LMFDB - Embedded newform 1183.2.a.n.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(1,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, 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("1183.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.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:	$9.44630255912$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.1279733.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 6x^{4} + 10x^{3} + 10x^{2} - 11x - 1 $ x^6 - 2x^5 - 6x^4 + 10x^3 + 10x^2 - 11*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.54570$ of defining polynomial
Character	$\chi$	$=$	1183.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.312100 q^{2} +1.10066 q^{3} -1.90259 q^{4} -1.93488 q^{5} -0.343514 q^{6} +1.00000 q^{7} +1.21800 q^{8} -1.78856 q^{9} +O(q^{10})$	\(q-0.312100 q^{2} +1.10066 q^{3} -1.90259 q^{4} -1.93488 q^{5} -0.343514 q^{6} +1.00000 q^{7} +1.21800 q^{8} -1.78856 q^{9} +0.603875 q^{10} +3.30407 q^{11} -2.09410 q^{12} -0.312100 q^{14} -2.12964 q^{15} +3.42505 q^{16} -2.68336 q^{17} +0.558208 q^{18} +3.97514 q^{19} +3.68129 q^{20} +1.10066 q^{21} -1.03120 q^{22} -0.249801 q^{23} +1.34060 q^{24} -1.25624 q^{25} -5.27055 q^{27} -1.90259 q^{28} -6.85160 q^{29} +0.664659 q^{30} -8.16283 q^{31} -3.50495 q^{32} +3.63665 q^{33} +0.837477 q^{34} -1.93488 q^{35} +3.40290 q^{36} +1.51991 q^{37} -1.24064 q^{38} -2.35668 q^{40} -1.36739 q^{41} -0.343514 q^{42} -10.5877 q^{43} -6.28630 q^{44} +3.46064 q^{45} +0.0779628 q^{46} +2.89468 q^{47} +3.76980 q^{48} +1.00000 q^{49} +0.392072 q^{50} -2.95346 q^{51} -11.3581 q^{53} +1.64494 q^{54} -6.39298 q^{55} +1.21800 q^{56} +4.37526 q^{57} +2.13838 q^{58} -13.9836 q^{59} +4.05183 q^{60} +13.7088 q^{61} +2.54762 q^{62} -1.78856 q^{63} -5.75621 q^{64} -1.13500 q^{66} -2.82526 q^{67} +5.10535 q^{68} -0.274945 q^{69} +0.603875 q^{70} +9.17197 q^{71} -2.17846 q^{72} -8.47003 q^{73} -0.474362 q^{74} -1.38269 q^{75} -7.56308 q^{76} +3.30407 q^{77} -8.68165 q^{79} -6.62706 q^{80} -0.435397 q^{81} +0.426761 q^{82} -8.89470 q^{83} -2.09410 q^{84} +5.19199 q^{85} +3.30441 q^{86} -7.54126 q^{87} +4.02435 q^{88} +7.50252 q^{89} -1.08007 q^{90} +0.475270 q^{92} -8.98447 q^{93} -0.903430 q^{94} -7.69142 q^{95} -3.85775 q^{96} +8.70065 q^{97} -0.312100 q^{98} -5.90952 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 8 q^{6} + 6 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 8 * q^6 + 6 * q^7 - 3 * q^8	$ 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 8 q^{6} + 6 q^{7} - 3 q^{8} - 14 q^{10} - 8 q^{11} - 23 q^{12} - 2 q^{14} - 3 q^{15} - 23 q^{17} - 26 q^{18} + 13 q^{19} + 4 q^{20} - 4 q^{21} - 4 q^{22} - 18 q^{23} + 26 q^{24} - 10 q^{25} - 10 q^{27} + 8 q^{28} - 15 q^{29} + 14 q^{30} - 3 q^{31} - 28 q^{32} - 3 q^{33} + 29 q^{34} - 2 q^{35} + 22 q^{36} + 13 q^{37} - 11 q^{38} - 14 q^{40} + 4 q^{41} + 8 q^{42} - 18 q^{43} + 19 q^{45} - 10 q^{46} + 16 q^{47} - 11 q^{48} + 6 q^{49} + 10 q^{50} + 14 q^{51} - 25 q^{53} + 31 q^{54} - 3 q^{56} + 4 q^{57} + 13 q^{58} - 18 q^{59} - 22 q^{60} + 16 q^{61} - 9 q^{62} - 7 q^{64} + 16 q^{66} - 16 q^{67} - 34 q^{68} - q^{69} - 14 q^{70} - 25 q^{71} - 39 q^{72} + 5 q^{73} - 14 q^{74} + 15 q^{75} - 7 q^{76} - 8 q^{77} + 2 q^{79} + 27 q^{80} - 6 q^{81} - 10 q^{82} + 7 q^{83} - 23 q^{84} - 9 q^{85} + 3 q^{86} + 13 q^{87} - 48 q^{88} + 10 q^{89} - 32 q^{92} - 35 q^{93} - 14 q^{94} - 7 q^{95} + 14 q^{96} + 5 q^{97} - 2 q^{98} + 15 q^{99}+O(q^{100}) $ 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 8 * q^6 + 6 * q^7 - 3 * q^8 - 14 * q^10 - 8 * q^11 - 23 * q^12 - 2 * q^14 - 3 * q^15 - 23 * q^17 - 26 * q^18 + 13 * q^19 + 4 * q^20 - 4 * q^21 - 4 * q^22 - 18 * q^23 + 26 * q^24 - 10 * q^25 - 10 * q^27 + 8 * q^28 - 15 * q^29 + 14 * q^30 - 3 * q^31 - 28 * q^32 - 3 * q^33 + 29 * q^34 - 2 * q^35 + 22 * q^36 + 13 * q^37 - 11 * q^38 - 14 * q^40 + 4 * q^41 + 8 * q^42 - 18 * q^43 + 19 * q^45 - 10 * q^46 + 16 * q^47 - 11 * q^48 + 6 * q^49 + 10 * q^50 + 14 * q^51 - 25 * q^53 + 31 * q^54 - 3 * q^56 + 4 * q^57 + 13 * q^58 - 18 * q^59 - 22 * q^60 + 16 * q^61 - 9 * q^62 - 7 * q^64 + 16 * q^66 - 16 * q^67 - 34 * q^68 - q^69 - 14 * q^70 - 25 * q^71 - 39 * q^72 + 5 * q^73 - 14 * q^74 + 15 * q^75 - 7 * q^76 - 8 * q^77 + 2 * q^79 + 27 * q^80 - 6 * q^81 - 10 * q^82 + 7 * q^83 - 23 * q^84 - 9 * q^85 + 3 * q^86 + 13 * q^87 - 48 * q^88 + 10 * q^89 - 32 * q^92 - 35 * q^93 - 14 * q^94 - 7 * q^95 + 14 * q^96 + 5 * q^97 - 2 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.312100	−0.220688	−0.110344	−	0.993893i	$-0.535195\pi$
$2$	−0.312100	−0.220688	−0.110344	+	0.993893i	$0.535195\pi$
$3$	1.10066	0.635464	0.317732	−	0.948181i	$-0.397079\pi$
$3$	1.10066	0.635464	0.317732	+	0.948181i	$0.397079\pi$
$4$	−1.90259	−0.951297
$5$	−1.93488	−0.865305	−0.432652	−	0.901561i	$-0.642422\pi$
$5$	−1.93488	−0.865305	−0.432652	+	0.901561i	$0.642422\pi$
$6$	−0.343514	−0.140239
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.21800	0.430627
$9$	−1.78856	−0.596185
$10$	0.603875	0.190962
$11$	3.30407	0.996215	0.498107	−	0.867115i	$-0.334029\pi$
$11$	3.30407	0.996215	0.498107	+	0.867115i	$0.334029\pi$
$12$	−2.09410	−0.604515
$13$	0	0
$13$	0	0
$14$	−0.312100	−0.0834122
$15$	−2.12964	−0.549870
$16$	3.42505	0.856263
$17$	−2.68336	−0.650811	−0.325406	−	0.945574i	$-0.605501\pi$
$17$	−2.68336	−0.650811	−0.325406	+	0.945574i	$0.605501\pi$
$18$	0.558208	0.131571
$19$	3.97514	0.911960	0.455980	−	0.889990i	$-0.349289\pi$
$19$	3.97514	0.911960	0.455980	+	0.889990i	$0.349289\pi$
$20$	3.68129	0.823162
$21$	1.10066	0.240183
$22$	−1.03120	−0.219852
$23$	−0.249801	−0.0520871	−0.0260435	−	0.999661i	$-0.508291\pi$
$23$	−0.249801	−0.0520871	−0.0260435	+	0.999661i	$0.508291\pi$
$24$	1.34060	0.273648
$25$	−1.25624	−0.251248
$26$	0	0
$27$	−5.27055	−1.01432
$28$	−1.90259	−0.359556
$29$	−6.85160	−1.27231	−0.636155	−	0.771561i	$-0.719476\pi$
$29$	−6.85160	−1.27231	−0.636155	+	0.771561i	$0.719476\pi$
$30$	0.664659	0.121350
$31$	−8.16283	−1.46609	−0.733044	−	0.680181i	$-0.761901\pi$
