LMFDB - Embedded newform 833.2.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(1,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("833.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.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:	$6.65153848837$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 119)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.24698$ of defining polynomial
Character	$\chi$	$=$	833.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.24698 q^{2} +1.24698 q^{3} -0.445042 q^{4} -2.24698 q^{5} +1.55496 q^{6} -3.04892 q^{8} -1.44504 q^{9} +O(q^{10})$	\(q+1.24698 q^{2} +1.24698 q^{3} -0.445042 q^{4} -2.24698 q^{5} +1.55496 q^{6} -3.04892 q^{8} -1.44504 q^{9} -2.80194 q^{10} -4.15883 q^{11} -0.554958 q^{12} +0.643104 q^{13} -2.80194 q^{15} -2.91185 q^{16} +1.00000 q^{17} -1.80194 q^{18} +0.109916 q^{19} +1.00000 q^{20} -5.18598 q^{22} -5.38404 q^{23} -3.80194 q^{24} +0.0489173 q^{25} +0.801938 q^{26} -5.54288 q^{27} +5.31767 q^{29} -3.49396 q^{30} +1.26875 q^{31} +2.46681 q^{32} -5.18598 q^{33} +1.24698 q^{34} +0.643104 q^{36} -10.2959 q^{37} +0.137063 q^{38} +0.801938 q^{39} +6.85086 q^{40} +10.4058 q^{41} -5.21983 q^{43} +1.85086 q^{44} +3.24698 q^{45} -6.71379 q^{46} -3.93362 q^{47} -3.63102 q^{48} +0.0609989 q^{50} +1.24698 q^{51} -0.286208 q^{52} +10.2567 q^{53} -6.91185 q^{54} +9.34481 q^{55} +0.137063 q^{57} +6.63102 q^{58} +6.85086 q^{59} +1.24698 q^{60} +0.246980 q^{61} +1.58211 q^{62} +8.89977 q^{64} -1.44504 q^{65} -6.46681 q^{66} -11.6310 q^{67} -0.445042 q^{68} -6.71379 q^{69} +0.878002 q^{71} +4.40581 q^{72} -15.8823 q^{73} -12.8388 q^{74} +0.0609989 q^{75} -0.0489173 q^{76} +1.00000 q^{78} +1.67994 q^{79} +6.54288 q^{80} -2.57673 q^{81} +12.9758 q^{82} +15.0954 q^{83} -2.24698 q^{85} -6.50902 q^{86} +6.63102 q^{87} +12.6799 q^{88} -3.56033 q^{89} +4.04892 q^{90} +2.39612 q^{92} +1.58211 q^{93} -4.90515 q^{94} -0.246980 q^{95} +3.07606 q^{96} -7.40581 q^{97} +6.00969 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} - q^{3} - q^{4} - 2 q^{5} + 5 q^{6} - 4 q^{9}+O(q^{10}) $ 3 * q - q^2 - q^3 - q^4 - 2 * q^5 + 5 * q^6 - 4 * q^9	$ 3 q - q^{2} - q^{3} - q^{4} - 2 q^{5} + 5 q^{6} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 2 q^{12} + 6 q^{13} - 4 q^{15} - 5 q^{16} + 3 q^{17} - q^{18} + q^{19} + 3 q^{20} - q^{22} - 6 q^{23} - 7 q^{24} - 9 q^{25} - 2 q^{26} + 2 q^{27} - q^{29} - q^{30} - 4 q^{31} + 4 q^{32} - q^{33} - q^{34} + 6 q^{36} - 17 q^{37} - 5 q^{38} - 2 q^{39} + 7 q^{40} + 18 q^{41} - 17 q^{43} - 8 q^{44} + 5 q^{45} - 12 q^{46} - 5 q^{47} + 4 q^{48} + 10 q^{50} - q^{51} - 9 q^{52} + 4 q^{53} - 17 q^{54} + 5 q^{55} - 5 q^{57} + 5 q^{58} + 7 q^{59} - q^{60} - 4 q^{61} - q^{62} + 4 q^{64} - 4 q^{65} - 16 q^{66} - 20 q^{67} - q^{68} - 12 q^{69} - 17 q^{71} - 9 q^{73} - 6 q^{74} + 10 q^{75} + 9 q^{76} + 3 q^{78} - 19 q^{79} + q^{80} - 5 q^{81} + q^{82} - 14 q^{83} - 2 q^{85} + 15 q^{86} + 5 q^{87} + 14 q^{88} - 8 q^{89} + 3 q^{90} + 16 q^{92} - q^{93} + 11 q^{94} + 4 q^{95} - 6 q^{96} - 9 q^{97} - 4 q^{99}+O(q^{100}) $ 3 * q - q^2 - q^3 - q^4 - 2 * q^5 + 5 * q^6 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 2 * q^12 + 6 * q^13 - 4 * q^15 - 5 * q^16 + 3 * q^17 - q^18 + q^19 + 3 * q^20 - q^22 - 6 * q^23 - 7 * q^24 - 9 * q^25 - 2 * q^26 + 2 * q^27 - q^29 - q^30 - 4 * q^31 + 4 * q^32 - q^33 - q^34 + 6 * q^36 - 17 * q^37 - 5 * q^38 - 2 * q^39 + 7 * q^40 + 18 * q^41 - 17 * q^43 - 8 * q^44 + 5 * q^45 - 12 * q^46 - 5 * q^47 + 4 * q^48 + 10 * q^50 - q^51 - 9 * q^52 + 4 * q^53 - 17 * q^54 + 5 * q^55 - 5 * q^57 + 5 * q^58 + 7 * q^59 - q^60 - 4 * q^61 - q^62 + 4 * q^64 - 4 * q^65 - 16 * q^66 - 20 * q^67 - q^68 - 12 * q^69 - 17 * q^71 - 9 * q^73 - 6 * q^74 + 10 * q^75 + 9 * q^76 + 3 * q^78 - 19 * q^79 + q^80 - 5 * q^81 + q^82 - 14 * q^83 - 2 * q^85 + 15 * q^86 + 5 * q^87 + 14 * q^88 - 8 * q^89 + 3 * q^90 + 16 * q^92 - q^93 + 11 * q^94 + 4 * q^95 - 6 * q^96 - 9 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.24698	0.881748	0.440874	−	0.897569i	$-0.354669\pi$
$2$	1.24698	0.881748	0.440874	+	0.897569i	$0.354669\pi$
$3$	1.24698	0.719944	0.359972	−	0.932963i	$-0.382786\pi$
$3$	1.24698	0.719944	0.359972	+	0.932963i	$0.382786\pi$
$4$	−0.445042	−0.222521
$5$	−2.24698	−1.00488	−0.502440	−	0.864612i	$-0.667564\pi$
$5$	−2.24698	−1.00488	−0.502440	+	0.864612i	$0.667564\pi$
$6$	1.55496	0.634809
$7$	0	0
$7$	0	0
$8$	−3.04892	−1.07796
$9$	−1.44504	−0.481681
$10$	−2.80194	−0.886051
$11$	−4.15883	−1.25394	−0.626968	−	0.779045i	$-0.715704\pi$
$11$	−4.15883	−1.25394	−0.626968	+	0.779045i	$0.715704\pi$
$12$	−0.554958	−0.160203
$13$	0.643104	0.178365	0.0891825	−	0.996015i	$-0.471575\pi$
$13$	0.643104	0.178365	0.0891825	+	0.996015i	$0.471575\pi$
$14$	0	0
$15$	−2.80194	−0.723457
$16$	−2.91185	−0.727963
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.80194	−0.424721
$19$	0.109916	0.0252165	0.0126083	−	0.999921i	$-0.495987\pi$
$19$	0.109916	0.0252165	0.0126083	+	0.999921i	$0.495987\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	−5.18598	−1.10565
$23$	−5.38404	−1.12265	−0.561325	−	0.827595i	$-0.689708\pi$
$23$	−5.38404	−1.12265	−0.561325	+	0.827595i	$0.689708\pi$
$24$	−3.80194	−0.776067
$25$	0.0489173	0.00978347
$26$	0.801938	0.157273
$27$	−5.54288	−1.06673
$28$	0	0
$29$	5.31767	0.987466	0.493733	−	0.869614i	$-0.335632\pi$
$29$	5.31767	0.987466	0.493733	+	0.869614i	$0.335632\pi$
$30$	−3.49396	−0.637907
$31$	1.26875	0.227874	0.113937	−	0.993488i	$-0.463654\pi$
$31$	1.26875	0.227874	0.113937	+	0.993488i	$0.463654\pi$
$32$	2.46681	0.436075
$33$	−5.18598	−0.902763
$34$	1.24698	0.213855
$35$	0	0
$36$	0.643104	0.107184
$37$	−10.2959	−1.69264	−0.846318	−	0.532679i	$-0.821185\pi$
$37$	−10.2959	−1.69264	−0.846318	+	0.532679i	$0.821185\pi$
$38$	0.137063	0.0222346
$39$	0.801938	0.128413
$40$	6.85086	1.08322
