{62} - 12 q^{64} + q^{65} - 9 q^{66} + 24 q^{67} + 3 q^{68} + 28 q^{69} + 16 q^{71} + 18 q^{72} + 30 q^{73} - 20 q^{74} + q^{75} - 4 q^{76} - 28 q^{78} + 15 q^{79} - 3 q^{80} - 9 q^{81} - 25 q^{82} + 21 q^{83} - 3 q^{85} - 23 q^{86} - 8 q^{87} - 6 q^{88} + 19 q^{89} - 7 q^{90} + 11 q^{92} + 24 q^{93} + 12 q^{94} - 4 q^{95} - 6 q^{96} - 3 q^{97} - 7 q^{98}+O(q^{100}) $ 3 * q + q^2 + q^3 + 3 * q^4 - 3 * q^5 + 9 * q^6 + 6 * q^8 - q^10 - 3 * q^11 + 8 * q^12 - q^13 - q^15 + 3 * q^16 + 3 * q^17 + 7 * q^18 + 4 * q^19 - 3 * q^20 - q^22 + q^23 + 9 * q^24 + 3 * q^25 - 16 * q^26 + 4 * q^27 - 3 * q^29 - 9 * q^30 + 10 * q^31 + 8 * q^32 - q^33 + q^34 + 18 * q^36 - 3 * q^37 + 22 * q^38 - 16 * q^39 - 6 * q^40 - 7 * q^41 + 9 * q^43 - 3 * q^44 + 28 * q^46 - 6 * q^47 + 20 * q^48 - 21 * q^49 + q^50 + q^51 - 26 * q^52 - 10 * q^53 - 9 * q^54 + 3 * q^55 + 22 * q^57 - 8 * q^58 - 17 * q^59 - 8 * q^60 + 21 * q^61 + 24 * q^62 - 12 * q^64 + q^65 - 9 * q^66 + 24 * q^67 + 3 * q^68 + 28 * q^69 + 16 * q^71 + 18 * q^72 + 30 * q^73 - 20 * q^74 + q^75 - 4 * q^76 - 28 * q^78 + 15 * q^79 - 3 * q^80 - 9 * q^81 - 25 * q^82 + 21 * q^83 - 3 * q^85 - 23 * q^86 - 8 * q^87 - 6 * q^88 + 19 * q^89 - 7 * q^90 + 11 * q^92 + 24 * q^93 + 12 * q^94 - 4 * q^95 - 6 * q^96 - 3 * q^97 - 7 * q^98

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 $

$2$	0.239123	0.169086	0.0845428	−	0.996420i	$-0.473057\pi$
$2$	0.239123	0.169086	0.0845428	+	0.996420i	$0.473057\pi$
$3$	0.239123	0.138058	0.0690289	−	0.997615i	$-0.478010\pi$
$3$	0.239123	0.138058	0.0690289	+	0.997615i	$0.478010\pi$
$4$	−1.94282	−0.971410
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.0571799	0.0233436
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	−0.942820	−0.333337
$9$	−2.94282	−0.980940
$10$	−0.239123	−0.0756174
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.464574	−0.134111
$13$	2.70370	0.749871	0.374935	−	0.927051i	$-0.377665\pi$
$13$	2.70370	0.749871	0.374935	+	0.927051i	$0.377665\pi$
$14$	0	0
$15$	−0.239123	−0.0617414
$16$	3.66019	0.915047
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.703697	−0.165863
$19$	6.84213	1.56969	0.784847	−	0.619690i	$-0.212742\pi$
$19$	6.84213	1.56969	0.784847	+	0.619690i	$0.212742\pi$
$20$	1.94282	0.434428
$21$	0	0
$22$	−0.239123	−0.0509813
$23$	2.89931	0.604549	0.302274	−	0.953221i	$-0.402254\pi$
$23$	2.89931	0.604549	0.302274	+	0.953221i	$0.402254\pi$
$24$	−0.225450	−0.0460198
$25$	1.00000	0.200000
$26$	0.646517	0.126792
$27$	−1.42107	−0.273484
$28$	0	0
$29$	1.94282	0.360773	0.180386	−	0.983596i	$-0.442265\pi$
$29$	1.94282	0.360773	0.180386	+	0.983596i	$0.442265\pi$
$30$	−0.0571799	−0.0104396
$31$	8.84213	1.58809	0.794047	−	0.607856i	$-0.207970\pi$
$31$	8.84213	1.58809	0.794047	+	0.607856i	$0.207970\pi$
$32$	2.76088	0.488059
$33$	−0.239123	−0.0416260
$34$	0.239123	0.0410093
$35$	0	0
$36$	5.71737	0.952895
$37$	−3.66019	−0.601732	−0.300866	−	0.953667i	$-0.597276\pi$
$37$	−3.66019	−0.601732	−0.300866	+	0.953667i	$0.597276\pi$
$38$	1.63611	0.265413
$39$	0.646517	0.103526
$40$	0.942820	0.149073
$41$	3.64652	0.569490	0.284745	−	0.958603i	$-0.408091\pi$
$41$	3.64652	0.569490	0.284745	+	0.958603i	$0.408091\pi$
$42$	0	0
$43$	3.28263	0.500596	0.250298	−	0.968169i	$-0.419471\pi$
$43$	3.28263	0.500596	0.250298	+	0.968169i	$0.419471\pi$
$44$	1.94282	0.292891
$45$	2.94282	0.438690
$46$	0.693293	0.102221
$47$	−7.88564	−1.15024	−0.575119	−	0.818069i	$-0.695044\pi$
$47$	−7.88564	−1.15024	−0.575119	+	0.818069i	$0.695044\pi$
$48$	0.875237	0.126330
$49$	−7.00000	−1.00000
$50$	0.239123	0.0338171
$51$	0.239123	0.0334840
$52$	−5.25280	−0.728432
$53$	2.36389	0.324705	0.162352	−	0.986733i	$-0.448092\pi$
$53$	2.36389	0.324705	0.162352	+	0.986733i	$0.448092\pi$
$54$	−0.339810	−0.0462423
$55$	1.00000	0.134840
$56$	0	0
$57$	1.63611	0.216709
$58$	0.464574	0.0610015
$59$	−8.70370	−1.13312	−0.566562	−	0.824019i	$-0.691727\pi$
$59$	−8.70370	−1.13312	−0.566562	+	0.824019i	$0.691727\pi$
$60$	0.464574	0.0599762
$61$	10.2255	1.30923	0.654617	−	0.755960i	$-0.272830\pi$
$61$	10.2255	1.30923	0.654617	+	0.755960i	$0.272830\pi$
$62$	2.11436	0.268524
$63$	0	0
$64$	−6.66019	−0.832524
$65$	−2.70370	−0.335352
$66$	−0.0571799	−0.00703836
$67$	13.8856	1.69640	0.848200	−	0.529675i	$-0.177686\pi$
$67$	13.8856	1.69640	0.848200	+	0.529675i	$0.177686\pi$
$68$	−1.94282	−0.235602
$69$	0.693293	0.0834627
$70$	0	0
$71$	−0.363887	−0.0431854	−0.0215927	−	0.999767i	$-0.506874\pi$
$71$	−0.363887	−0.0431854	−0.0215927	+	0.999767i	$0.506874\pi$
$72$	2.77455	0.326984
$73$	4.11436	0.481549	0.240775	−	0.970581i	$-0.422599\pi$
$73$	4.11436	0.481549	0.240775	+	0.970581i	$0.422599\pi$
$74$	−0.875237	−0.101744
$75$	0.239123	0.0276116
$76$	−13.2930	−1.52482
$77$	0	0
$78$	0.154597	0.0175047
$79$	5.28263	0.594342	0.297171	−	0.954824i	$-0.403957\pi$
$79$	5.28263	0.594342	0.297171	+	0.954824i	$0.403957\pi$
$80$	−3.66019	−0.409222
$81$	8.48865	0.943183
$82$	0.871967	0.0962927
$83$	15.5458	1.70638	0.853188	−	0.521603i	$-0.174666\pi$
$83$	15.5458	1.70638	0.853188	+	0.521603i	$0.174666\pi$
$84$	0	0
$85$	−1.00000	−0.108465
$86$	0.784953	0.0846437
$87$	0.464574	0.0498075
$88$	0.942820	0.100505
$89$	0.353483	0.0374691	0.0187346	−	0.999824i	$-0.494036\pi$
$89$	0.353483	0.0374691	0.0187346	+	0.999824i	$0.494036\pi$
$90$	0.703697	0.0741762
$91$	0	0
$92$	−5.63284	−0.587265
$93$	2.11436	0.219249
$94$	−1.88564	−0.194489
$95$	−6.84213	−0.701988
$96$	0.660190	0.0673803
$97$	−15.1488	−1.53813	−0.769066	−	0.639170i	$-0.779278\pi$
$97$	−15.1488	−1.53813	−0.769066	+	0.639170i	$0.779278\pi$