$31$	−8.16283	−1.46609	−0.733044	+	0.680181i	$0.761901\pi$
$32$	−3.50495	−0.619594
$33$	3.63665	0.633059
$34$	0.837477	0.143626
$35$	−1.93488	−0.327054
$36$	3.40290	0.567149
$37$	1.51991	0.249871	0.124935	−	0.992165i	$-0.460128\pi$
$37$	1.51991	0.249871	0.124935	+	0.992165i	$0.460128\pi$
$38$	−1.24064	−0.201258
$39$	0	0
$40$	−2.35668	−0.372624
$41$	−1.36739	−0.213550	−0.106775	−	0.994283i	$-0.534052\pi$
$41$	−1.36739	−0.213550	−0.106775	+	0.994283i	$0.534052\pi$
$42$	−0.343514	−0.0530054
$43$	−10.5877	−1.61460	−0.807302	−	0.590138i	$-0.799073\pi$
$43$	−10.5877	−1.61460	−0.807302	+	0.590138i	$0.799073\pi$
$44$	−6.28630	−0.947696
$45$	3.46064	0.515882
$46$	0.0779628	0.0114950
$47$	2.89468	0.422233	0.211117	−	0.977461i	$-0.432290\pi$
$47$	2.89468	0.422233	0.211117	+	0.977461i	$0.432290\pi$
$48$	3.76980	0.544124
$49$	1.00000	0.142857
$50$	0.392072	0.0554474
$51$	−2.95346	−0.413567
$52$	0	0
$53$	−11.3581	−1.56015	−0.780077	−	0.625683i	$-0.784820\pi$
$53$	−11.3581	−1.56015	−0.780077	+	0.625683i	$0.784820\pi$
$54$	1.64494	0.223848
$55$	−6.39298	−0.862029
$56$	1.21800	0.162762
$57$	4.37526	0.579518
$58$	2.13838	0.280783
$59$	−13.9836	−1.82052	−0.910258	−	0.414042i	$-0.864117\pi$
$59$	−13.9836	−1.82052	−0.910258	+	0.414042i	$0.864117\pi$
$60$	4.05183	0.523090
$61$	13.7088	1.75523	0.877616	−	0.479365i	$-0.159133\pi$
$61$	13.7088	1.75523	0.877616	+	0.479365i	$0.159133\pi$
$62$	2.54762	0.323548
$63$	−1.78856	−0.225337
$64$	−5.75621	−0.719526
$65$	0	0
$66$	−1.13500	−0.139708
$67$	−2.82526	−0.345161	−0.172580	−	0.984995i	$-0.555210\pi$
$67$	−2.82526	−0.345161	−0.172580	+	0.984995i	$0.555210\pi$
$68$	5.10535	0.619115
$69$	−0.274945	−0.0330995
$70$	0.603875	0.0721769
$71$	9.17197	1.08851	0.544256	−	0.838919i	$-0.316812\pi$
$71$	9.17197	1.08851	0.544256	+	0.838919i	$0.316812\pi$
$72$	−2.17846	−0.256734
$73$	−8.47003	−0.991342	−0.495671	−	0.868510i	$-0.665078\pi$
$73$	−8.47003	−0.991342	−0.495671	+	0.868510i	$0.665078\pi$
$74$	−0.474362	−0.0551435
$75$	−1.38269	−0.159659
$76$	−7.56308	−0.867544
$77$	3.30407	0.376534
$78$	0	0
$79$	−8.68165	−0.976762	−0.488381	−	0.872631i	$-0.662412\pi$
$79$	−8.68165	−0.976762	−0.488381	+	0.872631i	$0.662412\pi$
$80$	−6.62706	−0.740928
$81$	−0.435397	−0.0483775
$82$	0.426761	0.0471279
$83$	−8.89470	−0.976320	−0.488160	−	0.872754i	$-0.662332\pi$
$83$	−8.89470	−0.976320	−0.488160	+	0.872754i	$0.662332\pi$
$84$	−2.09410	−0.228485
$85$	5.19199	0.563150
$86$	3.30441	0.356324
$87$	−7.54126	−0.808508
$88$	4.02435	0.428997
$89$	7.50252	0.795265	0.397633	−	0.917545i	$-0.369832\pi$
$89$	7.50252	0.795265	0.397633	+	0.917545i	$0.369832\pi$
$90$	−1.08007	−0.113849
$91$	0	0
$92$	0.475270	0.0495503
$93$	−8.98447	−0.931646
$94$	−0.903430	−0.0931817
$95$	−7.69142	−0.789123
$96$	−3.85775	−0.393730
$97$	8.70065	0.883418	0.441709	−	0.897158i	$-0.354372\pi$
$97$	8.70065	0.883418	0.441709	+	0.897158i	$0.354372\pi$
$98$	−0.312100	−0.0315268
$99$	−5.90952	−0.593929
$100$	2.39011	0.239011
$101$	−7.66968	−0.763162	−0.381581	−	0.924335i	$-0.624620\pi$
$101$	−7.66968	−0.763162	−0.381581	+	0.924335i	$0.624620\pi$
$102$	0.921774	0.0912693
$103$	−9.35776	−0.922048	−0.461024	−	0.887388i	$-0.652518\pi$
$103$	−9.35776	−0.922048	−0.461024	+	0.887388i	$0.652518\pi$
$104$	0	0
$105$	−2.12964	−0.207831
$106$	3.54486	0.344307
$107$	9.36508	0.905357	0.452678	−	0.891674i	$-0.350469\pi$
$107$	9.36508	0.905357	0.452678	+	0.891674i	$0.350469\pi$
$108$	10.0277	0.964918
$109$	19.9277	1.90872	0.954362	−	0.298652i	$-0.0965371\pi$
$109$	19.9277	1.90872	0.954362	+	0.298652i	$0.0965371\pi$
$110$	1.99525	0.190239
$111$	1.67289	0.158784
$112$	3.42505	0.323637
$113$	−4.65777	−0.438166	−0.219083	−	0.975706i	$-0.570307\pi$
$113$	−4.65777	−0.438166	−0.219083	+	0.975706i	$0.570307\pi$
$114$	−1.36552	−0.127892
$115$	0.483335	0.0450712
$116$	13.0358	1.21035
$117$	0	0
$118$	4.36429	0.401766
$119$	−2.68336	−0.245984
$120$	−2.59389	−0.236789
$121$	−0.0831177	−0.00755616
$122$	−4.27851	−0.387358
$123$	−1.50502	−0.135703
$124$	15.5306	1.39468
$125$	12.1051	1.08271
$126$	0.558208	0.0497291
$127$	7.56559	0.671338	0.335669	−	0.941980i	$-0.391038\pi$
$127$	7.56559	0.671338	0.335669	+	0.941980i	$0.391038\pi$
$128$	8.80642	0.778385
$129$	−11.6534	−1.02602
$130$	0	0
$131$	20.5380	1.79441	0.897205	−	0.441615i	$-0.145594\pi$
$131$	20.5380	1.79441	0.897205	+	0.441615i	$0.145594\pi$
$132$	−6.91906	−0.602227
$133$	3.97514	0.344688
$134$	0.881764	0.0761728
$135$	10.1979	0.877694
$136$	−3.26833	−0.280257
$137$	−10.5347	−0.900043	−0.450021	−	0.893018i	$-0.648584\pi$
$137$	−10.5347	−0.900043	−0.450021	+	0.893018i	$0.648584\pi$
$138$	0.0858102	0.00730465
$139$	−5.42605	−0.460231	−0.230116	−	0.973163i	$-0.573910\pi$
$139$	−5.42605	−0.460231	−0.230116	+	0.973163i	$0.573910\pi$
$140$	3.68129	0.311126
$141$	3.18605	0.268314
$142$	−2.86257	−0.240222
$143$	0	0
$144$	−6.12590	−0.510491
$145$	13.2570	1.10094
$146$	2.64349	0.218777
$147$	1.10066	0.0907806
$148$	−2.89176	−0.237701
$149$	−19.3141	−1.58227	−0.791136	−	0.611640i	$-0.790510\pi$
$149$	−19.3141	−1.58227	−0.791136	+	0.611640i	$0.790510\pi$
$150$	0.431537	0.0352348
$151$	−2.41011	−0.196132	−0.0980658	−	0.995180i	$-0.531266\pi$
$151$	−2.41011	−0.196132	−0.0980658	+	0.995180i	$0.531266\pi$
$152$	4.84171	0.392715
$153$	4.79935	0.388004
$154$	−1.03120	−0.0830964
$155$	15.7941	1.26861
$156$	0	0
$157$	6.27981	0.501183	0.250592	−	0.968093i	$-0.419375\pi$
$157$	6.27981	0.501183	0.250592	+	0.968093i	$0.419375\pi$
$158$	2.70954	0.215559
$159$	−12.5014	−0.991422
$160$	6.78167	0.536138
$161$	−0.249801	−0.0196871
$162$	0.135887	0.0106763
$163$	−14.7792	−1.15760	−0.578799	−	0.815470i	$-0.696478\pi$
$163$	−14.7792	−1.15760	−0.578799	+	0.815470i	$0.696478\pi$
$164$	2.60158	0.203149
$165$	−7.03647	−0.547789
$166$	2.77603	0.215462
$167$	−11.6656	−0.902709	−0.451355	−	0.892345i	$-0.649059\pi$
$167$	−11.6656	−0.902709	−0.451355	+	0.892345i	$0.649059\pi$
$168$	1.34060	0.103429
$169$	0	0
$170$	−1.62042	−0.124280
$171$	−7.10976	−0.543697
$172$	20.1440	1.53597
$173$	−14.4438	−1.09814	−0.549072	−	0.835775i	$-0.685019\pi$
