LMFDB - Embedded newform 1183.2.a.j.1.3

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:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
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			1.3
Root			$-1.48119$ 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)

$f(q)$	$=$	$q+2.48119 q^{2} +1.67513 q^{3} +4.15633 q^{4} -0.675131 q^{5} +4.15633 q^{6} -1.00000 q^{7} +5.35026 q^{8} -0.193937 q^{9} +O(q^{10})$	\(q+2.48119 q^{2} +1.67513 q^{3} +4.15633 q^{4} -0.675131 q^{5} +4.15633 q^{6} -1.00000 q^{7} +5.35026 q^{8} -0.193937 q^{9} -1.67513 q^{10} +4.48119 q^{11} +6.96239 q^{12} -2.48119 q^{14} -1.13093 q^{15} +4.96239 q^{16} +3.28726 q^{17} -0.481194 q^{18} +5.21933 q^{19} -2.80606 q^{20} -1.67513 q^{21} +11.1187 q^{22} -4.76845 q^{23} +8.96239 q^{24} -4.54420 q^{25} -5.35026 q^{27} -4.15633 q^{28} -9.31265 q^{29} -2.80606 q^{30} -1.63752 q^{31} +1.61213 q^{32} +7.50659 q^{33} +8.15633 q^{34} +0.675131 q^{35} -0.806063 q^{36} -1.44358 q^{37} +12.9502 q^{38} -3.61213 q^{40} +7.92478 q^{41} -4.15633 q^{42} +4.61213 q^{43} +18.6253 q^{44} +0.130933 q^{45} -11.8315 q^{46} +7.86907 q^{47} +8.31265 q^{48} +1.00000 q^{49} -11.2750 q^{50} +5.50659 q^{51} -3.15633 q^{53} -13.2750 q^{54} -3.02539 q^{55} -5.35026 q^{56} +8.74306 q^{57} -23.1065 q^{58} -2.54420 q^{59} -4.70052 q^{60} -2.31265 q^{61} -4.06300 q^{62} +0.193937 q^{63} -5.92478 q^{64} +18.6253 q^{66} -7.35026 q^{67} +13.6629 q^{68} -7.98778 q^{69} +1.67513 q^{70} -7.75623 q^{71} -1.03761 q^{72} -15.1441 q^{73} -3.58181 q^{74} -7.61213 q^{75} +21.6932 q^{76} -4.48119 q^{77} +14.6629 q^{79} -3.35026 q^{80} -8.38058 q^{81} +19.6629 q^{82} +1.45088 q^{83} -6.96239 q^{84} -2.21933 q^{85} +11.4436 q^{86} -15.5999 q^{87} +23.9756 q^{88} -7.79384 q^{89} +0.324869 q^{90} -19.8192 q^{92} -2.74306 q^{93} +19.5247 q^{94} -3.52373 q^{95} +2.70052 q^{96} +17.9805 q^{97} +2.48119 q^{98} -0.869067 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} + 2 q^{4} + 3 q^{5} + 2 q^{6} - 3 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 + 2 * q^4 + 3 * q^5 + 2 * q^6 - 3 * q^7 + 6 * q^8 - q^9	$ 3 q + 2 q^{2} + 2 q^{4} + 3 q^{5} + 2 q^{6} - 3 q^{7} + 6 q^{8} - q^{9} + 8 q^{11} + 10 q^{12} - 2 q^{14} - 8 q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} + q^{19} - 8 q^{20} + 12 q^{22} - 3 q^{23} + 16 q^{24} - 4 q^{25} - 6 q^{27} - 2 q^{28} - 7 q^{29} - 8 q^{30} + 11 q^{31} + 4 q^{32} + 2 q^{33} + 14 q^{34} - 3 q^{35} - 2 q^{36} + 12 q^{37} + 2 q^{38} - 10 q^{40} + 2 q^{41} - 2 q^{42} + 13 q^{43} + 14 q^{44} + 5 q^{45} - 20 q^{46} + 19 q^{47} + 4 q^{48} + 3 q^{49} - 2 q^{50} - 4 q^{51} + q^{53} - 8 q^{54} + 6 q^{55} - 6 q^{56} + 30 q^{57} - 22 q^{58} + 2 q^{59} + 6 q^{60} + 14 q^{61} - 8 q^{62} + q^{63} + 4 q^{64} + 14 q^{66} - 12 q^{67} + 10 q^{68} + 2 q^{69} + 14 q^{71} - 14 q^{72} - 9 q^{73} - 12 q^{74} - 22 q^{75} + 32 q^{76} - 8 q^{77} + 13 q^{79} - 13 q^{81} + 28 q^{82} + q^{83} - 10 q^{84} + 8 q^{85} + 18 q^{86} - 20 q^{87} + 20 q^{88} + 3 q^{89} + 6 q^{90} - 18 q^{92} - 12 q^{93} + 10 q^{94} - 29 q^{95} - 12 q^{96} + 15 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) $ 3 * q + 2 * q^2 + 2 * q^4 + 3 * q^5 + 2 * q^6 - 3 * q^7 + 6 * q^8 - q^9 + 8 * q^11 + 10 * q^12 - 2 * q^14 - 8 * q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 + q^19 - 8 * q^20 + 12 * q^22 - 3 * q^23 + 16 * q^24 - 4 * q^25 - 6 * q^27 - 2 * q^28 - 7 * q^29 - 8 * q^30 + 11 * q^31 + 4 * q^32 + 2 * q^33 + 14 * q^34 - 3 * q^35 - 2 * q^36 + 12 * q^37 + 2 * q^38 - 10 * q^40 + 2 * q^41 - 2 * q^42 + 13 * q^43 + 14 * q^44 + 5 * q^45 - 20 * q^46 + 19 * q^47 + 4 * q^48 + 3 * q^49 - 2 * q^50 - 4 * q^51 + q^53 - 8 * q^54 + 6 * q^55 - 6 * q^56 + 30 * q^57 - 22 * q^58 + 2 * q^59 + 6 * q^60 + 14 * q^61 - 8 * q^62 + q^63 + 4 * q^64 + 14 * q^66 - 12 * q^67 + 10 * q^68 + 2 * q^69 + 14 * q^71 - 14 * q^72 - 9 * q^73 - 12 * q^74 - 22 * q^75 + 32 * q^76 - 8 * q^77 + 13 * q^79 - 13 * q^81 + 28 * q^82 + q^83 - 10 * q^84 + 8 * q^85 + 18 * q^86 - 20 * q^87 + 20 * q^88 + 3 * q^89 + 6 * q^90 - 18 * q^92 - 12 * q^93 + 10 * q^94 - 29 * q^95 - 12 * q^96 + 15 * q^97 + 2 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.48119	1.75447	0.877235	−	0.480062i	$-0.159386\pi$
$2$	2.48119	1.75447	0.877235	+	0.480062i	$0.159386\pi$
$3$	1.67513	0.967137	0.483569	−	0.875306i	$-0.339340\pi$
$3$	1.67513	0.967137	0.483569	+	0.875306i	$0.339340\pi$
$4$	4.15633	2.07816
$5$	−0.675131	−0.301928	−0.150964	−	0.988539i	$-0.548238\pi$
$5$	−0.675131	−0.301928	−0.150964	+	0.988539i	$0.548238\pi$
$6$	4.15633	1.69681
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	5.35026	1.89160
$9$	−0.193937	−0.0646455
$10$	−1.67513	−0.529723
$11$	4.48119	1.35113	0.675565	−	0.737300i	$-0.263900\pi$
$11$	4.48119	1.35113	0.675565	+	0.737300i	$0.263900\pi$
$12$	6.96239	2.00987
$13$	0	0
$13$	0	0
$14$	−2.48119	−0.663127
$15$	−1.13093	−0.292006
$16$	4.96239	1.24060
$17$	3.28726	0.797277	0.398639	−	0.917108i	$-0.369483\pi$
$17$	3.28726	0.797277	0.398639	+	0.917108i	$0.369483\pi$
$18$	−0.481194	−0.113419
$19$	5.21933	1.19740	0.598698	−	0.800975i	$-0.295685\pi$
$19$	5.21933	1.19740	0.598698	+	0.800975i	$0.295685\pi$
$20$	−2.80606	−0.627455
$21$	−1.67513	−0.365544
$22$	11.1187	2.37052
$23$	−4.76845	−0.994291	−0.497145	−	0.867667i	$-0.665618\pi$
$23$	−4.76845	−0.994291	−0.497145	+	0.867667i	$0.665618\pi$
$24$	8.96239	1.82944
$25$	−4.54420	−0.908840
$26$	0	0
