LMFDB - Embedded newform 1183.2.a.m.1.6

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:	6.6.7674048.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 2 $ x^6 - 2x^5 - 5x^4 + 8x^3 + 7x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$2.38595$ 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)

$f(q)$	$=$	$q+1.38595 q^{2} -2.82577 q^{3} -0.0791355 q^{4} +0.518957 q^{5} -3.91639 q^{6} +1.00000 q^{7} -2.88158 q^{8} +4.98500 q^{9} +O(q^{10})$	\(q+1.38595 q^{2} -2.82577 q^{3} -0.0791355 q^{4} +0.518957 q^{5} -3.91639 q^{6} +1.00000 q^{7} -2.88158 q^{8} +4.98500 q^{9} +0.719250 q^{10} +1.62416 q^{11} +0.223619 q^{12} +1.38595 q^{14} -1.46646 q^{15} -3.83547 q^{16} +1.94825 q^{17} +6.90897 q^{18} +2.49115 q^{19} -0.0410679 q^{20} -2.82577 q^{21} +2.25101 q^{22} -9.14058 q^{23} +8.14270 q^{24} -4.73068 q^{25} -5.60916 q^{27} -0.0791355 q^{28} -5.22996 q^{29} -2.03244 q^{30} +5.79391 q^{31} +0.447392 q^{32} -4.58951 q^{33} +2.70019 q^{34} +0.518957 q^{35} -0.394491 q^{36} -10.2293 q^{37} +3.45262 q^{38} -1.49542 q^{40} -4.20903 q^{41} -3.91639 q^{42} -0.997311 q^{43} -0.128529 q^{44} +2.58700 q^{45} -12.6684 q^{46} -4.51725 q^{47} +10.8382 q^{48} +1.00000 q^{49} -6.55650 q^{50} -5.50532 q^{51} -8.89651 q^{53} -7.77403 q^{54} +0.842869 q^{55} -2.88158 q^{56} -7.03944 q^{57} -7.24847 q^{58} +6.20526 q^{59} +0.116049 q^{60} -13.4707 q^{61} +8.03008 q^{62} +4.98500 q^{63} +8.29100 q^{64} -6.36084 q^{66} +8.37266 q^{67} -0.154176 q^{68} +25.8292 q^{69} +0.719250 q^{70} -5.19809 q^{71} -14.3647 q^{72} -11.8395 q^{73} -14.1773 q^{74} +13.3678 q^{75} -0.197139 q^{76} +1.62416 q^{77} +0.982310 q^{79} -1.99044 q^{80} +0.895217 q^{81} -5.83352 q^{82} -8.91851 q^{83} +0.223619 q^{84} +1.01106 q^{85} -1.38223 q^{86} +14.7787 q^{87} -4.68015 q^{88} -12.0190 q^{89} +3.58546 q^{90} +0.723345 q^{92} -16.3723 q^{93} -6.26070 q^{94} +1.29280 q^{95} -1.26423 q^{96} +4.42228 q^{97} +1.38595 q^{98} +8.09643 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{2} + 4 q^{4} - 6 q^{5} - 4 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) $ 6 * q - 4 * q^2 + 4 * q^4 - 6 * q^5 - 4 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9	$ 6 q - 4 q^{2} + 4 q^{4} - 6 q^{5} - 4 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9} + 12 q^{10} - 4 q^{11} + 2 q^{12} - 4 q^{14} - 20 q^{15} + 8 q^{16} - 4 q^{17} + 16 q^{18} - 2 q^{19} - 26 q^{20} - 6 q^{22} - 12 q^{23} - 2 q^{24} + 10 q^{25} + 6 q^{27} + 4 q^{28} - 8 q^{29} + 8 q^{30} + 14 q^{31} - 8 q^{32} - 16 q^{33} + 2 q^{34} - 6 q^{35} - 10 q^{36} - 12 q^{37} - 2 q^{38} + 46 q^{40} - 28 q^{41} - 4 q^{42} + 2 q^{43} + 20 q^{44} - 16 q^{45} - 20 q^{46} - 14 q^{47} + 2 q^{48} + 6 q^{49} - 32 q^{50} - 26 q^{51} - 22 q^{53} - 14 q^{54} + 6 q^{55} - 12 q^{56} - 4 q^{58} + 2 q^{59} - 14 q^{61} - 4 q^{62} + 4 q^{63} + 26 q^{64} - 26 q^{66} - 24 q^{67} + 8 q^{68} + 4 q^{69} + 12 q^{70} - 4 q^{71} - 8 q^{72} - 36 q^{73} - 6 q^{74} + 46 q^{75} + 26 q^{76} - 4 q^{77} - 28 q^{79} - 36 q^{80} - 2 q^{81} + 14 q^{82} - 26 q^{83} + 2 q^{84} + 20 q^{85} + 24 q^{86} + 2 q^{87} - 14 q^{88} - 42 q^{89} - 12 q^{90} + 12 q^{92} - 4 q^{94} - 22 q^{95} + 42 q^{96} - 24 q^{97} - 4 q^{98} - 16 q^{99}+O(q^{100}) $ 6 * q - 4 * q^2 + 4 * q^4 - 6 * q^5 - 4 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9 + 12 * q^10 - 4 * q^11 + 2 * q^12 - 4 * q^14 - 20 * q^15 + 8 * q^16 - 4 * q^17 + 16 * q^18 - 2 * q^19 - 26 * q^20 - 6 * q^22 - 12 * q^23 - 2 * q^24 + 10 * q^25 + 6 * q^27 + 4 * q^28 - 8 * q^29 + 8 * q^30 + 14 * q^31 - 8 * q^32 - 16 * q^33 + 2 * q^34 - 6 * q^35 - 10 * q^36 - 12 * q^37 - 2 * q^38 + 46 * q^40 - 28 * q^41 - 4 * q^42 + 2 * q^43 + 20 * q^44 - 16 * q^45 - 20 * q^46 - 14 * q^47 + 2 * q^48 + 6 * q^49 - 32 * q^50 - 26 * q^51 - 22 * q^53 - 14 * q^54 + 6 * q^55 - 12 * q^56 - 4 * q^58 + 2 * q^59 - 14 * q^61 - 4 * q^62 + 4 * q^63 + 26 * q^64 - 26 * q^66 - 24 * q^67 + 8 * q^68 + 4 * q^69 + 12 * q^70 - 4 * q^71 - 8 * q^72 - 36 * q^73 - 6 * q^74 + 46 * q^75 + 26 * q^76 - 4 * q^77 - 28 * q^79 - 36 * q^80 - 2 * q^81 + 14 * q^82 - 26 * q^83 + 2 * q^84 + 20 * q^85 + 24 * q^86 + 2 * q^87 - 14 * q^88 - 42 * q^89 - 12 * q^90 + 12 * q^92 - 4 * q^94 - 22 * q^95 + 42 * q^96 - 24 * q^97 - 4 * q^98 - 16 * 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 $

$2$	1.38595	0.980016	0.490008	−	0.871718i	$-0.336994\pi$
$2$	1.38595	0.980016	0.490008	+	0.871718i	$0.336994\pi$
$3$	−2.82577	−1.63146	−0.815731	−	0.578432i	$-0.803665\pi$
$3$	−2.82577	−1.63146	−0.815731	+	0.578432i	$0.803665\pi$
$4$	−0.0791355	−0.0395678
$5$	0.518957	0.232085	0.116042	−	0.993244i	$-0.462979\pi$
$5$	0.518957	0.232085	0.116042	+	0.993244i	$0.462979\pi$
$6$	−3.91639	−1.59886
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.88158	−1.01879
$9$	4.98500	1.66167
$10$	0.719250	0.227447
$11$	1.62416	0.489702	0.244851	−	0.969561i	$-0.421261\pi$
$11$	1.62416	0.489702	0.244851	+	0.969561i	$0.421261\pi$
$12$	0.223619	0.0645533
$13$	0	0
$13$	0	0
$14$	1.38595	0.370411
$15$	−1.46646	−0.378637
$16$	−3.83547	−0.958867
$17$	1.94825	0.472521	0.236260	−	0.971690i	$-0.424078\pi$
$17$	1.94825	0.472521	0.236260	+	0.971690i	$0.424078\pi$
$18$	6.90897	1.62846
$19$	2.49115	0.571510	0.285755	−	0.958303i	$-0.407756\pi$
$19$	2.49115	0.571510	0.285755	+	0.958303i	$0.407756\pi$
$20$	−0.0410679	−0.00918307
$21$	−2.82577	−0.616634
$22$	2.25101	0.479916
$23$	−9.14058	−1.90594	−0.952971	−	0.303060i	$-0.901992\pi$
$23$	−9.14058	−1.90594	−0.952971	+	0.303060i	$0.901992\pi$
$24$	8.14270	1.66212
$25$	−4.73068	−0.946137
$26$	0	0
$27$	−5.60916	−1.07948
$28$	−0.0791355	−0.0149552
$29$	−5.22996	−0.971179	−0.485589	−	0.874187i	$-0.661395\pi$
$29$	−5.22996	−0.971179	−0.485589	+	0.874187i	$0.661395\pi$
$30$	−2.03244	−0.371071
$31$	5.79391	1.04062	0.520308	−	0.853978i	$-0.325817\pi$
$31$	5.79391	1.04062	0.520308	+	0.853978i	$0.325817\pi$
$32$	0.447392	0.0790885
$33$	−4.58951	−0.798931
$34$	2.70019	0.463078
$35$	0.518957	0.0877197
$36$	−0.394491	−0.0657484
$37$	−10.2293	−1.68168	−0.840840	−	0.541284i	$-0.817938\pi$
$37$	−10.2293	−1.68168	−0.840840	+	0.541284i	$0.817938\pi$
$38$	3.45262	0.560089
$39$	0	0
$40$	−1.49542	−0.236446