$98$	−1.67386	−0.169086
$99$	2.94282	0.295765
$100$	−1.94282	−0.194282
$101$	−2.47825	−0.246595	−0.123297	−	0.992370i	$-0.539347\pi$
$101$	−2.47825	−0.246595	−0.123297	+	0.992370i	$0.539347\pi$
$102$	0.0571799	0.00566166
$103$	−10.7278	−1.05704	−0.528519	−	0.848921i	$-0.677253\pi$
$103$	−10.7278	−1.05704	−0.528519	+	0.848921i	$0.677253\pi$
$104$	−2.54910	−0.249960
$105$	0	0
$106$	0.565260	0.0549029
$107$	9.20602	0.889980	0.444990	−	0.895536i	$-0.353207\pi$
$107$	9.20602	0.889980	0.444990	+	0.895536i	$0.353207\pi$
$108$	2.76088	0.265665
$109$	0.603010	0.0577579	0.0288789	−	0.999583i	$-0.490806\pi$
$109$	0.603010	0.0577579	0.0288789	+	0.999583i	$0.490806\pi$
$110$	0.239123	0.0227995
$111$	−0.875237	−0.0830738
$112$	0	0
$113$	9.29630	0.874523	0.437261	−	0.899334i	$-0.355948\pi$
$113$	9.29630	0.874523	0.437261	+	0.899334i	$0.355948\pi$
$114$	0.391233	0.0366423
$115$	−2.89931	−0.270362
$116$	−3.77455	−0.350458
$117$	−7.95649	−0.735578
$118$	−2.08126	−0.191595
$119$	0	0
$120$	0.225450	0.0205807
$121$	1.00000	0.0909091
$122$	2.44514	0.221373
$123$	0.871967	0.0786226
$124$	−17.1787	−1.54269
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−1.94282	−0.172397	−0.0861987	−	0.996278i	$-0.527472\pi$
$127$	−1.94282	−0.172397	−0.0861987	+	0.996278i	$0.527472\pi$
$128$	−7.11436	−0.628827
$129$	0.784953	0.0691113
$130$	−0.646517	−0.0567033
$131$	−18.1592	−1.58658	−0.793290	−	0.608844i	$-0.791634\pi$
$131$	−18.1592	−1.58658	−0.793290	+	0.608844i	$0.791634\pi$
$132$	0.464574	0.0404359
$133$	0	0
$134$	3.32038	0.286837
$135$	1.42107	0.122306
$136$	−0.942820	−0.0808462
$137$	9.97265	0.852021	0.426011	−	0.904718i	$-0.359919\pi$
$137$	9.97265	0.852021	0.426011	+	0.904718i	$0.359919\pi$
$138$	0.165783	0.0141123
$139$	−16.4750	−1.39739	−0.698695	−	0.715420i	$-0.746235\pi$
$139$	−16.4750	−1.39739	−0.698695	+	0.715420i	$0.746235\pi$
$140$	0	0
$141$	−1.88564	−0.158800
$142$	−0.0870138	−0.00730203
$143$	−2.70370	−0.226094
$144$	−10.7713	−0.897607
$145$	−1.94282	−0.161342
$146$	0.983839	0.0814231
$147$	−1.67386	−0.138058
$148$	7.11109	0.584528
$149$	10.8148	0.885982	0.442991	−	0.896526i	$-0.353917\pi$
$149$	10.8148	0.885982	0.442991	+	0.896526i	$0.353917\pi$
$150$	0.0571799	0.00466872
$151$	12.1625	0.989771	0.494886	−	0.868958i	$-0.335210\pi$
$151$	12.1625	0.989771	0.494886	+	0.868958i	$0.335210\pi$
$152$	−6.45090	−0.523237
$153$	−2.94282	−0.237913
$154$	0	0
$155$	−8.84213	−0.710217
$156$	−1.25607	−0.100566
$157$	21.6569	1.72841	0.864205	−	0.503140i	$-0.167822\pi$
$157$	21.6569	1.72841	0.864205	+	0.503140i	$0.167822\pi$
$158$	1.26320	0.100495
$159$	0.565260	0.0448281
$160$	−2.76088	−0.218266
$161$	0	0
$162$	2.02983	0.159479
$163$	−9.71410	−0.760867	−0.380434	−	0.924808i	$-0.624225\pi$
$163$	−9.71410	−0.760867	−0.380434	+	0.924808i	$0.624225\pi$
$164$	−7.08453	−0.553209
$165$	0.239123	0.0186157
$166$	3.71737	0.288524
$167$	14.2495	1.10266	0.551331	−	0.834287i	$-0.314120\pi$
$167$	14.2495	1.10266	0.551331	+	0.834287i	$0.314120\pi$
$168$	0	0
$169$	−5.69002	−0.437694
$170$	−0.239123	−0.0183399
$171$	−20.1352	−1.53977
$172$	−6.37756	−0.486284
$173$	−5.60877	−0.426427	−0.213213	−	0.977006i	$-0.568393\pi$
$173$	−5.60877	−0.426427	−0.213213	+	0.977006i	$0.568393\pi$
$174$	0.111090	0.00842174
$175$	0	0
$176$	−3.66019	−0.275897
$177$	−2.08126	−0.156437
$178$	0.0845261	0.00633550
$179$	−8.50808	−0.635924	−0.317962	−	0.948103i	$-0.602998\pi$
$179$	−8.50808	−0.635924	−0.317962	+	0.948103i	$0.602998\pi$
$180$	−5.71737	−0.426148
$181$	4.20137	0.312286	0.156143	−	0.987734i	$-0.450094\pi$
$181$	4.20137	0.312286	0.156143	+	0.987734i	$0.450094\pi$
$182$	0	0
$183$	2.44514	0.180750
$184$	−2.73353	−0.201519
$185$	3.66019	0.269103
$186$	0.505593	0.0370719
$187$	−1.00000	−0.0731272
$188$	15.3204	1.11735
$189$	0	0
$190$	−1.63611	−0.118696
$191$	0.736800	0.0533130	0.0266565	−	0.999645i	$-0.491514\pi$
$191$	0.736800	0.0533130	0.0266565	+	0.999645i	$0.491514\pi$
$192$	−1.59261	−0.114936
$193$	1.15787	0.0833451	0.0416725	−	0.999131i	$-0.486731\pi$
$193$	1.15787	0.0833451	0.0416725	+	0.999131i	$0.486731\pi$
$194$	−3.62244	−0.260076
$195$	−0.646517	−0.0462980
$196$	13.5997	0.971410
$197$	−18.8421	−1.34245	−0.671223	−	0.741255i	$-0.734231\pi$
$197$	−18.8421	−1.34245	−0.671223	+	0.741255i	$0.734231\pi$
$198$	0.703697	0.0500096
$199$	17.4074	1.23398	0.616989	−	0.786972i	$-0.288352\pi$
$199$	17.4074	1.23398	0.616989	+	0.786972i	$0.288352\pi$
$200$	−0.942820	−0.0666674
$201$	3.32038	0.234202
$202$	−0.592606	−0.0416956
$203$	0	0
$204$	−0.464574	−0.0325267
$205$	−3.64652	−0.254684
$206$	−2.56526	−0.178730
$207$	−8.53216	−0.593026
$208$	9.89604	0.686167
$209$	−6.84213	−0.473280
$210$	0	0
$211$	1.57893	0.108698	0.0543491	−	0.998522i	$-0.482692\pi$
$211$	1.57893	0.108698	0.0543491	+	0.998522i	$0.482692\pi$
$212$	−4.59261	−0.315422
$213$	−0.0870138	−0.00596209
$214$	2.20137	0.150483
$215$	−3.28263	−0.223874
$216$	1.33981	0.0911625
$217$	0	0
$218$	0.144194	0.00976603
$219$	0.983839	0.0664817
$220$	−1.94282	−0.130985
$221$	2.70370	0.181870
$222$	−0.209289	−0.0140466
$223$	25.0917	1.68026	0.840131	−	0.542384i	$-0.182478\pi$
$223$	25.0917	1.68026	0.840131	+	0.542384i	$0.182478\pi$
$224$	0	0
$225$	−2.94282	−0.196188
$226$	2.22296	0.147869
$227$	11.6569	0.773697	0.386848	−	0.922143i	$-0.373564\pi$
$227$	11.6569	0.773697	0.386848	+	0.922143i	$0.373564\pi$
$228$	−3.17867	−0.210513
$229$	−8.12476	−0.536899	−0.268450	−	0.963294i	$-0.586511\pi$
$229$	−8.12476	−0.536899	−0.268450	+	0.963294i	$0.586511\pi$
$230$	−0.693293	−0.0457144