$27$	−5.35026	−1.02966
$28$	−4.15633	−0.785472
$29$	−9.31265	−1.72932	−0.864658	−	0.502361i	$-0.832465\pi$
$29$	−9.31265	−1.72932	−0.864658	+	0.502361i	$0.832465\pi$
$30$	−2.80606	−0.512315
$31$	−1.63752	−0.294107	−0.147054	−	0.989129i	$-0.546979\pi$
$31$	−1.63752	−0.294107	−0.147054	+	0.989129i	$0.546979\pi$
$32$	1.61213	0.284986
$33$	7.50659	1.30673
$34$	8.15633	1.39880
$35$	0.675131	0.114118
$36$	−0.806063	−0.134344
$37$	−1.44358	−0.237324	−0.118662	−	0.992935i	$-0.537860\pi$
$37$	−1.44358	−0.237324	−0.118662	+	0.992935i	$0.537860\pi$
$38$	12.9502	2.10079
$39$	0	0
$40$	−3.61213	−0.571127
$41$	7.92478	1.23764	0.618821	−	0.785532i	$-0.287611\pi$
$41$	7.92478	1.23764	0.618821	+	0.785532i	$0.287611\pi$
$42$	−4.15633	−0.641335
$43$	4.61213	0.703343	0.351671	−	0.936124i	$-0.385613\pi$
$43$	4.61213	0.703343	0.351671	+	0.936124i	$0.385613\pi$
$44$	18.6253	2.80787
$45$	0.130933	0.0195183
$46$	−11.8315	−1.74445
$47$	7.86907	1.14782	0.573911	−	0.818918i	$-0.305426\pi$
$47$	7.86907	1.14782	0.573911	+	0.818918i	$0.305426\pi$
$48$	8.31265	1.19983
$49$	1.00000	0.142857
$50$	−11.2750	−1.59453
$51$	5.50659	0.771076
$52$	0	0
$53$	−3.15633	−0.433555	−0.216777	−	0.976221i	$-0.569555\pi$
$53$	−3.15633	−0.433555	−0.216777	+	0.976221i	$0.569555\pi$
$54$	−13.2750	−1.80650
$55$	−3.02539	−0.407944
$56$	−5.35026	−0.714959
$57$	8.74306	1.15805
$58$	−23.1065	−3.03403
$59$	−2.54420	−0.331226	−0.165613	−	0.986191i	$-0.552960\pi$
$59$	−2.54420	−0.331226	−0.165613	+	0.986191i	$0.552960\pi$
$60$	−4.70052	−0.606835
$61$	−2.31265	−0.296105	−0.148052	−	0.988980i	$-0.547300\pi$
$61$	−2.31265	−0.296105	−0.148052	+	0.988980i	$0.547300\pi$
$62$	−4.06300	−0.516002
$63$	0.193937	0.0244337
$64$	−5.92478	−0.740597
$65$	0	0
$66$	18.6253	2.29262
$67$	−7.35026	−0.897977	−0.448989	−	0.893537i	$-0.648216\pi$
$67$	−7.35026	−0.897977	−0.448989	+	0.893537i	$0.648216\pi$
$68$	13.6629	1.65687
$69$	−7.98778	−0.961616
$70$	1.67513	0.200216
$71$	−7.75623	−0.920496	−0.460248	−	0.887791i	$-0.652239\pi$
$71$	−7.75623	−0.920496	−0.460248	+	0.887791i	$0.652239\pi$
$72$	−1.03761	−0.122284
$73$	−15.1441	−1.77248	−0.886242	−	0.463223i	$-0.846693\pi$
$73$	−15.1441	−1.77248	−0.886242	+	0.463223i	$0.846693\pi$
$74$	−3.58181	−0.416377
$75$	−7.61213	−0.878973
$76$	21.6932	2.48838
$77$	−4.48119	−0.510679
$78$	0	0
$79$	14.6629	1.64971	0.824853	−	0.565347i	$-0.191258\pi$
$79$	14.6629	1.64971	0.824853	+	0.565347i	$0.191258\pi$
$80$	−3.35026	−0.374571
$81$	−8.38058	−0.931175
$82$	19.6629	2.17141
$83$	1.45088	0.159254	0.0796272	−	0.996825i	$-0.474627\pi$
$83$	1.45088	0.159254	0.0796272	+	0.996825i	$0.474627\pi$
$84$	−6.96239	−0.759659
$85$	−2.21933	−0.240720
$86$	11.4436	1.23399
$87$	−15.5999	−1.67249
$88$	23.9756	2.55580
$89$	−7.79384	−0.826146	−0.413073	−	0.910698i	$-0.635545\pi$
$89$	−7.79384	−0.826146	−0.413073	+	0.910698i	$0.635545\pi$
$90$	0.324869	0.0342442
$91$	0	0
$92$	−19.8192	−2.06630
$93$	−2.74306	−0.284442
$94$	19.5247	2.01382
$95$	−3.52373	−0.361527
$96$	2.70052	0.275621
$97$	17.9805	1.82564	0.912821	−	0.408360i	$-0.133899\pi$
$97$	17.9805	1.82564	0.912821	+	0.408360i	$0.133899\pi$
$98$	2.48119	0.250638
$99$	−0.869067	−0.0873446
$100$	−18.8872	−1.88872
$101$	−9.33804	−0.929170	−0.464585	−	0.885529i	$-0.653796\pi$
$101$	−9.33804	−0.929170	−0.464585	+	0.885529i	$0.653796\pi$
$102$	13.6629	1.35283
$103$	−6.23743	−0.614592	−0.307296	−	0.951614i	$-0.599424\pi$
$103$	−6.23743	−0.614592	−0.307296	+	0.951614i	$0.599424\pi$
$104$	0	0
$105$	1.13093	0.110368
$106$	−7.83146	−0.760658
$107$	7.24472	0.700374	0.350187	−	0.936680i	$-0.386118\pi$
$107$	7.24472	0.700374	0.350187	+	0.936680i	$0.386118\pi$
$108$	−22.2374	−2.13980
$109$	−4.79384	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$109$	−4.79384	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$110$	−7.50659	−0.715725
$111$	−2.41819	−0.229524
$112$	−4.96239	−0.468902
$113$	−9.34297	−0.878912	−0.439456	−	0.898264i	$-0.644829\pi$
$113$	−9.34297	−0.878912	−0.439456	+	0.898264i	$0.644829\pi$
$114$	21.6932	2.03176
$115$	3.21933	0.300204
$116$	−38.7064	−3.59380
$117$	0	0
$118$	−6.31265	−0.581127
$119$	−3.28726	−0.301342
$120$	−6.05079	−0.552359
$121$	9.08110	0.825555
$122$	−5.73813	−0.519506
$123$	13.2750	1.19697
$124$	−6.80606	−0.611203
$125$	6.44358	0.576332
$126$	0.481194	0.0428682
$127$	1.38058	0.122507	0.0612533	−	0.998122i	$-0.480490\pi$
$127$	1.38058	0.122507	0.0612533	+	0.998122i	$0.480490\pi$
$128$	−17.9248	−1.58434
$129$	7.72592	0.680229
$130$	0	0
$131$	12.4993	1.09207	0.546034	−	0.837763i	$-0.316137\pi$
$131$	12.4993	1.09207	0.546034	+	0.837763i	$0.316137\pi$
$132$	31.1998	2.71560
$133$	−5.21933	−0.452573
$134$	−18.2374	−1.57547
$135$	3.61213	0.310882
$136$	17.5877	1.50813
$137$	3.20616	0.273920	0.136960	−	0.990577i	$-0.456267\pi$
$137$	3.20616	0.273920	0.136960	+	0.990577i	$0.456267\pi$
$138$	−19.8192	−1.68713
$139$	−0.249646	−0.0211747	−0.0105874	−	0.999944i	$-0.503370\pi$
$139$	−0.249646	−0.0211747	−0.0105874	+	0.999944i	$0.503370\pi$
$140$	2.80606	0.237156
$141$	13.1817	1.11010
$142$	−19.2447	−1.61498
$143$	0	0
$144$	−0.962389	−0.0801991
$145$	6.28726	0.522128
$146$	−37.5755	−3.10977
$147$	1.67513	0.138162
$148$	−6.00000	−0.493197
$149$	4.03269	0.330371	0.165185	−	0.986263i	$-0.447178\pi$
$149$	4.03269	0.330371	0.165185	+	0.986263i	$0.447178\pi$
$150$	−18.8872	−1.54213
$151$	1.56959	0.127731	0.0638657	−	0.997958i	$-0.479657\pi$