$41$	−4.20903	−0.657340	−0.328670	−	0.944445i	$-0.606600\pi$
$41$	−4.20903	−0.657340	−0.328670	+	0.944445i	$0.606600\pi$
$42$	−3.91639	−0.604312
$43$	−0.997311	−0.152088	−0.0760442	−	0.997104i	$-0.524229\pi$
$43$	−0.997311	−0.152088	−0.0760442	+	0.997104i	$0.524229\pi$
$44$	−0.128529	−0.0193764
$45$	2.58700	0.385647
$46$	−12.6684	−1.86786
$47$	−4.51725	−0.658909	−0.329455	−	0.944171i	$-0.606865\pi$
$47$	−4.51725	−0.658909	−0.329455	+	0.944171i	$0.606865\pi$
$48$	10.8382	1.56435
$49$	1.00000	0.142857
$50$	−6.55650	−0.927230
$51$	−5.50532	−0.770899
$52$	0	0
$53$	−8.89651	−1.22203	−0.611015	−	0.791619i	$-0.709238\pi$
$53$	−8.89651	−1.22203	−0.611015	+	0.791619i	$0.709238\pi$
$54$	−7.77403	−1.05791
$55$	0.842869	0.113652
$56$	−2.88158	−0.385068
$57$	−7.03944	−0.932397
$58$	−7.24847	−0.951771
$59$	6.20526	0.807856	0.403928	−	0.914791i	$-0.367645\pi$
$59$	6.20526	0.807856	0.403928	+	0.914791i	$0.367645\pi$
$60$	0.116049	0.0149818
$61$	−13.4707	−1.72475	−0.862375	−	0.506270i	$-0.831024\pi$
$61$	−13.4707	−1.72475	−0.862375	+	0.506270i	$0.831024\pi$
$62$	8.03008	1.01982
$63$	4.98500	0.628051
$64$	8.29100	1.03637
$65$	0	0
$66$	−6.36084	−0.782965
$67$	8.37266	1.02288	0.511442	−	0.859318i	$-0.329112\pi$
$67$	8.37266	1.02288	0.511442	+	0.859318i	$0.329112\pi$
$68$	−0.154176	−0.0186966
$69$	25.8292	3.10947
$70$	0.719250	0.0859668
$71$	−5.19809	−0.616900	−0.308450	−	0.951241i	$-0.599810\pi$
$71$	−5.19809	−0.616900	−0.308450	+	0.951241i	$0.599810\pi$
$72$	−14.3647	−1.69289
$73$	−11.8395	−1.38571	−0.692856	−	0.721076i	$-0.743648\pi$
$73$	−11.8395	−1.38571	−0.692856	+	0.721076i	$0.743648\pi$
$74$	−14.1773	−1.64807
$75$	13.3678	1.54359
$76$	−0.197139	−0.0226134
$77$	1.62416	0.185090
$78$	0	0
$79$	0.982310	0.110518	0.0552592	−	0.998472i	$-0.482401\pi$
$79$	0.982310	0.110518	0.0552592	+	0.998472i	$0.482401\pi$
$80$	−1.99044	−0.222538
$81$	0.895217	0.0994686
$82$	−5.83352	−0.644204
$83$	−8.91851	−0.978934	−0.489467	−	0.872022i	$-0.662809\pi$
$83$	−8.91851	−0.978934	−0.489467	+	0.872022i	$0.662809\pi$
$84$	0.223619	0.0243989
$85$	1.01106	0.109665
$86$	−1.38223	−0.149049
$87$	14.7787	1.58444
$88$	−4.68015	−0.498906
$89$	−12.0190	−1.27401	−0.637005	−	0.770860i	$-0.719827\pi$
$89$	−12.0190	−1.27401	−0.637005	+	0.770860i	$0.719827\pi$
$90$	3.58546	0.377941
$91$	0	0
$92$	0.723345	0.0754139
$93$	−16.3723	−1.69773
$94$	−6.26070	−0.645742
$95$	1.29280	0.132639
$96$	−1.26423	−0.129030
$97$	4.42228	0.449015	0.224507	−	0.974472i	$-0.427923\pi$
$97$	4.42228	0.449015	0.224507	+	0.974472i	$0.427923\pi$
$98$	1.38595	0.140002
$99$	8.09643	0.813722
$100$	0.374365	0.0374365
$101$	18.3026	1.82118	0.910591	−	0.413309i	$-0.135627\pi$
$101$	18.3026	1.82118	0.910591	+	0.413309i	$0.135627\pi$
$102$	−7.63012	−0.755494
$103$	5.02046	0.494680	0.247340	−	0.968929i	$-0.420444\pi$
$103$	5.02046	0.494680	0.247340	+	0.968929i	$0.420444\pi$
$104$	0	0
$105$	−1.46646	−0.143111
$106$	−12.3301	−1.19761
$107$	6.14456	0.594017	0.297008	−	0.954875i	$-0.404011\pi$
$107$	6.14456	0.594017	0.297008	+	0.954875i	$0.404011\pi$
$108$	0.443884	0.0427127
$109$	11.8962	1.13945	0.569727	−	0.821834i	$-0.307049\pi$
$109$	11.8962	1.13945	0.569727	+	0.821834i	$0.307049\pi$
$110$	1.16818	0.111381
$111$	28.9056	2.74359
$112$	−3.83547	−0.362418
$113$	3.55612	0.334532	0.167266	−	0.985912i	$-0.446506\pi$
$113$	3.55612	0.334532	0.167266	+	0.985912i	$0.446506\pi$
$114$	−9.75633	−0.913764
$115$	−4.74357	−0.442340
$116$	0.413875	0.0384274
$117$	0	0
$118$	8.60020	0.791713
$119$	1.94825	0.178596
$120$	4.22571	0.385753
$121$	−8.36211	−0.760191
$122$	−18.6698	−1.69028
$123$	11.8938	1.07243
$124$	−0.458504	−0.0411749
$125$	−5.04981	−0.451668
$126$	6.90897	0.615500
$127$	−1.42350	−0.126315	−0.0631575	−	0.998004i	$-0.520117\pi$
$127$	−1.42350	−0.126315	−0.0631575	+	0.998004i	$0.520117\pi$
$128$	10.5961	0.936576
$129$	2.81818	0.248127
$130$	0	0
$131$	8.67374	0.757828	0.378914	−	0.925432i	$-0.376298\pi$
$131$	8.67374	0.757828	0.378914	+	0.925432i	$0.376298\pi$
$132$	0.363193	0.0316119
$133$	2.49115	0.216011
$134$	11.6041	1.00244
$135$	−2.91091	−0.250531
$136$	−5.61405	−0.481401
$137$	−8.51784	−0.727728	−0.363864	−	0.931452i	$-0.618543\pi$
$137$	−8.51784	−0.727728	−0.363864	+	0.931452i	$0.618543\pi$
$138$	35.7981	3.04733
$139$	−5.03844	−0.427355	−0.213677	−	0.976904i	$-0.568544\pi$
$139$	−5.03844	−0.427355	−0.213677	+	0.976904i	$0.568544\pi$
$140$	−0.0410679	−0.00347087
$141$	12.7647	1.07499
$142$	−7.20431	−0.604572
$143$	0	0
$144$	−19.1198	−1.59332
$145$	−2.71412	−0.225396
$146$	−16.4090	−1.35802
$147$	−2.82577	−0.233066
$148$	0.809498	0.0665403
$149$	3.36490	0.275663	0.137832	−	0.990456i	$-0.455987\pi$
$149$	3.36490	0.275663	0.137832	+	0.990456i	$0.455987\pi$
$150$	18.5272	1.51274
$151$	12.6566	1.02998	0.514991	−	0.857196i	$-0.327795\pi$
$151$	12.6566	1.02998	0.514991	+	0.857196i	$0.327795\pi$
$152$	−7.17847	−0.582251
$153$	9.71204	0.785172
$154$	2.25101	0.181391
$155$	3.00679	0.241511
$156$	0	0
$157$	10.3691	0.827547	0.413773	−	0.910380i	$-0.364211\pi$
$157$	10.3691	0.827547	0.413773	+	0.910380i	$0.364211\pi$
$158$	1.36143	0.108310
$159$	25.1395	1.99369
$160$	0.232177	0.0183552
$161$	−9.14058	−0.720379
$162$	1.24073	0.0974808
$163$	−15.7534	−1.23390	−0.616950	−	0.787002i	$-0.711632\pi$
$163$	−15.7534	−1.23390	−0.616950	+	0.787002i	$0.711632\pi$
$164$	0.333084	0.0260095
$165$	−2.38176	−0.185420
$166$	−12.3606	−0.959371
$167$	−16.3986	−1.26896	−0.634481	−	0.772939i	$-0.718786\pi$
$167$	−16.3986	−1.26896	−0.634481	+	0.772939i	$0.718786\pi$
$168$	8.14270	0.628223
$169$	0	0
$170$	1.40128	0.107473
$171$	12.4184	0.949659
$172$	0.0789227	0.00601780
$173$	−0.301355	−0.0229116	−0.0114558	−	0.999934i	$-0.503647\pi$
$173$	−0.301355	−0.0229116	−0.0114558	+	0.999934i	$0.503647\pi$
$174$	20.4825	1.55278
$175$	−4.73068	−0.357606
$176$	−6.22941	−0.469559
$177$	−17.5347	−1.31799
$178$	−16.6577	−1.24855
$179$	−9.81582	−0.733669	−0.366834	−	0.930286i	$-0.619558\pi$
$179$	−9.81582	−0.733669	−0.366834	+	0.930286i	$0.619558\pi$
$180$	−0.204724	−0.0152592
$181$	−12.4320	−0.924062	−0.462031	−	0.886864i	$-0.652879\pi$
$181$	−12.4320	−0.924062	−0.462031	+	0.886864i	$0.652879\pi$
$182$	0	0
$183$	38.0652	2.81386