$231$	0	0
$232$	−1.83173	−0.120259
$233$	22.8903	1.49959	0.749796	−	0.661669i	$-0.230151\pi$
$233$	22.8903	1.49959	0.749796	+	0.661669i	$0.230151\pi$
$234$	−1.90258	−0.124376
$235$	7.88564	0.514402
$236$	16.9097	1.10073
$237$	1.26320	0.0820536
$238$	0	0
$239$	−16.3365	−1.05672	−0.528361	−	0.849020i	$-0.677193\pi$
$239$	−16.3365	−1.05672	−0.528361	+	0.849020i	$0.677193\pi$
$240$	−0.875237	−0.0564963
$241$	−6.78495	−0.437057	−0.218529	−	0.975831i	$-0.570126\pi$
$241$	−6.78495	−0.437057	−0.218529	+	0.975831i	$0.570126\pi$
$242$	0.239123	0.0153714
$243$	6.29303	0.403698
$244$	−19.8662	−1.27180
$245$	7.00000	0.447214
$246$	0.208508	0.0132940
$247$	18.4991	1.17707
$248$	−8.33654	−0.529371
$249$	3.71737	0.235579
$250$	−0.239123	−0.0151235
$251$	−5.03310	−0.317687	−0.158843	−	0.987304i	$-0.550776\pi$
$251$	−5.03310	−0.317687	−0.158843	+	0.987304i	$0.550776\pi$
$252$	0	0
$253$	−2.89931	−0.182278
$254$	−0.464574	−0.0291499
$255$	−0.239123	−0.0149745
$256$	11.6192	0.726198
$257$	−20.9773	−1.30853	−0.654264	−	0.756266i	$-0.727021\pi$
$257$	−20.9773	−1.30853	−0.654264	+	0.756266i	$0.727021\pi$
$258$	0.187701	0.0116857
$259$	0	0
$260$	5.25280	0.325765
$261$	−5.71737	−0.353896
$262$	−4.34230	−0.268268
$263$	−22.8799	−1.41083	−0.705417	−	0.708793i	$-0.749240\pi$
$263$	−22.8799	−1.41083	−0.705417	+	0.708793i	$0.749240\pi$
$264$	0.225450	0.0138755
$265$	−2.36389	−0.145212
$266$	0	0
$267$	0.0845261	0.00517291
$268$	−26.9773	−1.64790
$269$	5.20602	0.317417	0.158708	−	0.987326i	$-0.449267\pi$
$269$	5.20602	0.317417	0.158708	+	0.987326i	$0.449267\pi$
$270$	0.339810	0.0206802
$271$	−15.2930	−0.928986	−0.464493	−	0.885577i	$-0.653763\pi$
$271$	−15.2930	−0.928986	−0.464493	+	0.885577i	$0.653763\pi$
$272$	3.66019	0.221932
$273$	0	0
$274$	2.38469	0.144065
$275$	−1.00000	−0.0603023
$276$	−1.34694	−0.0810765
$277$	5.49441	0.330127	0.165063	−	0.986283i	$-0.447217\pi$
$277$	5.49441	0.330127	0.165063	+	0.986283i	$0.447217\pi$
$278$	−3.93955	−0.236279
$279$	−26.0208	−1.55782
$280$	0	0
$281$	3.72313	0.222103	0.111052	−	0.993815i	$-0.464578\pi$
$281$	3.72313	0.222103	0.111052	+	0.993815i	$0.464578\pi$
$282$	−0.450900	−0.0268507
$283$	25.2060	1.49834	0.749171	−	0.662376i	$-0.230452\pi$
$283$	25.2060	1.49834	0.749171	+	0.662376i	$0.230452\pi$
$284$	0.706966	0.0419507
$285$	−1.63611	−0.0969150
$286$	−0.646517	−0.0382293
$287$	0	0
$288$	−8.12476	−0.478756
$289$	1.00000	0.0588235
$290$	−0.464574	−0.0272807
$291$	−3.62244	−0.212351
$292$	−7.99346	−0.467782
$293$	−23.0813	−1.34842	−0.674211	−	0.738539i	$-0.735516\pi$
$293$	−23.0813	−1.34842	−0.674211	+	0.738539i	$0.735516\pi$
$294$	−0.400260	−0.0233436
$295$	8.70370	0.506749
$296$	3.45090	0.200580
$297$	1.42107	0.0824586
$298$	2.58607	0.149807
$299$	7.83886	0.453333
$300$	−0.464574	−0.0268222
$301$	0	0
$302$	2.90834	0.167356
$303$	−0.592606	−0.0340444
$304$	25.0435	1.43634
$305$	−10.2255	−0.585508
$306$	−0.703697	−0.0402277
$307$	7.62709	0.435301	0.217650	−	0.976027i	$-0.430161\pi$
$307$	7.62709	0.435301	0.217650	+	0.976027i	$0.430161\pi$
$308$	0	0
$309$	−2.56526	−0.145933
$310$	−2.11436	−0.120088
$311$	−21.0046	−1.19106	−0.595532	−	0.803332i	$-0.703059\pi$
$311$	−21.0046	−1.19106	−0.595532	+	0.803332i	$0.703059\pi$
$312$	−0.609549	−0.0345089
$313$	11.3100	0.639278	0.319639	−	0.947539i	$-0.396438\pi$
$313$	11.3100	0.639278	0.319639	+	0.947539i	$0.396438\pi$
$314$	5.17867	0.292249
$315$	0	0
$316$	−10.2632	−0.577350
$317$	12.2118	0.685882	0.342941	−	0.939357i	$-0.388577\pi$
$317$	12.2118	0.685882	0.342941	+	0.939357i	$0.388577\pi$
$318$	0.135167	0.00757978
$319$	−1.94282	−0.108777
$320$	6.66019	0.372316
$321$	2.20137	0.122869
$322$	0	0
$323$	6.84213	0.380706
$324$	−16.4919	−0.916218
$325$	2.70370	0.149974
$326$	−2.32287	−0.128652
$327$	0.144194	0.00797393
$328$	−3.43801	−0.189832
$329$	0	0
$330$	0.0571799	0.00314765
$331$	−21.2826	−1.16980	−0.584900	−	0.811106i	$-0.698866\pi$
$331$	−21.2826	−1.16980	−0.584900	+	0.811106i	$0.698866\pi$
$332$	−30.2028	−1.65759
$333$	10.7713	0.590263
$334$	3.40739	0.186444
$335$	−13.8856	−0.758654
$336$	0	0
$337$	18.2495	0.994115	0.497058	−	0.867718i	$-0.334414\pi$
$337$	18.2495	0.994115	0.497058	+	0.867718i	$0.334414\pi$
$338$	−1.36062	−0.0740078
$339$	2.22296	0.120735
$340$	1.94282	0.105364
$341$	−8.84213	−0.478828
$342$	−4.81479	−0.260354
$343$	0	0
$344$	−3.09493	−0.166867
$345$	−0.693293	−0.0373257
$346$	−1.34119	−0.0721026
$347$	10.4782	0.562502	0.281251	−	0.959634i	$-0.409251\pi$
$347$	10.4782	0.562502	0.281251	+	0.959634i	$0.409251\pi$
$348$	−0.902583	−0.0483835
$349$	−18.5264	−0.991695	−0.495848	−	0.868409i	$-0.665143\pi$
$349$	−18.5264	−0.991695	−0.495848	+	0.868409i	$0.665143\pi$
$350$	0	0
$351$	−3.84213	−0.205078
$352$	−2.76088	−0.147155
$353$	17.1579	0.913221	0.456611	−	0.889667i	$-0.349063\pi$
$353$	17.1579	0.913221	0.456611	+	0.889667i	$0.349063\pi$
$354$	−0.497677	−0.0264512
$355$	0.363887	0.0193131
$356$	−0.686754	−0.0363979
$357$	0	0
$358$	−2.03448	−0.107526
$359$	2.33654	0.123318	0.0616589	−	0.998097i	$-0.480361\pi$
$359$	2.33654	0.123318	0.0616589	+	0.998097i	$0.480361\pi$
$360$	−2.77455	−0.146232
$361$	27.8148	1.46394
$362$	1.00465	0.0528030
$363$	0.239123	0.0125507
$364$	0	0
$365$	−4.11436	−0.215355
$366$	0.584691	0.0305623
$367$	−20.4991	−1.07004	−0.535021	−	0.844839i	$-0.679696\pi$
$367$	−20.4991	−1.07004	−0.535021	+	0.844839i	$0.679696\pi$
$368$	10.6120	0.553191
$369$	−10.7310	−0.558636
$370$	0.875237	0.0455014
$371$	0	0
$372$	−4.10782	−0.212981
$373$	22.7278	1.17680	0.588400	−	0.808570i	$-0.299758\pi$