$151$	1.56959	0.127731	0.0638657	+	0.997958i	$0.479657\pi$
$152$	27.9248	2.26500
$153$	−0.637519	−0.0515404
$154$	−11.1187	−0.895971
$155$	1.10554	0.0887991
$156$	0	0
$157$	2.89938	0.231396	0.115698	−	0.993284i	$-0.463090\pi$
$157$	2.89938	0.231396	0.115698	+	0.993284i	$0.463090\pi$
$158$	36.3815	2.89436
$159$	−5.28726	−0.419307
$160$	−1.08840	−0.0860453
$161$	4.76845	0.375807
$162$	−20.7938	−1.63372
$163$	17.2750	1.35309	0.676543	−	0.736403i	$-0.263477\pi$
$163$	17.2750	1.35309	0.676543	+	0.736403i	$0.263477\pi$
$164$	32.9380	2.57202
$165$	−5.06793	−0.394538
$166$	3.59991	0.279407
$167$	16.2931	1.26080	0.630400	−	0.776270i	$-0.282891\pi$
$167$	16.2931	1.26080	0.630400	+	0.776270i	$0.282891\pi$
$168$	−8.96239	−0.691463
$169$	0	0
$170$	−5.50659	−0.422336
$171$	−1.01222	−0.0774063
$172$	19.1695	1.46166
$173$	−2.17442	−0.165318	−0.0826592	−	0.996578i	$-0.526341\pi$
$173$	−2.17442	−0.165318	−0.0826592	+	0.996578i	$0.526341\pi$
$174$	−38.7064	−2.93432
$175$	4.54420	0.343509
$176$	22.2374	1.67621
$177$	−4.26187	−0.320341
$178$	−19.3380	−1.44945
$179$	0.551493	0.0412205	0.0206102	−	0.999788i	$-0.493439\pi$
$179$	0.551493	0.0412205	0.0206102	+	0.999788i	$0.493439\pi$
$180$	0.544198	0.0405621
$181$	−0.511511	−0.0380203	−0.0190102	−	0.999819i	$-0.506051\pi$
$181$	−0.511511	−0.0380203	−0.0190102	+	0.999819i	$0.506051\pi$
$182$	0	0
$183$	−3.87399	−0.286374
$184$	−25.5125	−1.88080
$185$	0.974607	0.0716546
$186$	−6.80606	−0.499045
$187$	14.7308	1.07723
$188$	32.7064	2.38536
$189$	5.35026	0.389174
$190$	−8.74306	−0.634288
$191$	−16.5442	−1.19710	−0.598548	−	0.801087i	$-0.704255\pi$
$191$	−16.5442	−1.19710	−0.598548	+	0.801087i	$0.704255\pi$
$192$	−9.92478	−0.716259
$193$	7.41090	0.533448	0.266724	−	0.963773i	$-0.414059\pi$
$193$	7.41090	0.533448	0.266724	+	0.963773i	$0.414059\pi$
$194$	44.6131	3.20303
$195$	0	0
$196$	4.15633	0.296880
$197$	−7.14903	−0.509347	−0.254674	−	0.967027i	$-0.581968\pi$
$197$	−7.14903	−0.509347	−0.254674	+	0.967027i	$0.581968\pi$
$198$	−2.15633	−0.153243
$199$	−5.10062	−0.361573	−0.180787	−	0.983522i	$-0.557864\pi$
$199$	−5.10062	−0.361573	−0.180787	+	0.983522i	$0.557864\pi$
$200$	−24.3127	−1.71916
$201$	−12.3127	−0.868467
$202$	−23.1695	−1.63020
$203$	9.31265	0.653620
$204$	22.8872	1.60242
$205$	−5.35026	−0.373678
$206$	−15.4763	−1.07828
$207$	0.924777	0.0642765
$208$	0	0
$209$	23.3888	1.61784
$210$	2.80606	0.193637
$211$	0.193937	0.0133511	0.00667557	−	0.999978i	$-0.497875\pi$
$211$	0.193937	0.0133511	0.00667557	+	0.999978i	$0.497875\pi$
$212$	−13.1187	−0.900997
$213$	−12.9927	−0.890246
$214$	17.9756	1.22878
$215$	−3.11379	−0.212359
$216$	−28.6253	−1.94771
$217$	1.63752	0.111162
$218$	−11.8945	−0.805594
$219$	−25.3684	−1.71423
$220$	−12.5745	−0.847774
$221$	0	0
$222$	−6.00000	−0.402694
$223$	−5.83875	−0.390992	−0.195496	−	0.980705i	$-0.562632\pi$
$223$	−5.83875	−0.390992	−0.195496	+	0.980705i	$0.562632\pi$
$224$	−1.61213	−0.107715
$225$	0.881286	0.0587524
$226$	−23.1817	−1.54202
$227$	3.68735	0.244738	0.122369	−	0.992485i	$-0.460951\pi$
$227$	3.68735	0.244738	0.122369	+	0.992485i	$0.460951\pi$
$228$	36.3390	2.40661
$229$	−5.65703	−0.373827	−0.186914	−	0.982376i	$-0.559848\pi$
$229$	−5.65703	−0.373827	−0.186914	+	0.982376i	$0.559848\pi$
$230$	7.98778	0.526699
$231$	−7.50659	−0.493897
$232$	−49.8251	−3.27118
$233$	10.3258	0.676467	0.338234	−	0.941062i	$-0.390171\pi$
$233$	10.3258	0.676467	0.338234	+	0.941062i	$0.390171\pi$
$234$	0	0
$235$	−5.31265	−0.346559
$236$	−10.5745	−0.688342
$237$	24.5623	1.59549
$238$	−8.15633	−0.528696
$239$	22.2882	1.44170	0.720852	−	0.693089i	$-0.243751\pi$
$239$	22.2882	1.44170	0.720852	+	0.693089i	$0.243751\pi$
$240$	−5.61213	−0.362261
$241$	29.4264	1.89552	0.947762	−	0.318979i	$-0.103340\pi$
$241$	29.4264	1.89552	0.947762	+	0.318979i	$0.103340\pi$
$242$	22.5320	1.44841
$243$	2.01222	0.129084
$244$	−9.61213	−0.615353
$245$	−0.675131	−0.0431325
$246$	32.9380	2.10005
$247$	0	0
$248$	−8.76116	−0.556334
$249$	2.43041	0.154021
$250$	15.9878	1.01116
$251$	21.5247	1.35863	0.679313	−	0.733849i	$-0.262278\pi$
$251$	21.5247	1.35863	0.679313	+	0.733849i	$0.262278\pi$
$252$	0.806063	0.0507772
$253$	−21.3684	−1.34342
$254$	3.42548	0.214934
$255$	−3.71767	−0.232809
$256$	−32.6253	−2.03908
$257$	−0.661957	−0.0412917	−0.0206459	−	0.999787i	$-0.506572\pi$
$257$	−0.661957	−0.0412917	−0.0206459	+	0.999787i	$0.506572\pi$
$258$	19.1695	1.19344
$259$	1.44358	0.0896999
$260$	0	0
$261$	1.80606	0.111793
$262$	31.0132	1.91600
$263$	5.18664	0.319822	0.159911	−	0.987131i	$-0.448879\pi$
$263$	5.18664	0.319822	0.159911	+	0.987131i	$0.448879\pi$
$264$	40.1622	2.47181
$265$	2.13093	0.130902
$266$	−12.9502	−0.794026
$267$	−13.0557	−0.798996
$268$	−30.5501	−1.86614
$269$	27.2506	1.66150	0.830749	−	0.556647i	$-0.187912\pi$
$269$	27.2506	1.66150	0.830749	+	0.556647i	$0.187912\pi$
$270$	8.96239	0.545434
$271$	−18.7612	−1.13966	−0.569830	−	0.821763i	$-0.692991\pi$
$271$	−18.7612	−1.13966	−0.569830	+	0.821763i	$0.692991\pi$
$272$	16.3127	0.989100
$273$	0	0
$274$	7.95509	0.480585
$275$	−20.3634	−1.22796
$276$	−33.1998	−1.99839
$277$	15.4241	0.926743	0.463371	−	0.886164i	$-0.346640\pi$
$277$	15.4241	0.926743	0.463371	+	0.886164i	$0.346640\pi$
$278$	−0.619421	−0.0371504
$279$	0.317575	0.0190127
$280$	3.61213	0.215866
$281$	−24.8446	−1.48211	−0.741053	−	0.671446i	$-0.765673\pi$
$281$	−24.8446	−1.48211	−0.741053	+	0.671446i	$0.765673\pi$