$184$	26.3393	1.94176
$185$	−5.30854	−0.390292
$186$	−22.6912	−1.66380
$187$	3.16427	0.231395
$188$	0.357475	0.0260716
$189$	−5.60916	−0.408006
$190$	1.79176	0.129988
$191$	−12.2469	−0.886156	−0.443078	−	0.896483i	$-0.646114\pi$
$191$	−12.2469	−0.886156	−0.443078	+	0.896483i	$0.646114\pi$
$192$	−23.4285	−1.69081
$193$	−11.6338	−0.837422	−0.418711	−	0.908119i	$-0.637518\pi$
$193$	−11.6338	−0.837422	−0.418711	+	0.908119i	$0.637518\pi$
$194$	6.12908	0.440042
$195$	0	0
$196$	−0.0791355	−0.00565254
$197$	1.80114	0.128326	0.0641631	−	0.997939i	$-0.479562\pi$
$197$	1.80114	0.128326	0.0641631	+	0.997939i	$0.479562\pi$
$198$	11.2213	0.797461
$199$	6.59313	0.467375	0.233687	−	0.972312i	$-0.424921\pi$
$199$	6.59313	0.467375	0.233687	+	0.972312i	$0.424921\pi$
$200$	13.6319	0.963918
$201$	−23.6592	−1.66879
$202$	25.3666	1.78479
$203$	−5.22996	−0.367071
$204$	0.435667	0.0305028
$205$	−2.18431	−0.152559
$206$	6.95811	0.484795
$207$	−45.5658	−3.16704
$208$	0	0
$209$	4.04603	0.279870
$210$	−2.03244	−0.140252
$211$	10.7199	0.737990	0.368995	−	0.929431i	$-0.379702\pi$
$211$	10.7199	0.737990	0.368995	+	0.929431i	$0.379702\pi$
$212$	0.704030	0.0483530
$213$	14.6886	1.00645
$214$	8.51607	0.582146
$215$	−0.517562	−0.0352974
$216$	16.1633	1.09977
$217$	5.79391	0.393316
$218$	16.4876	1.11668
$219$	33.4558	2.26074
$220$	−0.0667009	−0.00449697
$221$	0	0
$222$	40.0617	2.68877
$223$	12.8878	0.863034	0.431517	−	0.902105i	$-0.357979\pi$
$223$	12.8878	0.863034	0.431517	+	0.902105i	$0.357979\pi$
$224$	0.447392	0.0298926
$225$	−23.5825	−1.57216
$226$	4.92862	0.327847
$227$	−0.699155	−0.0464045	−0.0232023	−	0.999731i	$-0.507386\pi$
$227$	−0.699155	−0.0464045	−0.0232023	+	0.999731i	$0.507386\pi$
$228$	0.557070	0.0368929
$229$	18.2868	1.20843	0.604214	−	0.796822i	$-0.293487\pi$
$229$	18.2868	1.20843	0.604214	+	0.796822i	$0.293487\pi$
$230$	−6.57436	−0.433501
$231$	−4.58951	−0.301967
$232$	15.0706	0.989431
$233$	26.7796	1.75439	0.877194	−	0.480137i	$-0.159413\pi$
$233$	26.7796	1.75439	0.877194	+	0.480137i	$0.159413\pi$
$234$	0	0
$235$	−2.34426	−0.152923
$236$	−0.491057	−0.0319651
$237$	−2.77579	−0.180307
$238$	2.70019	0.175027
$239$	−16.6177	−1.07491	−0.537454	−	0.843293i	$-0.680614\pi$
$239$	−16.6177	−1.07491	−0.537454	+	0.843293i	$0.680614\pi$
$240$	5.62454	0.363063
$241$	−17.4129	−1.12166	−0.560830	−	0.827931i	$-0.689518\pi$
$241$	−17.4129	−1.12166	−0.560830	+	0.827931i	$0.689518\pi$
$242$	−11.5895	−0.745000
$243$	14.2978	0.917204
$244$	1.06601	0.0682445
$245$	0.518957	0.0331549
$246$	16.4842	1.05099
$247$	0	0
$248$	−16.6956	−1.06017
$249$	25.2017	1.59709
$250$	−6.99879	−0.442642
$251$	−6.44982	−0.407109	−0.203554	−	0.979064i	$-0.565249\pi$
$251$	−6.44982	−0.407109	−0.203554	+	0.979064i	$0.565249\pi$
$252$	−0.394491	−0.0248506
$253$	−14.8458	−0.933345
$254$	−1.97290	−0.123791
$255$	−2.85703	−0.178914
$256$	−1.89624	−0.118515
$257$	−3.67156	−0.229025	−0.114513	−	0.993422i	$-0.536531\pi$
$257$	−3.67156	−0.229025	−0.114513	+	0.993422i	$0.536531\pi$
$258$	3.90586	0.243168
$259$	−10.2293	−0.635615
$260$	0	0
$261$	−26.0713	−1.61377
$262$	12.0214	0.742684
$263$	18.3193	1.12961	0.564807	−	0.825223i	$-0.308950\pi$
$263$	18.3193	1.12961	0.564807	+	0.825223i	$0.308950\pi$
$264$	13.2250	0.813945
$265$	−4.61690	−0.283614
$266$	3.45262	0.211694
$267$	33.9629	2.07850
$268$	−0.662575	−0.0404732
$269$	27.5429	1.67932	0.839661	−	0.543111i	$-0.182754\pi$
$269$	27.5429	1.67932	0.839661	+	0.543111i	$0.182754\pi$
$270$	−4.03439	−0.245525
$271$	6.51923	0.396015	0.198007	−	0.980201i	$-0.436553\pi$
$271$	6.51923	0.396015	0.198007	+	0.980201i	$0.436553\pi$
$272$	−7.47246	−0.453084
$273$	0	0
$274$	−11.8053	−0.713186
$275$	−7.68338	−0.463325
$276$	−2.04401	−0.123035
$277$	5.44186	0.326970	0.163485	−	0.986546i	$-0.447727\pi$
$277$	5.44186	0.326970	0.163485	+	0.986546i	$0.447727\pi$
$278$	−6.98304	−0.418815
$279$	28.8826	1.72916
$280$	−1.49542	−0.0893683
$281$	3.54237	0.211320	0.105660	−	0.994402i	$-0.466304\pi$
$281$	3.54237	0.211320	0.105660	+	0.994402i	$0.466304\pi$
$282$	17.6913	1.05350
$283$	−14.1391	−0.840484	−0.420242	−	0.907412i	$-0.638055\pi$
$283$	−14.1391	−0.840484	−0.420242	+	0.907412i	$0.638055\pi$
$284$	0.411354	0.0244094
$285$	−3.65317	−0.216395
$286$	0	0
$287$	−4.20903	−0.248451
$288$	2.23025	0.131419
$289$	−13.2043	−0.776724
$290$	−3.76165	−0.220891
$291$	−12.4964	−0.732551
$292$	0.936928	0.0548295
$293$	8.34931	0.487772	0.243886	−	0.969804i	$-0.421578\pi$
$293$	8.34931	0.487772	0.243886	+	0.969804i	$0.421578\pi$
$294$	−3.91639	−0.228408
$295$	3.22027	0.187491
$296$	29.4765	1.71328
$297$	−9.11017	−0.528626
$298$	4.66359	0.270155
$299$	0	0
$300$	−1.05787	−0.0610762
$301$	−0.997311	−0.0574840
$302$	17.5415	1.00940
$303$	−51.7192	−2.97119
$304$	−9.55474	−0.548002
$305$	−6.99073	−0.400288
$306$	13.4604	0.769481
$307$	−8.33362	−0.475625	−0.237813	−	0.971311i	$-0.576430\pi$
$307$	−8.33362	−0.475625	−0.237813	+	0.971311i	$0.576430\pi$
$308$	−0.128529	−0.00732360
$309$	−14.1867	−0.807052
$310$	4.16727	0.236685
$311$	−14.6227	−0.829176	−0.414588	−	0.910009i	$-0.636074\pi$
$311$	−14.6227	−0.829176	−0.414588	+	0.910009i	$0.636074\pi$
$312$	0	0
$313$	17.1328	0.968404	0.484202	−	0.874956i	$-0.339110\pi$
$313$	17.1328	0.968404	0.484202	+	0.874956i	$0.339110\pi$
$314$	14.3711	0.811009
$315$	2.58700	0.145761
$316$	−0.0777356	−0.00437297
$317$	−14.0000	−0.786320	−0.393160	−	0.919470i	$-0.628618\pi$
$317$	−14.0000	−0.786320	−0.393160	+	0.919470i	$0.628618\pi$
$318$	34.8422	1.95385
$319$	−8.49428	−0.475589
$320$	4.30267	0.240527
$321$	−17.3631	−0.969116
$322$	−12.6684	−0.705983
$323$	4.85340	0.270050
$324$	−0.0708435	−0.00393575
$325$	0	0
$326$	−21.8334	−1.20924
$327$	−33.6161	−1.85897
$328$	12.1287	0.669694
$329$	−4.51725	−0.249044
$330$	−3.30100	−0.181714
$331$	6.91996	0.380355	0.190178	−	0.981750i	$-0.439094\pi$
$331$	6.91996	0.380355	0.190178	+	0.981750i	$0.439094\pi$
$332$	0.705771	0.0387342
$333$	−50.9928	−2.79439
$334$	−22.7277	−1.24360
$335$	4.34505	0.237395
$336$	10.8382	0.591270
$337$	−11.1559	−0.607703	−0.303852	−	0.952719i	$-0.598273\pi$
$337$	−11.1559	−0.607703	−0.303852	+	0.952719i	$0.598273\pi$
$338$	0	0
$339$	−10.0488	−0.545776