$41$	10.4058	1.62511	0.812557	−	0.582881i	$-0.198075\pi$
$41$	10.4058	1.62511	0.812557	+	0.582881i	$0.198075\pi$
$42$	0	0
$43$	−5.21983	−0.796017	−0.398008	−	0.917382i	$-0.630299\pi$
$43$	−5.21983	−0.796017	−0.398008	+	0.917382i	$0.630299\pi$
$44$	1.85086	0.279027
$45$	3.24698	0.484031
$46$	−6.71379	−0.989895
$47$	−3.93362	−0.573778	−0.286889	−	0.957964i	$-0.592621\pi$
$47$	−3.93362	−0.573778	−0.286889	+	0.957964i	$0.592621\pi$
$48$	−3.63102	−0.524093
$49$	0	0
$50$	0.0609989	0.00862655
$51$	1.24698	0.174612
$52$	−0.286208	−0.0396899
$53$	10.2567	1.40886	0.704431	−	0.709773i	$-0.251202\pi$
$53$	10.2567	1.40886	0.704431	+	0.709773i	$0.251202\pi$
$54$	−6.91185	−0.940584
$55$	9.34481	1.26005
$56$	0	0
$57$	0.137063	0.0181545
$58$	6.63102	0.870696
$59$	6.85086	0.891905	0.445953	−	0.895057i	$-0.352865\pi$
$59$	6.85086	0.891905	0.445953	+	0.895057i	$0.352865\pi$
$60$	1.24698	0.160984
$61$	0.246980	0.0316225	0.0158112	−	0.999875i	$-0.494967\pi$
$61$	0.246980	0.0316225	0.0158112	+	0.999875i	$0.494967\pi$
$62$	1.58211	0.200928
$63$	0	0
$64$	8.89977	1.11247
$65$	−1.44504	−0.179235
$66$	−6.46681	−0.796010
$67$	−11.6310	−1.42096	−0.710478	−	0.703720i	$-0.751521\pi$
$67$	−11.6310	−1.42096	−0.710478	+	0.703720i	$0.751521\pi$
$68$	−0.445042	−0.0539693
$69$	−6.71379	−0.808246
$70$	0	0
$71$	0.878002	0.104200	0.0520998	−	0.998642i	$-0.483409\pi$
$71$	0.878002	0.104200	0.0520998	+	0.998642i	$0.483409\pi$
$72$	4.40581	0.519230
$73$	−15.8823	−1.85888	−0.929442	−	0.368968i	$-0.879711\pi$
$73$	−15.8823	−1.85888	−0.929442	+	0.368968i	$0.879711\pi$
$74$	−12.8388	−1.49248
$75$	0.0609989	0.00704355
$76$	−0.0489173	−0.00561120
$77$	0	0
$78$	1.00000	0.113228
$79$	1.67994	0.189008	0.0945040	−	0.995524i	$-0.469873\pi$
$79$	1.67994	0.189008	0.0945040	+	0.995524i	$0.469873\pi$
$80$	6.54288	0.731516
$81$	−2.57673	−0.286303
$82$	12.9758	1.43294
$83$	15.0954	1.65694	0.828470	−	0.560033i	$-0.189212\pi$
$83$	15.0954	1.65694	0.828470	+	0.560033i	$0.189212\pi$
$84$	0	0
$85$	−2.24698	−0.243719
$86$	−6.50902	−0.701886
$87$	6.63102	0.710920
$88$	12.6799	1.35169
$89$	−3.56033	−0.377395	−0.188697	−	0.982035i	$-0.560427\pi$
$89$	−3.56033	−0.377395	−0.188697	+	0.982035i	$0.560427\pi$
$90$	4.04892	0.426793
$91$	0	0
$92$	2.39612	0.249813
$93$	1.58211	0.164057
$94$	−4.90515	−0.505928
$95$	−0.246980	−0.0253396
$96$	3.07606	0.313950
$97$	−7.40581	−0.751946	−0.375973	−	0.926631i	$-0.622692\pi$
$97$	−7.40581	−0.751946	−0.375973	+	0.926631i	$0.622692\pi$
$98$	0	0
$99$	6.00969	0.603996
$100$	−0.0217703	−0.00217703
$101$	−12.1129	−1.20528	−0.602639	−	0.798014i	$-0.705884\pi$
$101$	−12.1129	−1.20528	−0.602639	+	0.798014i	$0.705884\pi$
$102$	1.55496	0.153964
$103$	−3.93900	−0.388121	−0.194061	−	0.980990i	$-0.562166\pi$
$103$	−3.93900	−0.388121	−0.194061	+	0.980990i	$0.562166\pi$
$104$	−1.96077	−0.192269
$105$	0	0
$106$	12.7899	1.24226
$107$	−2.02177	−0.195452	−0.0977260	−	0.995213i	$-0.531157\pi$
$107$	−2.02177	−0.195452	−0.0977260	+	0.995213i	$0.531157\pi$
$108$	2.46681	0.237369
$109$	4.65279	0.445657	0.222828	−	0.974858i	$-0.428471\pi$
$109$	4.65279	0.445657	0.222828	+	0.974858i	$0.428471\pi$
$110$	11.6528	1.11105
$111$	−12.8388	−1.21860
$112$	0	0
$113$	2.74094	0.257846	0.128923	−	0.991655i	$-0.458848\pi$
$113$	2.74094	0.257846	0.128923	+	0.991655i	$0.458848\pi$
$114$	0.170915	0.0160077
$115$	12.0978	1.12813
$116$	−2.36658	−0.219732
$117$	−0.929312	−0.0859150
$118$	8.54288	0.786436
$119$	0	0
$120$	8.54288	0.779854
$121$	6.29590	0.572354
$122$	0.307979	0.0278831
$123$	12.9758	1.16999
$124$	−0.564647	−0.0507068
$125$	11.1250	0.995049
$126$	0	0
$127$	−9.66487	−0.857619	−0.428809	−	0.903395i	$-0.641067\pi$
$127$	−9.66487	−0.857619	−0.428809	+	0.903395i	$0.641067\pi$
$128$	6.16421	0.544844
$129$	−6.50902	−0.573088
$130$	−1.80194	−0.158040
$131$	10.6582	0.931209	0.465604	−	0.884993i	$-0.345837\pi$
$131$	10.6582	0.931209	0.465604	+	0.884993i	$0.345837\pi$
$132$	2.30798	0.200884
$133$	0	0
$134$	−14.5036	−1.25292
$135$	12.4547	1.07193
$136$	−3.04892	−0.261443
$137$	14.4450	1.23412	0.617062	−	0.786915i	$-0.288323\pi$
$137$	14.4450	1.23412	0.617062	+	0.786915i	$0.288323\pi$
$138$	−8.37196	−0.712669
$139$	−18.8019	−1.59476	−0.797380	−	0.603478i	$-0.793781\pi$
$139$	−18.8019	−1.59476	−0.797380	+	0.603478i	$0.793781\pi$
$140$	0	0
$141$	−4.90515	−0.413088
$142$	1.09485	0.0918778
$143$	−2.67456	−0.223658
$144$	4.20775	0.350646
$145$	−11.9487	−0.992285
$146$	−19.8049	−1.63907
$147$	0	0
$148$	4.58211	0.376647
$149$	1.81402	0.148610	0.0743051	−	0.997236i	$-0.476326\pi$
$149$	1.81402	0.148610	0.0743051	+	0.997236i	$0.476326\pi$
$150$	0.0760644	0.00621063
$151$	−7.54288	−0.613831	−0.306915	−	0.951737i	$-0.599297\pi$
$151$	−7.54288	−0.613831	−0.306915	+	0.951737i	$0.599297\pi$
$152$	−0.335126	−0.0271823
$153$	−1.44504	−0.116825
$154$	0	0
$155$	−2.85086	−0.228986
$156$	−0.356896	−0.0285745
$157$	11.7506	0.937802	0.468901	−	0.883251i	$-0.344650\pi$
$157$	11.7506	0.937802	0.468901	+	0.883251i	$0.344650\pi$
$158$	2.09485	0.166657
$159$	12.7899	1.01430
$160$	−5.54288	−0.438203
$161$	0	0
$162$	−3.21313	−0.252447
$163$	21.8146	1.70865	0.854326	−	0.519737i	$-0.173970\pi$
$163$	21.8146	1.70865	0.854326	+	0.519737i	$0.173970\pi$
$164$	−4.63102	−0.361622
$165$	11.6528	0.907169
$166$	18.8237	1.46100
$167$	−21.6136	−1.67251	−0.836254	−	0.548342i	$-0.815259\pi$
$167$	−21.6136	−1.67251	−0.836254	+	0.548342i	$0.815259\pi$
$168$	0	0
$169$	−12.5864	−0.968186
$170$	−2.80194	−0.214899
$171$	−0.158834	−0.0121463
$172$	2.32304	0.177130
$173$	−15.6799	−1.19212	−0.596062	−	0.802939i	$-0.703269\pi$
$173$	−15.6799	−1.19212	−0.596062	+	0.802939i	$0.703269\pi$
$174$	8.26875	0.626852
$175$	0	0
$176$	12.1099	0.912819
$177$	8.54288	0.642122
$178$	−4.43967	−0.332767
$179$	−16.7168	−1.24947	−0.624735	−	0.780837i	$-0.714793\pi$
$179$	−16.7168	−1.24947	−0.624735	+	0.780837i	$0.714793\pi$
$180$	−1.44504	−0.107707