$282$	32.7064	1.94764
$283$	22.8872	1.36050	0.680250	−	0.732980i	$-0.261871\pi$
$283$	22.8872	1.36050	0.680250	+	0.732980i	$0.261871\pi$
$284$	−32.2374	−1.91294
$285$	−5.90271	−0.349646
$286$	0	0
$287$	−7.92478	−0.467785
$288$	−0.312650	−0.0184231
$289$	−6.19394	−0.364349
$290$	15.5999	0.916058
$291$	30.1197	1.76565
$292$	−62.9438	−3.68351
$293$	25.2193	1.47333	0.736664	−	0.676258i	$-0.236400\pi$
$293$	25.2193	1.47333	0.736664	+	0.676258i	$0.236400\pi$
$294$	4.15633	0.242402
$295$	1.71767	0.100006
$296$	−7.72355	−0.448922
$297$	−23.9756	−1.39120
$298$	10.0059	0.579625
$299$	0	0
$300$	−31.6385	−1.82665
$301$	−4.61213	−0.265839
$302$	3.89446	0.224101
$303$	−15.6424	−0.898635
$304$	25.9003	1.48549
$305$	1.56134	0.0894022
$306$	−1.58181	−0.0904260
$307$	7.24965	0.413759	0.206880	−	0.978366i	$-0.433669\pi$
$307$	7.24965	0.413759	0.206880	+	0.978366i	$0.433669\pi$
$308$	−18.6253	−1.06128
$309$	−10.4485	−0.594395
$310$	2.74306	0.155795
$311$	−20.2398	−1.14769	−0.573847	−	0.818963i	$-0.694550\pi$
$311$	−20.2398	−1.14769	−0.573847	+	0.818963i	$0.694550\pi$
$312$	0	0
$313$	−33.1368	−1.87300	−0.936502	−	0.350663i	$-0.885956\pi$
$313$	−33.1368	−1.87300	−0.936502	+	0.350663i	$0.885956\pi$
$314$	7.19394	0.405977
$315$	−0.130933	−0.00737721
$316$	60.9438	3.42836
$317$	−17.0132	−0.955555	−0.477778	−	0.878481i	$-0.658557\pi$
$317$	−17.0132	−0.955555	−0.477778	+	0.878481i	$0.658557\pi$
$318$	−13.1187	−0.735661
$319$	−41.7318	−2.33653
$320$	4.00000	0.223607
$321$	12.1359	0.677357
$322$	11.8315	0.659341
$323$	17.1573	0.954657
$324$	−34.8324	−1.93513
$325$	0	0
$326$	42.8627	2.37395
$327$	−8.03032	−0.444078
$328$	42.3996	2.34113
$329$	−7.86907	−0.433836
$330$	−12.5745	−0.692204
$331$	10.8364	0.595621	0.297811	−	0.954625i	$-0.403744\pi$
$331$	10.8364	0.595621	0.297811	+	0.954625i	$0.403744\pi$
$332$	6.03032	0.330957
$333$	0.279964	0.0153419
$334$	40.4264	2.21204
$335$	4.96239	0.271124
$336$	−8.31265	−0.453492
$337$	2.96968	0.161769	0.0808845	−	0.996723i	$-0.474226\pi$
$337$	2.96968	0.161769	0.0808845	+	0.996723i	$0.474226\pi$
$338$	0	0
$339$	−15.6507	−0.850029
$340$	−9.22425	−0.500255
$341$	−7.33804	−0.397377
$342$	−2.51151	−0.135807
$343$	−1.00000	−0.0539949
$344$	24.6761	1.33045
$345$	5.39280	0.290338
$346$	−5.39517	−0.290046
$347$	30.7367	1.65003	0.825017	−	0.565108i	$-0.191166\pi$
$347$	30.7367	1.65003	0.825017	+	0.565108i	$0.191166\pi$
$348$	−64.8383	−3.47570
$349$	2.00492	0.107321	0.0536606	−	0.998559i	$-0.482911\pi$
$349$	2.00492	0.107321	0.0536606	+	0.998559i	$0.482911\pi$
$350$	11.2750	0.602676
$351$	0	0
$352$	7.22425	0.385054
$353$	17.2546	0.918368	0.459184	−	0.888341i	$-0.348142\pi$
$353$	17.2546	0.918368	0.459184	+	0.888341i	$0.348142\pi$
$354$	−10.5745	−0.562029
$355$	5.23647	0.277923
$356$	−32.3938	−1.71687
$357$	−5.50659	−0.291439
$358$	1.36836	0.0723201
$359$	−7.10650	−0.375066	−0.187533	−	0.982258i	$-0.560049\pi$
$359$	−7.10650	−0.375066	−0.187533	+	0.982258i	$0.560049\pi$
$360$	0.700523	0.0369208
$361$	8.24140	0.433758
$362$	−1.26916	−0.0667055
$363$	15.2120	0.798425
$364$	0	0
$365$	10.2243	0.535162
$366$	−9.61213	−0.502434
$367$	−27.2628	−1.42311	−0.711554	−	0.702632i	$-0.752008\pi$
$367$	−27.2628	−1.42311	−0.711554	+	0.702632i	$0.752008\pi$
$368$	−23.6629	−1.23351
$369$	−1.53690	−0.0800080
$370$	2.41819	0.125716
$371$	3.15633	0.163868
$372$	−11.4010	−0.591117
$373$	−5.91890	−0.306469	−0.153234	−	0.988190i	$-0.548969\pi$
$373$	−5.91890	−0.306469	−0.153234	+	0.988190i	$0.548969\pi$
$374$	36.5501	1.88996
$375$	10.7938	0.557392
$376$	42.1016	2.17122
$377$	0	0
$378$	13.2750	0.682794
$379$	−28.9706	−1.48812	−0.744061	−	0.668112i	$-0.767103\pi$
$379$	−28.9706	−1.48812	−0.744061	+	0.668112i	$0.767103\pi$
$380$	−14.6458	−0.751312
$381$	2.31265	0.118481
$382$	−41.0494	−2.10027
$383$	23.2243	1.18670	0.593352	−	0.804943i	$-0.297804\pi$
$383$	23.2243	1.18670	0.593352	+	0.804943i	$0.297804\pi$
$384$	−30.0263	−1.53228
$385$	3.02539	0.154188
$386$	18.3879	0.935918
$387$	−0.894460	−0.0454680
$388$	74.7328	3.79398
$389$	16.1319	0.817919	0.408960	−	0.912552i	$-0.365892\pi$
$389$	16.1319	0.817919	0.408960	+	0.912552i	$0.365892\pi$
$390$	0	0
$391$	−15.6751	−0.792725
$392$	5.35026	0.270229
$393$	20.9380	1.05618
$394$	−17.7381	−0.893634
$395$	−9.89938	−0.498092
$396$	−3.61213	−0.181516
$397$	24.0557	1.20732	0.603661	−	0.797241i	$-0.293708\pi$
$397$	24.0557	1.20732	0.603661	+	0.797241i	$0.293708\pi$
$398$	−12.6556	−0.634369
$399$	−8.74306	−0.437700
$400$	−22.5501	−1.12750
$401$	2.77575	0.138614	0.0693071	−	0.997595i	$-0.477921\pi$
$401$	2.77575	0.138614	0.0693071	+	0.997595i	$0.477921\pi$
$402$	−30.5501	−1.52370
$403$	0	0
$404$	−38.8119	−1.93097
$405$	5.65799	0.281148
$406$	23.1065	1.14676
$407$	−6.46898	−0.320655
$408$	29.4617	1.45857
$409$	−20.1309	−0.995411	−0.497705	−	0.867346i	$-0.665824\pi$
$409$	−20.1309	−0.995411	−0.497705	+	0.867346i	$0.665824\pi$
$410$	−13.2750	−0.655607
$411$	5.37073	0.264919
$412$	−25.9248	−1.27722
$413$	2.54420	0.125192
$414$	2.29455	0.112771
$415$	−0.979532	−0.0480833
$416$	0	0
$417$	−0.418190	−0.0204789
$418$	58.0322	2.83845
$419$	−0.385503	−0.0188331	−0.00941654	−	0.999956i	$-0.502997\pi$
$419$	−0.385503	−0.0188331	−0.00941654	+	0.999956i	$0.502997\pi$
$420$	4.70052	0.229362
$421$	15.6810	0.764246	0.382123	−	0.924112i	$-0.375193\pi$
$421$	15.6810	0.764246	0.382123	+	0.924112i	$0.375193\pi$
$422$	0.481194	0.0234242