$340$	−0.0800108	−0.00433919
$341$	9.41023	0.509593
$342$	17.2113	0.930682
$343$	1.00000	0.0539949
$344$	2.87383	0.154947
$345$	13.4043	0.721661
$346$	−0.417663	−0.0224537
$347$	−4.92511	−0.264393	−0.132197	−	0.991223i	$-0.542203\pi$
$347$	−4.92511	−0.264393	−0.132197	+	0.991223i	$0.542203\pi$
$348$	−1.16952	−0.0626928
$349$	1.52335	0.0815430	0.0407715	−	0.999168i	$-0.487018\pi$
$349$	1.52335	0.0815430	0.0407715	+	0.999168i	$0.487018\pi$
$350$	−6.55650	−0.350460
$351$	0	0
$352$	0.726636	0.0387298
$353$	−17.9280	−0.954212	−0.477106	−	0.878846i	$-0.658314\pi$
$353$	−17.9280	−0.954212	−0.477106	+	0.878846i	$0.658314\pi$
$354$	−24.3022	−1.29165
$355$	−2.69759	−0.143173
$356$	0.951129	0.0504097
$357$	−5.50532	−0.291373
$358$	−13.6043	−0.719007
$359$	−20.0014	−1.05563	−0.527816	−	0.849359i	$-0.676989\pi$
$359$	−20.0014	−1.05563	−0.527816	+	0.849359i	$0.676989\pi$
$360$	−7.45466	−0.392895
$361$	−12.7941	−0.673376
$362$	−17.2301	−0.905596
$363$	23.6294	1.24022
$364$	0	0
$365$	−6.14421	−0.321602
$366$	52.7566	2.75763
$367$	27.4157	1.43109	0.715544	−	0.698568i	$-0.246179\pi$
$367$	27.4157	1.43109	0.715544	+	0.698568i	$0.246179\pi$
$368$	35.0584	1.82754
$369$	−20.9820	−1.09228
$370$	−7.35739	−0.382492
$371$	−8.89651	−0.461884
$372$	1.29563	0.0671752
$373$	−15.8929	−0.822901	−0.411451	−	0.911432i	$-0.634978\pi$
$373$	−15.8929	−0.822901	−0.411451	+	0.911432i	$0.634978\pi$
$374$	4.38553	0.226771
$375$	14.2696	0.736880
$376$	13.0168	0.671292
$377$	0	0
$378$	−7.77403	−0.399853
$379$	−8.77900	−0.450947	−0.225474	−	0.974249i	$-0.572393\pi$
$379$	−8.77900	−0.450947	−0.225474	+	0.974249i	$0.572393\pi$
$380$	−0.102307	−0.00524822
$381$	4.02249	0.206078
$382$	−16.9736	−0.868447
$383$	7.96237	0.406858	0.203429	−	0.979090i	$-0.434791\pi$
$383$	7.96237	0.406858	0.203429	+	0.979090i	$0.434791\pi$
$384$	−29.9423	−1.52799
$385$	0.842869	0.0429566
$386$	−16.1240	−0.820688
$387$	−4.97159	−0.252720
$388$	−0.349960	−0.0177665
$389$	32.0434	1.62467	0.812333	−	0.583194i	$-0.198197\pi$
$389$	32.0434	1.62467	0.812333	+	0.583194i	$0.198197\pi$
$390$	0	0
$391$	−17.8082	−0.900598
$392$	−2.88158	−0.145542
$393$	−24.5100	−1.23637
$394$	2.49630	0.125762
$395$	0.509777	0.0256496
$396$	−0.640716	−0.0321972
$397$	−6.43457	−0.322942	−0.161471	−	0.986877i	$-0.551624\pi$
$397$	−6.43457	−0.322942	−0.161471	+	0.986877i	$0.551624\pi$
$398$	9.13777	0.458035
$399$	−7.03944	−0.352413
$400$	18.1444	0.907219
$401$	−0.533577	−0.0266456	−0.0133228	−	0.999911i	$-0.504241\pi$
$401$	−0.533577	−0.0266456	−0.0133228	+	0.999911i	$0.504241\pi$
$402$	−32.7906	−1.63545
$403$	0	0
$404$	−1.44839	−0.0720601
$405$	0.464579	0.0230851
$406$	−7.24847	−0.359736
$407$	−16.6139	−0.823522
$408$	15.8640	0.785387
$409$	−39.7528	−1.96565	−0.982824	−	0.184547i	$-0.940918\pi$
$409$	−39.7528	−1.96565	−0.982824	+	0.184547i	$0.940918\pi$
$410$	−3.02735	−0.149510
$411$	24.0695	1.18726
$412$	−0.397296	−0.0195734
$413$	6.20526	0.305341
$414$	−63.1520	−3.10375
$415$	−4.62832	−0.227195
$416$	0	0
$417$	14.2375	0.697213
$418$	5.60761	0.274277
$419$	23.8176	1.16357	0.581783	−	0.813344i	$-0.302355\pi$
$419$	23.8176	1.16357	0.581783	+	0.813344i	$0.302355\pi$
$420$	0.116049	0.00566260
$421$	23.2419	1.13274	0.566370	−	0.824151i	$-0.308347\pi$
$421$	23.2419	1.13274	0.566370	+	0.824151i	$0.308347\pi$
$422$	14.8573	0.723243
$423$	−22.5185	−1.09489
$424$	25.6360	1.24500
$425$	−9.21657	−0.447069
$426$	20.3578	0.986336
$427$	−13.4707	−0.651894
$428$	−0.486253	−0.0235039
$429$	0	0
$430$	−0.717316	−0.0345920
$431$	2.70689	0.130386	0.0651932	−	0.997873i	$-0.479234\pi$
$431$	2.70689	0.130386	0.0651932	+	0.997873i	$0.479234\pi$
$432$	21.5137	1.03508
$433$	−5.81890	−0.279638	−0.139819	−	0.990177i	$-0.544652\pi$
$433$	−5.81890	−0.279638	−0.139819	+	0.990177i	$0.544652\pi$
$434$	8.03008	0.385456
$435$	7.66950	0.367724
$436$	−0.941416	−0.0450856
$437$	−22.7706	−1.08927
$438$	46.3682	2.21556
$439$	38.1702	1.82176	0.910882	−	0.412668i	$-0.135403\pi$
$439$	38.1702	1.82176	0.910882	+	0.412668i	$0.135403\pi$
$440$	−2.42880	−0.115788
$441$	4.98500	0.237381
$442$	0	0
$443$	−31.6740	−1.50488	−0.752440	−	0.658661i	$-0.771123\pi$
$443$	−31.6740	−1.50488	−0.752440	+	0.658661i	$0.771123\pi$
$444$	−2.28746	−0.108558
$445$	−6.23734	−0.295678
$446$	17.8619	0.845787
$447$	−9.50845	−0.449734
$448$	8.29100	0.391713
$449$	−31.4049	−1.48209	−0.741045	−	0.671455i	$-0.765669\pi$
$449$	−31.4049	−1.48209	−0.741045	+	0.671455i	$0.765669\pi$
$450$	−32.6842	−1.54075
$451$	−6.83614	−0.321901
$452$	−0.281416	−0.0132367
$453$	−35.7648	−1.68037
$454$	−0.968995	−0.0454772
$455$	0	0
$456$	20.2847	0.949920
$457$	−31.8281	−1.48886	−0.744429	−	0.667702i	$-0.767278\pi$
$457$	−31.8281	−1.48886	−0.744429	+	0.667702i	$0.767278\pi$
$458$	25.3447	1.18428
$459$	−10.9281	−0.510078
$460$	0.375385	0.0175024
$461$	1.16631	0.0543203	0.0271601	−	0.999631i	$-0.491354\pi$
$461$	1.16631	0.0543203	0.0271601	+	0.999631i	$0.491354\pi$
$462$	−6.36084	−0.295933
$463$	20.3441	0.945469	0.472734	−	0.881205i	$-0.343267\pi$
$463$	20.3441	0.945469	0.472734	+	0.881205i	$0.343267\pi$
$464$	20.0593	0.931231
$465$	−8.49651	−0.394016
$466$	37.1152	1.71933
$467$	−1.56939	−0.0726229	−0.0363114	−	0.999341i	$-0.511561\pi$
$467$	−1.56939	−0.0726229	−0.0363114	+	0.999341i	$0.511561\pi$
$468$	0	0
$469$	8.37266	0.386614
$470$	−3.24903	−0.149867
$471$	−29.3008	−1.35011
$472$	−17.8810	−0.823039
$473$	−1.61979	−0.0744781
$474$	−3.84711	−0.176703
$475$	−11.7849	−0.540727
$476$	−0.154176	−0.00706665
$477$	−44.3491	−2.03060
$478$	−23.0313	−1.05343
$479$	7.71918	0.352699	0.176349	−	0.984328i	$-0.443571\pi$
$479$	7.71918	0.352699	0.176349	+	0.984328i	$0.443571\pi$
$480$	−0.656080	−0.0299458
$481$	0	0
$482$	−24.1334	−1.09925
$483$	25.8292	1.17527
$484$	0.661740	0.0300791
$485$	2.29498	0.104209
$486$	19.8161	0.898875
$487$	−0.0761801	−0.00345205	−0.00172602	−	0.999999i	$-0.500549\pi$
$487$	−0.0761801	−0.00345205	−0.00172602	+	0.999999i	$0.500549\pi$
$488$	38.8170	1.75716
$489$	44.5155	2.01306
$490$	0.719250	0.0324924
$491$	1.78715	0.0806529	0.0403264	−	0.999187i	$-0.487160\pi$
$491$	1.78715	0.0806529	0.0403264	+	0.999187i	$0.487160\pi$
$492$	−0.941220	−0.0424335