$173$	−14.4438	−1.09814	−0.549072	+	0.835775i	$0.685019\pi$
$174$	2.35362	0.178428
$175$	−1.25624	−0.0949628
$176$	11.3166	0.853021
$177$	−15.3912	−1.15687
$178$	−2.34153	−0.175505
$179$	−5.40993	−0.404357	−0.202179	−	0.979349i	$-0.564802\pi$
$179$	−5.40993	−0.404357	−0.202179	+	0.979349i	$0.564802\pi$
$180$	−6.58420	−0.490757
$181$	6.75171	0.501851	0.250926	−	0.968006i	$-0.419265\pi$
$181$	6.75171	0.501851	0.250926	+	0.968006i	$0.419265\pi$
$182$	0	0
$183$	15.0887	1.11539
$184$	−0.304257	−0.0224301
$185$	−2.94084	−0.216215
$186$	2.80405	0.205603
$187$	−8.86602	−0.648348
$188$	−5.50741	−0.401669
$189$	−5.27055	−0.383376
$190$	2.40049	0.174150
$191$	−13.0918	−0.947290	−0.473645	−	0.880716i	$-0.657062\pi$
$191$	−13.0918	−0.947290	−0.473645	+	0.880716i	$0.657062\pi$
$192$	−6.33560	−0.457233
$193$	8.06247	0.580350	0.290175	−	0.956974i	$-0.406287\pi$
$193$	8.06247	0.580350	0.290175	+	0.956974i	$0.406287\pi$
$194$	−2.71547	−0.194960
$195$	0	0
$196$	−1.90259	−0.135900
$197$	14.9630	1.06607	0.533033	−	0.846094i	$-0.321052\pi$
$197$	14.9630	1.06607	0.533033	+	0.846094i	$0.321052\pi$
$198$	1.84436	0.131073
$199$	10.2781	0.728597	0.364299	−	0.931282i	$-0.381309\pi$
$199$	10.2781	0.728597	0.364299	+	0.931282i	$0.381309\pi$
$200$	−1.53010	−0.108194
$201$	−3.10964	−0.219337
$202$	2.39370	0.168420
$203$	−6.85160	−0.480888
$204$	5.61924	0.393425
$205$	2.64573	0.184786
$206$	2.92056	0.203485
$207$	0.446783	0.0310536
$208$	0	0
$209$	13.1341	0.908508
$210$	0.664659	0.0458658
$211$	−7.19246	−0.495150	−0.247575	−	0.968869i	$-0.579634\pi$
$211$	−7.19246	−0.495150	−0.247575	+	0.968869i	$0.579634\pi$
$212$	21.6098	1.48417
$213$	10.0952	0.691711
$214$	−2.92284	−0.199801
$215$	20.4859	1.39713
$216$	−6.41953	−0.436793
$217$	−8.16283	−0.554129
$218$	−6.21942	−0.421232
$219$	−9.32259	−0.629962
$220$	12.1632	0.820046
$221$	0	0
$222$	−0.522110	−0.0350417
$223$	29.7080	1.98939	0.994697	−	0.102851i	$-0.0327966\pi$
$223$	29.7080	1.98939	0.994697	+	0.102851i	$0.0327966\pi$
$224$	−3.50495	−0.234185
$225$	2.24686	0.149790
$226$	1.45369	0.0966980
$227$	−12.8350	−0.851891	−0.425946	−	0.904749i	$-0.640059\pi$
$227$	−12.8350	−0.851891	−0.425946	+	0.904749i	$0.640059\pi$
$228$	−8.32435	−0.551293
$229$	−12.9893	−0.858360	−0.429180	−	0.903219i	$-0.641197\pi$
$229$	−12.9893	−0.858360	−0.429180	+	0.903219i	$0.641197\pi$
$230$	−0.150849	−0.00994667
$231$	3.63665	0.239274
$232$	−8.34524	−0.547892
$233$	20.7043	1.35638	0.678192	−	0.734884i	$-0.262764\pi$
$233$	20.7043	1.35638	0.678192	+	0.734884i	$0.262764\pi$
$234$	0	0
$235$	−5.60087	−0.365360
$236$	26.6052	1.73185
$237$	−9.55551	−0.620697
$238$	0.837477	0.0542856
$239$	−14.2812	−0.923772	−0.461886	−	0.886939i	$-0.652827\pi$
$239$	−14.2812	−0.923772	−0.461886	+	0.886939i	$0.652827\pi$
$240$	−7.29412	−0.470833
$241$	−12.8333	−0.826665	−0.413332	−	0.910580i	$-0.635635\pi$
$241$	−12.8333	−0.826665	−0.413332	+	0.910580i	$0.635635\pi$
$242$	0.0259410	0.00166755
$243$	15.3324	0.983576
$244$	−26.0823	−1.66975
$245$	−1.93488	−0.123615
$246$	0.469717	0.0299481
$247$	0	0
$248$	−9.94232	−0.631338
$249$	−9.79000	−0.620416
$250$	−3.77799	−0.238941
$251$	−15.1961	−0.959168	−0.479584	−	0.877496i	$-0.659212\pi$
$251$	−15.1961	−0.959168	−0.479584	+	0.877496i	$0.659212\pi$
$252$	3.40290	0.214362
$253$	−0.825360	−0.0518899
$254$	−2.36122	−0.148156
$255$	5.71459	0.357862
$256$	8.76393	0.547746
$257$	−30.4182	−1.89744	−0.948718	−	0.316125i	$-0.897618\pi$
$257$	−30.4182	−1.89744	−0.948718	+	0.316125i	$0.897618\pi$
$258$	3.63702	0.226431
$259$	1.51991	0.0944424
$260$	0	0
$261$	12.2545	0.758533
$262$	−6.40989	−0.396004
$263$	4.87591	0.300662	0.150331	−	0.988636i	$-0.451966\pi$
$263$	4.87591	0.300662	0.150331	+	0.988636i	$0.451966\pi$
$264$	4.42943	0.272612
$265$	21.9766	1.35001
$266$	−1.24064	−0.0760685
$267$	8.25769	0.505362
$268$	5.37533	0.328350
$269$	−6.89823	−0.420592	−0.210296	−	0.977638i	$-0.567443\pi$
$269$	−6.89823	−0.420592	−0.210296	+	0.977638i	$0.567443\pi$
$270$	−3.18276	−0.193696
$271$	2.14946	0.130570	0.0652851	−	0.997867i	$-0.479204\pi$
$271$	2.14946	0.130570	0.0652851	+	0.997867i	$0.479204\pi$
$272$	−9.19066	−0.557266
$273$	0	0
$274$	3.28789	0.198629
$275$	−4.15071	−0.250297
$276$	0.523108	0.0314874
$277$	27.8905	1.67577	0.837887	−	0.545843i	$-0.183791\pi$
$277$	27.8905	1.67577	0.837887	+	0.545843i	$0.183791\pi$
$278$	1.69347	0.101567
$279$	14.5997	0.874060
$280$	−2.35668	−0.140839
$281$	1.76846	0.105498	0.0527488	−	0.998608i	$-0.483202\pi$
$281$	1.76846	0.105498	0.0527488	+	0.998608i	$0.483202\pi$
$282$	−0.994366	−0.0592136
$283$	18.6963	1.11138	0.555690	−	0.831390i	$-0.312454\pi$
$283$	18.6963	1.11138	0.555690	+	0.831390i	$0.312454\pi$
$284$	−17.4505	−1.03550
$285$	−8.46561	−0.501459
$286$	0	0
$287$	−1.36739	−0.0807143
$288$	6.26881	0.369393
$289$	−9.79956	−0.576444
$290$	−4.13751	−0.242963
$291$	9.57643	0.561380
$292$	16.1150	0.943061
$293$	−9.71217	−0.567391	−0.283695	−	0.958914i	$-0.591560\pi$
$293$	−9.71217	−0.567391	−0.283695	+	0.958914i	$0.591560\pi$
$294$	−0.343514	−0.0200342
$295$	27.0567	1.57530
$296$	1.85124	0.107601
$297$	−17.4143	−1.01048
$298$	6.02792	0.349188
$299$	0	0
$300$	2.63069	0.151883
$301$	−10.5877	−0.610263
$302$	0.752193	0.0432839
$303$	−8.44168	−0.484962
$304$	13.6151	0.780877
$305$	−26.5249	−1.51881
$306$	−1.49788	−0.0856278
$307$	−3.92435	−0.223975	−0.111987	−	0.993710i	$-0.535722\pi$
$307$	−3.92435	−0.223975	−0.111987	+	0.993710i	$0.535722\pi$
$308$	−6.28630	−0.358195
$309$	−10.2997	−0.585928
$310$	−4.92933	−0.279967
$311$	22.5407	1.27817	0.639084	−	0.769137i	$-0.279314\pi$
$311$	22.5407	1.27817	0.639084	+	0.769137i	$0.279314\pi$
$312$	0	0
$313$	33.2674	1.88038	0.940191	−	0.340647i	$-0.110646\pi$
$313$	33.2674	1.88038	0.940191	+	0.340647i	$0.110646\pi$
$314$	−1.95993	−0.110605
$315$	3.46064	0.194985
$316$	16.5177	0.929191
$317$	16.5373	0.928827	0.464413	−	0.885618i	$-0.346265\pi$
$317$	16.5373	0.928827	0.464413	+	0.885618i	$0.346265\pi$
$318$	3.90167	0.218795
$319$	−22.6382	−1.26749
$320$	11.1376	0.622609