$373$	22.7278	1.17680	0.588400	+	0.808570i	$0.299758\pi$
$374$	−0.239123	−0.0123648
$375$	−0.239123	−0.0123483
$376$	7.43474	0.383417
$377$	5.25280	0.270533
$378$	0	0
$379$	31.1190	1.59848	0.799238	−	0.601015i	$-0.205237\pi$
$379$	31.1190	1.59848	0.799238	+	0.601015i	$0.205237\pi$
$380$	13.2930	0.681918
$381$	−0.464574	−0.0238008
$382$	0.176186	0.00901446
$383$	−12.0208	−0.614235	−0.307117	−	0.951672i	$-0.599364\pi$
$383$	−12.0208	−0.614235	−0.307117	+	0.951672i	$0.599364\pi$
$384$	−1.70121	−0.0868145
$385$	0	0
$386$	0.276873	0.0140925
$387$	−9.66019	−0.491055
$388$	29.4315	1.49416
$389$	−5.08126	−0.257630	−0.128815	−	0.991669i	$-0.541117\pi$
$389$	−5.08126	−0.257630	−0.128815	+	0.991669i	$0.541117\pi$
$390$	−0.154597	−0.00782833
$391$	2.89931	0.146625
$392$	6.59974	0.333337
$393$	−4.34230	−0.219040
$394$	−4.50559	−0.226988
$395$	−5.28263	−0.265798
$396$	−5.71737	−0.287309
$397$	35.8090	1.79720	0.898602	−	0.438765i	$-0.144584\pi$
$397$	35.8090	1.79720	0.898602	+	0.438765i	$0.144584\pi$
$398$	4.16251	0.208648
$399$	0	0
$400$	3.66019	0.183009
$401$	−25.0046	−1.24867	−0.624336	−	0.781156i	$-0.714630\pi$
$401$	−25.0046	−1.24867	−0.624336	+	0.781156i	$0.714630\pi$
$402$	0.793980	0.0396001
$403$	23.9064	1.19086
$404$	4.81479	0.239545
$405$	−8.48865	−0.421804
$406$	0	0
$407$	3.66019	0.181429
$408$	−0.225450	−0.0111614
$409$	−29.3685	−1.45218	−0.726090	−	0.687599i	$-0.758665\pi$
$409$	−29.3685	−1.45218	−0.726090	+	0.687599i	$0.758665\pi$
$410$	−0.871967	−0.0430634
$411$	2.38469	0.117628
$412$	20.8421	1.02682
$413$	0	0
$414$	−2.04024	−0.100272
$415$	−15.5458	−0.763115
$416$	7.46457	0.365981
$417$	−3.93955	−0.192921
$418$	−1.63611	−0.0800249
$419$	9.04351	0.441804	0.220902	−	0.975296i	$-0.429100\pi$
$419$	9.04351	0.441804	0.220902	+	0.975296i	$0.429100\pi$
$420$	0	0
$421$	29.4854	1.43703	0.718515	−	0.695512i	$-0.244822\pi$
$421$	29.4854	1.43703	0.718515	+	0.695512i	$0.244822\pi$
$422$	0.377560	0.0183793
$423$	23.2060	1.12832
$424$	−2.22872	−0.108236
$425$	1.00000	0.0485071
$426$	−0.0208070	−0.00100810
$427$	0	0
$428$	−17.8856	−0.864535
$429$	−0.646517	−0.0312141
$430$	−0.784953	−0.0378538
$431$	3.52502	0.169794	0.0848972	−	0.996390i	$-0.472944\pi$
$431$	3.52502	0.169794	0.0848972	+	0.996390i	$0.472944\pi$
$432$	−5.20137	−0.250251
$433$	33.9064	1.62944	0.814720	−	0.579855i	$-0.196891\pi$
$433$	33.9064	1.62944	0.814720	+	0.579855i	$0.196891\pi$
$434$	0	0
$435$	−0.464574	−0.0222746
$436$	−1.17154	−0.0561066
$437$	19.8375	0.948956
$438$	0.235259	0.0112411
$439$	−36.3250	−1.73370	−0.866849	−	0.498570i	$-0.833859\pi$
$439$	−36.3250	−1.73370	−0.866849	+	0.498570i	$0.833859\pi$
$440$	−0.942820	−0.0449472
$441$	20.5997	0.980940
$442$	0.646517	0.0307517
$443$	−30.1078	−1.43047	−0.715233	−	0.698886i	$-0.753679\pi$
$443$	−30.1078	−1.43047	−0.715233	+	0.698886i	$0.753679\pi$
$444$	1.70043	0.0806987
$445$	−0.353483	−0.0167567
$446$	6.00000	0.284108
$447$	2.58607	0.122317
$448$	0	0
$449$	40.4717	1.90998	0.954989	−	0.296641i	$-0.0958666\pi$
$449$	40.4717	1.90998	0.954989	+	0.296641i	$0.0958666\pi$
$450$	−0.703697	−0.0331726
$451$	−3.64652	−0.171708
$452$	−18.0610	−0.849520
$453$	2.90834	0.136646
$454$	2.78744	0.130821
$455$	0	0
$456$	−1.54256	−0.0722370
$457$	18.3743	0.859513	0.429757	−	0.902945i	$-0.358599\pi$
$457$	18.3743	0.859513	0.429757	+	0.902945i	$0.358599\pi$
$458$	−1.94282	−0.0907820
$459$	−1.42107	−0.0663297
$460$	5.63284	0.262633
$461$	−8.31573	−0.387302	−0.193651	−	0.981070i	$-0.562033\pi$
$461$	−8.31573	−0.387302	−0.193651	+	0.981070i	$0.562033\pi$
$462$	0	0
$463$	−14.7551	−0.685729	−0.342864	−	0.939385i	$-0.611397\pi$
$463$	−14.7551	−0.685729	−0.342864	+	0.939385i	$0.611397\pi$
$464$	7.11109	0.330124
$465$	−2.11436	−0.0980511
$466$	5.47360	0.253560
$467$	−4.84213	−0.224067	−0.112034	−	0.993704i	$-0.535736\pi$
$467$	−4.84213	−0.224067	−0.112034	+	0.993704i	$0.535736\pi$
$468$	15.4580	0.714548
$469$	0	0
$470$	1.88564	0.0869781
$471$	5.17867	0.238621
$472$	8.20602	0.377713
$473$	−3.28263	−0.150935
$474$	0.302060	0.0138741
$475$	6.84213	0.313939
$476$	0	0
$477$	−6.95649	−0.318516
$478$	−3.90645	−0.178677
$479$	23.6479	1.08050	0.540250	−	0.841505i	$-0.318330\pi$
$479$	23.6479	1.08050	0.540250	+	0.841505i	$0.318330\pi$
$480$	−0.660190	−0.0301334
$481$	−9.89604	−0.451221
$482$	−1.62244	−0.0739001
$483$	0	0
$484$	−1.94282	−0.0883100
$485$	15.1488	0.687873
$486$	1.50481	0.0682596
$487$	−3.99673	−0.181109	−0.0905546	−	0.995891i	$-0.528864\pi$
$487$	−3.99673	−0.181109	−0.0905546	+	0.995891i	$0.528864\pi$
$488$	−9.64076	−0.436417
$489$	−2.32287	−0.105044
$490$	1.67386	0.0756174
$491$	−33.7713	−1.52408	−0.762038	−	0.647532i	$-0.775801\pi$
$491$	−33.7713	−1.52408	−0.762038	+	0.647532i	$0.775801\pi$
$492$	−1.69408	−0.0763748
$493$	1.94282	0.0875002
$494$	4.42355	0.199025
$495$	−2.94282	−0.132270
$496$	32.3639	1.45318
$497$	0	0
$498$	0.888910	0.0398330
$499$	3.09166	0.138402	0.0692009	−	0.997603i	$-0.477955\pi$
$499$	3.09166	0.138402	0.0692009	+	0.997603i	$0.477955\pi$
$500$	1.94282	0.0868856
$501$	3.40739	0.152231
$502$	−1.20353	−0.0537163
$503$	34.0208	1.51691	0.758456	−	0.651724i	$-0.225954\pi$
$503$	34.0208	1.51691	0.758456	+	0.651724i	$0.225954\pi$
$504$	0	0
$505$	2.47825	0.110281
$506$	−0.693293	−0.0308206
$507$	−1.36062	−0.0604271
$508$	3.77455	0.167469
$509$	−7.91547	−0.350847	−0.175424	−	0.984493i	$-0.556130\pi$
$509$	−7.91547	−0.350847	−0.175424	+	0.984493i	$0.556130\pi$
$510$	−0.0571799	−0.00253197
$511$	0	0
$512$	17.0071	0.751616
$513$	−9.72313	−0.429287
$514$	−5.01616	−0.221253