$181$	−16.5362	−1.22912	−0.614562	−	0.788869i	$-0.710667\pi$
$181$	−16.5362	−1.22912	−0.614562	+	0.788869i	$0.710667\pi$
$182$	0	0
$183$	0.307979	0.0227664
$184$	16.4155	1.21017
$185$	23.1347	1.70089
$186$	1.97285	0.144657
$187$	−4.15883	−0.304124
$188$	1.75063	0.127678
$189$	0	0
$190$	−0.307979	−0.0223431
$191$	−2.19567	−0.158873	−0.0794365	−	0.996840i	$-0.525312\pi$
$191$	−2.19567	−0.158873	−0.0794365	+	0.996840i	$0.525312\pi$
$192$	11.0978	0.800917
$193$	−15.7409	−1.13306	−0.566529	−	0.824042i	$-0.691714\pi$
$193$	−15.7409	−1.13306	−0.566529	+	0.824042i	$0.691714\pi$
$194$	−9.23490	−0.663027
$195$	−1.80194	−0.129039
$196$	0	0
$197$	−14.2228	−1.01333	−0.506667	−	0.862142i	$-0.669123\pi$
$197$	−14.2228	−1.01333	−0.506667	+	0.862142i	$0.669123\pi$
$198$	7.49396	0.532572
$199$	2.06398	0.146312	0.0731559	−	0.997321i	$-0.476693\pi$
$199$	2.06398	0.146312	0.0731559	+	0.997321i	$0.476693\pi$
$200$	−0.149145	−0.0105461
$201$	−14.5036	−1.02301
$202$	−15.1045	−1.06275
$203$	0	0
$204$	−0.554958	−0.0388548
$205$	−23.3817	−1.63305
$206$	−4.91185	−0.342225
$207$	7.78017	0.540759
$208$	−1.87263	−0.129843
$209$	−0.457123	−0.0316199
$210$	0	0
$211$	−2.19136	−0.150859	−0.0754296	−	0.997151i	$-0.524033\pi$
$211$	−2.19136	−0.150859	−0.0754296	+	0.997151i	$0.524033\pi$
$212$	−4.56465	−0.313501
$213$	1.09485	0.0750179
$214$	−2.52111	−0.172339
$215$	11.7289	0.799901
$216$	16.8998	1.14988
$217$	0	0
$218$	5.80194	0.392957
$219$	−19.8049	−1.33829
$220$	−4.15883	−0.280389
$221$	0.643104	0.0432599
$222$	−16.0097	−1.07450
$223$	13.1414	0.880012	0.440006	−	0.897995i	$-0.354976\pi$
$223$	13.1414	0.880012	0.440006	+	0.897995i	$0.354976\pi$
$224$	0	0
$225$	−0.0706876	−0.00471251
$226$	3.41789	0.227355
$227$	3.60388	0.239198	0.119599	−	0.992822i	$-0.461839\pi$
$227$	3.60388	0.239198	0.119599	+	0.992822i	$0.461839\pi$
$228$	−0.0609989	−0.00403975
$229$	−0.928247	−0.0613403	−0.0306702	−	0.999530i	$-0.509764\pi$
$229$	−0.928247	−0.0613403	−0.0306702	+	0.999530i	$0.509764\pi$
$230$	15.0858	0.994725
$231$	0	0
$232$	−16.2131	−1.06444
$233$	−5.79954	−0.379941	−0.189970	−	0.981790i	$-0.560839\pi$
$233$	−5.79954	−0.379941	−0.189970	+	0.981790i	$0.560839\pi$
$234$	−1.15883	−0.0757553
$235$	8.83877	0.576578
$236$	−3.04892	−0.198468
$237$	2.09485	0.136075
$238$	0	0
$239$	−8.36227	−0.540910	−0.270455	−	0.962733i	$-0.587174\pi$
$239$	−8.36227	−0.540910	−0.270455	+	0.962733i	$0.587174\pi$
$240$	8.15883	0.526650
$241$	27.5652	1.77563	0.887817	−	0.460198i	$-0.152221\pi$
$241$	27.5652	1.77563	0.887817	+	0.460198i	$0.152221\pi$
$242$	7.85086	0.504672
$243$	13.4155	0.860605
$244$	−0.109916	−0.00703667
$245$	0	0
$246$	16.1806	1.03164
$247$	0.0706876	0.00449774
$248$	−3.86831	−0.245638
$249$	18.8237	1.19290
$250$	13.8726	0.877382
$251$	25.9541	1.63821	0.819103	−	0.573646i	$-0.194472\pi$
$251$	25.9541	1.63821	0.819103	+	0.573646i	$0.194472\pi$
$252$	0	0
$253$	22.3913	1.40773
$254$	−12.0519	−0.756204
$255$	−2.80194	−0.175464
$256$	−10.1129	−0.632056
$257$	13.0737	0.815513	0.407757	−	0.913091i	$-0.366311\pi$
$257$	13.0737	0.815513	0.407757	+	0.913091i	$0.366311\pi$
$258$	−8.11662	−0.505319
$259$	0	0
$260$	0.643104	0.0398836
$261$	−7.68425	−0.475643
$262$	13.2905	0.821091
$263$	−9.59850	−0.591869	−0.295934	−	0.955208i	$-0.595631\pi$
$263$	−9.59850	−0.591869	−0.295934	+	0.955208i	$0.595631\pi$
$264$	15.8116	0.973138
$265$	−23.0465	−1.41574
$266$	0	0
$267$	−4.43967	−0.271703
$268$	5.17629	0.316192
$269$	−13.6722	−0.833607	−0.416803	−	0.908997i	$-0.636850\pi$
$269$	−13.6722	−0.833607	−0.416803	+	0.908997i	$0.636850\pi$
$270$	15.5308	0.945174
$271$	25.1196	1.52591	0.762954	−	0.646453i	$-0.223748\pi$
$271$	25.1196	1.52591	0.762954	+	0.646453i	$0.223748\pi$
$272$	−2.91185	−0.176557
$273$	0	0
$274$	18.0127	1.08819
$275$	−0.203439	−0.0122678
$276$	2.98792	0.179852
$277$	−10.6963	−0.642680	−0.321340	−	0.946964i	$-0.604133\pi$
$277$	−10.6963	−0.642680	−0.321340	+	0.946964i	$0.604133\pi$
$278$	−23.4456	−1.40618
$279$	−1.83340	−0.109763
$280$	0	0
$281$	13.4233	0.800765	0.400383	−	0.916348i	$-0.368877\pi$
$281$	13.4233	0.800765	0.400383	+	0.916348i	$0.368877\pi$
$282$	−6.11662	−0.364239
$283$	2.78017	0.165264	0.0826319	−	0.996580i	$-0.473667\pi$
$283$	2.78017	0.165264	0.0826319	+	0.996580i	$0.473667\pi$
$284$	−0.390748	−0.0231866
$285$	−0.307979	−0.0182431
$286$	−3.33513	−0.197210
$287$	0	0
$288$	−3.56465	−0.210049
$289$	1.00000	0.0588235
$290$	−14.8998	−0.874945
$291$	−9.23490	−0.541359
$292$	7.06829	0.413641
$293$	−11.1414	−0.650886	−0.325443	−	0.945562i	$-0.605513\pi$
$293$	−11.1414	−0.650886	−0.325443	+	0.945562i	$0.605513\pi$
$294$	0	0
$295$	−15.3937	−0.896258
$296$	31.3913	1.82458
$297$	23.0519	1.33761
$298$	2.26205	0.131037
$299$	−3.46250	−0.200242
$300$	−0.0271471	−0.00156734
$301$	0	0
$302$	−9.40581	−0.541244
$303$	−15.1045	−0.867733
$304$	−0.320060	−0.0183567
$305$	−0.554958	−0.0317768
$306$	−1.80194	−0.103010
$307$	6.76032	0.385832	0.192916	−	0.981215i	$-0.438206\pi$
$307$	6.76032	0.385832	0.192916	+	0.981215i	$0.438206\pi$
$308$	0	0
$309$	−4.91185	−0.279426
$310$	−3.55496	−0.201908
$311$	−17.6515	−1.00092	−0.500461	−	0.865759i	$-0.666836\pi$
$311$	−17.6515	−1.00092	−0.500461	+	0.865759i	$0.666836\pi$
$312$	−2.44504	−0.138423
$313$	19.7409	1.11582	0.557912	−	0.829900i	$-0.311603\pi$
$313$	19.7409	1.11582	0.557912	+	0.829900i	$0.311603\pi$
$314$	14.6528	0.826905
$315$	0	0
$316$	−0.747644	−0.0420582
$317$	2.14675	0.120574	0.0602868	−	0.998181i	$-0.480798\pi$
$317$	2.14675	0.120574	0.0602868	+	0.998181i	$0.480798\pi$
$318$	15.9487	0.894358
$319$	−22.1153	−1.23822
$320$	−19.9976	−1.11790
$321$	−2.52111	−0.140714
$322$	0	0
$323$	0.109916	0.00611590
$324$	1.14675	0.0637084
$325$	0.0314589	0.00174503
$326$	27.2024	1.50660
$327$	5.80194	0.320848
$328$	−31.7265	−1.75180
$329$	0	0
$330$	14.5308	0.799894
$331$	10.0653	0.553240	0.276620	−	0.960979i	$-0.410786\pi$