$321$	10.3077	0.575322
$322$	0.0779628	0.00434470
$323$	−10.6667	−0.593514
$324$	0.828384	0.0460214
$325$	0	0
$326$	4.61259	0.255468
$327$	21.9335	1.21293
$328$	−1.66548	−0.0919605
$329$	2.89468	0.159589
$330$	2.19608	0.120890
$331$	10.3115	0.566769	0.283384	−	0.959006i	$-0.408543\pi$
$331$	10.3115	0.566769	0.283384	+	0.959006i	$0.408543\pi$
$332$	16.9230	0.928770
$333$	−2.71844	−0.148969
$334$	3.64082	0.199217
$335$	5.46654	0.298669
$336$	3.76980	0.205660
$337$	−27.0447	−1.47322	−0.736610	−	0.676318i	$-0.763575\pi$
$337$	−27.0447	−1.47322	−0.736610	+	0.676318i	$0.763575\pi$
$338$	0	0
$339$	−5.12660	−0.278439
$340$	−9.87824	−0.535723
$341$	−26.9706	−1.46054
$342$	2.21895	0.119987
$343$	1.00000	0.0539949
$344$	−12.8958	−0.695293
$345$	0.531985	0.0286411
$346$	4.50792	0.242347
$347$	−28.3496	−1.52189	−0.760943	−	0.648818i	$-0.775264\pi$
$347$	−28.3496	−1.52189	−0.760943	+	0.648818i	$0.775264\pi$
$348$	14.3479	0.769131
$349$	18.6769	0.999751	0.499876	−	0.866097i	$-0.333379\pi$
$349$	18.6769	0.999751	0.499876	+	0.866097i	$0.333379\pi$
$350$	0.392072	0.0209571
$351$	0	0
$352$	−11.5806	−0.617249
$353$	18.8456	1.00305	0.501526	−	0.865142i	$-0.332772\pi$
$353$	18.8456	1.00305	0.501526	+	0.865142i	$0.332772\pi$
$354$	4.80358	0.255308
$355$	−17.7467	−0.941895
$356$	−14.2742	−0.756533
$357$	−2.95346	−0.156314
$358$	1.68844	0.0892368
$359$	−3.46550	−0.182902	−0.0914509	−	0.995810i	$-0.529150\pi$
$359$	−3.46550	−0.182902	−0.0914509	+	0.995810i	$0.529150\pi$
$360$	4.21506	0.222153
$361$	−3.19826	−0.168330
$362$	−2.10721	−0.110752
$363$	−0.0914840	−0.00480167
$364$	0	0
$365$	16.3885	0.857813
$366$	−4.70917	−0.246152
$367$	31.0976	1.62328	0.811640	−	0.584158i	$-0.198575\pi$
$367$	31.0976	1.62328	0.811640	+	0.584158i	$0.198575\pi$
$368$	−0.855581	−0.0446002
$369$	2.44565	0.127315
$370$	0.917834	0.0477159
$371$	−11.3581	−0.589683
$372$	17.0938	0.886272
$373$	−10.8655	−0.562597	−0.281298	−	0.959620i	$-0.590765\pi$
$373$	−10.8655	−0.562597	−0.281298	+	0.959620i	$0.590765\pi$
$374$	2.76708	0.143083
$375$	13.3235	0.688024
$376$	3.52572	0.181825
$377$	0	0
$378$	1.64494	0.0846065
$379$	−1.88019	−0.0965786	−0.0482893	−	0.998833i	$-0.515377\pi$
$379$	−1.88019	−0.0965786	−0.0482893	+	0.998833i	$0.515377\pi$
$380$	14.6336	0.750690
$381$	8.32712	0.426611
$382$	4.08595	0.209055
$383$	35.2053	1.79891	0.899454	−	0.437016i	$-0.143965\pi$
$383$	35.2053	1.79891	0.899454	+	0.437016i	$0.143965\pi$
$384$	9.69284	0.494636
$385$	−6.39298	−0.325816
$386$	−2.51630	−0.128076
$387$	18.9366	0.962604
$388$	−16.5538	−0.840392
$389$	−14.7871	−0.749738	−0.374869	−	0.927078i	$-0.622312\pi$
$389$	−14.7871	−0.749738	−0.374869	+	0.927078i	$0.622312\pi$
$390$	0	0
$391$	0.670307	0.0338989
$392$	1.21800	0.0615182
$393$	22.6052	1.14028
$394$	−4.66994	−0.235268
$395$	16.7980	0.845197
$396$	11.2434	0.565003
$397$	29.0277	1.45686	0.728428	−	0.685122i	$-0.240251\pi$
$397$	29.0277	1.45686	0.728428	+	0.685122i	$0.240251\pi$
$398$	−3.20780	−0.160792
$399$	4.37526	0.219037
$400$	−4.30268	−0.215134
$401$	20.5046	1.02395	0.511974	−	0.859001i	$-0.328914\pi$
$401$	20.5046	1.02395	0.511974	+	0.859001i	$0.328914\pi$
$402$	0.970518	0.0484051
$403$	0	0
$404$	14.5923	0.725993
$405$	0.842442	0.0418613
$406$	2.13838	0.106126
$407$	5.02188	0.248925
$408$	−3.59731	−0.178093
$409$	−2.31717	−0.114576	−0.0572882	−	0.998358i	$-0.518245\pi$
$409$	−2.31717	−0.114576	−0.0572882	+	0.998358i	$0.518245\pi$
$410$	−0.825732	−0.0407800
$411$	−11.5951	−0.571945
$412$	17.8040	0.877141
$413$	−13.9836	−0.688090
$414$	−0.139441	−0.00685314
$415$	17.2102	0.844814
$416$	0	0
$417$	−5.97221	−0.292460
$418$	−4.09916	−0.200497
$419$	−10.1990	−0.498254	−0.249127	−	0.968471i	$-0.580144\pi$
$419$	−10.1990	−0.498254	−0.249127	+	0.968471i	$0.580144\pi$
$420$	4.05183	0.197709
$421$	−8.80131	−0.428950	−0.214475	−	0.976730i	$-0.568804\pi$
$421$	−8.80131	−0.428950	−0.214475	+	0.976730i	$0.568804\pi$
$422$	2.24477	0.109274
$423$	−5.17731	−0.251729
$424$	−13.8341	−0.671845
$425$	3.37095	0.163515
$426$	−3.15070	−0.152652
$427$	13.7088	0.663415
$428$	−17.8179	−0.861263
$429$	0	0
$430$	−6.39364	−0.308328
$431$	−15.7687	−0.759552	−0.379776	−	0.925078i	$-0.623999\pi$
$431$	−15.7687	−0.759552	−0.379776	+	0.925078i	$0.623999\pi$
$432$	−18.0519	−0.868523
$433$	20.9710	1.00780	0.503901	−	0.863761i	$-0.331898\pi$
$433$	20.9710	1.00780	0.503901	+	0.863761i	$0.331898\pi$
$434$	2.54762	0.122290
$435$	14.5914	0.699605
$436$	−37.9142	−1.81576
$437$	−0.992994	−0.0475013
$438$	2.90958	0.139025
$439$	22.2439	1.06164	0.530822	−	0.847483i	$-0.321883\pi$
$439$	22.2439	1.06164	0.530822	+	0.847483i	$0.321883\pi$
$440$	−7.78664	−0.371213
$441$	−1.78856	−0.0851693
$442$	0	0
$443$	−22.6025	−1.07388	−0.536939	−	0.843621i	$-0.680419\pi$
$443$	−22.6025	−1.07388	−0.536939	+	0.843621i	$0.680419\pi$
$444$	−3.18284	−0.151051
$445$	−14.5165	−0.688147
$446$	−9.27185	−0.439035
$447$	−21.2582	−1.00548
$448$	−5.75621	−0.271955
$449$	33.6781	1.58937	0.794685	−	0.607022i	$-0.207636\pi$
$449$	33.6781	1.58937	0.794685	+	0.607022i	$0.207636\pi$
$450$	−0.701243	−0.0330569
$451$	−4.51794	−0.212742
$452$	8.86185	0.416826
$453$	−2.65270	−0.124635
$454$	4.00581	0.188002
$455$	0	0
$456$	5.32906	0.249556
$457$	−29.9328	−1.40020	−0.700099	−	0.714046i	$-0.746861\pi$
$457$	−29.9328	−1.40020	−0.700099	+	0.714046i	$0.746861\pi$
$458$	4.05397	0.189430
$459$	14.1428	0.660130
$460$	−0.919590	−0.0428761
$461$	−11.8887	−0.553714	−0.276857	−	0.960911i	$-0.589293\pi$
$461$	−11.8887	−0.553714	−0.276857	+	0.960911i	$0.589293\pi$
$462$	−1.13500	−0.0528048
$463$	−17.1606	−0.797522	−0.398761	−	0.917055i	$-0.630560\pi$
$463$	−17.1606	−0.797522	−0.398761	+	0.917055i	$0.630560\pi$
$464$	−23.4671	−1.08943
$465$	17.3839	0.806158
$466$	−6.46181	−0.299338
$467$	−5.83855	−0.270176	−0.135088	−	0.990834i	$-0.543132\pi$
$467$	−5.83855	−0.270176	−0.135088	+	0.990834i	$0.543132\pi$
$468$	0	0
$469$	−2.82526	−0.130459
$470$	1.74803	0.0806306
$471$	6.91191	0.318484
$472$	−17.0321	−0.783964
$473$	−34.9824	−1.60849
$474$	2.98227	0.136980