$515$	10.7278	0.472722
$516$	−1.52502	−0.0671354
$517$	7.88564	0.346810
$518$	0	0
$519$	−1.34119	−0.0588716
$520$	2.54910	0.111785
$521$	22.0690	0.966859	0.483429	−	0.875383i	$-0.339391\pi$
$521$	22.0690	0.966859	0.483429	+	0.875383i	$0.339391\pi$
$522$	−1.36716	−0.0598388
$523$	−20.4692	−0.895056	−0.447528	−	0.894270i	$-0.647696\pi$
$523$	−20.4692	−0.895056	−0.447528	+	0.894270i	$0.647696\pi$
$524$	35.2801	1.54122
$525$	0	0
$526$	−5.47111	−0.238552
$527$	8.84213	0.385169
$528$	−0.875237	−0.0380898
$529$	−14.5940	−0.634521
$530$	−0.565260	−0.0245533
$531$	25.6134	1.11153
$532$	0	0
$533$	9.85908	0.427044
$534$	0.0202121	0.000874665 0
$535$	−9.20602	−0.398011
$536$	−13.0917	−0.565474
$537$	−2.03448	−0.0877943
$538$	1.24488	0.0536706
$539$	7.00000	0.301511
$540$	−2.76088	−0.118809
$541$	31.2840	1.34500	0.672502	−	0.740095i	$-0.265220\pi$
$541$	31.2840	1.34500	0.672502	+	0.740095i	$0.265220\pi$
$542$	−3.65692	−0.157078
$543$	1.00465	0.0431135
$544$	2.76088	0.118372
$545$	−0.603010	−0.0258301
$546$	0	0
$547$	−20.7874	−0.888807	−0.444403	−	0.895827i	$-0.646584\pi$
$547$	−20.7874	−0.888807	−0.444403	+	0.895827i	$0.646584\pi$
$548$	−19.3751	−0.827662
$549$	−30.0917	−1.28428
$550$	−0.239123	−0.0101963
$551$	13.2930	0.566302
$552$	−0.653651	−0.0278212
$553$	0	0
$554$	1.31384	0.0558197
$555$	0.875237	0.0371517
$556$	32.0079	1.35744
$557$	−2.58220	−0.109411	−0.0547057	−	0.998503i	$-0.517422\pi$
$557$	−2.58220	−0.109411	−0.0547057	+	0.998503i	$0.517422\pi$
$558$	−6.22218	−0.263406
$559$	8.87524	0.375383
$560$	0	0
$561$	−0.239123	−0.0100958
$562$	0.890286	0.0375545
$563$	−46.5861	−1.96337	−0.981684	−	0.190515i	$-0.938984\pi$
$563$	−46.5861	−1.96337	−0.981684	+	0.190515i	$0.938984\pi$
$564$	3.66346	0.154259
$565$	−9.29630	−0.391098
$566$	6.02735	0.253348
$567$	0	0
$568$	0.343080	0.0143953
$569$	−29.7439	−1.24693	−0.623465	−	0.781851i	$-0.714276\pi$
$569$	−29.7439	−1.24693	−0.623465	+	0.781851i	$0.714276\pi$
$570$	−0.391233	−0.0163869
$571$	−7.84789	−0.328424	−0.164212	−	0.986425i	$-0.552508\pi$
$571$	−7.84789	−0.328424	−0.164212	+	0.986425i	$0.552508\pi$
$572$	5.25280	0.219630
$573$	0.176186	0.00736028
$574$	0	0
$575$	2.89931	0.120910
$576$	19.5997	0.816656
$577$	33.1672	1.38077	0.690383	−	0.723444i	$-0.257442\pi$
$577$	33.1672	1.38077	0.690383	+	0.723444i	$0.257442\pi$
$578$	0.239123	0.00994622
$579$	0.276873	0.0115064
$580$	3.77455	0.156730
$581$	0	0
$582$	−0.866210	−0.0359056
$583$	−2.36389	−0.0979022
$584$	−3.87910	−0.160518
$585$	7.95649	0.328961
$586$	−5.51927	−0.227999
$587$	11.2722	0.465255	0.232627	−	0.972566i	$-0.425268\pi$
$587$	11.2722	0.465255	0.232627	+	0.972566i	$0.425268\pi$
$588$	3.25201	0.134111
$589$	60.4991	2.49282
$590$	2.08126	0.0856840
$591$	−4.50559	−0.185335
$592$	−13.3970	−0.550613
$593$	−0.387963	−0.0159317	−0.00796587	−	0.999968i	$-0.502536\pi$
$593$	−0.387963	−0.0159317	−0.00796587	+	0.999968i	$0.502536\pi$
$594$	0.339810	0.0139426
$595$	0	0
$596$	−21.0112	−0.860652
$597$	4.16251	0.170360
$598$	1.87445	0.0766522
$599$	5.88237	0.240347	0.120174	−	0.992753i	$-0.461655\pi$
$599$	5.88237	0.240347	0.120174	+	0.992753i	$0.461655\pi$
$600$	−0.225450	−0.00920397
$601$	37.4257	1.52663	0.763313	−	0.646028i	$-0.223571\pi$
$601$	37.4257	1.52663	0.763313	+	0.646028i	$0.223571\pi$
$602$	0	0
$603$	−40.8629	−1.66407
$604$	−23.6296	−0.961474
$605$	−1.00000	−0.0406558
$606$	−0.141706	−0.00575641
$607$	−38.8421	−1.57655	−0.788277	−	0.615321i	$-0.789026\pi$
$607$	−38.8421	−1.57655	−0.788277	+	0.615321i	$0.789026\pi$
$608$	18.8903	0.766102
$609$	0	0
$610$	−2.44514	−0.0990010
$611$	−21.3204	−0.862530
$612$	5.71737	0.231111
$613$	−13.7896	−0.556957	−0.278478	−	0.960443i	$-0.589830\pi$
$613$	−13.7896	−0.556957	−0.278478	+	0.960443i	$0.589830\pi$
$614$	1.82381	0.0736031
$615$	−0.871967	−0.0351611
$616$	0	0
$617$	−29.6752	−1.19468	−0.597340	−	0.801988i	$-0.703776\pi$
$617$	−29.6752	−1.19468	−0.597340	+	0.801988i	$0.703776\pi$
$618$	−0.613413	−0.0246751
$619$	36.2495	1.45699	0.728496	−	0.685050i	$-0.240220\pi$
$619$	36.2495	1.45699	0.728496	+	0.685050i	$0.240220\pi$
$620$	17.1787	0.689912
$621$	−4.12012	−0.165335
$622$	−5.02270	−0.201392
$623$	0	0
$624$	2.36637	0.0947308
$625$	1.00000	0.0400000
$626$	2.70448	0.108093
$627$	−1.63611	−0.0653401
$628$	−42.0755	−1.67900
$629$	−3.66019	−0.145941
$630$	0	0
$631$	−23.2416	−0.925234	−0.462617	−	0.886558i	$-0.653089\pi$
$631$	−23.2416	−0.925234	−0.462617	+	0.886558i	$0.653089\pi$
$632$	−4.98057	−0.198116
$633$	0.377560	0.0150067
$634$	2.92012	0.115973
$635$	1.94282	0.0770985
$636$	−1.09820	−0.0435464
$637$	−18.9259	−0.749871
$638$	−0.464574	−0.0183926
$639$	1.07085	0.0423623
$640$	7.11436	0.281220
$641$	−12.5264	−0.494763	−0.247382	−	0.968918i	$-0.579570\pi$
$641$	−12.5264	−0.494763	−0.247382	+	0.968918i	$0.579570\pi$
$642$	0.526400	0.0207753
$643$	−0.00326955	−0.000128938 0	−6.44691e−5	−	1.00000i	$-0.500021\pi$
$643$	−0.00326955	−0.000128938 0	−6.44691e−5		1.00000i	$0.500021\pi$
$644$	0	0
$645$	−0.784953	−0.0309075
$646$	1.63611	0.0643720
$647$	43.7532	1.72012	0.860058	−	0.510196i	$-0.170427\pi$
$647$	43.7532	1.72012	0.860058	+	0.510196i	$0.170427\pi$
$648$	−8.00327	−0.314398
$649$	8.70370	0.341650
$650$	0.646517	0.0253585
$651$	0	0
$652$	18.8727	0.739114
$653$	0.744716	0.0291430	0.0145715	−	0.999894i	$-0.495362\pi$
$653$	0.744716	0.0291430	0.0145715	+	0.999894i	$0.495362\pi$
$654$	0.0344801	0.00134828
$655$	18.1592	0.709540
$656$	13.3469	0.521111
$657$	−12.1078	−0.472371
$658$	0	0
$659$	−22.5537	−0.878569	−0.439285	−	0.898348i	$-0.644768\pi$