$423$	−1.52610	−0.0742015
$424$	−16.8872	−0.820113
$425$	−14.9380	−0.724597
$426$	−32.2374	−1.56191
$427$	2.31265	0.111917
$428$	30.1114	1.45549
$429$	0	0
$430$	−7.72592	−0.372577
$431$	1.53690	0.0740301	0.0370150	−	0.999315i	$-0.488215\pi$
$431$	1.53690	0.0740301	0.0370150	+	0.999315i	$0.488215\pi$
$432$	−26.5501	−1.27739
$433$	−26.0362	−1.25122	−0.625610	−	0.780136i	$-0.715150\pi$
$433$	−26.0362	−1.25122	−0.625610	+	0.780136i	$0.715150\pi$
$434$	4.06300	0.195030
$435$	10.5320	0.504970
$436$	−19.9248	−0.954224
$437$	−24.8881	−1.19056
$438$	−62.9438	−3.00757
$439$	19.1246	0.912767	0.456384	−	0.889783i	$-0.349145\pi$
$439$	19.1246	0.912767	0.456384	+	0.889783i	$0.349145\pi$
$440$	−16.1866	−0.771668
$441$	−0.193937	−0.00923507
$442$	0	0
$443$	−12.6180	−0.599500	−0.299750	−	0.954018i	$-0.596903\pi$
$443$	−12.6180	−0.599500	−0.299750	+	0.954018i	$0.596903\pi$
$444$	−10.0508	−0.476989
$445$	5.26187	0.249436
$446$	−14.4871	−0.685983
$447$	6.75528	0.319514
$448$	5.92478	0.279919
$449$	−1.02302	−0.0482794	−0.0241397	−	0.999709i	$-0.507685\pi$
$449$	−1.02302	−0.0482794	−0.0241397	+	0.999709i	$0.507685\pi$
$450$	2.18664	0.103079
$451$	35.5125	1.67222
$452$	−38.8324	−1.82652
$453$	2.62927	0.123534
$454$	9.14903	0.429385
$455$	0	0
$456$	46.7777	2.19056
$457$	28.5320	1.33467	0.667335	−	0.744758i	$-0.267435\pi$
$457$	28.5320	1.33467	0.667335	+	0.744758i	$0.267435\pi$
$458$	−14.0362	−0.655868
$459$	−17.5877	−0.820923
$460$	13.3806	0.623873
$461$	25.3503	1.18068	0.590340	−	0.807155i	$-0.298994\pi$
$461$	25.3503	1.18068	0.590340	+	0.807155i	$0.298994\pi$
$462$	−18.6253	−0.866527
$463$	39.6810	1.84413	0.922066	−	0.387032i	$-0.126500\pi$
$463$	39.6810	1.84413	0.922066	+	0.387032i	$0.126500\pi$
$464$	−46.2130	−2.14538
$465$	1.85192	0.0858809
$466$	25.6204	1.18684
$467$	1.95158	0.0903086	0.0451543	−	0.998980i	$-0.485622\pi$
$467$	1.95158	0.0903086	0.0451543	+	0.998980i	$0.485622\pi$
$468$	0	0
$469$	7.35026	0.339404
$470$	−13.1817	−0.608027
$471$	4.85685	0.223792
$472$	−13.6121	−0.626549
$473$	20.6678	0.950308
$474$	60.9438	2.79924
$475$	−23.7177	−1.08824
$476$	−13.6629	−0.626239
$477$	0.612127	0.0280274
$478$	55.3014	2.52943
$479$	−26.1368	−1.19422	−0.597111	−	0.802159i	$-0.703685\pi$
$479$	−26.1368	−1.19422	−0.597111	+	0.802159i	$0.703685\pi$
$480$	−1.82321	−0.0832176
$481$	0	0
$482$	73.0127	3.32564
$483$	7.98778	0.363457
$484$	37.7440	1.71564
$485$	−12.1392	−0.551212
$486$	4.99271	0.226474
$487$	−20.9624	−0.949896	−0.474948	−	0.880014i	$-0.657533\pi$
$487$	−20.9624	−0.949896	−0.474948	+	0.880014i	$0.657533\pi$
$488$	−12.3733	−0.560112
$489$	28.9380	1.30862
$490$	−1.67513	−0.0756747
$491$	−2.95651	−0.133425	−0.0667127	−	0.997772i	$-0.521251\pi$
$491$	−2.95651	−0.133425	−0.0667127	+	0.997772i	$0.521251\pi$
$492$	55.1754	2.48750
$493$	−30.6131	−1.37874
$494$	0	0
$495$	0.586734	0.0263717
$496$	−8.12601	−0.364869
$497$	7.75623	0.347915
$498$	6.03032	0.270225
$499$	−2.85448	−0.127784	−0.0638920	−	0.997957i	$-0.520351\pi$
$499$	−2.85448	−0.127784	−0.0638920	+	0.997957i	$0.520351\pi$
$500$	26.7816	1.19771
$501$	27.2931	1.21937
$502$	53.4069	2.38367
$503$	23.8641	1.06405	0.532025	−	0.846729i	$-0.321431\pi$
$503$	23.8641	1.06405	0.532025	+	0.846729i	$0.321431\pi$
$504$	1.03761	0.0462189
$505$	6.30440	0.280542
$506$	−53.0191	−2.35698
$507$	0	0
$508$	5.73813	0.254589
$509$	−11.1949	−0.496205	−0.248102	−	0.968734i	$-0.579807\pi$
$509$	−11.1949	−0.496205	−0.248102	+	0.968734i	$0.579807\pi$
$510$	−9.22425	−0.408457
$511$	15.1441	0.669936
$512$	−45.1002	−1.99316
$513$	−27.9248	−1.23291
$514$	−1.64244	−0.0724451
$515$	4.21108	0.185562
$516$	32.1114	1.41363
$517$	35.2628	1.55086
$518$	3.58181	0.157376
$519$	−3.64244	−0.159886
$520$	0	0
$521$	−26.4894	−1.16052	−0.580262	−	0.814430i	$-0.697050\pi$
$521$	−26.4894	−1.16052	−0.580262	+	0.814430i	$0.697050\pi$
$522$	4.48119	0.196137
$523$	−12.9525	−0.566375	−0.283188	−	0.959065i	$-0.591392\pi$
$523$	−12.9525	−0.566375	−0.283188	+	0.959065i	$0.591392\pi$
$524$	51.9511	2.26950
$525$	7.61213	0.332220
$526$	12.8691	0.561118
$527$	−5.38295	−0.234485
$528$	37.2506	1.62112
$529$	−0.261865	−0.0113854
$530$	5.28726	0.229664
$531$	0.493413	0.0214123
$532$	−21.6932	−0.940521
$533$	0	0
$534$	−32.3938	−1.40181
$535$	−4.89114	−0.211462
$536$	−39.3258	−1.69862
$537$	0.923822	0.0398659
$538$	67.6140	2.91505
$539$	4.48119	0.193019
$540$	15.0132	0.646064
$541$	−28.0933	−1.20783	−0.603913	−	0.797050i	$-0.706393\pi$
$541$	−28.0933	−1.20783	−0.603913	+	0.797050i	$0.706393\pi$
$542$	−46.5501	−1.99950
$543$	−0.856849	−0.0367709
$544$	5.29948	0.227213
$545$	3.23647	0.138635
$546$	0	0
$547$	14.8192	0.633625	0.316812	−	0.948488i	$-0.397387\pi$
$547$	14.8192	0.633625	0.316812	+	0.948488i	$0.397387\pi$
$548$	13.3258	0.569251
$549$	0.448507	0.0191418
$550$	−50.5256	−2.15442
$551$	−48.6058	−2.07068
$552$	−42.7367	−1.81900
$553$	−14.6629	−0.623530
$554$	38.2701	1.62594
$555$	1.63259	0.0692998
$556$	−1.03761	−0.0440045
$557$	18.3879	0.779119	0.389560	−	0.921001i	$-0.372627\pi$
$557$	18.3879	0.779119	0.389560	+	0.921001i	$0.372627\pi$
$558$	0.787965	0.0333572
$559$	0	0
$560$	3.35026	0.141574
$561$	24.6761	1.04183
$562$	−61.6444	−2.60031
$563$	−15.3357	−0.646322	−0.323161	−	0.946344i	$-0.604745\pi$
$563$	−15.3357	−0.646322	−0.323161	+	0.946344i	$0.604745\pi$
$564$	54.7875	2.30697
$565$	6.30773	0.265368
$566$	56.7875	2.38696
$567$	8.38058	0.351951
$568$	−41.4979	−1.74121