$475$	−4.99373	−0.229128
$476$	5.10535	0.234003
$477$	20.3146	0.930141
$478$	4.45715	0.203865
$479$	15.9848	0.730364	0.365182	−	0.930936i	$-0.381007\pi$
$479$	15.9848	0.730364	0.365182	+	0.930936i	$0.381007\pi$
$480$	7.46428	0.340696
$481$	0	0
$482$	4.00527	0.182435
$483$	−0.274945	−0.0125104
$484$	0.158139	0.00718815
$485$	−16.8347	−0.764425
$486$	−4.78525	−0.217063
$487$	−16.9216	−0.766790	−0.383395	−	0.923585i	$-0.625245\pi$
$487$	−16.9216	−0.766790	−0.383395	+	0.923585i	$0.625245\pi$
$488$	16.6973	0.755851
$489$	−16.2668	−0.735612
$490$	0.603875	0.0272803
$491$	−6.03131	−0.272189	−0.136095	−	0.990696i	$-0.543455\pi$
$491$	−6.03131	−0.272189	−0.136095	+	0.990696i	$0.543455\pi$
$492$	2.86345	0.129094
$493$	18.3853	0.828034
$494$	0	0
$495$	11.4342	0.513929
$496$	−27.9581	−1.25536
$497$	9.17197	0.411419
$498$	3.05546	0.136918
$499$	20.3622	0.911537	0.455768	−	0.890098i	$-0.349365\pi$
$499$	20.3622	0.911537	0.455768	+	0.890098i	$0.349365\pi$
$500$	−23.0310	−1.02998
$501$	−12.8398	−0.573639
$502$	4.74269	0.211677
$503$	−14.7571	−0.657986	−0.328993	−	0.944332i	$-0.606709\pi$
$503$	−14.7571	−0.657986	−0.328993	+	0.944332i	$0.606709\pi$
$504$	−2.17846	−0.0970363
$505$	14.8399	0.660367
$506$	0.257595	0.0114515
$507$	0	0
$508$	−14.3943	−0.638642
$509$	8.19735	0.363341	0.181670	−	0.983359i	$-0.441850\pi$
$509$	8.19735	0.363341	0.181670	+	0.983359i	$0.441850\pi$
$510$	−1.78352	−0.0789757
$511$	−8.47003	−0.374692
$512$	−20.3481	−0.899266
$513$	−20.9512	−0.925018
$514$	9.49351	0.418741
$515$	18.1061	0.797852
$516$	22.1717	0.976053
$517$	9.56424	0.420635
$518$	−0.474362	−0.0208423
$519$	−15.8977	−0.697831
$520$	0	0
$521$	−36.4358	−1.59628	−0.798141	−	0.602471i	$-0.794183\pi$
$521$	−36.4358	−1.59628	−0.798141	+	0.602471i	$0.794183\pi$
$522$	−3.82462	−0.167399
$523$	3.12730	0.136747	0.0683737	−	0.997660i	$-0.478219\pi$
$523$	3.12730	0.136747	0.0683737	+	0.997660i	$0.478219\pi$
$524$	−39.0754	−1.70702
$525$	−1.38269	−0.0603454
$526$	−1.52177	−0.0663523
$527$	21.9038	0.954147
$528$	12.4557	0.542064
$529$	−22.9376	−0.997287
$530$	−6.85888	−0.297931
$531$	25.0105	1.08536
$532$	−7.56308	−0.327901
$533$	0	0
$534$	−2.57722	−0.111527
$535$	−18.1203	−0.783409
$536$	−3.44117	−0.148636
$537$	−5.95448	−0.256955
$538$	2.15294	0.0928196
$539$	3.30407	0.142316
$540$	−19.4024	−0.834948
$541$	40.2086	1.72870	0.864351	−	0.502889i	$-0.167730\pi$
$541$	40.2086	1.72870	0.864351	+	0.502889i	$0.167730\pi$
$542$	−0.670845	−0.0288153
$543$	7.43132	0.318908
$544$	9.40507	0.403239
$545$	−38.5576	−1.65163
$546$	0	0
$547$	−32.0924	−1.37217	−0.686086	−	0.727521i	$-0.740673\pi$
$547$	−32.0924	−1.37217	−0.686086	+	0.727521i	$0.740673\pi$
$548$	20.0433	0.856208
$549$	−24.5190	−1.04644
$550$	1.29543	0.0552375
$551$	−27.2361	−1.16030
$552$	−0.334882	−0.0142535
$553$	−8.68165	−0.369181
$554$	−8.70460	−0.369823
$555$	−3.23685	−0.137397
$556$	10.3236	0.437817
$557$	−24.3334	−1.03104	−0.515520	−	0.856877i	$-0.672401\pi$
$557$	−24.3334	−1.03104	−0.515520	+	0.856877i	$0.672401\pi$
$558$	−4.55656	−0.192894
$559$	0	0
$560$	−6.62706	−0.280044
$561$	−9.75844	−0.412002
$562$	−0.551936	−0.0232820
$563$	−25.0355	−1.05512	−0.527559	−	0.849518i	$-0.676893\pi$
$563$	−25.0355	−1.05512	−0.527559	+	0.849518i	$0.676893\pi$
$564$	−6.06176	−0.255246
$565$	9.01223	0.379147
$566$	−5.83511	−0.245268
$567$	−0.435397	−0.0182850
$568$	11.1714	0.468744
$569$	−21.6212	−0.906407	−0.453203	−	0.891407i	$-0.649719\pi$
$569$	−21.6212	−0.906407	−0.453203	+	0.891407i	$0.649719\pi$
$570$	2.64211	0.110666
$571$	16.6372	0.696246	0.348123	−	0.937449i	$-0.386819\pi$
$571$	16.6372	0.696246	0.348123	+	0.937449i	$0.386819\pi$
$572$	0	0
$573$	−14.4096	−0.601969
$574$	0.426761	0.0178127
$575$	0.313810	0.0130868
$576$	10.2953	0.428971
$577$	−0.909053	−0.0378444	−0.0189222	−	0.999821i	$-0.506023\pi$
$577$	−0.909053	−0.0378444	−0.0189222	+	0.999821i	$0.506023\pi$
$578$	3.05844	0.127214
$579$	8.87401	0.368791
$580$	−25.2227	−1.04732
$581$	−8.89470	−0.369014
$582$	−2.98880	−0.123890
$583$	−37.5280	−1.55425
$584$	−10.3165	−0.426899
$585$	0	0
$586$	3.03116	0.125216
$587$	41.1599	1.69885	0.849424	−	0.527710i	$-0.176949\pi$
$587$	41.1599	1.69885	0.849424	+	0.527710i	$0.176949\pi$
$588$	−2.09410	−0.0863593
$589$	−32.4484	−1.33701
$590$	−8.44438	−0.347650
$591$	16.4691	0.677447
$592$	5.20575	0.213955
$593$	7.37079	0.302682	0.151341	−	0.988482i	$-0.451641\pi$
$593$	7.37079	0.302682	0.151341	+	0.988482i	$0.451641\pi$
$594$	5.43499	0.223000
$595$	5.19199	0.212851
$596$	36.7469	1.50521
$597$	11.3127	0.462997
$598$	0	0
$599$	−14.4698	−0.591220	−0.295610	−	0.955309i	$-0.595523\pi$
$599$	−14.4698	−0.591220	−0.295610	+	0.955309i	$0.595523\pi$
$600$	−1.68411	−0.0687536
$601$	4.85844	0.198180	0.0990900	−	0.995078i	$-0.468407\pi$
$601$	4.85844	0.198180	0.0990900	+	0.995078i	$0.468407\pi$
$602$	3.30441	0.134678
$603$	5.05314	0.205780
$604$	4.58545	0.186579
$605$	0.160823	0.00653838
$606$	2.63465	0.107025
$607$	11.4226	0.463628	0.231814	−	0.972760i	$-0.425534\pi$
$607$	11.4226	0.463628	0.231814	+	0.972760i	$0.425534\pi$
$608$	−13.9327	−0.565045
$609$	−7.54126	−0.305587
$610$	8.27841	0.335183
$611$	0	0
$612$	−9.13121	−0.369107
$613$	−31.2929	−1.26391	−0.631955	−	0.775005i	$-0.717747\pi$
$613$	−31.2929	−1.26391	−0.631955	+	0.775005i	$0.717747\pi$
$614$	1.22479	0.0494285
$615$	2.91204	0.117425
$616$	4.02435	0.162146
$617$	20.5067	0.825567	0.412784	−	0.910829i	$-0.364557\pi$
$617$	20.5067	0.825567	0.412784	+	0.910829i	$0.364557\pi$
$618$	3.21453	0.129307
$619$	15.1362	0.608373	0.304187	−	0.952612i	$-0.401615\pi$
$619$	15.1362	0.608373	0.304187	+	0.952612i	$0.401615\pi$
$620$	−30.0498	−1.20683
$621$	1.31659	0.0528329
$622$	−7.03495	−0.282076
$623$	7.50252	0.300582
$624$	0	0
$625$	−17.1407	−0.685626
$626$	−10.3827	−0.414977
$627$	14.4562	0.577324
$628$	−11.9479	−0.476774
$629$	−4.07846	−0.162619
$630$	−1.08007	−0.0430308
$631$	−14.0749	−0.560313	−0.280157	−	0.959954i	$-0.590386\pi$
$631$	−14.0749	−0.560313	−0.280157	+	0.959954i	$0.590386\pi$
$632$	−10.5742	−0.420621