$659$	−22.5537	−0.878569	−0.439285	+	0.898348i	$0.644768\pi$
$660$	−0.464574	−0.0180835
$661$	2.17154	0.0844631	0.0422316	−	0.999108i	$-0.486553\pi$
$661$	2.17154	0.0844631	0.0422316	+	0.999108i	$0.486553\pi$
$662$	−5.08917	−0.197796
$663$	0.646517	0.0251086
$664$	−14.6569	−0.568799
$665$	0	0
$666$	2.57566	0.0998049
$667$	5.63284	0.218105
$668$	−27.6843	−1.07114
$669$	6.00000	0.231973
$670$	−3.32038	−0.128277
$671$	−10.2255	−0.394749
$672$	0	0
$673$	40.2977	1.55336	0.776681	−	0.629895i	$-0.216902\pi$
$673$	40.2977	1.55336	0.776681	+	0.629895i	$0.216902\pi$
$674$	4.36389	0.168091
$675$	−1.42107	−0.0546969
$676$	11.0547	0.425180
$677$	−12.1833	−0.468243	−0.234122	−	0.972207i	$-0.575221\pi$
$677$	−12.1833	−0.468243	−0.234122	+	0.972207i	$0.575221\pi$
$678$	0.531562	0.0204145
$679$	0	0
$680$	0.942820	0.0361555
$681$	2.78744	0.106815
$682$	−2.11436	−0.0809630
$683$	−13.7357	−0.525582	−0.262791	−	0.964853i	$-0.584643\pi$
$683$	−13.7357	−0.525582	−0.262791	+	0.964853i	$0.584643\pi$
$684$	39.1190	1.49575
$685$	−9.97265	−0.381036
$686$	0	0
$687$	−1.94282	−0.0741232
$688$	12.0150	0.458069
$689$	6.39123	0.243487
$690$	−0.165783	−0.00631123
$691$	−7.32038	−0.278480	−0.139240	−	0.990259i	$-0.544466\pi$
$691$	−7.32038	−0.278480	−0.139240	+	0.990259i	$0.544466\pi$
$692$	10.8968	0.414235
$693$	0	0
$694$	2.50559	0.0951110
$695$	16.4750	0.624931
$696$	−0.438009	−0.0166027
$697$	3.64652	0.138122
$698$	−4.43009	−0.167682
$699$	5.47360	0.207031
$700$	0	0
$701$	−39.9064	−1.50725	−0.753623	−	0.657307i	$-0.771695\pi$
$701$	−39.9064	−1.50725	−0.753623	+	0.657307i	$0.771695\pi$
$702$	−0.918743	−0.0346757
$703$	−25.0435	−0.944534
$704$	6.66019	0.251015
$705$	1.88564	0.0710173
$706$	4.10285	0.154413
$707$	0	0
$708$	4.04351	0.151964
$709$	9.65692	0.362673	0.181337	−	0.983421i	$-0.441958\pi$
$709$	9.65692	0.362673	0.181337	+	0.983421i	$0.441958\pi$
$710$	0.0870138	0.00326557
$711$	−15.5458	−0.583014
$712$	−0.333271	−0.0124899
$713$	25.6361	0.960080
$714$	0	0
$715$	2.70370	0.101113
$716$	16.5297	0.617743
$717$	−3.90645	−0.145889
$718$	0.558721	0.0208513
$719$	−43.7532	−1.63172	−0.815860	−	0.578249i	$-0.803736\pi$
$719$	−43.7532	−1.63172	−0.815860	+	0.578249i	$0.803736\pi$
$720$	10.7713	0.401422
$721$	0	0
$722$	6.65116	0.247531
$723$	−1.62244	−0.0603392
$724$	−8.16251	−0.303357
$725$	1.94282	0.0721545
$726$	0.0571799	0.00212215
$727$	0.793980	0.0294471	0.0147235	−	0.999892i	$-0.495313\pi$
$727$	0.793980	0.0294471	0.0147235	+	0.999892i	$0.495313\pi$
$728$	0	0
$729$	−23.9611	−0.887450
$730$	−0.983839	−0.0364135
$731$	3.28263	0.121412
$732$	−4.75047	−0.175583
$733$	−10.3535	−0.382415	−0.191207	−	0.981550i	$-0.561240\pi$
$733$	−10.3535	−0.382415	−0.191207	+	0.981550i	$0.561240\pi$
$734$	−4.90180	−0.180929
$735$	1.67386	0.0617414
$736$	8.00465	0.295055
$737$	−13.8856	−0.511484
$738$	−2.56604	−0.0944573
$739$	12.8033	0.470976	0.235488	−	0.971877i	$-0.424331\pi$
$739$	12.8033	0.470976	0.235488	+	0.971877i	$0.424331\pi$
$740$	−7.11109	−0.261409
$741$	4.42355	0.162503
$742$	0	0
$743$	−33.7713	−1.23895	−0.619474	−	0.785017i	$-0.712654\pi$
$743$	−33.7713	−1.23895	−0.619474	+	0.785017i	$0.712654\pi$
$744$	−1.99346	−0.0730838
$745$	−10.8148	−0.396223
$746$	5.43474	0.198980
$747$	−45.7486	−1.67385
$748$	1.94282	0.0710365
$749$	0	0
$750$	−0.0571799	−0.00208792
$751$	−7.85829	−0.286753	−0.143377	−	0.989668i	$-0.545796\pi$
$751$	−7.85829	−0.286753	−0.143377	+	0.989668i	$0.545796\pi$
$752$	−28.8629	−1.05252
$753$	−1.20353	−0.0438592
$754$	1.25607	0.0457432
$755$	−12.1625	−0.442639
$756$	0	0
$757$	4.30422	0.156440	0.0782198	−	0.996936i	$-0.475076\pi$
$757$	4.30422	0.156440	0.0782198	+	0.996936i	$0.475076\pi$
$758$	7.44128	0.270279
$759$	−0.693293	−0.0251650
$760$	6.45090	0.233999
$761$	−28.5264	−1.03408	−0.517041	−	0.855961i	$-0.672966\pi$
$761$	−28.5264	−1.03408	−0.517041	+	0.855961i	$0.672966\pi$
$762$	−0.111090	−0.00402438
$763$	0	0
$764$	−1.43147	−0.0517888
$765$	2.94282	0.106398
$766$	−2.87445	−0.103858
$767$	−23.5322	−0.849697
$768$	2.77841	0.100257
$769$	34.2495	1.23507	0.617535	−	0.786544i	$-0.288131\pi$
$769$	34.2495	1.23507	0.617535	+	0.786544i	$0.288131\pi$
$770$	0	0
$771$	−5.01616	−0.180653
$772$	−2.24953	−0.0809622
$773$	−7.34773	−0.264279	−0.132140	−	0.991231i	$-0.542185\pi$
$773$	−7.34773	−0.264279	−0.132140	+	0.991231i	$0.542185\pi$
$774$	−2.30998	−0.0830304
$775$	8.84213	0.317619
$776$	14.2826	0.512717
$777$	0	0
$778$	−1.21505	−0.0435615
$779$	24.9500	0.893925
$780$	1.25607	0.0449744
$781$	0.363887	0.0130209
$782$	0.693293	0.0247921
$783$	−2.76088	−0.0986657
$784$	−25.6213	−0.915047
$785$	−21.6569	−0.772969
$786$	−1.03834	−0.0370365
$787$	−48.4328	−1.72644	−0.863222	−	0.504824i	$-0.831557\pi$
$787$	−48.4328	−1.72644	−0.863222	+	0.504824i	$0.831557\pi$
$788$	36.6069	1.30407
$789$	−5.47111	−0.194777
$790$	−1.26320	−0.0449426
$791$	0	0
$792$	−2.77455	−0.0985893
$793$	27.6465	0.981757
$794$	8.56277	0.303881
$795$	−0.565260	−0.0200477
$796$	−33.8194	−1.19870
$797$	34.5472	1.22372	0.611862	−	0.790964i	$-0.290421\pi$
$797$	34.5472	1.22372	0.611862	+	0.790964i	$0.290421\pi$
$798$	0	0
$799$	−7.88564	−0.278974
$800$	2.76088	0.0976117
$801$	−1.04024	−0.0367550
$802$	−5.97919	−0.211133
$803$	−4.11436	−0.145193
$804$	−6.45090	−0.227506
$805$	0	0
$806$	5.71659	0.201358
$807$	1.24488	0.0438219
$808$	2.33654	0.0821992
$809$	36.8148	1.29434	0.647169	−	0.762346i	$-0.275953\pi$
$809$	36.8148	1.29434	0.647169	+	0.762346i	$0.275953\pi$
$810$	−2.02983	−0.0713211
$811$	14.8058	0.519901	0.259950	−	0.965622i	$-0.416294\pi$