$569$	1.32250	0.0554421	0.0277210	−	0.999616i	$-0.491175\pi$
$569$	1.32250	0.0554421	0.0277210	+	0.999616i	$0.491175\pi$
$570$	−14.6458	−0.613444
$571$	−37.9175	−1.58680	−0.793399	−	0.608702i	$-0.791690\pi$
$571$	−37.9175	−1.58680	−0.793399	+	0.608702i	$0.791690\pi$
$572$	0	0
$573$	−27.7137	−1.15776
$574$	−19.6629	−0.820714
$575$	21.6688	0.903651
$576$	1.14903	0.0478763
$577$	−12.8627	−0.535482	−0.267741	−	0.963491i	$-0.586277\pi$
$577$	−12.8627	−0.535482	−0.267741	+	0.963491i	$0.586277\pi$
$578$	−15.3684	−0.639240
$579$	12.4142	0.515917
$580$	26.1319	1.08507
$581$	−1.45088	−0.0601925
$582$	74.7328	3.09777
$583$	−14.1441	−0.585789
$584$	−81.0249	−3.35284
$585$	0	0
$586$	62.5741	2.58491
$587$	−31.0240	−1.28050	−0.640248	−	0.768168i	$-0.721169\pi$
$587$	−31.0240	−1.28050	−0.640248	+	0.768168i	$0.721169\pi$
$588$	6.96239	0.287124
$589$	−8.54675	−0.352163
$590$	4.26187	0.175458
$591$	−11.9756	−0.492609
$592$	−7.16362	−0.294423
$593$	−11.4119	−0.468629	−0.234314	−	0.972161i	$-0.575284\pi$
$593$	−11.4119	−0.468629	−0.234314	+	0.972161i	$0.575284\pi$
$594$	−59.4880	−2.44082
$595$	2.21933	0.0909836
$596$	16.7612	0.686564
$597$	−8.54420	−0.349691
$598$	0	0
$599$	7.37328	0.301264	0.150632	−	0.988590i	$-0.451869\pi$
$599$	7.37328	0.301264	0.150632	+	0.988590i	$0.451869\pi$
$600$	−40.7269	−1.66267
$601$	17.2144	0.702190	0.351095	−	0.936340i	$-0.385809\pi$
$601$	17.2144	0.702190	0.351095	+	0.936340i	$0.385809\pi$
$602$	−11.4436	−0.466406
$603$	1.42548	0.0580502
$604$	6.52373	0.265447
$605$	−6.13093	−0.249258
$606$	−38.8119	−1.57663
$607$	32.4264	1.31615	0.658074	−	0.752953i	$-0.271371\pi$
$607$	32.4264	1.31615	0.658074	+	0.752953i	$0.271371\pi$
$608$	8.41422	0.341242
$609$	15.5999	0.632140
$610$	3.87399	0.156853
$611$	0	0
$612$	−2.64974	−0.107109
$613$	−35.6991	−1.44187	−0.720937	−	0.693001i	$-0.756288\pi$
$613$	−35.6991	−1.44187	−0.720937	+	0.693001i	$0.756288\pi$
$614$	17.9878	0.725928
$615$	−8.96239	−0.361398
$616$	−23.9756	−0.966003
$617$	20.3733	0.820198	0.410099	−	0.912041i	$-0.365494\pi$
$617$	20.3733	0.820198	0.410099	+	0.912041i	$0.365494\pi$
$618$	−25.9248	−1.04285
$619$	−40.0118	−1.60821	−0.804104	−	0.594488i	$-0.797355\pi$
$619$	−40.0118	−1.60821	−0.804104	+	0.594488i	$0.797355\pi$
$620$	4.59498	0.184539
$621$	25.5125	1.02378
$622$	−50.2189	−2.01359
$623$	7.79384	0.312254
$624$	0	0
$625$	18.3707	0.734829
$626$	−82.2189	−3.28613
$627$	39.1793	1.56467
$628$	12.0508	0.480879
$629$	−4.74543	−0.189213
$630$	−0.324869	−0.0129431
$631$	−16.3879	−0.652391	−0.326195	−	0.945302i	$-0.605767\pi$
$631$	−16.3879	−0.652391	−0.326195	+	0.945302i	$0.605767\pi$
$632$	78.4504	3.12059
$633$	0.324869	0.0129124
$634$	−42.2130	−1.67649
$635$	−0.932071	−0.0369881
$636$	−21.9756	−0.871388
$637$	0	0
$638$	−103.545	−4.09937
$639$	1.50422	0.0595059
$640$	12.1016	0.478357
$641$	−8.23884	−0.325415	−0.162707	−	0.986674i	$-0.552023\pi$
$641$	−8.23884	−0.325415	−0.162707	+	0.986674i	$0.552023\pi$
$642$	30.1114	1.18840
$643$	−30.4847	−1.20220	−0.601100	−	0.799174i	$-0.705271\pi$
$643$	−30.4847	−1.20220	−0.601100	+	0.799174i	$0.705271\pi$
$644$	19.8192	0.780987
$645$	−5.21600	−0.205380
$646$	42.5705	1.67492
$647$	28.8388	1.13377	0.566884	−	0.823798i	$-0.308149\pi$
$647$	28.8388	1.13377	0.566884	+	0.823798i	$0.308149\pi$
$648$	−44.8383	−1.76141
$649$	−11.4010	−0.447530
$650$	0	0
$651$	2.74306	0.107509
$652$	71.8007	2.81193
$653$	21.4518	0.839475	0.419738	−	0.907646i	$-0.362122\pi$
$653$	21.4518	0.839475	0.419738	+	0.907646i	$0.362122\pi$
$654$	−19.9248	−0.779120
$655$	−8.43866	−0.329726
$656$	39.3258	1.53542
$657$	2.93700	0.114583
$658$	−19.5247	−0.761151
$659$	−50.6589	−1.97339	−0.986696	−	0.162575i	$-0.948020\pi$
$659$	−50.6589	−1.97339	−0.986696	+	0.162575i	$0.948020\pi$
$660$	−21.0640	−0.819913
$661$	−15.5477	−0.604736	−0.302368	−	0.953191i	$-0.597777\pi$
$661$	−15.5477	−0.604736	−0.302368	+	0.953191i	$0.597777\pi$
$662$	26.8872	1.04500
$663$	0	0
$664$	7.76257	0.301246
$665$	3.52373	0.136644
$666$	0.694644	0.0269169
$667$	44.4069	1.71944
$668$	67.7196	2.62015
$669$	−9.78067	−0.378143
$670$	12.3127	0.475679
$671$	−10.3634	−0.400076
$672$	−2.70052	−0.104175
$673$	−26.8700	−1.03576	−0.517882	−	0.855452i	$-0.673279\pi$
$673$	−26.8700	−1.03576	−0.517882	+	0.855452i	$0.673279\pi$
$674$	7.36836	0.283819
$675$	24.3127	0.935794
$676$	0	0
$677$	16.3757	0.629368	0.314684	−	0.949197i	$-0.398102\pi$
$677$	16.3757	0.629368	0.314684	+	0.949197i	$0.398102\pi$
$678$	−38.8324	−1.49135
$679$	−17.9805	−0.690028
$680$	−11.8740	−0.455347
$681$	6.17679	0.236695
$682$	−18.2071	−0.697186
$683$	−15.7988	−0.604523	−0.302262	−	0.953225i	$-0.597742\pi$
$683$	−15.7988	−0.604523	−0.302262	+	0.953225i	$0.597742\pi$
$684$	−4.20711	−0.160863
$685$	−2.16457	−0.0827041
$686$	−2.48119	−0.0947324
$687$	−9.47627	−0.361542
$688$	22.8872	0.872565
$689$	0	0
$690$	13.3806	0.509390
$691$	7.56818	0.287907	0.143953	−	0.989584i	$-0.454018\pi$
$691$	7.56818	0.287907	0.143953	+	0.989584i	$0.454018\pi$
$692$	−9.03761	−0.343558
$693$	0.869067	0.0330131
$694$	76.2638	2.89493
$695$	0.168544	0.00639324
$696$	−83.4636	−3.16368
$697$	26.0508	0.986744
$698$	4.97461	0.188292
$699$	17.2971	0.654237
$700$	18.8872	0.713868
$701$	32.6629	1.23366	0.616831	−	0.787096i	$-0.288416\pi$
$701$	32.6629	1.23366	0.616831	+	0.787096i	$0.288416\pi$
$702$	0	0
$703$	−7.53453	−0.284170
$704$	−26.5501	−1.00064
$705$	−8.89938	−0.335170