$633$	−7.91643	−0.314650
$634$	−5.16129	−0.204981
$635$	−14.6385	−0.580912
$636$	23.7850	0.943137
$637$	0	0
$638$	7.06537	0.279721
$639$	−16.4046	−0.648955
$640$	−17.0394	−0.673540
$641$	5.65089	0.223197	0.111598	−	0.993753i	$-0.464403\pi$
$641$	5.65089	0.223197	0.111598	+	0.993753i	$0.464403\pi$
$642$	−3.21704	−0.126966
$643$	13.5494	0.534335	0.267167	−	0.963650i	$-0.413912\pi$
$643$	13.5494	0.534335	0.267167	+	0.963650i	$0.413912\pi$
$644$	0.475270	0.0187283
$645$	22.5479	0.887823
$646$	3.32909	0.130981
$647$	−29.6278	−1.16479	−0.582395	−	0.812906i	$-0.697884\pi$
$647$	−29.6278	−1.16479	−0.582395	+	0.812906i	$0.697884\pi$
$648$	−0.530313	−0.0208327
$649$	−46.2029	−1.81362
$650$	0	0
$651$	−8.98447	−0.352129
$652$	28.1189	1.10122
$653$	−16.6538	−0.651714	−0.325857	−	0.945419i	$-0.605653\pi$
$653$	−16.6538	−0.651714	−0.325857	+	0.945419i	$0.605653\pi$
$654$	−6.84544	−0.267678
$655$	−39.7385	−1.55271
$656$	−4.68337	−0.182855
$657$	15.1491	0.591024
$658$	−0.903430	−0.0352194
$659$	−14.5002	−0.564850	−0.282425	−	0.959289i	$-0.591139\pi$
$659$	−14.5002	−0.564850	−0.282425	+	0.959289i	$0.591139\pi$
$660$	13.3875	0.521110
$661$	32.7213	1.27271	0.636355	−	0.771396i	$-0.280441\pi$
$661$	32.7213	1.27271	0.636355	+	0.771396i	$0.280441\pi$
$662$	−3.21820	−0.125079
$663$	0	0
$664$	−10.8337	−0.420430
$665$	−7.69142	−0.298260
$666$	0.848423	0.0328757
$667$	1.71154	0.0662710
$668$	22.1948	0.858744
$669$	32.6983	1.26419
$670$	−1.70611	−0.0659127
$671$	45.2948	1.74859
$672$	−3.85775	−0.148816
$673$	−14.6250	−0.563751	−0.281875	−	0.959451i	$-0.590956\pi$
$673$	−14.6250	−0.563751	−0.281875	+	0.959451i	$0.590956\pi$
$674$	8.44065	0.325122
$675$	6.62108	0.254845
$676$	0	0
$677$	−41.1507	−1.58155	−0.790774	−	0.612108i	$-0.790322\pi$
$677$	−41.1507	−1.58155	−0.790774	+	0.612108i	$0.790322\pi$
$678$	1.60001	0.0614481
$679$	8.70065	0.333900
$680$	6.32383	0.242508
$681$	−14.1270	−0.541346
$682$	8.41751	0.322323
$683$	−31.0900	−1.18963	−0.594813	−	0.803864i	$-0.702774\pi$
$683$	−31.0900	−1.18963	−0.594813	+	0.803864i	$0.702774\pi$
$684$	13.5270	0.517217
$685$	20.3834	0.778811
$686$	−0.312100	−0.0119160
$687$	−14.2968	−0.545457
$688$	−36.2633	−1.38253
$689$	0	0
$690$	−0.166032	−0.00632075
$691$	−10.4806	−0.398700	−0.199350	−	0.979928i	$-0.563883\pi$
$691$	−10.4806	−0.398700	−0.199350	+	0.979928i	$0.563883\pi$
$692$	27.4808	1.04466
$693$	−5.90952	−0.224484
$694$	8.84790	0.335862
$695$	10.4987	0.398240
$696$	−9.18524	−0.348166
$697$	3.66920	0.138981
$698$	−5.82905	−0.220633
$699$	22.7883	0.861934
$700$	2.39011	0.0903378
$701$	30.9900	1.17047	0.585237	−	0.810862i	$-0.301001\pi$
$701$	30.9900	1.17047	0.585237	+	0.810862i	$0.301001\pi$
$702$	0	0
$703$	6.04184	0.227872
$704$	−19.0189	−0.716802
$705$	−6.16463	−0.232173
$706$	−5.88172	−0.221362
$707$	−7.66968	−0.288448
$708$	29.2832	1.10053
$709$	−9.26922	−0.348113	−0.174056	−	0.984736i	$-0.555688\pi$
$709$	−9.26922	−0.348113	−0.174056	+	0.984736i	$0.555688\pi$
$710$	5.53873	0.207865
$711$	15.5276	0.582331
$712$	9.13805	0.342463
$713$	2.03908	0.0763643
$714$	0.921774	0.0344965
$715$	0	0
$716$	10.2929	0.384664
$717$	−15.7187	−0.587024
$718$	1.08158	0.0403642
$719$	12.6772	0.472779	0.236389	−	0.971658i	$-0.424036\pi$
$719$	12.6772	0.472779	0.236389	+	0.971658i	$0.424036\pi$
$720$	11.8529	0.441730
$721$	−9.35776	−0.348501
$722$	0.998177	0.0371483
$723$	−14.1250	−0.525316
$724$	−12.8458	−0.477409
$725$	8.60726	0.319665
$726$	0.0285521	0.00105967
$727$	−20.4565	−0.758691	−0.379345	−	0.925255i	$-0.623851\pi$
$727$	−20.4565	−0.758691	−0.379345	+	0.925255i	$0.623851\pi$
$728$	0	0
$729$	18.1819	0.673405
$730$	−5.11484	−0.189309
$731$	28.4106	1.05080
$732$	−28.7076	−1.06106
$733$	−1.20844	−0.0446347	−0.0223174	−	0.999751i	$-0.507104\pi$
$733$	−1.20844	−0.0446347	−0.0223174	+	0.999751i	$0.507104\pi$
$734$	−9.70554	−0.358238
$735$	−2.12964	−0.0785529
$736$	0.875541	0.0322729
$737$	−9.33487	−0.343854
$738$	−0.763286	−0.0280970
$739$	27.7387	1.02038	0.510192	−	0.860061i	$-0.329574\pi$
$739$	27.7387	1.02038	0.510192	+	0.860061i	$0.329574\pi$
$740$	5.59521	0.205684
$741$	0	0
$742$	3.54486	0.130136
$743$	−0.529188	−0.0194140	−0.00970702	−	0.999953i	$-0.503090\pi$
$743$	−0.529188	−0.0194140	−0.00970702	+	0.999953i	$0.503090\pi$
$744$	−10.9431	−0.401192
$745$	37.3704	1.36915
$746$	3.39113	0.124158
$747$	15.9087	0.582068
$748$	16.8684	0.616771
$749$	9.36508	0.342193
$750$	−4.15827	−0.151838
$751$	−11.7927	−0.430323	−0.215161	−	0.976578i	$-0.569028\pi$
$751$	−11.7927	−0.430323	−0.215161	+	0.976578i	$0.569028\pi$
$752$	9.91444	0.361542
$753$	−16.7257	−0.609517
$754$	0	0
$755$	4.66326	0.169714
$756$	10.0277	0.364705
$757$	−30.2288	−1.09868	−0.549342	−	0.835598i	$-0.685121\pi$
$757$	−30.2288	−1.09868	−0.549342	+	0.835598i	$0.685121\pi$
$758$	0.586805	0.0213137
$759$	−0.908437	−0.0329742
$760$	−9.36814	−0.339818
$761$	16.9978	0.616170	0.308085	−	0.951359i	$-0.400312\pi$
$761$	16.9978	0.616170	0.308085	+	0.951359i	$0.400312\pi$
$762$	−2.59889	−0.0941479
$763$	19.9277	0.721430
$764$	24.9084	0.901154
$765$	−9.28616	−0.335742
$766$	−10.9876	−0.396997
$767$	0	0
$768$	9.64607	0.348073
$769$	2.13537	0.0770035	0.0385017	−	0.999259i	$-0.487741\pi$
$769$	2.13537	0.0770035	0.0385017	+	0.999259i	$0.487741\pi$
$770$	1.99525	0.0719037
$771$	−33.4800	−1.20575
$772$	−15.3396	−0.552085
$773$	−41.9443	−1.50863	−0.754316	−	0.656512i	$-0.772031\pi$
$773$	−41.9443	−1.50863	−0.754316	+	0.656512i	$0.772031\pi$
$774$	−5.91012	−0.212435
$775$	10.2545	0.368352
$776$	10.5974	0.380424
$777$	1.67289	0.0600147
$778$	4.61506	0.165458
$779$	−5.43556	−0.194749
$780$	0	0
$781$	30.3048	1.08439
$782$	−0.209203	−0.00748107
$783$	36.1117	1.29053
$784$	3.42505	0.122323
$785$	−12.1507	−0.433676
$786$	−7.05508	−0.251646
$787$	5.31182	0.189346	0.0946729	−	0.995508i	$-0.469819\pi$
$787$	5.31182	0.189346	0.0946729	+	0.995508i	$0.469819\pi$
$788$	−28.4684	−1.01415
$789$	5.36670	0.191060
$790$	−5.24264	−0.186525
$791$	−4.65777	−0.165611
$792$	−7.19778	−0.255762
$793$	0	0
$794$	−9.05953	−0.321511