$331$	10.0653	0.553240	0.276620	+	0.960979i	$0.410786\pi$
$332$	−6.71810	−0.368704
$333$	14.8780	0.815309
$334$	−26.9517	−1.47473
$335$	26.1347	1.42789
$336$	0	0
$337$	−36.3696	−1.98118	−0.990588	−	0.136875i	$-0.956294\pi$
$337$	−36.3696	−1.98118	−0.990588	+	0.136875i	$0.956294\pi$
$338$	−15.6950	−0.853696
$339$	3.41789	0.185635
$340$	1.00000	0.0542326
$341$	−5.27652	−0.285740
$342$	−0.198062	−0.0107100
$343$	0	0
$344$	15.9148	0.858071
$345$	15.0858	0.812190
$346$	−19.5526	−1.05115
$347$	−35.6775	−1.91527	−0.957636	−	0.287983i	$-0.907015\pi$
$347$	−35.6775	−1.91527	−0.957636	+	0.287983i	$0.907015\pi$
$348$	−2.95108	−0.158195
$349$	10.8140	0.578861	0.289431	−	0.957199i	$-0.406534\pi$
$349$	10.8140	0.578861	0.289431	+	0.957199i	$0.406534\pi$
$350$	0	0
$351$	−3.56465	−0.190267
$352$	−10.2591	−0.546810
$353$	11.1250	0.592123	0.296062	−	0.955169i	$-0.404327\pi$
$353$	11.1250	0.592123	0.296062	+	0.955169i	$0.404327\pi$
$354$	10.6528	0.566190
$355$	−1.97285	−0.104708
$356$	1.58450	0.0839782
$357$	0	0
$358$	−20.8455	−1.10172
$359$	−17.3177	−0.913992	−0.456996	−	0.889469i	$-0.651075\pi$
$359$	−17.3177	−0.913992	−0.456996	+	0.889469i	$0.651075\pi$
$360$	−9.89977	−0.521764
$361$	−18.9879	−0.999364
$362$	−20.6203	−1.08378
$363$	7.85086	0.412063
$364$	0	0
$365$	35.6872	1.86796
$366$	0.384043	0.0200742
$367$	−36.3400	−1.89693	−0.948467	−	0.316876i	$-0.897366\pi$
$367$	−36.3400	−1.89693	−0.948467	+	0.316876i	$0.897366\pi$
$368$	15.6775	0.817249
$369$	−15.0368	−0.782786
$370$	28.8485	1.49976
$371$	0	0
$372$	−0.704103	−0.0365060
$373$	24.4403	1.26547	0.632734	−	0.774369i	$-0.281933\pi$
$373$	24.4403	1.26547	0.632734	+	0.774369i	$0.281933\pi$
$374$	−5.18598	−0.268161
$375$	13.8726	0.716379
$376$	11.9933	0.618507
$377$	3.41981	0.176129
$378$	0	0
$379$	−13.2862	−0.682467	−0.341233	−	0.939979i	$-0.610845\pi$
$379$	−13.2862	−0.682467	−0.341233	+	0.939979i	$0.610845\pi$
$380$	0.109916	0.00563859
$381$	−12.0519	−0.617438
$382$	−2.73795	−0.140086
$383$	−33.1540	−1.69409	−0.847046	−	0.531519i	$-0.821621\pi$
$383$	−33.1540	−1.69409	−0.847046	+	0.531519i	$0.821621\pi$
$384$	7.68664	0.392257
$385$	0	0
$386$	−19.6286	−0.999071
$387$	7.54288	0.383426
$388$	3.29590	0.167324
$389$	23.1424	1.17337	0.586684	−	0.809816i	$-0.300433\pi$
$389$	23.1424	1.17337	0.586684	+	0.809816i	$0.300433\pi$
$390$	−2.24698	−0.113780
$391$	−5.38404	−0.272283
$392$	0	0
$393$	13.2905	0.670418
$394$	−17.7356	−0.893505
$395$	−3.77479	−0.189930
$396$	−2.67456	−0.134402
$397$	4.96615	0.249244	0.124622	−	0.992204i	$-0.460228\pi$
$397$	4.96615	0.249244	0.124622	+	0.992204i	$0.460228\pi$
$398$	2.57374	0.129010
$399$	0	0
$400$	−0.142440	−0.00712201
$401$	16.9463	0.846258	0.423129	−	0.906070i	$-0.360932\pi$
$401$	16.9463	0.846258	0.423129	+	0.906070i	$0.360932\pi$
$402$	−18.0858	−0.902035
$403$	0.815938	0.0406448
$404$	5.39075	0.268200
$405$	5.78986	0.287700
$406$	0	0
$407$	42.8189	2.12246
$408$	−3.80194	−0.188224
$409$	−8.05861	−0.398472	−0.199236	−	0.979951i	$-0.563846\pi$
$409$	−8.05861	−0.398472	−0.199236	+	0.979951i	$0.563846\pi$
$410$	−29.1564	−1.43993
$411$	18.0127	0.888500
$412$	1.75302	0.0863651
$413$	0	0
$414$	9.70171	0.476813
$415$	−33.9191	−1.66503
$416$	1.58642	0.0777805
$417$	−23.4456	−1.14814
$418$	−0.570024	−0.0278808
$419$	−24.8256	−1.21281	−0.606406	−	0.795155i	$-0.707389\pi$
$419$	−24.8256	−1.21281	−0.606406	+	0.795155i	$0.707389\pi$
$420$	0	0
$421$	10.0731	0.490932	0.245466	−	0.969405i	$-0.421059\pi$
$421$	10.0731	0.490932	0.245466	+	0.969405i	$0.421059\pi$
$422$	−2.73258	−0.133020
$423$	5.68425	0.276378
$424$	−31.2717	−1.51869
$425$	0.0489173	0.00237284
$426$	1.36526	0.0661469
$427$	0	0
$428$	0.899772	0.0434921
$429$	−3.33513	−0.161021
$430$	14.6256	0.705311
$431$	13.7429	0.661970	0.330985	−	0.943636i	$-0.392619\pi$
$431$	13.7429	0.661970	0.330985	+	0.943636i	$0.392619\pi$
$432$	16.1400	0.776538
$433$	27.8780	1.33973	0.669866	−	0.742482i	$-0.266352\pi$
$433$	27.8780	1.33973	0.669866	+	0.742482i	$0.266352\pi$
$434$	0	0
$435$	−14.8998	−0.714389
$436$	−2.07069	−0.0991680
$437$	−0.591794	−0.0283093
$438$	−24.6963	−1.18004
$439$	−8.79763	−0.419888	−0.209944	−	0.977713i	$-0.567328\pi$
$439$	−8.79763	−0.419888	−0.209944	+	0.977713i	$0.567328\pi$
$440$	−28.4916	−1.35828
$441$	0	0
$442$	0.801938	0.0381443
$443$	−19.6963	−0.935801	−0.467901	−	0.883781i	$-0.654989\pi$
$443$	−19.6963	−0.935801	−0.467901	+	0.883781i	$0.654989\pi$
$444$	5.71379	0.271165
$445$	8.00000	0.379236
$446$	16.3870	0.775948
$447$	2.26205	0.106991
$448$	0	0
$449$	−9.96508	−0.470281	−0.235141	−	0.971961i	$-0.575555\pi$
$449$	−9.96508	−0.470281	−0.235141	+	0.971961i	$0.575555\pi$
$450$	−0.0881460	−0.00415524
$451$	−43.2760	−2.03779
$452$	−1.21983	−0.0573761
$453$	−9.40581	−0.441924
$454$	4.49396	0.210912
$455$	0	0
$456$	−0.417895	−0.0195697
$457$	−36.7101	−1.71722	−0.858612	−	0.512625i	$-0.828673\pi$
$457$	−36.7101	−1.71722	−0.858612	+	0.512625i	$0.828673\pi$
$458$	−1.15751	−0.0540867
$459$	−5.54288	−0.258719
$460$	−5.38404	−0.251032
$461$	−11.5840	−0.539522	−0.269761	−	0.962927i	$-0.586945\pi$
$461$	−11.5840	−0.539522	−0.269761	+	0.962927i	$0.586945\pi$
$462$	0	0
$463$	−17.4504	−0.810990	−0.405495	−	0.914097i	$-0.632901\pi$
$463$	−17.4504	−0.810990	−0.405495	+	0.914097i	$0.632901\pi$
$464$	−15.4843	−0.718839
$465$	−3.55496	−0.164857
$466$	−7.23191	−0.335012
$467$	37.5961	1.73974	0.869870	−	0.493281i	$-0.164202\pi$
$467$	37.5961	1.73974	0.869870	+	0.493281i	$0.164202\pi$
$468$	0.413583	0.0191179
$469$	0	0
$470$	11.0218	0.508396
$471$	14.6528	0.675165
$472$	−20.8877	−0.961434
$473$	21.7084	0.998154
$474$	2.61224	0.119984
$475$	0.00537681	0.000246705 0
$476$	0	0
$477$	−14.8213	−0.678621
$478$	−10.4276	−0.476947
$479$	−24.5767	−1.12294	−0.561470	−	0.827497i	$-0.689764\pi$
$479$	−24.5767	−1.12294	−0.561470	+	0.827497i	$0.689764\pi$