$706$	42.8119	1.61125
$707$	9.33804	0.351193
$708$	−17.7137	−0.665722
$709$	25.0214	0.939699	0.469850	−	0.882746i	$-0.344308\pi$
$709$	25.0214	0.939699	0.469850	+	0.882746i	$0.344308\pi$
$710$	12.9927	0.487608
$711$	−2.84367	−0.106646
$712$	−41.6991	−1.56274
$713$	7.80843	0.292428
$714$	−13.6629	−0.511322
$715$	0	0
$716$	2.29218	0.0856629
$717$	37.3357	1.39433
$718$	−17.6326	−0.658043
$719$	−1.85192	−0.0690651	−0.0345326	−	0.999404i	$-0.510994\pi$
$719$	−1.85192	−0.0690651	−0.0345326	+	0.999404i	$0.510994\pi$
$720$	0.649738	0.0242143
$721$	6.23743	0.232294
$722$	20.4485	0.761015
$723$	49.2931	1.83323
$724$	−2.12601	−0.0790125
$725$	42.3185	1.57167
$726$	37.7440	1.40081
$727$	10.8265	0.401534	0.200767	−	0.979639i	$-0.435657\pi$
$727$	10.8265	0.401534	0.200767	+	0.979639i	$0.435657\pi$
$728$	0	0
$729$	28.5125	1.05602
$730$	25.3684	0.938925
$731$	15.1612	0.560759
$732$	−16.1016	−0.595131
$733$	−23.4264	−0.865275	−0.432638	−	0.901568i	$-0.642417\pi$
$733$	−23.4264	−0.865275	−0.432638	+	0.901568i	$0.642417\pi$
$734$	−67.6444	−2.49680
$735$	−1.13093	−0.0417151
$736$	−7.68735	−0.283359
$737$	−32.9380	−1.21329
$738$	−3.81336	−0.140372
$739$	0.481194	0.0177010	0.00885051	−	0.999961i	$-0.497183\pi$
$739$	0.481194	0.0177010	0.00885051	+	0.999961i	$0.497183\pi$
$740$	4.05079	0.148910
$741$	0	0
$742$	7.83146	0.287502
$743$	13.7889	0.505866	0.252933	−	0.967484i	$-0.418605\pi$
$743$	13.7889	0.505866	0.252933	+	0.967484i	$0.418605\pi$
$744$	−14.6761	−0.538051
$745$	−2.72259	−0.0997480
$746$	−14.6859	−0.537690
$747$	−0.281378	−0.0102951
$748$	61.2262	2.23865
$749$	−7.24472	−0.264716
$750$	26.7816	0.977927
$751$	−26.4617	−0.965600	−0.482800	−	0.875731i	$-0.660380\pi$
$751$	−26.4617	−0.965600	−0.482800	+	0.875731i	$0.660380\pi$
$752$	39.0494	1.42398
$753$	36.0567	1.31398
$754$	0	0
$755$	−1.05968	−0.0385657
$756$	22.2374	0.808767
$757$	−21.1114	−0.767308	−0.383654	−	0.923477i	$-0.625334\pi$
$757$	−21.1114	−0.767308	−0.383654	+	0.923477i	$0.625334\pi$
$758$	−71.8818	−2.61086
$759$	−35.7948	−1.29927
$760$	−18.8529	−0.683866
$761$	−28.5247	−1.03402	−0.517010	−	0.855980i	$-0.672955\pi$
$761$	−28.5247	−1.03402	−0.517010	+	0.855980i	$0.672955\pi$
$762$	5.73813	0.207871
$763$	4.79384	0.173549
$764$	−68.7631	−2.48776
$765$	0.430409	0.0155615
$766$	57.6239	2.08204
$767$	0	0
$768$	−54.6516	−1.97207
$769$	25.8388	0.931769	0.465885	−	0.884845i	$-0.345736\pi$
$769$	25.8388	0.931769	0.465885	+	0.884845i	$0.345736\pi$
$770$	7.50659	0.270519
$771$	−1.10886	−0.0399348
$772$	30.8021	1.10859
$773$	27.4010	0.985547	0.492774	−	0.870158i	$-0.335983\pi$
$773$	27.4010	0.985547	0.492774	+	0.870158i	$0.335983\pi$
$774$	−2.21933	−0.0797721
$775$	7.44121	0.267296
$776$	96.2003	3.45339
$777$	2.41819	0.0867521
$778$	40.0263	1.43501
$779$	41.3620	1.48195
$780$	0	0
$781$	−34.7572	−1.24371
$782$	−38.8930	−1.39081
$783$	49.8251	1.78060
$784$	4.96239	0.177228
$785$	−1.95746	−0.0698649
$786$	51.9511	1.85304
$787$	31.0240	1.10589	0.552943	−	0.833219i	$-0.313505\pi$
$787$	31.0240	1.10589	0.552943	+	0.833219i	$0.313505\pi$
$788$	−29.7137	−1.05851
$789$	8.68830	0.309312
$790$	−24.5623	−0.873887
$791$	9.34297	0.332198
$792$	−4.64974	−0.165221
$793$	0	0
$794$	59.6869	2.11821
$795$	3.56959	0.126600
$796$	−21.1998	−0.751408
$797$	16.1378	0.571629	0.285815	−	0.958285i	$-0.407736\pi$
$797$	16.1378	0.571629	0.285815	+	0.958285i	$0.407736\pi$
$798$	−21.6932	−0.767932
$799$	25.8677	0.915132
$800$	−7.32582	−0.259007
$801$	1.51151	0.0534066
$802$	6.88717	0.243194
$803$	−67.8637	−2.39486
$804$	−51.1754	−1.80482
$805$	−3.21933	−0.113466
$806$	0	0
$807$	45.6483	1.60690
$808$	−49.9610	−1.75762
$809$	−10.3503	−0.363896	−0.181948	−	0.983308i	$-0.558240\pi$
$809$	−10.3503	−0.363896	−0.181948	+	0.983308i	$0.558240\pi$
$810$	14.0386	0.493265
$811$	46.3752	1.62845	0.814227	−	0.580547i	$-0.197161\pi$
$811$	46.3752	1.62845	0.814227	+	0.580547i	$0.197161\pi$
$812$	38.7064	1.35833
$813$	−31.4274	−1.10221
$814$	−16.0508	−0.562580
$815$	−11.6629	−0.408534
$816$	27.3258	0.956595
$817$	24.0722	0.842180
$818$	−49.9488	−1.74642
$819$	0	0
$820$	−22.2374	−0.776565
$821$	55.5388	1.93832	0.969159	−	0.246436i	$-0.0792596\pi$
$821$	55.5388	1.93832	0.969159	+	0.246436i	$0.0792596\pi$
$822$	13.3258	0.464791
$823$	−20.8324	−0.726172	−0.363086	−	0.931756i	$-0.618277\pi$
$823$	−20.8324	−0.726172	−0.363086	+	0.931756i	$0.618277\pi$
$824$	−33.3719	−1.16256
$825$	−34.1114	−1.18761
$826$	6.31265	0.219645
$827$	2.47295	0.0859927	0.0429964	−	0.999075i	$-0.486310\pi$
$827$	2.47295	0.0859927	0.0429964	+	0.999075i	$0.486310\pi$
$828$	3.84367	0.133577
$829$	−34.5623	−1.20040	−0.600199	−	0.799851i	$-0.704912\pi$
$829$	−34.5623	−1.20040	−0.600199	+	0.799851i	$0.704912\pi$
$830$	−2.43041	−0.0843607
$831$	25.8373	0.896287
$832$	0	0
$833$	3.28726	0.113897
$834$	−1.03761	−0.0359295
$835$	−11.0000	−0.380671
$836$	97.2116	3.36213
$837$	8.76116	0.302830
$838$	−0.956509	−0.0330421
$839$	−39.9149	−1.37802	−0.689008	−	0.724754i	$-0.741954\pi$
$839$	−39.9149	−1.37802	−0.689008	+	0.724754i	$0.741954\pi$
$840$	6.05079	0.208772
$841$	57.7255	1.99053
$842$	38.9076	1.34085
$843$	−41.6180	−1.43340
$844$	0.806063	0.0277458
$845$	0	0
$846$	−3.78655	−0.130184
$847$	−9.08110	−0.312030
$848$	−15.6629	−0.537867
$849$	38.3390	1.31579
$850$	−37.0640	−1.27128
$851$	6.88366	0.235969
$852$	−54.0019	−1.85007
$853$	−32.6507	−1.11794	−0.558969	−	0.829188i	$-0.688803\pi$