$811$	14.8058	0.519901	0.259950	+	0.965622i	$0.416294\pi$
$812$	0	0
$813$	−3.65692	−0.128254
$814$	0.875237	0.0306770
$815$	9.71410	0.340270
$816$	0.875237	0.0306394
$817$	22.4602	0.785783
$818$	−7.02270	−0.245543
$819$	0	0
$820$	7.08453	0.247402
$821$	−52.1456	−1.81989	−0.909946	−	0.414726i	$-0.863878\pi$
$821$	−52.1456	−1.81989	−0.909946	+	0.414726i	$0.863878\pi$
$822$	0.570236	0.0198893
$823$	−7.30206	−0.254534	−0.127267	−	0.991869i	$-0.540620\pi$
$823$	−7.30206	−0.254534	−0.127267	+	0.991869i	$0.540620\pi$
$824$	10.1144	0.352350
$825$	−0.239123	−0.00832520
$826$	0	0
$827$	7.49441	0.260606	0.130303	−	0.991474i	$-0.458405\pi$
$827$	7.49441	0.260606	0.130303	+	0.991474i	$0.458405\pi$
$828$	16.5764	0.576071
$829$	−18.7303	−0.650529	−0.325264	−	0.945623i	$-0.605453\pi$
$829$	−18.7303	−0.650529	−0.325264	+	0.945623i	$0.605453\pi$
$830$	−3.71737	−0.129032
$831$	1.31384	0.0455766
$832$	−18.0071	−0.624285
$833$	−7.00000	−0.242536
$834$	−0.942038	−0.0326201
$835$	−14.2495	−0.493125
$836$	13.2930	0.459749
$837$	−12.5653	−0.434319
$838$	2.16251	0.0747028
$839$	−39.2542	−1.35520	−0.677602	−	0.735429i	$-0.736981\pi$
$839$	−39.2542	−1.35520	−0.677602	+	0.735429i	$0.736981\pi$
$840$	0	0
$841$	−25.2255	−0.869843
$842$	7.05064	0.242981
$843$	0.890286	0.0306631
$844$	−3.06758	−0.105591
$845$	5.69002	0.195743
$846$	5.54910	0.190782
$847$	0	0
$848$	8.65227	0.297120
$849$	6.02735	0.206858
$850$	0.239123	0.00820186
$851$	−10.6120	−0.363776
$852$	0.169052	0.00579163
$853$	−38.1078	−1.30479	−0.652393	−	0.757880i	$-0.726235\pi$
$853$	−38.1078	−1.30479	−0.652393	+	0.757880i	$0.726235\pi$
$854$	0	0
$855$	20.1352	0.688608
$856$	−8.67962	−0.296663
$857$	38.5472	1.31675	0.658374	−	0.752691i	$-0.271245\pi$
$857$	38.5472	1.31675	0.658374	+	0.752691i	$0.271245\pi$
$858$	−0.154597	−0.00527786
$859$	26.1111	0.890899	0.445449	−	0.895307i	$-0.353044\pi$
$859$	26.1111	0.890899	0.445449	+	0.895307i	$0.353044\pi$
$860$	6.37756	0.217473
$861$	0	0
$862$	0.842915	0.0287098
$863$	−31.7439	−1.08058	−0.540288	−	0.841480i	$-0.681685\pi$
$863$	−31.7439	−1.08058	−0.540288	+	0.841480i	$0.681685\pi$
$864$	−3.92339	−0.133476
$865$	5.60877	0.190704
$866$	8.10782	0.275515
$867$	0.239123	0.00812105
$868$	0	0
$869$	−5.28263	−0.179201
$870$	−0.111090	−0.00376632
$871$	37.5426	1.27208
$872$	−0.568530	−0.0192529
$873$	44.5803	1.50881
$874$	4.74360	0.160455
$875$	0	0
$876$	−1.91142	−0.0645810
$877$	6.30422	0.212878	0.106439	−	0.994319i	$-0.466055\pi$
$877$	6.30422	0.212878	0.106439	+	0.994319i	$0.466055\pi$
$878$	−8.68616	−0.293144
$879$	−5.51927	−0.186160
$880$	3.66019	0.123385
$881$	10.9773	0.369835	0.184917	−	0.982754i	$-0.440798\pi$
$881$	10.9773	0.369835	0.184917	+	0.982754i	$0.440798\pi$
$882$	4.92588	0.165863
$883$	−20.0482	−0.674674	−0.337337	−	0.941384i	$-0.609526\pi$
$883$	−20.0482	−0.674674	−0.337337	+	0.941384i	$0.609526\pi$
$884$	−5.25280	−0.176671
$885$	2.08126	0.0699607
$886$	−7.19948	−0.241871
$887$	−12.8903	−0.432813	−0.216407	−	0.976303i	$-0.569434\pi$
$887$	−12.8903	−0.432813	−0.216407	+	0.976303i	$0.569434\pi$
$888$	0.825191	0.0276916
$889$	0	0
$890$	−0.0845261	−0.00283332
$891$	−8.48865	−0.284380
$892$	−48.7486	−1.63222
$893$	−53.9546	−1.80552
$894$	0.618389	0.0206820
$895$	8.50808	0.284394
$896$	0	0
$897$	1.87445	0.0625862
$898$	9.67773	0.322950
$899$	17.1787	0.572941
$900$	5.71737	0.190579
$901$	2.36389	0.0787525
$902$	−0.871967	−0.0290333
$903$	0	0
$904$	−8.76474	−0.291511
$905$	−4.20137	−0.139658
$906$	0.695452	0.0231048
$907$	5.91299	0.196337	0.0981687	−	0.995170i	$-0.468702\pi$
$907$	5.91299	0.196337	0.0981687	+	0.995170i	$0.468702\pi$
$908$	−22.6473	−0.751577
$909$	7.29303	0.241895
$910$	0	0
$911$	−32.9565	−1.09190	−0.545949	−	0.837819i	$-0.683831\pi$
$911$	−32.9565	−1.09190	−0.545949	+	0.837819i	$0.683831\pi$
$912$	5.98849	0.198299
$913$	−15.5458	−0.514492
$914$	4.39372	0.145331
$915$	−2.44514	−0.0808339
$916$	15.7850	0.521550
$917$	0	0
$918$	−0.339810	−0.0112154
$919$	15.2449	0.502882	0.251441	−	0.967873i	$-0.419096\pi$
$919$	15.2449	0.502882	0.251441	+	0.967873i	$0.419096\pi$
$920$	2.73353	0.0901218
$921$	1.82381	0.0600967
$922$	−1.98849	−0.0654873
$923$	−0.983839	−0.0323835
$924$	0	0
$925$	−3.66019	−0.120346
$926$	−3.52829	−0.115947
$927$	31.5699	1.03689
$928$	5.36389	0.176078
$929$	41.7532	1.36988	0.684939	−	0.728600i	$-0.259829\pi$
$929$	41.7532	1.36988	0.684939	+	0.728600i	$0.259829\pi$
$930$	−0.505593	−0.0165790
$931$	−47.8949	−1.56969
$932$	−44.4717	−1.45672
$933$	−5.02270	−0.164436
$934$	−1.15787	−0.0378866
$935$	1.00000	0.0327035
$936$	7.50154	0.245196
$937$	1.07988	0.0352781	0.0176391	−	0.999844i	$-0.494385\pi$
$937$	1.07988	0.0352781	0.0176391	+	0.999844i	$0.494385\pi$
$938$	0	0
$939$	2.70448	0.0882573
$940$	−15.3204	−0.499696
$941$	−60.1833	−1.96192	−0.980960	−	0.194209i	$-0.937786\pi$
$941$	−60.1833	−1.96192	−0.980960	+	0.194209i	$0.937786\pi$
$942$	1.23834	0.0403473
$943$	10.5724	0.344285
$944$	−31.8572	−1.03686
$945$	0	0
$946$	−0.784953	−0.0255210
$947$	22.4088	0.728187	0.364094	−	0.931362i	$-0.381379\pi$
$947$	22.4088	0.728187	0.364094	+	0.931362i	$0.381379\pi$
$948$	−2.45417	−0.0797077
$949$	11.1240	0.361100
$950$	1.63611	0.0530825
$951$	2.92012	0.0946914
$952$	0	0
$953$	−10.4815	−0.339530	−0.169765	−	0.985485i	$-0.554301\pi$
$953$	−10.4815	−0.339530	−0.169765	+	0.985485i	$0.554301\pi$
$954$	−1.66346	−0.0538565
$955$	−0.736800	−0.0238423
$956$	31.7390	1.02651
$957$	−0.464574	−0.0150175
$958$	5.65476	0.182697
$959$	0	0
$960$	1.59261	0.0514012
$961$	47.1833	1.52204