$480$	−6.91185	−0.315482
$481$	−6.62133	−0.301907
$482$	34.3733	1.56566
$483$	0	0
$484$	−2.80194	−0.127361
$485$	16.6407	0.755616
$486$	16.7289	0.758836
$487$	−1.93602	−0.0877293	−0.0438647	−	0.999037i	$-0.513967\pi$
$487$	−1.93602	−0.0877293	−0.0438647	+	0.999037i	$0.513967\pi$
$488$	−0.753020	−0.0340876
$489$	27.2024	1.23013
$490$	0	0
$491$	18.6340	0.840941	0.420470	−	0.907306i	$-0.361865\pi$
$491$	18.6340	0.840941	0.420470	+	0.907306i	$0.361865\pi$
$492$	−5.77479	−0.260348
$493$	5.31767	0.239496
$494$	0.0881460	0.00396588
$495$	−13.5036	−0.606944
$496$	−3.69441	−0.165884
$497$	0	0
$498$	23.4728	1.05184
$499$	13.5483	0.606503	0.303252	−	0.952911i	$-0.401928\pi$
$499$	13.5483	0.606503	0.303252	+	0.952911i	$0.401928\pi$
$500$	−4.95108	−0.221419
$501$	−26.9517	−1.20411
$502$	32.3642	1.44448
$503$	1.94331	0.0866480	0.0433240	−	0.999061i	$-0.486205\pi$
$503$	1.94331	0.0866480	0.0433240	+	0.999061i	$0.486205\pi$
$504$	0	0
$505$	27.2174	1.21116
$506$	27.9215	1.24126
$507$	−15.6950	−0.697040
$508$	4.30127	0.190838
$509$	2.26444	0.100369	0.0501847	−	0.998740i	$-0.484019\pi$
$509$	2.26444	0.100369	0.0501847	+	0.998740i	$0.484019\pi$
$510$	−3.49396	−0.154715
$511$	0	0
$512$	−24.9390	−1.10216
$513$	−0.609252	−0.0268991
$514$	16.3026	0.719077
$515$	8.85086	0.390015
$516$	2.89679	0.127524
$517$	16.3593	0.719481
$518$	0	0
$519$	−19.5526	−0.858262
$520$	4.40581	0.193208
$521$	−3.70410	−0.162280	−0.0811399	−	0.996703i	$-0.525856\pi$
$521$	−3.70410	−0.162280	−0.0811399	+	0.996703i	$0.525856\pi$
$522$	−9.58211	−0.419397
$523$	21.3690	0.934400	0.467200	−	0.884152i	$-0.345263\pi$
$523$	21.3690	0.934400	0.467200	+	0.884152i	$0.345263\pi$
$524$	−4.74333	−0.207213
$525$	0	0
$526$	−11.9691	−0.521879
$527$	1.26875	0.0552676
$528$	15.1008	0.657179
$529$	5.98792	0.260344
$530$	−28.7385	−1.24832
$531$	−9.89977	−0.429614
$532$	0	0
$533$	6.69202	0.289864
$534$	−5.53617	−0.239574
$535$	4.54288	0.196406
$536$	35.4620	1.53173
$537$	−20.8455	−0.899549
$538$	−17.0489	−0.735031
$539$	0	0
$540$	−5.54288	−0.238527
$541$	−0.670251	−0.0288164	−0.0144082	−	0.999896i	$-0.504586\pi$
$541$	−0.670251	−0.0288164	−0.0144082	+	0.999896i	$0.504586\pi$
$542$	31.3236	1.34547
$543$	−20.6203	−0.884900
$544$	2.46681	0.105764
$545$	−10.4547	−0.447831
$546$	0	0
$547$	−22.0204	−0.941526	−0.470763	−	0.882260i	$-0.656021\pi$
$547$	−22.0204	−0.941526	−0.470763	+	0.882260i	$0.656021\pi$
$548$	−6.42865	−0.274618
$549$	−0.356896	−0.0152319
$550$	−0.253684	−0.0108171
$551$	0.584498	0.0249005
$552$	20.4698	0.871252
$553$	0	0
$554$	−13.3381	−0.566682
$555$	28.8485	1.22455
$556$	8.36765	0.354867
$557$	5.97179	0.253033	0.126516	−	0.991965i	$-0.459620\pi$
$557$	5.97179	0.253033	0.126516	+	0.991965i	$0.459620\pi$
$558$	−2.28621	−0.0967829
$559$	−3.35690	−0.141982
$560$	0	0
$561$	−5.18598	−0.218952
$562$	16.7385	0.706073
$563$	26.0954	1.09979	0.549896	−	0.835233i	$-0.314667\pi$
$563$	26.0954	1.09979	0.549896	+	0.835233i	$0.314667\pi$
$564$	2.18300	0.0919207
$565$	−6.15883	−0.259104
$566$	3.46681	0.145721
$567$	0	0
$568$	−2.67696	−0.112323
$569$	6.24267	0.261706	0.130853	−	0.991402i	$-0.458228\pi$
$569$	6.24267	0.261706	0.130853	+	0.991402i	$0.458228\pi$
$570$	−0.384043	−0.0160858
$571$	−2.32065	−0.0971162	−0.0485581	−	0.998820i	$-0.515463\pi$
$571$	−2.32065	−0.0971162	−0.0485581	+	0.998820i	$0.515463\pi$
$572$	1.19029	0.0497686
$573$	−2.73795	−0.114380
$574$	0	0
$575$	−0.263373	−0.0109834
$576$	−12.8605	−0.535856
$577$	36.2650	1.50973	0.754866	−	0.655879i	$-0.227702\pi$
$577$	36.2650	1.50973	0.754866	+	0.655879i	$0.227702\pi$
$578$	1.24698	0.0518675
$579$	−19.6286	−0.815738
$580$	5.31767	0.220804
$581$	0	0
$582$	−11.5157	−0.477342
$583$	−42.6558	−1.76662
$584$	48.4239	2.00379
$585$	2.08815	0.0863342
$586$	−13.8931	−0.573917
$587$	−19.0747	−0.787299	−0.393649	−	0.919261i	$-0.628788\pi$
$587$	−19.0747	−0.787299	−0.393649	+	0.919261i	$0.628788\pi$
$588$	0	0
$589$	0.139456	0.00574619
$590$	−19.1957	−0.790273
$591$	−17.7356	−0.729544
$592$	29.9801	1.23218
$593$	−29.2271	−1.20021	−0.600107	−	0.799920i	$-0.704875\pi$
$593$	−29.2271	−1.20021	−0.600107	+	0.799920i	$0.704875\pi$
$594$	28.7453	1.17943
$595$	0	0
$596$	−0.807315	−0.0330689
$597$	2.57374	0.105336
$598$	−4.31767	−0.176563
$599$	−13.5496	−0.553621	−0.276810	−	0.960925i	$-0.589277\pi$
$599$	−13.5496	−0.553621	−0.276810	+	0.960925i	$0.589277\pi$
$600$	−0.185981	−0.00759263
$601$	40.4292	1.64914	0.824572	−	0.565758i	$-0.191416\pi$
$601$	40.4292	1.64914	0.824572	+	0.565758i	$0.191416\pi$
$602$	0	0
$603$	16.8073	0.684447
$604$	3.35690	0.136590
$605$	−14.1468	−0.575147
$606$	−18.8351	−0.765122
$607$	−18.4631	−0.749394	−0.374697	−	0.927147i	$-0.622253\pi$
$607$	−18.4631	−0.749394	−0.374697	+	0.927147i	$0.622253\pi$
$608$	0.271143	0.0109963
$609$	0	0
$610$	−0.692021	−0.0280191
$611$	−2.52973	−0.102342
$612$	0.643104	0.0259959
$613$	18.9172	0.764060	0.382030	−	0.924150i	$-0.375225\pi$
$613$	18.9172	0.764060	0.382030	+	0.924150i	$0.375225\pi$
$614$	8.42998	0.340206
$615$	−29.1564	−1.17570
$616$	0	0
$617$	6.15751	0.247892	0.123946	−	0.992289i	$-0.460445\pi$
$617$	6.15751	0.247892	0.123946	+	0.992289i	$0.460445\pi$
$618$	−6.12498	−0.246383
$619$	1.35152	0.0543221	0.0271611	−	0.999631i	$-0.491353\pi$
$619$	1.35152	0.0543221	0.0271611	+	0.999631i	$0.491353\pi$
$620$	1.26875	0.0509542
$621$	29.8431	1.19756
$622$	−22.0110	−0.882561
$623$	0	0
$624$	−2.33513	−0.0934798
$625$	−25.2422	−1.00969
$626$	24.6165	0.983875
$627$	−0.570024	−0.0227646
$628$	−5.22952	−0.208681
$629$	−10.2959	−0.410524
$630$	0	0
$631$	−8.67217	−0.345234	−0.172617	−	0.984989i	$-0.555222\pi$
$631$	−8.67217	−0.345234	−0.172617	+	0.984989i	$0.555222\pi$
$632$	−5.12200	−0.203742
$633$	−2.73258	−0.108610
$634$	2.67696	0.106316
$635$	21.7168	0.861804
$636$	−5.69202	−0.225703
$637$	0	0
$638$	−27.5773	−1.09180
$639$	−1.26875	−0.0501910
$640$	−13.8509	−0.547503