$795$	24.1886	0.857882
$796$	−19.5551	−0.693112
$797$	1.28506	0.0455191	0.0227596	−	0.999741i	$-0.492755\pi$
$797$	1.28506	0.0455191	0.0227596	+	0.999741i	$0.492755\pi$
$798$	−1.36552	−0.0483388
$799$	−7.76749	−0.274794
$800$	4.40306	0.155672
$801$	−13.4187	−0.474126
$802$	−6.39947	−0.225973
$803$	−27.9856	−0.987590
$804$	5.91639	0.208655
$805$	0.483335	0.0170353
$806$	0	0
$807$	−7.59258	−0.267271
$808$	−9.34166	−0.328638
$809$	−7.67690	−0.269905	−0.134953	−	0.990852i	$-0.543088\pi$
$809$	−7.67690	−0.269905	−0.134953	+	0.990852i	$0.543088\pi$
$810$	−0.262926	−0.00923827
$811$	9.69738	0.340521	0.170261	−	0.985399i	$-0.445539\pi$
$811$	9.69738	0.340521	0.170261	+	0.985399i	$0.445539\pi$
$812$	13.0358	0.457467
$813$	2.36581	0.0829727
$814$	−1.56733	−0.0549348
$815$	28.5960	1.00167
$816$	−10.1158	−0.354122
$817$	−42.0875	−1.47245
$818$	0.723187	0.0252856
$819$	0	0
$820$	−5.03375	−0.175786
$821$	−28.7275	−1.00260	−0.501298	−	0.865275i	$-0.667144\pi$
$821$	−28.7275	−1.00260	−0.501298	+	0.865275i	$0.667144\pi$
$822$	3.61883	0.126221
$823$	−2.15032	−0.0749553	−0.0374777	−	0.999297i	$-0.511932\pi$
$823$	−2.15032	−0.0749553	−0.0374777	+	0.999297i	$0.511932\pi$
$824$	−11.3977	−0.397059
$825$	−4.56850	−0.159055
$826$	4.36429	0.151853
$827$	−38.5500	−1.34051	−0.670257	−	0.742129i	$-0.733816\pi$
$827$	−38.5500	−1.34051	−0.670257	+	0.742129i	$0.733816\pi$
$828$	−0.850047	−0.0295412
$829$	8.11579	0.281873	0.140936	−	0.990019i	$-0.454989\pi$
$829$	8.11579	0.281873	0.140936	+	0.990019i	$0.454989\pi$
$830$	−5.37129	−0.186440
$831$	30.6978	1.06489
$832$	0	0
$833$	−2.68336	−0.0929731
$834$	1.86393	0.0645425
$835$	22.5715	0.781118
$836$	−24.9889	−0.864261
$837$	43.0226	1.48708
$838$	3.18311	0.109959
$839$	19.0949	0.659228	0.329614	−	0.944116i	$-0.393081\pi$
$839$	19.0949	0.659228	0.329614	+	0.944116i	$0.393081\pi$
$840$	−2.59389	−0.0894979
$841$	17.9445	0.618774
$842$	2.74689	0.0946640
$843$	1.94647	0.0670399
$844$	13.6843	0.471034
$845$	0	0
$846$	1.61584	0.0555536
$847$	−0.0831177	−0.00285596
$848$	−38.9021	−1.33590
$849$	20.5782	0.706242
$850$	−1.05207	−0.0360858
$851$	−0.379674	−0.0130151
$852$	−19.2070	−0.658022
$853$	49.0402	1.67910	0.839551	−	0.543280i	$-0.182818\pi$
$853$	49.0402	1.67910	0.839551	+	0.543280i	$0.182818\pi$
$854$	−4.27851	−0.146408
$855$	13.7565	0.470464
$856$	11.4067	0.389871
$857$	−50.1325	−1.71249	−0.856247	−	0.516566i	$-0.827210\pi$
$857$	−50.1325	−1.71249	−0.856247	+	0.516566i	$0.827210\pi$
$858$	0	0
$859$	34.5583	1.17912	0.589558	−	0.807726i	$-0.299302\pi$
$859$	34.5583	1.17912	0.589558	+	0.807726i	$0.299302\pi$
$860$	−38.9763	−1.32908
$861$	−1.50502	−0.0512910
$862$	4.92141	0.167624
$863$	8.86279	0.301693	0.150846	−	0.988557i	$-0.451800\pi$
$863$	8.86279	0.301693	0.150846	+	0.988557i	$0.451800\pi$
$864$	18.4730	0.628466
$865$	27.9471	0.950230
$866$	−6.54504	−0.222410
$867$	−10.7859	−0.366310
$868$	15.5306	0.527141
$869$	−28.6848	−0.973065
$870$	−4.55398	−0.154394
$871$	0	0
$872$	24.2719	0.821949
$873$	−15.5616	−0.526681
$874$	0.309913	0.0104830
$875$	12.1051	0.409226
$876$	17.7371	0.599281
$877$	−10.2278	−0.345367	−0.172683	−	0.984977i	$-0.555244\pi$
$877$	−10.2278	−0.345367	−0.172683	+	0.984977i	$0.555244\pi$
$878$	−6.94232	−0.234292
$879$	−10.6898	−0.360557
$880$	−21.8963	−0.738123
$881$	28.8841	0.973131	0.486565	−	0.873644i	$-0.338250\pi$
$881$	28.8841	0.973131	0.486565	+	0.873644i	$0.338250\pi$
$882$	0.558208	0.0187958
$883$	−3.42325	−0.115202	−0.0576008	−	0.998340i	$-0.518345\pi$
$883$	−3.42325	−0.115202	−0.0576008	+	0.998340i	$0.518345\pi$
$884$	0	0
$885$	29.7801	1.00105
$886$	7.05423	0.236992
$887$	6.79837	0.228267	0.114133	−	0.993465i	$-0.463591\pi$
$887$	6.79837	0.228267	0.114133	+	0.993465i	$0.463591\pi$
$888$	2.03758	0.0683768
$889$	7.56559	0.253742
$890$	4.53059	0.151866
$891$	−1.43858	−0.0481944
$892$	−56.5222	−1.89250
$893$	11.5068	0.385060
$894$	6.63467	0.221897
$895$	10.4676	0.349892
$896$	8.80642	0.294202
$897$	0	0
$898$	−10.5109	−0.350755
$899$	55.9285	1.86532
$900$	−4.27485	−0.142495
$901$	30.4779	1.01537
$902$	1.41005	0.0469495
$903$	−11.6534	−0.387800
$904$	−5.67316	−0.188686
$905$	−13.0638	−0.434254
$906$	0.827906	0.0275053
$907$	50.9386	1.69139	0.845694	−	0.533668i	$-0.179187\pi$
$907$	50.9386	1.69139	0.845694	+	0.533668i	$0.179187\pi$
$908$	24.4199	0.810402
$909$	13.7177	0.454986
$910$	0	0
$911$	−28.4847	−0.943742	−0.471871	−	0.881668i	$-0.656421\pi$
$911$	−28.4847	−0.943742	−0.471871	+	0.881668i	$0.656421\pi$
$912$	14.9855	0.496219
$913$	−29.3887	−0.972624
$914$	9.34202	0.309007
$915$	−29.1948	−0.965149
$916$	24.7134	0.816555
$917$	20.5380	0.678223
$918$	−4.41397	−0.145683
$919$	44.6522	1.47294	0.736470	−	0.676470i	$-0.236491\pi$
$919$	44.6522	1.47294	0.736470	+	0.676470i	$0.236491\pi$
$920$	0.588701	0.0194089
$921$	−4.31936	−0.142328
$922$	3.71047	0.122198
$923$	0	0
$924$	−6.91906	−0.227620
$925$	−1.90937	−0.0627796
$926$	5.35583	0.176003
$927$	16.7369	0.549712
$928$	24.0146	0.788316
$929$	−35.6955	−1.17113	−0.585565	−	0.810625i	$-0.699127\pi$
$929$	−35.6955	−1.17113	−0.585565	+	0.810625i	$0.699127\pi$
$930$	−5.42550	−0.177909
$931$	3.97514	0.130280
$932$	−39.3919	−1.29032
$933$	24.8096	0.812229
$934$	1.82221	0.0596245
$935$	17.1547	0.561018
$936$	0	0
$937$	−8.92893	−0.291695	−0.145848	−	0.989307i	$-0.546591\pi$
$937$	−8.92893	−0.291695	−0.145848	+	0.989307i	$0.546591\pi$
$938$	0.881764	0.0287906
$939$	36.6159	1.19492
$940$	10.6562	0.347566
$941$	−10.5470	−0.343821	−0.171911	−	0.985113i	$-0.554994\pi$
$941$	−10.5470	−0.343821	−0.171911	+	0.985113i	$0.554994\pi$
$942$	−2.15721	−0.0702856
$943$	0.341575	0.0111232
$944$	−47.8947	−1.55884
$945$	10.1979	0.331737
$946$	10.9180	0.354975
$947$	9.84312	0.319858	0.159929	−	0.987128i	$-0.448873\pi$
$947$	9.84312	0.319858	0.159929	+	0.987128i	$0.448873\pi$
$948$	18.1803	0.590467
$949$	0	0
$950$	1.55854	0.0505658
$951$	18.2019	0.590236
$952$	−3.26833	−0.105927
$953$	−10.8735	−0.352226	−0.176113	−	0.984370i	$-0.556352\pi$
$953$	−10.8735	−0.352226	−0.176113	+	0.984370i	$0.556352\pi$