$493$	−10.1893	−0.458902
$494$	0	0
$495$	4.20170	0.188852
$496$	−22.2223	−0.997813
$497$	−5.19809	−0.233166
$498$	34.9284	1.56518
$499$	8.33493	0.373123	0.186561	−	0.982443i	$-0.440266\pi$
$499$	8.33493	0.373123	0.186561	+	0.982443i	$0.440266\pi$
$500$	0.399619	0.0178715
$501$	46.3387	2.07026
$502$	−8.93914	−0.398973
$503$	1.44048	0.0642277	0.0321138	−	0.999484i	$-0.489776\pi$
$503$	1.44048	0.0642277	0.0321138	+	0.999484i	$0.489776\pi$
$504$	−14.3647	−0.639854
$505$	9.49829	0.422668
$506$	−20.5755	−0.914693
$507$	0	0
$508$	0.112649	0.00499801
$509$	−14.8256	−0.657135	−0.328568	−	0.944480i	$-0.606566\pi$
$509$	−14.8256	−0.657135	−0.328568	+	0.944480i	$0.606566\pi$
$510$	−3.95970	−0.175339
$511$	−11.8395	−0.523750
$512$	−23.8204	−1.05272
$513$	−13.9733	−0.616935
$514$	−5.08860	−0.224449
$515$	2.60540	0.114808
$516$	−0.223018	−0.00981781
$517$	−7.33674	−0.322670
$518$	−14.1773	−0.622913
$519$	0.851561	0.0373794
$520$	0	0
$521$	−0.334388	−0.0146498	−0.00732489	−	0.999973i	$-0.502332\pi$
$521$	−0.334388	−0.0146498	−0.00732489	+	0.999973i	$0.502332\pi$
$522$	−36.1336	−1.58153
$523$	−32.5065	−1.42141	−0.710705	−	0.703490i	$-0.751624\pi$
$523$	−32.5065	−1.42141	−0.710705	+	0.703490i	$0.751624\pi$
$524$	−0.686401	−0.0299856
$525$	13.3678	0.583420
$526$	25.3896	1.10704
$527$	11.2880	0.491713
$528$	17.6029	0.766068
$529$	60.5502	2.63262
$530$	−6.39881	−0.277947
$531$	30.9332	1.34239
$532$	−0.197139	−0.00854706
$533$	0	0
$534$	47.0710	2.03696
$535$	3.18876	0.137862
$536$	−24.1265	−1.04211
$537$	27.7373	1.19695
$538$	38.1732	1.64576
$539$	1.62416	0.0699575
$540$	0.230357	0.00991297
$541$	10.6015	0.455796	0.227898	−	0.973685i	$-0.426815\pi$
$541$	10.6015	0.455796	0.227898	+	0.973685i	$0.426815\pi$
$542$	9.03534	0.388101
$543$	35.1300	1.50757
$544$	0.871633	0.0373709
$545$	6.17364	0.264450
$546$	0	0
$547$	10.2327	0.437519	0.218760	−	0.975779i	$-0.429799\pi$
$547$	10.2327	0.437519	0.218760	+	0.975779i	$0.429799\pi$
$548$	0.674064	0.0287946
$549$	−67.1515	−2.86596
$550$	−10.6488	−0.454067
$551$	−13.0286	−0.555038
$552$	−74.4290	−3.16791
$553$	0.982310	0.0417721
$554$	7.54216	0.320436
$555$	15.0007	0.636746
$556$	0.398720	0.0169095
$557$	31.9930	1.35559	0.677793	−	0.735253i	$-0.262937\pi$
$557$	31.9930	1.35559	0.677793	+	0.735253i	$0.262937\pi$
$558$	40.0300	1.69460
$559$	0	0
$560$	−1.99044	−0.0841115
$561$	−8.94152	−0.377511
$562$	4.90956	0.207097
$563$	10.7913	0.454800	0.227400	−	0.973801i	$-0.426978\pi$
$563$	10.7913	0.454800	0.227400	+	0.973801i	$0.426978\pi$
$564$	−1.01014	−0.0425348
$565$	1.84547	0.0776397
$566$	−19.5962	−0.823688
$567$	0.895217	0.0375956
$568$	14.9787	0.628494
$569$	−24.6014	−1.03134	−0.515672	−	0.856786i	$-0.672458\pi$
$569$	−24.6014	−1.03134	−0.515672	+	0.856786i	$0.672458\pi$
$570$	−5.06312	−0.212071
$571$	16.5724	0.693534	0.346767	−	0.937951i	$-0.387279\pi$
$571$	16.5724	0.693534	0.346767	+	0.937951i	$0.387279\pi$
$572$	0	0
$573$	34.6070	1.44573
$574$	−5.83352	−0.243486
$575$	43.2412	1.80328
$576$	41.3306	1.72211
$577$	14.6611	0.610348	0.305174	−	0.952297i	$-0.401285\pi$
$577$	14.6611	0.610348	0.305174	+	0.952297i	$0.401285\pi$
$578$	−18.3005	−0.761202
$579$	32.8746	1.36622
$580$	0.214784	0.00891840
$581$	−8.91851	−0.370002
$582$	−17.3194	−0.717912
$583$	−14.4493	−0.598431
$584$	34.1166	1.41175
$585$	0	0
$586$	11.5717	0.478024
$587$	−35.3336	−1.45837	−0.729186	−	0.684315i	$-0.760101\pi$
$587$	−35.3336	−1.45837	−0.729186	+	0.684315i	$0.760101\pi$
$588$	0.223619	0.00922190
$589$	14.4335	0.594723
$590$	4.46313	0.183744
$591$	−5.08963	−0.209359
$592$	39.2340	1.61251
$593$	16.4294	0.674675	0.337338	−	0.941384i	$-0.390474\pi$
$593$	16.4294	0.674675	0.337338	+	0.941384i	$0.390474\pi$
$594$	−12.6263	−0.518062
$595$	1.01106	0.0414494
$596$	−0.266283	−0.0109074
$597$	−18.6307	−0.762504
$598$	0	0
$599$	12.0819	0.493653	0.246826	−	0.969060i	$-0.420612\pi$
$599$	12.0819	0.493653	0.246826	+	0.969060i	$0.420612\pi$
$600$	−38.5206	−1.57259
$601$	7.81486	0.318775	0.159387	−	0.987216i	$-0.449048\pi$
$601$	7.81486	0.318775	0.159387	+	0.987216i	$0.449048\pi$
$602$	−1.38223	−0.0563353
$603$	41.7377	1.69969
$604$	−1.00159	−0.0407541
$605$	−4.33957	−0.176429
$606$	−71.6803	−2.91181
$607$	35.5649	1.44354	0.721768	−	0.692135i	$-0.243330\pi$
$607$	35.5649	1.44354	0.721768	+	0.692135i	$0.243330\pi$
$608$	1.11452	0.0451999
$609$	14.7787	0.598862
$610$	−9.68882	−0.392289
$611$	0	0
$612$	−0.768568	−0.0310675
$613$	11.9368	0.482122	0.241061	−	0.970510i	$-0.422505\pi$
$613$	11.9368	0.482122	0.241061	+	0.970510i	$0.422505\pi$
$614$	−11.5500	−0.466120
$615$	6.17236	0.248893
$616$	−4.68015	−0.188569
$617$	−23.5702	−0.948901	−0.474450	−	0.880282i	$-0.657353\pi$
$617$	−23.5702	−0.948901	−0.474450	+	0.880282i	$0.657353\pi$
$618$	−19.6621	−0.790924
$619$	28.5571	1.14781	0.573904	−	0.818923i	$-0.305428\pi$
$619$	28.5571	1.14781	0.573904	+	0.818923i	$0.305428\pi$
$620$	−0.237944	−0.00955606
$621$	51.2710	2.05743
$622$	−20.2663	−0.812607
$623$	−12.0190	−0.481530
$624$	0	0
$625$	21.0328	0.841311
$626$	23.7453	0.949052
$627$	−11.4332	−0.456597
$628$	−0.820567	−0.0327442
$629$	−19.9292	−0.794628
$630$	3.58546	0.142848
$631$	44.9925	1.79112	0.895561	−	0.444938i	$-0.146774\pi$
$631$	44.9925	1.79112	0.895561	+	0.444938i	$0.146774\pi$
$632$	−2.83061	−0.112596
$633$	−30.2921	−1.20400
$634$	−19.4034	−0.770607
$635$	−0.738735	−0.0293158
$636$	−1.98943	−0.0788860
$637$	0	0
$638$	−11.7727	−0.466085
$639$	−25.9125	−1.02508
$640$	5.49894	0.217365
$641$	−2.53300	−0.100048	−0.0500238	−	0.998748i	$-0.515930\pi$
$641$	−2.53300	−0.100048	−0.0500238	+	0.998748i	$0.515930\pi$
$642$	−24.0645	−0.949749
$643$	18.3771	0.724721	0.362360	−	0.932038i	$-0.381971\pi$
$643$	18.3771	0.724721	0.362360	+	0.932038i	$0.381971\pi$
$644$	0.723345	0.0285038
$645$	1.46251	0.0575863
$646$	6.72658	0.264654
$647$	20.9287	0.822791	0.411396	−	0.911457i	$-0.365041\pi$
$647$	20.9287	0.822791	0.411396	+	0.911457i	$0.365041\pi$
$648$	−2.57964	−0.101338
$649$	10.0783	0.395609
$650$	0	0
$651$	−16.3723	−0.641680
$652$	1.24665	0.0488227
$653$	−48.1160	−1.88292	−0.941461	−	0.337121i	$-0.890547\pi$
$653$	−48.1160	−1.88292	−0.941461	+	0.337121i	$0.890547\pi$