$962$	−2.36637	−0.0762950
$963$	−27.0917	−0.873017
$964$	13.1819	0.424562
$965$	−1.15787	−0.0372731
$966$	0	0
$967$	−13.6739	−0.439722	−0.219861	−	0.975531i	$-0.570560\pi$
$967$	−13.6739	−0.439722	−0.219861	+	0.975531i	$0.570560\pi$
$968$	−0.942820	−0.0303034
$969$	1.63611	0.0525595
$970$	3.62244	0.116310
$971$	12.4027	0.398023	0.199012	−	0.979997i	$-0.436227\pi$
$971$	12.4027	0.398023	0.199012	+	0.979997i	$0.436227\pi$
$972$	−12.2262	−0.392157
$973$	0	0
$974$	−0.955711	−0.0306230
$975$	0.646517	0.0207051
$976$	37.4271	1.19801
$977$	−9.29957	−0.297520	−0.148760	−	0.988873i	$-0.547528\pi$
$977$	−9.29957	−0.297520	−0.148760	+	0.988873i	$0.547528\pi$
$978$	−0.555452	−0.0177614
$979$	−0.353483	−0.0112974
$980$	−13.5997	−0.434428
$981$	−1.77455	−0.0566570
$982$	−8.07550	−0.257700
$983$	36.6764	1.16979	0.584897	−	0.811108i	$-0.301135\pi$
$983$	36.6764	1.16979	0.584897	+	0.811108i	$0.301135\pi$
$984$	−0.822108	−0.0262078
$985$	18.8421	0.600360
$986$	0.464574	0.0147950
$987$	0	0
$988$	−35.9403	−1.14341
$989$	9.51737	0.302635
$990$	−0.703697	−0.0223650
$991$	−30.1899	−0.959012	−0.479506	−	0.877538i	$-0.659184\pi$
$991$	−30.1899	−0.959012	−0.479506	+	0.877538i	$0.659184\pi$
$992$	24.4120	0.775083
$993$	−5.08917	−0.161500
$994$	0	0
$995$	−17.4074	−0.551851
$996$	−7.22218	−0.228844
$997$	−33.8676	−1.07260	−0.536299	−	0.844028i	$-0.680178\pi$
$997$	−33.8676	−1.07260	−0.536299	+	0.844028i	$0.680178\pi$
$998$	0.739288	0.0234017
$999$	5.20137	0.164564

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	935.2.a.f.1.2	✓	3
3.2	odd	2		8415.2.a.w.1.2		3
5.4	even	2		4675.2.a.w.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
935.2.a.f.1.2	✓	3	1.1	even	1	trivial
4675.2.a.w.1.2		3	5.4	even	2
8415.2.a.w.1.2		3	3.2	odd	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:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.a (trivial)

\(f(q)\)	\(=\)	\(q+0.239123 q^{2} +0.239123 q^{3} -1.94282 q^{4} -1.00000 q^{5} +0.0571799 q^{6} -0.942820 q^{8} -2.94282 q^{9} +O(q^{10})\)	\(q+0.239123 q^{2} +0.239123 q^{3} -1.94282 q^{4} -1.00000 q^{5} +0.0571799 q^{6} -0.942820 q^{8} -2.94282 q^{9} -0.239123 q^{10} -1.00000 q^{11} -0.464574 q^{12} +2.70370 q^{13} -0.239123 q^{15} +3.66019 q^{16} +1.00000 q^{17} -0.703697 q^{18} +6.84213 q^{19} +1.94282 q^{20} -0.239123 q^{22} +2.89931 q^{23} -0.225450 q^{24} +1.00000 q^{25} +0.646517 q^{26} -1.42107 q^{27} +1.94282 q^{29} -0.0571799 q^{30} +8.84213 q^{31} +2.76088 q^{32} -0.239123 q^{33} +0.239123 q^{34} +5.71737 q^{36} -3.66019 q^{37} +1.63611 q^{38} +0.646517 q^{39} +0.942820 q^{40} +3.64652 q^{41} +3.28263 q^{43} +1.94282 q^{44} +2.94282 q^{45} +0.693293 q^{46} -7.88564 q^{47} +0.875237 q^{48} -7.00000 q^{49} +0.239123 q^{50} +0.239123 q^{51} -5.25280 q^{52} +2.36389 q^{53} -0.339810 q^{54} +1.00000 q^{55} +1.63611 q^{57} +0.464574 q^{58} -8.70370 q^{59} +0.464574 q^{60} +10.2255 q^{61} +2.11436 q^{62} -6.66019 q^{64} -2.70370 q^{65} -0.0571799 q^{66} +13.8856 q^{67} -1.94282 q^{68} +0.693293 q^{69} -0.363887 q^{71} +2.77455 q^{72} +4.11436 q^{73} -0.875237 q^{74} +0.239123 q^{75} -13.2930 q^{76} +0.154597 q^{78} +5.28263 q^{79} -3.66019 q^{80} +8.48865 q^{81} +0.871967 q^{82} +15.5458 q^{83} -1.00000 q^{85} +0.784953 q^{86} +0.464574 q^{87} +0.942820 q^{88} +0.353483 q^{89} +0.703697 q^{90} -5.63284 q^{92} +2.11436 q^{93} -1.88564 q^{94} -6.84213 q^{95} +0.660190 q^{96} -15.1488 q^{97} -1.67386 q^{98} +2.94282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + q^{3} + 3 q^{4} - 3 q^{5} + 9 q^{6} + 6 q^{8}+O(q^{10}) \) 3 * q + q^2 + q^3 + 3 * q^4 - 3 * q^5 + 9 * q^6 + 6 * q^8	\( 3 q + q^{2} + q^{3} + 3 q^{4} - 3 q^{5} + 9 q^{6} + 6 q^{8} - q^{10} - 3 q^{11} + 8 q^{12} - q^{13} - q^{15} + 3 q^{16} + 3 q^{17} + 7 q^{18} + 4 q^{19} - 3 q^{20} - q^{22} + q^{23} + 9 q^{24} + 3 q^{25} - 16 q^{26} + 4 q^{27} - 3 q^{29} - 9 q^{30} + 10 q^{31} + 8 q^{32} - q^{33} + q^{34} + 18 q^{36} - 3 q^{37} + 22 q^{38} - 16 q^{39} - 6 q^{40} - 7 q^{41} + 9 q^{43} - 3 q^{44} + 28 q^{46} - 6 q^{47} + 20 q^{48} - 21 q^{49} + q^{50} + q^{51} - 26 q^{52} - 10 q^{53} - 9 q^{54} + 3 q^{55} + 22 q^{57} - 8 q^{58} - 17 q^{59} - 8 q^{60} + 21 q^{61} + 24 q^{62} - 12 q^{64} + q^{65} - 9 q^{66} + 24 q^{67} + 3 q^{68} + 28 q^{69} + 16 q^{71} + 18 q^{72} + 30 q^{73} - 20 q^{74} + q^{75} - 4 q^{76} - 28 q^{78} + 15 q^{79} - 3 q^{80} - 9 q^{81} - 25 q^{82} + 21 q^{83} - 3 q^{85} - 23 q^{86} - 8 q^{87} - 6 q^{88} + 19 q^{89} - 7 q^{90} + 11 q^{92} + 24 q^{93} + 12 q^{94} - 4 q^{95} - 6 q^{96} - 3 q^{97} - 7 q^{98}+O(q^{100}) \) 3 * q + q^2 + q^3 + 3 * q^4 - 3 * q^5 + 9 * q^6 + 6 * q^8 - q^10 - 3 * q^11 + 8 * q^12 - q^13 - q^15 + 3 * q^16 + 3 * q^17 + 7 * q^18 + 4 * q^19 - 3 * q^20 - q^22 + q^23 + 9 * q^24 + 3 * q^25 - 16 * q^26 + 4 * q^27 - 3 * q^29 - 9 * q^30 + 10 * q^31 + 8 * q^32 - q^33 + q^34 + 18 * q^36 - 3 * q^37 + 22 * q^38 - 16 * q^39 - 6 * q^40 - 7 * q^41 + 9 * q^43 - 3 * q^44 + 28 * q^46 - 6 * q^47 + 20 * q^48 - 21 * q^49 + q^50 + q^51 - 26 * q^52 - 10 * q^53 - 9 * q^54 + 3 * q^55 + 22 * q^57 - 8 * q^58 - 17 * q^59 - 8 * q^60 + 21 * q^61 + 24 * q^62 - 12 * q^64 + q^65 - 9 * q^66 + 24 * q^67 + 3 * q^68 + 28 * q^69 + 16 * q^71 + 18 * q^72 + 30 * q^73 - 20 * q^74 + q^75 - 4 * q^76 - 28 * q^78 + 15 * q^79 - 3 * q^80 - 9 * q^81 - 25 * q^82 + 21 * q^83 - 3 * q^85 - 23 * q^86 - 8 * q^87 - 6 * q^88 + 19 * q^89 - 7 * q^90 + 11 * q^92 + 24 * q^93 + 12 * q^94 - 4 * q^95 - 6 * q^96 - 3 * q^97 - 7 * q^98

Introduction

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