$641$	−3.08708	−0.121932	−0.0609662	−	0.998140i	$-0.519418\pi$
$641$	−3.08708	−0.121932	−0.0609662	+	0.998140i	$0.519418\pi$
$642$	−3.14377	−0.124075
$643$	−5.17629	−0.204133	−0.102067	−	0.994778i	$-0.532545\pi$
$643$	−5.17629	−0.204133	−0.102067	+	0.994778i	$0.532545\pi$
$644$	0	0
$645$	14.6256	0.575884
$646$	0.137063	0.00539268
$647$	40.8039	1.60417	0.802083	−	0.597213i	$-0.203725\pi$
$647$	40.8039	1.60417	0.802083	+	0.597213i	$0.203725\pi$
$648$	7.85623	0.308622
$649$	−28.4916	−1.11839
$650$	0.0392287	0.00153867
$651$	0	0
$652$	−9.70841	−0.380211
$653$	14.7506	0.577237	0.288618	−	0.957444i	$-0.406804\pi$
$653$	14.7506	0.577237	0.288618	+	0.957444i	$0.406804\pi$
$654$	7.23490	0.282907
$655$	−23.9487	−0.935753
$656$	−30.3002	−1.18302
$657$	22.9506	0.895389
$658$	0	0
$659$	13.1056	0.510522	0.255261	−	0.966872i	$-0.417839\pi$
$659$	13.1056	0.510522	0.255261	+	0.966872i	$0.417839\pi$
$660$	−5.18598	−0.201864
$661$	−40.7318	−1.58429	−0.792143	−	0.610336i	$-0.791034\pi$
$661$	−40.7318	−1.58429	−0.792143	+	0.610336i	$0.791034\pi$
$662$	12.5512	0.487818
$663$	0.801938	0.0311447
$664$	−46.0248	−1.78611
$665$	0	0
$666$	18.5526	0.718897
$667$	−28.6305	−1.10858
$668$	9.61894	0.372168
$669$	16.3870	0.633559
$670$	32.5894	1.25904
$671$	−1.02715	−0.0396526
$672$	0	0
$673$	31.9506	1.23161	0.615803	−	0.787900i	$-0.288832\pi$
$673$	31.9506	1.23161	0.615803	+	0.787900i	$0.288832\pi$
$674$	−45.3521	−1.74690
$675$	−0.271143	−0.0104363
$676$	5.60148	0.215442
$677$	−7.24027	−0.278266	−0.139133	−	0.990274i	$-0.544432\pi$
$677$	−7.24027	−0.278266	−0.139133	+	0.990274i	$0.544432\pi$
$678$	4.26205	0.163683
$679$	0	0
$680$	6.85086	0.262718
$681$	4.49396	0.172209
$682$	−6.57971	−0.251950
$683$	1.53425	0.0587066	0.0293533	−	0.999569i	$-0.490655\pi$
$683$	1.53425	0.0587066	0.0293533	+	0.999569i	$0.490655\pi$
$684$	0.0706876	0.00270281
$685$	−32.4577	−1.24015
$686$	0	0
$687$	−1.15751	−0.0441616
$688$	15.1994	0.579471
$689$	6.59611	0.251292
$690$	18.8116	0.716146
$691$	−9.56763	−0.363970	−0.181985	−	0.983301i	$-0.558252\pi$
$691$	−9.56763	−0.363970	−0.181985	+	0.983301i	$0.558252\pi$
$692$	6.97823	0.265272
$693$	0	0
$694$	−44.4892	−1.68879
$695$	42.2476	1.60254
$696$	−20.2174	−0.766340
$697$	10.4058	0.394148
$698$	13.4849	0.510410
$699$	−7.23191	−0.273536
$700$	0	0
$701$	−35.4825	−1.34015	−0.670077	−	0.742291i	$-0.733739\pi$
$701$	−35.4825	−1.34015	−0.670077	+	0.742291i	$0.733739\pi$
$702$	−4.44504	−0.167767
$703$	−1.13169	−0.0426824
$704$	−37.0127	−1.39497
$705$	11.0218	0.415104
$706$	13.8726	0.522103
$707$	0	0
$708$	−3.80194	−0.142886
$709$	22.1153	0.830557	0.415279	−	0.909694i	$-0.363684\pi$
$709$	22.1153	0.830557	0.415279	+	0.909694i	$0.363684\pi$
$710$	−2.46011	−0.0923262
$711$	−2.42758	−0.0910415
$712$	10.8552	0.406815
$713$	−6.83100	−0.255823
$714$	0	0
$715$	6.00969	0.224750
$716$	7.43967	0.278033
$717$	−10.4276	−0.389425
$718$	−21.5948	−0.805910
$719$	−0.425665	−0.0158746	−0.00793730	−	0.999968i	$-0.502527\pi$
$719$	−0.425665	−0.0158746	−0.00793730	+	0.999968i	$0.502527\pi$
$720$	−9.45473	−0.352357
$721$	0	0
$722$	−23.6775	−0.881187
$723$	34.3733	1.27836
$724$	7.35929	0.273506
$725$	0.260126	0.00966084
$726$	9.78986	0.363336
$727$	−24.7676	−0.918580	−0.459290	−	0.888286i	$-0.651896\pi$
$727$	−24.7676	−0.918580	−0.459290	+	0.888286i	$0.651896\pi$
$728$	0	0
$729$	24.4590	0.905890
$730$	44.5013	1.64707
$731$	−5.21983	−0.193062
$732$	−0.137063	−0.00506601
$733$	41.3062	1.52568	0.762839	−	0.646588i	$-0.223805\pi$
$733$	41.3062	1.52568	0.762839	+	0.646588i	$0.223805\pi$
$734$	−45.3153	−1.67262
$735$	0	0
$736$	−13.2814	−0.489560
$737$	48.3715	1.78179
$738$	−18.7506	−0.690220
$739$	34.7458	1.27815	0.639073	−	0.769146i	$-0.279318\pi$
$739$	34.7458	1.27815	0.639073	+	0.769146i	$0.279318\pi$
$740$	−10.2959	−0.378485
$741$	0.0881460	0.00323812
$742$	0	0
$743$	16.0495	0.588799	0.294400	−	0.955682i	$-0.404880\pi$
$743$	16.0495	0.588799	0.294400	+	0.955682i	$0.404880\pi$
$744$	−4.82371	−0.176846
$745$	−4.07606	−0.149335
$746$	30.4765	1.11582
$747$	−21.8135	−0.798116
$748$	1.85086	0.0676740
$749$	0	0
$750$	17.2989	0.631666
$751$	−50.4553	−1.84114	−0.920570	−	0.390577i	$-0.872276\pi$
$751$	−50.4553	−1.84114	−0.920570	+	0.390577i	$0.872276\pi$
$752$	11.4541	0.417689
$753$	32.3642	1.17942
$754$	4.26444	0.155302
$755$	16.9487	0.616826
$756$	0	0
$757$	48.4204	1.75987	0.879935	−	0.475095i	$-0.157586\pi$
$757$	48.4204	1.75987	0.879935	+	0.475095i	$0.157586\pi$
$758$	−16.5676	−0.601763
$759$	27.9215	1.01349
$760$	0.753020	0.0273149
$761$	30.0097	1.08785	0.543925	−	0.839134i	$-0.316938\pi$
$761$	30.0097	1.08785	0.543925	+	0.839134i	$0.316938\pi$
$762$	−15.0285	−0.544424
$763$	0	0
$764$	0.977165	0.0353526
$765$	3.24698	0.117395
$766$	−41.3424	−1.49376
$767$	4.40581	0.159085
$768$	−12.6106	−0.455045
$769$	13.4470	0.484910	0.242455	−	0.970163i	$-0.422047\pi$
$769$	13.4470	0.484910	0.242455	+	0.970163i	$0.422047\pi$
$770$	0	0
$771$	16.3026	0.587124
$772$	7.00538	0.252129
$773$	8.13839	0.292718	0.146359	−	0.989232i	$-0.453245\pi$
$773$	8.13839	0.292718	0.146359	+	0.989232i	$0.453245\pi$
$774$	9.40581	0.338085
$775$	0.0620639	0.00222940
$776$	22.5797	0.810564
$777$	0	0
$778$	28.8582	1.03461
$779$	1.14377	0.0409797
$780$	0.801938	0.0287140
$781$	−3.65146	−0.130660
$782$	−6.71379	−0.240085
$783$	−29.4752	−1.05336
$784$	0	0
$785$	−26.4034	−0.942378
$786$	16.5730	0.591140
$787$	−14.1642	−0.504900	−0.252450	−	0.967610i	$-0.581236\pi$
$787$	−14.1642	−0.504900	−0.252450	+	0.967610i	$0.581236\pi$
$788$	6.32975	0.225488
$789$	−11.9691	−0.426112
$790$	−4.70709	−0.167471
$791$	0	0
$792$	−18.3230	−0.651081
$793$	0.158834	0.00564035
$794$	6.19269	0.219770
$795$	−28.7385	−1.01925
$796$	−0.918559	−0.0325575
$797$	−7.24937	−0.256786	−0.128393	−	0.991723i	$-0.540982\pi$
$797$	−7.24937	−0.256786	−0.128393	+	0.991723i	$0.540982\pi$
$798$	0	0