$654$	−46.5903	−1.82183
$655$	4.50130	0.175880
$656$	16.1436	0.630302
$657$	−59.0200	−2.30259
$658$	−6.26070	−0.244068
$659$	−2.21638	−0.0863379	−0.0431690	−	0.999068i	$-0.513745\pi$
$659$	−2.21638	−0.0863379	−0.0431690	+	0.999068i	$0.513745\pi$
$660$	0.188482	0.00733664
$661$	−0.637434	−0.0247933	−0.0123966	−	0.999923i	$-0.503946\pi$
$661$	−0.637434	−0.0247933	−0.0123966	+	0.999923i	$0.503946\pi$
$662$	9.59073	0.372754
$663$	0	0
$664$	25.6994	0.997331
$665$	1.29280	0.0501327
$666$	−70.6736	−2.73855
$667$	47.8048	1.85101
$668$	1.29771	0.0502100
$669$	−36.4181	−1.40801
$670$	6.02203	0.232651
$671$	−21.8786	−0.844614
$672$	−1.26423	−0.0487687
$673$	15.4069	0.593891	0.296945	−	0.954895i	$-0.404032\pi$
$673$	15.4069	0.593891	0.296945	+	0.954895i	$0.404032\pi$
$674$	−15.4616	−0.595559
$675$	26.5352	1.02134
$676$	0	0
$677$	−11.6812	−0.448945	−0.224473	−	0.974480i	$-0.572066\pi$
$677$	−11.6812	−0.448945	−0.224473	+	0.974480i	$0.572066\pi$
$678$	−13.9272	−0.534869
$679$	4.42228	0.169712
$680$	−2.91345	−0.111726
$681$	1.97565	0.0757072
$682$	13.0421	0.499409
$683$	−22.9114	−0.876680	−0.438340	−	0.898809i	$-0.644433\pi$
$683$	−22.9114	−0.876680	−0.438340	+	0.898809i	$0.644433\pi$
$684$	−0.982737	−0.0375759
$685$	−4.42039	−0.168895
$686$	1.38595	0.0529159
$687$	−51.6745	−1.97150
$688$	3.82515	0.145833
$689$	0	0
$690$	18.5777	0.707239
$691$	47.2325	1.79681	0.898405	−	0.439167i	$-0.144726\pi$
$691$	47.2325	1.79681	0.898405	+	0.439167i	$0.144726\pi$
$692$	0.0238479	0.000906560 0
$693$	8.09643	0.307558
$694$	−6.82596	−0.259110
$695$	−2.61473	−0.0991825
$696$	−42.5860	−1.61422
$697$	−8.20026	−0.310607
$698$	2.11129	0.0799135
$699$	−75.6730	−2.86222
$700$	0.374365	0.0141497
$701$	−12.2098	−0.461158	−0.230579	−	0.973054i	$-0.574062\pi$
$701$	−12.2098	−0.461158	−0.230579	+	0.973054i	$0.574062\pi$
$702$	0	0
$703$	−25.4827	−0.961097
$704$	13.4659	0.507515
$705$	6.62435	0.249488
$706$	−24.8474	−0.935144
$707$	18.3026	0.688342
$708$	1.38762	0.0521498
$709$	17.8875	0.671778	0.335889	−	0.941902i	$-0.390963\pi$
$709$	17.8875	0.671778	0.335889	+	0.941902i	$0.390963\pi$
$710$	−3.73873	−0.140312
$711$	4.89681	0.183645
$712$	34.6337	1.29795
$713$	−52.9597	−1.98336
$714$	−7.63012	−0.285550
$715$	0	0
$716$	0.776780	0.0290296
$717$	46.9578	1.75367
$718$	−27.7210	−1.03454
$719$	9.12634	0.340355	0.170178	−	0.985413i	$-0.445566\pi$
$719$	9.12634	0.340355	0.170178	+	0.985413i	$0.445566\pi$
$720$	−9.92235	−0.369784
$721$	5.02046	0.186972
$722$	−17.7321	−0.659920
$723$	49.2048	1.82995
$724$	0.983812	0.0365631
$725$	24.7413	0.918868
$726$	32.7493	1.21544
$727$	−33.6859	−1.24934	−0.624670	−	0.780889i	$-0.714767\pi$
$727$	−33.6859	−1.24934	−0.624670	+	0.780889i	$0.714767\pi$
$728$	0	0
$729$	−43.0880	−1.59585
$730$	−8.51558	−0.315176
$731$	−1.94301	−0.0718650
$732$	−3.01231	−0.111338
$733$	46.4344	1.71509	0.857547	−	0.514406i	$-0.171987\pi$
$733$	46.4344	1.71509	0.857547	+	0.514406i	$0.171987\pi$
$734$	37.9968	1.40249
$735$	−1.46646	−0.0540910
$736$	−4.08942	−0.150738
$737$	13.5985	0.500908
$738$	−29.0801	−1.07045
$739$	−1.85025	−0.0680627	−0.0340314	−	0.999421i	$-0.510835\pi$
$739$	−1.85025	−0.0680627	−0.0340314	+	0.999421i	$0.510835\pi$
$740$	0.420095	0.0154430
$741$	0	0
$742$	−12.3301	−0.452654
$743$	−33.1509	−1.21619	−0.608094	−	0.793865i	$-0.708066\pi$
$743$	−33.1509	−1.21619	−0.608094	+	0.793865i	$0.708066\pi$
$744$	47.1781	1.72963
$745$	1.74624	0.0639773
$746$	−22.0268	−0.806457
$747$	−44.4588	−1.62666
$748$	−0.250407	−0.00915577
$749$	6.14456	0.224517
$750$	19.7770	0.722154
$751$	−20.7743	−0.758064	−0.379032	−	0.925384i	$-0.623743\pi$
$751$	−20.7743	−0.758064	−0.379032	+	0.925384i	$0.623743\pi$
$752$	17.3258	0.631806
$753$	18.2257	0.664182
$754$	0	0
$755$	6.56824	0.239043
$756$	0.443884	0.0161439
$757$	43.6150	1.58521	0.792607	−	0.609733i	$-0.208723\pi$
$757$	43.6150	1.58521	0.792607	+	0.609733i	$0.208723\pi$
$758$	−12.1673	−0.441936
$759$	41.9508	1.52272
$760$	−3.72532	−0.135131
$761$	−12.3902	−0.449145	−0.224573	−	0.974457i	$-0.572099\pi$
$761$	−12.3902	−0.449145	−0.224573	+	0.974457i	$0.572099\pi$
$762$	5.57497	0.201960
$763$	11.8962	0.430673
$764$	0.969167	0.0350632
$765$	5.04013	0.182226
$766$	11.0355	0.398728
$767$	0	0
$768$	5.35835	0.193353
$769$	5.55359	0.200268	0.100134	−	0.994974i	$-0.468073\pi$
$769$	5.55359	0.200268	0.100134	+	0.994974i	$0.468073\pi$
$770$	1.16818	0.0420982
$771$	10.3750	0.373646
$772$	0.920651	0.0331349
$773$	43.8042	1.57553	0.787764	−	0.615977i	$-0.211239\pi$
$773$	43.8042	1.57553	0.787764	+	0.615977i	$0.211239\pi$
$774$	−6.89039	−0.247670
$775$	−27.4092	−0.984566
$776$	−12.7432	−0.457454
$777$	28.9056	1.03698
$778$	44.4107	1.59220
$779$	−10.4853	−0.375677
$780$	0	0
$781$	−8.44253	−0.302098
$782$	−24.6813	−0.882600
$783$	29.3357	1.04837
$784$	−3.83547	−0.136981
$785$	5.38113	0.192061
$786$	−33.9697	−1.21166
$787$	−24.8009	−0.884057	−0.442029	−	0.897001i	$-0.645741\pi$
$787$	−24.8009	−0.884057	−0.442029	+	0.897001i	$0.645741\pi$
$788$	−0.142535	−0.00507758
$789$	−51.7661	−1.84292
$790$	0.706526	0.0251371
$791$	3.55612	0.126441
$792$	−23.3305	−0.829015
$793$	0	0
$794$	−8.91801	−0.316489
$795$	13.0463	0.462706
$796$	−0.521751	−0.0184930
$797$	−16.4715	−0.583451	−0.291725	−	0.956502i	$-0.594229\pi$
$797$	−16.4715	−0.583451	−0.291725	+	0.956502i	$0.594229\pi$
$798$	−9.75633	−0.345370
$799$	−8.80076	−0.311348
$800$	−2.11647	−0.0748285
$801$	−59.9146	−2.11698
$802$	−0.739513	−0.0261131
$803$	−19.2293	−0.678587
$804$	1.87229	0.0660305
$805$	−4.74357	−0.167189
$806$	0	0
$807$	−77.8301	−2.73975
$808$	−52.7406	−1.85541
$809$	1.38194	0.0485863	0.0242932	−	0.999705i	$-0.492266\pi$
$809$	1.38194	0.0485863	0.0242932	+	0.999705i	$0.492266\pi$
$810$	0.643885	0.0226238
$811$	−6.83571	−0.240034	−0.120017	−	0.992772i	$-0.538295\pi$
$811$	−6.83571	−0.240034	−0.120017	+	0.992772i	$0.538295\pi$
$812$	0.413875	0.0145242
$813$	−18.4219	−0.646083
$814$	−23.0261	−0.807066
$815$	−8.17533	−0.286369
$816$	21.1155	0.739190
$817$	−2.48446	−0.0869201
$818$	−55.0954	−1.92637
$819$	0	0
$820$	0.172856	0.00603640
$821$	10.5425	0.367936	0.183968	−	0.982932i	$-0.441106\pi$
$821$	10.5425	0.367936	0.183968	+	0.982932i	$0.441106\pi$