$954$	−6.34018	−0.205271
$955$	25.3311	0.819695
$956$	27.1713	0.878781
$957$	−24.9168	−0.805447
$958$	−4.98885	−0.161183
$959$	−10.5347	−0.340184
$960$	12.2586	0.395646
$961$	35.6318	1.14941
$962$	0	0
$963$	−16.7500	−0.539761
$964$	24.4165	0.786404
$965$	−15.5999	−0.502179
$966$	0.0858102	0.00276090
$967$	33.7702	1.08598	0.542988	−	0.839741i	$-0.317293\pi$
$967$	33.7702	1.08598	0.542988	+	0.839741i	$0.317293\pi$
$968$	−0.101237	−0.00325389
$969$	−11.7404	−0.377157
$970$	5.25411	0.168699
$971$	44.4037	1.42498	0.712492	−	0.701680i	$-0.247567\pi$
$971$	44.4037	1.42498	0.712492	+	0.701680i	$0.247567\pi$
$972$	−29.1714	−0.935673
$973$	−5.42605	−0.173951
$974$	5.28122	0.169221
$975$	0	0
$976$	46.9533	1.50294
$977$	7.28864	0.233184	0.116592	−	0.993180i	$-0.462803\pi$
$977$	7.28864	0.233184	0.116592	+	0.993180i	$0.462803\pi$
$978$	5.07688	0.162341
$979$	24.7888	0.792255
$980$	3.68129	0.117595
$981$	−35.6417	−1.13795
$982$	1.88237	0.0600689
$983$	7.27754	0.232118	0.116059	−	0.993242i	$-0.462974\pi$
$983$	7.27754	0.232118	0.116059	+	0.993242i	$0.462974\pi$
$984$	−1.83312	−0.0584376
$985$	−28.9515	−0.922473
$986$	−5.73806	−0.182737
$987$	3.18605	0.101413
$988$	0	0
$989$	2.64481	0.0841001
$990$	−3.56861	−0.113418
$991$	−2.38406	−0.0757320	−0.0378660	−	0.999283i	$-0.512056\pi$
$991$	−2.38406	−0.0757320	−0.0378660	+	0.999283i	$0.512056\pi$
$992$	28.6103	0.908379
$993$	11.3494	0.360161
$994$	−2.86257	−0.0907952
$995$	−19.8869	−0.630458
$996$	18.6264	0.590200
$997$	−7.64905	−0.242248	−0.121124	−	0.992637i	$-0.538650\pi$
$997$	−7.64905	−0.242248	−0.121124	+	0.992637i	$0.538650\pi$
$998$	−6.35503	−0.201165
$999$	−8.01074	−0.253449

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.n.1.4	✓	6
7.6	odd	2		8281.2.a.cb.1.4		6
13.5	odd	4		1183.2.c.h.337.7		12
13.8	odd	4		1183.2.c.h.337.6		12
13.12	even	2		1183.2.a.o.1.3	yes	6
91.90	odd	2		8281.2.a.cg.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.n.1.4	✓	6	1.1	even	1	trivial
1183.2.a.o.1.3	yes	6	13.12	even	2
1183.2.c.h.337.6		12	13.8	odd	4
1183.2.c.h.337.7		12	13.5	odd	4
8281.2.a.cb.1.4		6	7.6	odd	2
8281.2.a.cg.1.3		6	91.90	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.a (trivial)

\(f(q)\)	\(=\)	\(q-0.312100 q^{2} +1.10066 q^{3} -1.90259 q^{4} -1.93488 q^{5} -0.343514 q^{6} +1.00000 q^{7} +1.21800 q^{8} -1.78856 q^{9} +O(q^{10})\)	\(q-0.312100 q^{2} +1.10066 q^{3} -1.90259 q^{4} -1.93488 q^{5} -0.343514 q^{6} +1.00000 q^{7} +1.21800 q^{8} -1.78856 q^{9} +0.603875 q^{10} +3.30407 q^{11} -2.09410 q^{12} -0.312100 q^{14} -2.12964 q^{15} +3.42505 q^{16} -2.68336 q^{17} +0.558208 q^{18} +3.97514 q^{19} +3.68129 q^{20} +1.10066 q^{21} -1.03120 q^{22} -0.249801 q^{23} +1.34060 q^{24} -1.25624 q^{25} -5.27055 q^{27} -1.90259 q^{28} -6.85160 q^{29} +0.664659 q^{30} -8.16283 q^{31} -3.50495 q^{32} +3.63665 q^{33} +0.837477 q^{34} -1.93488 q^{35} +3.40290 q^{36} +1.51991 q^{37} -1.24064 q^{38} -2.35668 q^{40} -1.36739 q^{41} -0.343514 q^{42} -10.5877 q^{43} -6.28630 q^{44} +3.46064 q^{45} +0.0779628 q^{46} +2.89468 q^{47} +3.76980 q^{48} +1.00000 q^{49} +0.392072 q^{50} -2.95346 q^{51} -11.3581 q^{53} +1.64494 q^{54} -6.39298 q^{55} +1.21800 q^{56} +4.37526 q^{57} +2.13838 q^{58} -13.9836 q^{59} +4.05183 q^{60} +13.7088 q^{61} +2.54762 q^{62} -1.78856 q^{63} -5.75621 q^{64} -1.13500 q^{66} -2.82526 q^{67} +5.10535 q^{68} -0.274945 q^{69} +0.603875 q^{70} +9.17197 q^{71} -2.17846 q^{72} -8.47003 q^{73} -0.474362 q^{74} -1.38269 q^{75} -7.56308 q^{76} +3.30407 q^{77} -8.68165 q^{79} -6.62706 q^{80} -0.435397 q^{81} +0.426761 q^{82} -8.89470 q^{83} -2.09410 q^{84} +5.19199 q^{85} +3.30441 q^{86} -7.54126 q^{87} +4.02435 q^{88} +7.50252 q^{89} -1.08007 q^{90} +0.475270 q^{92} -8.98447 q^{93} -0.903430 q^{94} -7.69142 q^{95} -3.85775 q^{96} +8.70065 q^{97} -0.312100 q^{98} -5.90952 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 8 q^{6} + 6 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 8 * q^6 + 6 * q^7 - 3 * q^8	\( 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 8 q^{6} + 6 q^{7} - 3 q^{8} - 14 q^{10} - 8 q^{11} - 23 q^{12} - 2 q^{14} - 3 q^{15} - 23 q^{17} - 26 q^{18} + 13 q^{19} + 4 q^{20} - 4 q^{21} - 4 q^{22} - 18 q^{23} + 26 q^{24} - 10 q^{25} - 10 q^{27} + 8 q^{28} - 15 q^{29} + 14 q^{30} - 3 q^{31} - 28 q^{32} - 3 q^{33} + 29 q^{34} - 2 q^{35} + 22 q^{36} + 13 q^{37} - 11 q^{38} - 14 q^{40} + 4 q^{41} + 8 q^{42} - 18 q^{43} + 19 q^{45} - 10 q^{46} + 16 q^{47} - 11 q^{48} + 6 q^{49} + 10 q^{50} + 14 q^{51} - 25 q^{53} + 31 q^{54} - 3 q^{56} + 4 q^{57} + 13 q^{58} - 18 q^{59} - 22 q^{60} + 16 q^{61} - 9 q^{62} - 7 q^{64} + 16 q^{66} - 16 q^{67} - 34 q^{68} - q^{69} - 14 q^{70} - 25 q^{71} - 39 q^{72} + 5 q^{73} - 14 q^{74} + 15 q^{75} - 7 q^{76} - 8 q^{77} + 2 q^{79} + 27 q^{80} - 6 q^{81} - 10 q^{82} + 7 q^{83} - 23 q^{84} - 9 q^{85} + 3 q^{86} + 13 q^{87} - 48 q^{88} + 10 q^{89} - 32 q^{92} - 35 q^{93} - 14 q^{94} - 7 q^{95} + 14 q^{96} + 5 q^{97} - 2 q^{98} + 15 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 8 * q^6 + 6 * q^7 - 3 * q^8 - 14 * q^10 - 8 * q^11 - 23 * q^12 - 2 * q^14 - 3 * q^15 - 23 * q^17 - 26 * q^18 + 13 * q^19 + 4 * q^20 - 4 * q^21 - 4 * q^22 - 18 * q^23 + 26 * q^24 - 10 * q^25 - 10 * q^27 + 8 * q^28 - 15 * q^29 + 14 * q^30 - 3 * q^31 - 28 * q^32 - 3 * q^33 + 29 * q^34 - 2 * q^35 + 22 * q^36 + 13 * q^37 - 11 * q^38 - 14 * q^40 + 4 * q^41 + 8 * q^42 - 18 * q^43 + 19 * q^45 - 10 * q^46 + 16 * q^47 - 11 * q^48 + 6 * q^49 + 10 * q^50 + 14 * q^51 - 25 * q^53 + 31 * q^54 - 3 * q^56 + 4 * q^57 + 13 * q^58 - 18 * q^59 - 22 * q^60 + 16 * q^61 - 9 * q^62 - 7 * q^64 + 16 * q^66 - 16 * q^67 - 34 * q^68 - q^69 - 14 * q^70 - 25 * q^71 - 39 * q^72 + 5 * q^73 - 14 * q^74 + 15 * q^75 - 7 * q^76 - 8 * q^77 + 2 * q^79 + 27 * q^80 - 6 * q^81 - 10 * q^82 + 7 * q^83 - 23 * q^84 - 9 * q^85 + 3 * q^86 + 13 * q^87 - 48 * q^88 + 10 * q^89 - 32 * q^92 - 35 * q^93 - 14 * q^94 - 7 * q^95 + 14 * q^96 + 5 * q^97 - 2 * q^98 + 15 * q^99

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