$799$	−3.93362	−0.139162
$800$	0.120670	0.00426632
$801$	5.14483	0.181784
$802$	21.1317	0.746186
$803$	66.0519	2.33092
$804$	6.45473	0.227641
$805$	0	0
$806$	1.01746	0.0358384
$807$	−17.0489	−0.600150
$808$	36.9312	1.29924
$809$	19.2174	0.675649	0.337825	−	0.941209i	$-0.390309\pi$
$809$	19.2174	0.675649	0.337825	+	0.941209i	$0.390309\pi$
$810$	7.21983	0.253679
$811$	−12.8224	−0.450255	−0.225127	−	0.974329i	$-0.572280\pi$
$811$	−12.8224	−0.450255	−0.225127	+	0.974329i	$0.572280\pi$
$812$	0	0
$813$	31.3236	1.09857
$814$	53.3943	1.87147
$815$	−49.0170	−1.71699
$816$	−3.63102	−0.127111
$817$	−0.573744	−0.0200728
$818$	−10.0489	−0.351352
$819$	0	0
$820$	10.4058	0.363387
$821$	55.3900	1.93312	0.966562	−	0.256432i	$-0.0825469\pi$
$821$	55.3900	1.93312	0.966562	+	0.256432i	$0.0825469\pi$
$822$	22.4614	0.783433
$823$	−25.3284	−0.882893	−0.441447	−	0.897288i	$-0.645535\pi$
$823$	−25.3284	−0.882893	−0.441447	+	0.897288i	$0.645535\pi$
$824$	12.0097	0.418377
$825$	−0.253684	−0.00883216
$826$	0	0
$827$	5.51334	0.191717	0.0958587	−	0.995395i	$-0.469440\pi$
$827$	5.51334	0.191717	0.0958587	+	0.995395i	$0.469440\pi$
$828$	−3.46250	−0.120330
$829$	53.6480	1.86327	0.931636	−	0.363392i	$-0.118382\pi$
$829$	53.6480	1.86327	0.931636	+	0.363392i	$0.118382\pi$
$830$	−42.2965	−1.46813
$831$	−13.3381	−0.462694
$832$	5.72348	0.198426
$833$	0	0
$834$	−29.2362	−1.01237
$835$	48.5652	1.68067
$836$	0.203439	0.00703609
$837$	−7.03252	−0.243080
$838$	−30.9571	−1.06939
$839$	3.05131	0.105343	0.0526715	−	0.998612i	$-0.483226\pi$
$839$	3.05131	0.105343	0.0526715	+	0.998612i	$0.483226\pi$
$840$	0	0
$841$	−0.722415	−0.0249109
$842$	12.5609	0.432878
$843$	16.7385	0.576506
$844$	0.975246	0.0335693
$845$	28.2814	0.972911
$846$	7.08815	0.243695
$847$	0	0
$848$	−29.8659	−1.02560
$849$	3.46681	0.118981
$850$	0.0609989	0.00209225
$851$	55.4336	1.90024
$852$	−0.487254	−0.0166931
$853$	−2.72827	−0.0934141	−0.0467070	−	0.998909i	$-0.514873\pi$
$853$	−2.72827	−0.0934141	−0.0467070	+	0.998909i	$0.514873\pi$
$854$	0	0
$855$	0.356896	0.0122056
$856$	6.16421	0.210688
$857$	19.2577	0.657832	0.328916	−	0.944359i	$-0.393317\pi$
$857$	19.2577	0.657832	0.328916	+	0.944359i	$0.393317\pi$
$858$	−4.15883	−0.141980
$859$	−7.78209	−0.265521	−0.132761	−	0.991148i	$-0.542384\pi$
$859$	−7.78209	−0.265521	−0.132761	+	0.991148i	$0.542384\pi$
$860$	−5.21983	−0.177995
$861$	0	0
$862$	17.1371	0.583691
$863$	43.7066	1.48779	0.743895	−	0.668296i	$-0.232976\pi$
$863$	43.7066	1.48779	0.743895	+	0.668296i	$0.232976\pi$
$864$	−13.6732	−0.465173
$865$	35.2325	1.19794
$866$	34.7633	1.18131
$867$	1.24698	0.0423496
$868$	0	0
$869$	−6.98659	−0.237004
$870$	−18.5797	−0.629911
$871$	−7.47996	−0.253449
$872$	−14.1860	−0.480398
$873$	10.7017	0.362198
$874$	−0.737955	−0.0249617
$875$	0	0
$876$	8.81402	0.297798
$877$	−41.3889	−1.39761	−0.698803	−	0.715314i	$-0.746283\pi$
$877$	−41.3889	−1.39761	−0.698803	+	0.715314i	$0.746283\pi$
$878$	−10.9705	−0.370235
$879$	−13.8931	−0.468602
$880$	−27.2107	−0.917274
$881$	−4.79763	−0.161636	−0.0808181	−	0.996729i	$-0.525753\pi$
$881$	−4.79763	−0.161636	−0.0808181	+	0.996729i	$0.525753\pi$
$882$	0	0
$883$	−11.3679	−0.382561	−0.191280	−	0.981535i	$-0.561264\pi$
$883$	−11.3679	−0.382561	−0.191280	+	0.981535i	$0.561264\pi$
$884$	−0.286208	−0.00962623
$885$	−19.1957	−0.645255
$886$	−24.5609	−0.825140
$887$	−6.14914	−0.206468	−0.103234	−	0.994657i	$-0.532919\pi$
$887$	−6.14914	−0.206468	−0.103234	+	0.994657i	$0.532919\pi$
$888$	39.1444	1.31360
$889$	0	0
$890$	9.97584	0.334391
$891$	10.7162	0.359006
$892$	−5.84846	−0.195821
$893$	−0.432369	−0.0144687
$894$	2.82072	0.0943391
$895$	37.5623	1.25557
$896$	0	0
$897$	−4.31767	−0.144163
$898$	−12.4263	−0.414670
$899$	6.74679	0.225018
$900$	0.0314589	0.00104863
$901$	10.2567	0.341699
$902$	−53.9643	−1.79682
$903$	0	0
$904$	−8.35690	−0.277946
$905$	37.1564	1.23512
$906$	−11.7289	−0.389665
$907$	−51.8353	−1.72116	−0.860582	−	0.509312i	$-0.829900\pi$
$907$	−51.8353	−1.72116	−0.860582	+	0.509312i	$0.829900\pi$
$908$	−1.60388	−0.0532265
$909$	17.5036	0.580559
$910$	0	0
$911$	20.2795	0.671890	0.335945	−	0.941882i	$-0.390944\pi$
$911$	20.2795	0.671890	0.335945	+	0.941882i	$0.390944\pi$
$912$	−0.399108	−0.0132158
$913$	−62.7794	−2.07770
$914$	−45.7767	−1.51416
$915$	−0.692021	−0.0228775
$916$	0.413109	0.0136495
$917$	0	0
$918$	−6.91185	−0.228125
$919$	17.1366	0.565284	0.282642	−	0.959225i	$-0.408789\pi$
$919$	17.1366	0.565284	0.282642	+	0.959225i	$0.408789\pi$
$920$	−36.8853	−1.21607
$921$	8.42998	0.277777
$922$	−14.4450	−0.475722
$923$	0.564647	0.0185856
$924$	0	0
$925$	−0.503648	−0.0165598
$926$	−21.7603	−0.715088
$927$	5.69202	0.186951
$928$	13.1177	0.430609
$929$	28.2331	0.926298	0.463149	−	0.886280i	$-0.346720\pi$
$929$	28.2331	0.926298	0.463149	+	0.886280i	$0.346720\pi$
$930$	−4.43296	−0.145362
$931$	0	0
$932$	2.58104	0.0845448
$933$	−22.0110	−0.720608
$934$	46.8816	1.53401
$935$	9.34481	0.305608
$936$	2.83340	0.0926125
$937$	59.5271	1.94466	0.972332	−	0.233602i	$-0.0750512\pi$
$937$	59.5271	1.94466	0.972332	+	0.233602i	$0.0750512\pi$
$938$	0	0
$939$	24.6165	0.803331
$940$	−3.93362	−0.128301
$941$	−1.11662	−0.0364008	−0.0182004	−	0.999834i	$-0.505794\pi$
$941$	−1.11662	−0.0364008	−0.0182004	+	0.999834i	$0.505794\pi$
$942$	18.2717	0.595325
$943$	−56.0253	−1.82444
$944$	−19.9487	−0.649275
$945$	0	0
$946$	27.0700	0.880120
$947$	21.9065	0.711865	0.355932	−	0.934512i	$-0.384163\pi$
$947$	21.9065	0.711865	0.355932	+	0.934512i	$0.384163\pi$
$948$	−0.932296	−0.0302796
$949$	−10.2140	−0.331560
$950$	0.00670477	0.000217532 0
$951$	2.67696	0.0868062
$952$	0	0
$953$	22.3588	0.724273	0.362137	−	0.932125i	$-0.382047\pi$
$953$	22.3588	0.724273	0.362137	+	0.932125i	$0.382047\pi$
$954$	−18.4819	−0.598373
$955$	4.93362	0.159648
$956$	3.72156	0.120364
$957$	−27.5773	−0.891448
$958$	−30.6467	−0.990149
$959$	0	0