$822$	33.3592	1.16353
$823$	14.8330	0.517047	0.258524	−	0.966005i	$-0.416764\pi$
$823$	14.8330	0.517047	0.258524	+	0.966005i	$0.416764\pi$
$824$	−14.4669	−0.503977
$825$	21.7115	0.755898
$826$	8.60020	0.299239
$827$	55.6758	1.93604	0.968018	−	0.250879i	$-0.0807197\pi$
$827$	55.6758	1.93604	0.968018	+	0.250879i	$0.0807197\pi$
$828$	3.60587	0.125313
$829$	−0.0464848	−0.00161448	−0.000807242	−	1.00000i	$-0.500257\pi$
$829$	−0.0464848	−0.00161448	−0.000807242		1.00000i	$0.500257\pi$
$830$	−6.41464	−0.222655
$831$	−15.3775	−0.533438
$832$	0	0
$833$	1.94825	0.0675030
$834$	19.7325	0.683280
$835$	−8.51016	−0.294506
$836$	−0.320185	−0.0110738
$837$	−32.4990	−1.12333
$838$	33.0100	1.14031
$839$	−25.5475	−0.881999	−0.440999	−	0.897507i	$-0.645376\pi$
$839$	−25.5475	−0.881999	−0.440999	+	0.897507i	$0.645376\pi$
$840$	4.22571	0.145801
$841$	−1.64755	−0.0568120
$842$	32.2121	1.11010
$843$	−10.0099	−0.344761
$844$	−0.848327	−0.0292006
$845$	0	0
$846$	−31.2096	−1.07301
$847$	−8.36211	−0.287325
$848$	34.1223	1.17176
$849$	39.9540	1.37122
$850$	−12.7737	−0.438135
$851$	93.5013	3.20518
$852$	−1.16239	−0.0398229
$853$	−22.6671	−0.776105	−0.388053	−	0.921637i	$-0.626852\pi$
$853$	−22.6671	−0.776105	−0.388053	+	0.921637i	$0.626852\pi$
$854$	−18.6698	−0.638867
$855$	6.44462	0.220401
$856$	−17.7061	−0.605181
$857$	−37.0535	−1.26572	−0.632862	−	0.774264i	$-0.718120\pi$
$857$	−37.0535	−1.26572	−0.632862	+	0.774264i	$0.718120\pi$
$858$	0	0
$859$	−4.24339	−0.144782	−0.0723912	−	0.997376i	$-0.523063\pi$
$859$	−4.24339	−0.144782	−0.0723912	+	0.997376i	$0.523063\pi$
$860$	0.0409575	0.00139664
$861$	11.8938	0.405339
$862$	3.75162	0.127781
$863$	−7.50051	−0.255320	−0.127660	−	0.991818i	$-0.540747\pi$
$863$	−7.50051	−0.255320	−0.127660	+	0.991818i	$0.540747\pi$
$864$	−2.50949	−0.0853746
$865$	−0.156390	−0.00531743
$866$	−8.06472	−0.274050
$867$	37.3124	1.26720
$868$	−0.458504	−0.0155626
$869$	1.59543	0.0541212
$870$	10.6296	0.360376
$871$	0	0
$872$	−34.2800	−1.16087
$873$	22.0451	0.746113
$874$	−31.5590	−1.06750
$875$	−5.04981	−0.170715
$876$	−2.64755	−0.0894523
$877$	−28.2897	−0.955274	−0.477637	−	0.878557i	$-0.658507\pi$
$877$	−28.2897	−0.955274	−0.477637	+	0.878557i	$0.658507\pi$
$878$	52.9021	1.78536
$879$	−23.5933	−0.795781
$880$	−3.23280	−0.108978
$881$	−39.5721	−1.33322	−0.666609	−	0.745408i	$-0.732255\pi$
$881$	−39.5721	−1.33322	−0.666609	+	0.745408i	$0.732255\pi$
$882$	6.90897	0.232637
$883$	28.3609	0.954419	0.477209	−	0.878790i	$-0.341648\pi$
$883$	28.3609	0.954419	0.477209	+	0.878790i	$0.341648\pi$
$884$	0	0
$885$	−9.09974	−0.305884
$886$	−43.8987	−1.47481
$887$	−43.7186	−1.46793	−0.733963	−	0.679189i	$-0.762331\pi$
$887$	−43.7186	−1.46793	−0.733963	+	0.679189i	$0.762331\pi$
$888$	−83.2938	−2.79516
$889$	−1.42350	−0.0477426
$890$	−8.64465	−0.289769
$891$	1.45398	0.0487100
$892$	−1.01989	−0.0341483
$893$	−11.2532	−0.376573
$894$	−13.1783	−0.440747
$895$	−5.09399	−0.170273
$896$	10.5961	0.353992
$897$	0	0
$898$	−43.5257	−1.45247
$899$	−30.3019	−1.01062
$900$	1.86621	0.0622070
$901$	−17.3326	−0.577434
$902$	−9.47456	−0.315468
$903$	2.81818	0.0937830
$904$	−10.2473	−0.340819
$905$	−6.45167	−0.214461
$906$	−49.5683	−1.64679
$907$	−36.6985	−1.21855	−0.609277	−	0.792957i	$-0.708540\pi$
$907$	−36.6985	−1.21855	−0.609277	+	0.792957i	$0.708540\pi$
$908$	0.0553280	0.00183612
$909$	91.2387	3.02620
$910$	0	0
$911$	−35.5211	−1.17686	−0.588432	−	0.808546i	$-0.700255\pi$
$911$	−35.5211	−1.17686	−0.588432	+	0.808546i	$0.700255\pi$
$912$	26.9995	0.894044
$913$	−14.4851	−0.479386
$914$	−44.1123	−1.45911
$915$	19.7542	0.653054
$916$	−1.44714	−0.0478148
$917$	8.67374	0.286432
$918$	−15.1458	−0.499885
$919$	21.9334	0.723516	0.361758	−	0.932272i	$-0.382177\pi$
$919$	21.9334	0.723516	0.361758	+	0.932272i	$0.382177\pi$
$920$	13.6690	0.450653
$921$	23.5489	0.775964
$922$	1.61644	0.0532348
$923$	0	0
$924$	0.363193	0.0119482
$925$	48.3914	1.59110
$926$	28.1959	0.926575
$927$	25.0270	0.821993
$928$	−2.33984	−0.0768090
$929$	−15.5172	−0.509102	−0.254551	−	0.967059i	$-0.581928\pi$
$929$	−15.5172	−0.509102	−0.254551	+	0.967059i	$0.581928\pi$
$930$	−11.7758	−0.386142
$931$	2.49115	0.0816443
$932$	−2.11922	−0.0694172
$933$	41.3204	1.35277
$934$	−2.17510	−0.0711716
$935$	1.64212	0.0537031
$936$	0	0
$937$	40.8110	1.33324	0.666618	−	0.745399i	$-0.267741\pi$
$937$	40.8110	1.33324	0.666618	+	0.745399i	$0.267741\pi$
$938$	11.6041	0.378888
$939$	−48.4135	−1.57991
$940$	0.185514	0.00605081
$941$	−51.5936	−1.68190	−0.840952	−	0.541109i	$-0.818004\pi$
$941$	−51.5936	−1.68190	−0.840952	+	0.541109i	$0.818004\pi$
$942$	−40.6096	−1.32313
$943$	38.4730	1.25285
$944$	−23.8001	−0.774627
$945$	−2.91091	−0.0946920
$946$	−2.24495	−0.0729898
$947$	−4.98209	−0.161896	−0.0809482	−	0.996718i	$-0.525795\pi$
$947$	−4.98209	−0.161896	−0.0809482	+	0.996718i	$0.525795\pi$
$948$	0.219663	0.00713433
$949$	0	0
$950$	−16.3333	−0.529921
$951$	39.5609	1.28285
$952$	−5.61405	−0.181953
$953$	30.2325	0.979328	0.489664	−	0.871911i	$-0.337119\pi$
$953$	30.2325	0.979328	0.489664	+	0.871911i	$0.337119\pi$
$954$	−61.4657	−1.99003
$955$	−6.35562	−0.205663
$956$	1.31505	0.0425317
$957$	24.0029	0.775904
$958$	10.6984	0.345650
$959$	−8.51784	−0.275055
$960$	−12.1584	−0.392410
$961$	2.56939	0.0828835
$962$	0	0
$963$	30.6306	0.987058
$964$	1.37798	0.0443816
$965$	−6.03746	−0.194353
$966$	35.7981	1.15178
$967$	−29.9990	−0.964703	−0.482352	−	0.875978i	$-0.660217\pi$
$967$	−29.9990	−0.964703	−0.482352	+	0.875978i	$0.660217\pi$
$968$	24.0961	0.774478
$969$	−13.7146	−0.440577
$970$	3.18073	0.102127
$971$	44.1240	1.41601	0.708003	−	0.706209i	$-0.249596\pi$
$971$	44.1240	1.41601	0.708003	+	0.706209i	$0.249596\pi$
$972$	−1.13146	−0.0362917
$973$	−5.03844	−0.161525
$974$	−0.105582	−0.00338306
$975$	0	0
$976$	51.6665	1.65380
$977$	15.0024	0.479970	0.239985	−	0.970777i	$-0.422858\pi$
$977$	15.0024	0.479970	0.239985	+	0.970777i	$0.422858\pi$
$978$	61.6964	1.97283
$979$	−19.5207	−0.623886
$980$	−0.0410679	−0.00131187
$981$	59.3028	1.89339
$982$	2.47690	0.0790411
$983$	−6.01856	−0.191962	−0.0959812	−	0.995383i	$-0.530599\pi$
$983$	−6.01856	−0.191962	−0.0959812	+	0.995383i	$0.530599\pi$