$960$	−24.9366	−0.804826
$961$	−29.3903	−0.948073
$962$	−8.25667	−0.266206
$963$	2.92154	0.0941454
$964$	−12.2677	−0.395116
$965$	35.3696	1.13859
$966$	0	0
$967$	−24.4590	−0.786550	−0.393275	−	0.919421i	$-0.628658\pi$
$967$	−24.4590	−0.786550	−0.393275	+	0.919421i	$0.628658\pi$
$968$	−19.1957	−0.616972
$969$	0.137063	0.00440311
$970$	20.7506	0.666262
$971$	−37.2954	−1.19687	−0.598434	−	0.801172i	$-0.704210\pi$
$971$	−37.2954	−1.19687	−0.598434	+	0.801172i	$0.704210\pi$
$972$	−5.97046	−0.191503
$973$	0	0
$974$	−2.41417	−0.0773551
$975$	0.0392287	0.00125632
$976$	−0.719169	−0.0230200
$977$	20.7767	0.664706	0.332353	−	0.943155i	$-0.392157\pi$
$977$	20.7767	0.664706	0.332353	+	0.943155i	$0.392157\pi$
$978$	33.9208	1.08467
$979$	14.8068	0.473229
$980$	0	0
$981$	−6.72348	−0.214664
$982$	23.2362	0.741498
$983$	−23.2862	−0.742715	−0.371357	−	0.928490i	$-0.621108\pi$
$983$	−23.2862	−0.742715	−0.371357	+	0.928490i	$0.621108\pi$
$984$	−39.5623	−1.26120
$985$	31.9584	1.01828
$986$	6.63102	0.211175
$987$	0	0
$988$	−0.0314589	−0.00100084
$989$	28.1038	0.893649
$990$	−16.8388	−0.535171
$991$	34.3159	1.09008	0.545040	−	0.838410i	$-0.316515\pi$
$991$	34.3159	1.09008	0.545040	+	0.838410i	$0.316515\pi$
$992$	3.12977	0.0993702
$993$	12.5512	0.398301
$994$	0	0
$995$	−4.63773	−0.147026
$996$	−8.37734	−0.265446
$997$	12.7138	0.402650	0.201325	−	0.979525i	$-0.435475\pi$
$997$	12.7138	0.402650	0.201325	+	0.979525i	$0.435475\pi$
$998$	16.8944	0.534783
$999$	57.0689	1.80558

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.a.b.1.3		3
3.2	odd	2		7497.2.a.bc.1.1		3
7.2	even	3		833.2.e.c.18.1		6
7.3	odd	6		119.2.e.a.86.1	yes	6
7.4	even	3		833.2.e.c.324.1		6
7.5	odd	6		119.2.e.a.18.1	✓	6
7.6	odd	2		833.2.a.c.1.3		3
21.5	even	6		1071.2.i.d.613.3		6
21.17	even	6		1071.2.i.d.919.3		6
21.20	even	2		7497.2.a.bb.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.e.a.18.1	✓	6	7.5	odd	6
119.2.e.a.86.1	yes	6	7.3	odd	6
833.2.a.b.1.3		3	1.1	even	1	trivial
833.2.a.c.1.3		3	7.6	odd	2
833.2.e.c.18.1		6	7.2	even	3
833.2.e.c.324.1		6	7.4	even	3
1071.2.i.d.613.3		6	21.5	even	6
1071.2.i.d.919.3		6	21.17	even	6
7497.2.a.bb.1.1		3	21.20	even	2
7497.2.a.bc.1.1		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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.a (trivial)

\(f(q)\)	\(=\)	\(q+1.24698 q^{2} +1.24698 q^{3} -0.445042 q^{4} -2.24698 q^{5} +1.55496 q^{6} -3.04892 q^{8} -1.44504 q^{9} +O(q^{10})\)	\(q+1.24698 q^{2} +1.24698 q^{3} -0.445042 q^{4} -2.24698 q^{5} +1.55496 q^{6} -3.04892 q^{8} -1.44504 q^{9} -2.80194 q^{10} -4.15883 q^{11} -0.554958 q^{12} +0.643104 q^{13} -2.80194 q^{15} -2.91185 q^{16} +1.00000 q^{17} -1.80194 q^{18} +0.109916 q^{19} +1.00000 q^{20} -5.18598 q^{22} -5.38404 q^{23} -3.80194 q^{24} +0.0489173 q^{25} +0.801938 q^{26} -5.54288 q^{27} +5.31767 q^{29} -3.49396 q^{30} +1.26875 q^{31} +2.46681 q^{32} -5.18598 q^{33} +1.24698 q^{34} +0.643104 q^{36} -10.2959 q^{37} +0.137063 q^{38} +0.801938 q^{39} +6.85086 q^{40} +10.4058 q^{41} -5.21983 q^{43} +1.85086 q^{44} +3.24698 q^{45} -6.71379 q^{46} -3.93362 q^{47} -3.63102 q^{48} +0.0609989 q^{50} +1.24698 q^{51} -0.286208 q^{52} +10.2567 q^{53} -6.91185 q^{54} +9.34481 q^{55} +0.137063 q^{57} +6.63102 q^{58} +6.85086 q^{59} +1.24698 q^{60} +0.246980 q^{61} +1.58211 q^{62} +8.89977 q^{64} -1.44504 q^{65} -6.46681 q^{66} -11.6310 q^{67} -0.445042 q^{68} -6.71379 q^{69} +0.878002 q^{71} +4.40581 q^{72} -15.8823 q^{73} -12.8388 q^{74} +0.0609989 q^{75} -0.0489173 q^{76} +1.00000 q^{78} +1.67994 q^{79} +6.54288 q^{80} -2.57673 q^{81} +12.9758 q^{82} +15.0954 q^{83} -2.24698 q^{85} -6.50902 q^{86} +6.63102 q^{87} +12.6799 q^{88} -3.56033 q^{89} +4.04892 q^{90} +2.39612 q^{92} +1.58211 q^{93} -4.90515 q^{94} -0.246980 q^{95} +3.07606 q^{96} -7.40581 q^{97} +6.00969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} - q^{3} - q^{4} - 2 q^{5} + 5 q^{6} - 4 q^{9}+O(q^{10}) \) 3 * q - q^2 - q^3 - q^4 - 2 * q^5 + 5 * q^6 - 4 * q^9	\( 3 q - q^{2} - q^{3} - q^{4} - 2 q^{5} + 5 q^{6} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 2 q^{12} + 6 q^{13} - 4 q^{15} - 5 q^{16} + 3 q^{17} - q^{18} + q^{19} + 3 q^{20} - q^{22} - 6 q^{23} - 7 q^{24} - 9 q^{25} - 2 q^{26} + 2 q^{27} - q^{29} - q^{30} - 4 q^{31} + 4 q^{32} - q^{33} - q^{34} + 6 q^{36} - 17 q^{37} - 5 q^{38} - 2 q^{39} + 7 q^{40} + 18 q^{41} - 17 q^{43} - 8 q^{44} + 5 q^{45} - 12 q^{46} - 5 q^{47} + 4 q^{48} + 10 q^{50} - q^{51} - 9 q^{52} + 4 q^{53} - 17 q^{54} + 5 q^{55} - 5 q^{57} + 5 q^{58} + 7 q^{59} - q^{60} - 4 q^{61} - q^{62} + 4 q^{64} - 4 q^{65} - 16 q^{66} - 20 q^{67} - q^{68} - 12 q^{69} - 17 q^{71} - 9 q^{73} - 6 q^{74} + 10 q^{75} + 9 q^{76} + 3 q^{78} - 19 q^{79} + q^{80} - 5 q^{81} + q^{82} - 14 q^{83} - 2 q^{85} + 15 q^{86} + 5 q^{87} + 14 q^{88} - 8 q^{89} + 3 q^{90} + 16 q^{92} - q^{93} + 11 q^{94} + 4 q^{95} - 6 q^{96} - 9 q^{97} - 4 q^{99}+O(q^{100}) \) 3 * q - q^2 - q^3 - q^4 - 2 * q^5 + 5 * q^6 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 2 * q^12 + 6 * q^13 - 4 * q^15 - 5 * q^16 + 3 * q^17 - q^18 + q^19 + 3 * q^20 - q^22 - 6 * q^23 - 7 * q^24 - 9 * q^25 - 2 * q^26 + 2 * q^27 - q^29 - q^30 - 4 * q^31 + 4 * q^32 - q^33 - q^34 + 6 * q^36 - 17 * q^37 - 5 * q^38 - 2 * q^39 + 7 * q^40 + 18 * q^41 - 17 * q^43 - 8 * q^44 + 5 * q^45 - 12 * q^46 - 5 * q^47 + 4 * q^48 + 10 * q^50 - q^51 - 9 * q^52 + 4 * q^53 - 17 * q^54 + 5 * q^55 - 5 * q^57 + 5 * q^58 + 7 * q^59 - q^60 - 4 * q^61 - q^62 + 4 * q^64 - 4 * q^65 - 16 * q^66 - 20 * q^67 - q^68 - 12 * q^69 - 17 * q^71 - 9 * q^73 - 6 * q^74 + 10 * q^75 + 9 * q^76 + 3 * q^78 - 19 * q^79 + q^80 - 5 * q^81 + q^82 - 14 * q^83 - 2 * q^85 + 15 * q^86 + 5 * q^87 + 14 * q^88 - 8 * q^89 + 3 * q^90 + 16 * q^92 - q^93 + 11 * q^94 + 4 * q^95 - 6 * q^96 - 9 * q^97 - 4 * q^99

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