$984$	−34.2729	−1.09258
$985$	0.934717	0.0297825
$986$	−14.1219	−0.449732
$987$	12.7647	0.406306
$988$	0	0
$989$	9.11600	0.289872
$990$	5.82336	0.185078
$991$	33.8400	1.07496	0.537482	−	0.843275i	$-0.319376\pi$
$991$	33.8400	1.07496	0.537482	+	0.843275i	$0.319376\pi$
$992$	2.59215	0.0823008
$993$	−19.5542	−0.620535
$994$	−7.20431	−0.228507
$995$	3.42155	0.108471
$996$	−1.99435	−0.0631934
$997$	26.3215	0.833610	0.416805	−	0.908996i	$-0.363150\pi$
$997$	26.3215	0.833610	0.416805	+	0.908996i	$0.363150\pi$
$998$	11.5518	0.365666
$999$	57.3775	1.81534

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.m.1.6		6
7.6	odd	2		8281.2.a.by.1.6		6
13.5	odd	4		1183.2.c.i.337.3		12
13.6	odd	12		91.2.q.a.36.2	✓	12
13.8	odd	4		1183.2.c.i.337.10		12
13.11	odd	12		91.2.q.a.43.2	yes	12
13.12	even	2		1183.2.a.p.1.1		6
39.11	even	12		819.2.ct.a.316.5		12
39.32	even	12		819.2.ct.a.127.5		12
52.11	even	12		1456.2.cc.c.225.1		12
52.19	even	12		1456.2.cc.c.673.1		12
91.6	even	12		637.2.q.h.491.2		12
91.11	odd	12		637.2.u.h.30.5		12
91.19	even	12		637.2.u.i.361.5		12
91.24	even	12		637.2.u.i.30.5		12
91.32	odd	12		637.2.k.h.569.2		12
91.37	odd	12		637.2.k.h.459.5		12
91.45	even	12		637.2.k.g.569.2		12
91.58	odd	12		637.2.u.h.361.5		12
91.76	even	12		637.2.q.h.589.2		12
91.89	even	12		637.2.k.g.459.5		12
91.90	odd	2		8281.2.a.ch.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.2	✓	12	13.6	odd	12
91.2.q.a.43.2	yes	12	13.11	odd	12
637.2.k.g.459.5		12	91.89	even	12
637.2.k.g.569.2		12	91.45	even	12
637.2.k.h.459.5		12	91.37	odd	12
637.2.k.h.569.2		12	91.32	odd	12
637.2.q.h.491.2		12	91.6	even	12
637.2.q.h.589.2		12	91.76	even	12
637.2.u.h.30.5		12	91.11	odd	12
637.2.u.h.361.5		12	91.58	odd	12
637.2.u.i.30.5		12	91.24	even	12
637.2.u.i.361.5		12	91.19	even	12
819.2.ct.a.127.5		12	39.32	even	12
819.2.ct.a.316.5		12	39.11	even	12
1183.2.a.m.1.6		6	1.1	even	1	trivial
1183.2.a.p.1.1		6	13.12	even	2
1183.2.c.i.337.3		12	13.5	odd	4
1183.2.c.i.337.10		12	13.8	odd	4
1456.2.cc.c.225.1		12	52.11	even	12
1456.2.cc.c.673.1		12	52.19	even	12
8281.2.a.by.1.6		6	7.6	odd	2
8281.2.a.ch.1.1		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)

\(f(q)\)	\(=\)	\(q+1.38595 q^{2} -2.82577 q^{3} -0.0791355 q^{4} +0.518957 q^{5} -3.91639 q^{6} +1.00000 q^{7} -2.88158 q^{8} +4.98500 q^{9} +O(q^{10})\)	\(q+1.38595 q^{2} -2.82577 q^{3} -0.0791355 q^{4} +0.518957 q^{5} -3.91639 q^{6} +1.00000 q^{7} -2.88158 q^{8} +4.98500 q^{9} +0.719250 q^{10} +1.62416 q^{11} +0.223619 q^{12} +1.38595 q^{14} -1.46646 q^{15} -3.83547 q^{16} +1.94825 q^{17} +6.90897 q^{18} +2.49115 q^{19} -0.0410679 q^{20} -2.82577 q^{21} +2.25101 q^{22} -9.14058 q^{23} +8.14270 q^{24} -4.73068 q^{25} -5.60916 q^{27} -0.0791355 q^{28} -5.22996 q^{29} -2.03244 q^{30} +5.79391 q^{31} +0.447392 q^{32} -4.58951 q^{33} +2.70019 q^{34} +0.518957 q^{35} -0.394491 q^{36} -10.2293 q^{37} +3.45262 q^{38} -1.49542 q^{40} -4.20903 q^{41} -3.91639 q^{42} -0.997311 q^{43} -0.128529 q^{44} +2.58700 q^{45} -12.6684 q^{46} -4.51725 q^{47} +10.8382 q^{48} +1.00000 q^{49} -6.55650 q^{50} -5.50532 q^{51} -8.89651 q^{53} -7.77403 q^{54} +0.842869 q^{55} -2.88158 q^{56} -7.03944 q^{57} -7.24847 q^{58} +6.20526 q^{59} +0.116049 q^{60} -13.4707 q^{61} +8.03008 q^{62} +4.98500 q^{63} +8.29100 q^{64} -6.36084 q^{66} +8.37266 q^{67} -0.154176 q^{68} +25.8292 q^{69} +0.719250 q^{70} -5.19809 q^{71} -14.3647 q^{72} -11.8395 q^{73} -14.1773 q^{74} +13.3678 q^{75} -0.197139 q^{76} +1.62416 q^{77} +0.982310 q^{79} -1.99044 q^{80} +0.895217 q^{81} -5.83352 q^{82} -8.91851 q^{83} +0.223619 q^{84} +1.01106 q^{85} -1.38223 q^{86} +14.7787 q^{87} -4.68015 q^{88} -12.0190 q^{89} +3.58546 q^{90} +0.723345 q^{92} -16.3723 q^{93} -6.26070 q^{94} +1.29280 q^{95} -1.26423 q^{96} +4.42228 q^{97} +1.38595 q^{98} +8.09643 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{2} + 4 q^{4} - 6 q^{5} - 4 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) \) 6 * q - 4 * q^2 + 4 * q^4 - 6 * q^5 - 4 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9	\( 6 q - 4 q^{2} + 4 q^{4} - 6 q^{5} - 4 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9} + 12 q^{10} - 4 q^{11} + 2 q^{12} - 4 q^{14} - 20 q^{15} + 8 q^{16} - 4 q^{17} + 16 q^{18} - 2 q^{19} - 26 q^{20} - 6 q^{22} - 12 q^{23} - 2 q^{24} + 10 q^{25} + 6 q^{27} + 4 q^{28} - 8 q^{29} + 8 q^{30} + 14 q^{31} - 8 q^{32} - 16 q^{33} + 2 q^{34} - 6 q^{35} - 10 q^{36} - 12 q^{37} - 2 q^{38} + 46 q^{40} - 28 q^{41} - 4 q^{42} + 2 q^{43} + 20 q^{44} - 16 q^{45} - 20 q^{46} - 14 q^{47} + 2 q^{48} + 6 q^{49} - 32 q^{50} - 26 q^{51} - 22 q^{53} - 14 q^{54} + 6 q^{55} - 12 q^{56} - 4 q^{58} + 2 q^{59} - 14 q^{61} - 4 q^{62} + 4 q^{63} + 26 q^{64} - 26 q^{66} - 24 q^{67} + 8 q^{68} + 4 q^{69} + 12 q^{70} - 4 q^{71} - 8 q^{72} - 36 q^{73} - 6 q^{74} + 46 q^{75} + 26 q^{76} - 4 q^{77} - 28 q^{79} - 36 q^{80} - 2 q^{81} + 14 q^{82} - 26 q^{83} + 2 q^{84} + 20 q^{85} + 24 q^{86} + 2 q^{87} - 14 q^{88} - 42 q^{89} - 12 q^{90} + 12 q^{92} - 4 q^{94} - 22 q^{95} + 42 q^{96} - 24 q^{97} - 4 q^{98} - 16 q^{99}+O(q^{100}) \) 6 * q - 4 * q^2 + 4 * q^4 - 6 * q^5 - 4 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9 + 12 * q^10 - 4 * q^11 + 2 * q^12 - 4 * q^14 - 20 * q^15 + 8 * q^16 - 4 * q^17 + 16 * q^18 - 2 * q^19 - 26 * q^20 - 6 * q^22 - 12 * q^23 - 2 * q^24 + 10 * q^25 + 6 * q^27 + 4 * q^28 - 8 * q^29 + 8 * q^30 + 14 * q^31 - 8 * q^32 - 16 * q^33 + 2 * q^34 - 6 * q^35 - 10 * q^36 - 12 * q^37 - 2 * q^38 + 46 * q^40 - 28 * q^41 - 4 * q^42 + 2 * q^43 + 20 * q^44 - 16 * q^45 - 20 * q^46 - 14 * q^47 + 2 * q^48 + 6 * q^49 - 32 * q^50 - 26 * q^51 - 22 * q^53 - 14 * q^54 + 6 * q^55 - 12 * q^56 - 4 * q^58 + 2 * q^59 - 14 * q^61 - 4 * q^62 + 4 * q^63 + 26 * q^64 - 26 * q^66 - 24 * q^67 + 8 * q^68 + 4 * q^69 + 12 * q^70 - 4 * q^71 - 8 * q^72 - 36 * q^73 - 6 * q^74 + 46 * q^75 + 26 * q^76 - 4 * q^77 - 28 * q^79 - 36 * q^80 - 2 * q^81 + 14 * q^82 - 26 * q^83 + 2 * q^84 + 20 * q^85 + 24 * q^86 + 2 * q^87 - 14 * q^88 - 42 * q^89 - 12 * q^90 + 12 * q^92 - 4 * q^94 - 22 * q^95 + 42 * q^96 - 24 * q^97 - 4 * q^98 - 16 * q^99

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