$853$	−32.6507	−1.11794	−0.558969	+	0.829188i	$0.688803\pi$
$854$	5.73813	0.196355
$855$	0.683380	0.0233711
$856$	38.7612	1.32483
$857$	−7.63656	−0.260860	−0.130430	−	0.991458i	$-0.541636\pi$
$857$	−7.63656	−0.260860	−0.130430	+	0.991458i	$0.541636\pi$
$858$	0	0
$859$	−8.96239	−0.305793	−0.152896	−	0.988242i	$-0.548860\pi$
$859$	−8.96239	−0.305793	−0.152896	+	0.988242i	$0.548860\pi$
$860$	−12.9419	−0.441316
$861$	−13.2750	−0.452412
$862$	3.81336	0.129883
$863$	−46.8021	−1.59316	−0.796581	−	0.604532i	$-0.793360\pi$
$863$	−46.8021	−1.59316	−0.796581	+	0.604532i	$0.793360\pi$
$864$	−8.62530	−0.293439
$865$	1.46802	0.0499142
$866$	−64.6009	−2.19523
$867$	−10.3757	−0.352376
$868$	6.80606	0.231013
$869$	65.7074	2.22897
$870$	26.1319	0.885954
$871$	0	0
$872$	−25.6483	−0.868562
$873$	−3.48707	−0.118020
$874$	−61.7523	−2.08880
$875$	−6.44358	−0.217833
$876$	−105.439	−3.56246
$877$	10.3406	0.349177	0.174589	−	0.984641i	$-0.444140\pi$
$877$	10.3406	0.349177	0.174589	+	0.984641i	$0.444140\pi$
$878$	47.4518	1.60142
$879$	42.2457	1.42491
$880$	−15.0132	−0.506094
$881$	15.1538	0.510543	0.255272	−	0.966869i	$-0.417835\pi$
$881$	15.1538	0.510543	0.255272	+	0.966869i	$0.417835\pi$
$882$	−0.481194	−0.0162027
$883$	−51.5983	−1.73642	−0.868211	−	0.496196i	$-0.834730\pi$
$883$	−51.5983	−1.73642	−0.868211	+	0.496196i	$0.834730\pi$
$884$	0	0
$885$	2.87732	0.0967199
$886$	−31.3077	−1.05180
$887$	4.18664	0.140574	0.0702868	−	0.997527i	$-0.477609\pi$
$887$	4.18664	0.140574	0.0702868	+	0.997527i	$0.477609\pi$
$888$	−12.9380	−0.434169
$889$	−1.38058	−0.0463031
$890$	13.0557	0.437628
$891$	−37.5550	−1.25814
$892$	−24.2677	−0.812544
$893$	41.0713	1.37440
$894$	16.7612	0.560577
$895$	−0.372330	−0.0124456
$896$	17.9248	0.598825
$897$	0	0
$898$	−2.53832	−0.0847048
$899$	15.2496	0.508604
$900$	3.66291	0.122097
$901$	−10.3757	−0.345663
$902$	88.1133	2.93385
$903$	−7.72592	−0.257102
$904$	−49.9873	−1.66255
$905$	0.345337	0.0114794
$906$	6.52373	0.216736
$907$	−9.60483	−0.318923	−0.159462	−	0.987204i	$-0.550976\pi$
$907$	−9.60483	−0.318923	−0.159462	+	0.987204i	$0.550976\pi$
$908$	15.3258	0.508605
$909$	1.81099	0.0600667
$910$	0	0
$911$	−1.82653	−0.0605157	−0.0302578	−	0.999542i	$-0.509633\pi$
$911$	−1.82653	−0.0605157	−0.0302578	+	0.999542i	$0.509633\pi$
$912$	43.3865	1.43667
$913$	6.50166	0.215174
$914$	70.7934	2.34164
$915$	2.61545	0.0864642
$916$	−23.5125	−0.776874
$917$	−12.4993	−0.412763
$918$	−43.6385	−1.44028
$919$	15.7842	0.520672	0.260336	−	0.965518i	$-0.416167\pi$
$919$	15.7842	0.520672	0.260336	+	0.965518i	$0.416167\pi$
$920$	17.2243	0.567867
$921$	12.1441	0.400162
$922$	62.8989	2.07147
$923$	0	0
$924$	−31.1998	−1.02640
$925$	6.55993	0.215689
$926$	98.4563	3.23547
$927$	1.20967	0.0397306
$928$	−15.0132	−0.492832
$929$	−16.8011	−0.551227	−0.275614	−	0.961268i	$-0.588881\pi$
$929$	−16.8011	−0.551227	−0.275614	+	0.961268i	$0.588881\pi$
$930$	4.59498	0.150675
$931$	5.21933	0.171057
$932$	42.9175	1.40581
$933$	−33.9043	−1.10998
$934$	4.84226	0.158444
$935$	−9.94525	−0.325244
$936$	0	0
$937$	−38.3004	−1.25122	−0.625610	−	0.780136i	$-0.715150\pi$
$937$	−38.3004	−1.25122	−0.625610	+	0.780136i	$0.715150\pi$
$938$	18.2374	0.595473
$939$	−55.5085	−1.81145
$940$	−22.0811	−0.720206
$941$	−45.2496	−1.47510	−0.737548	−	0.675295i	$-0.764017\pi$
$941$	−45.2496	−1.47510	−0.737548	+	0.675295i	$0.764017\pi$
$942$	12.0508	0.392636
$943$	−37.7889	−1.23058
$944$	−12.6253	−0.410919
$945$	−3.61213	−0.117502
$946$	51.2809	1.66729
$947$	4.73672	0.153923	0.0769614	−	0.997034i	$-0.475478\pi$
$947$	4.73672	0.153923	0.0769614	+	0.997034i	$0.475478\pi$
$948$	102.089	3.31569
$949$	0	0
$950$	−58.8481	−1.90929
$951$	−28.4993	−0.924153
$952$	−17.5877	−0.570020
$953$	44.8007	1.45124	0.725618	−	0.688098i	$-0.241554\pi$
$953$	44.8007	1.45124	0.725618	+	0.688098i	$0.241554\pi$
$954$	1.51881	0.0491732
$955$	11.1695	0.361436
$956$	92.6371	2.99610
$957$	−69.9062	−2.25975
$958$	−64.8505	−2.09522
$959$	−3.20616	−0.103532
$960$	6.70052	0.216258
$961$	−28.3185	−0.913501
$962$	0	0
$963$	−1.40502	−0.0452760
$964$	122.306	3.93921
$965$	−5.00332	−0.161063
$966$	19.8192	0.637674
$967$	−40.6843	−1.30832	−0.654160	−	0.756356i	$-0.726978\pi$
$967$	−40.6843	−1.30832	−0.654160	+	0.756356i	$0.726978\pi$
$968$	48.5863	1.56162
$969$	28.7407	0.923284
$970$	−30.1197	−0.967084
$971$	−41.4109	−1.32894	−0.664469	−	0.747315i	$-0.731342\pi$
$971$	−41.4109	−1.32894	−0.664469	+	0.747315i	$0.731342\pi$
$972$	8.36344	0.268257
$973$	0.249646	0.00800329
$974$	−52.0118	−1.66656
$975$	0	0
$976$	−11.4763	−0.367346
$977$	50.6072	1.61907	0.809534	−	0.587073i	$-0.199720\pi$
$977$	50.6072	1.61907	0.809534	+	0.587073i	$0.199720\pi$
$978$	71.8007	2.29593
$979$	−34.9257	−1.11623
$980$	−2.80606	−0.0896364
$981$	0.929702	0.0296831
$982$	−7.33567	−0.234091
$983$	24.5452	0.782869	0.391434	−	0.920206i	$-0.371979\pi$
$983$	24.5452	0.782869	0.391434	+	0.920206i	$0.371979\pi$
$984$	71.0249	2.26419
$985$	4.82653	0.153786
$986$	−75.9570	−2.41896
$987$	−13.1817	−0.419579
$988$	0	0
$989$	−21.9927	−0.699327
$990$	1.45580	0.0462684
$991$	−31.6542	−1.00553	−0.502764	−	0.864423i	$-0.667684\pi$
$991$	−31.6542	−1.00553	−0.502764	+	0.864423i	$0.667684\pi$
$992$	−2.63989	−0.0838166
$993$	18.1524	0.576048
$994$	19.2447	0.610406
$995$	3.44358	0.109169
$996$	10.1016	0.320081
$997$	−29.1852	−0.924305	−0.462153	−	0.886800i	$-0.652923\pi$
$997$	−29.1852	−0.924305	−0.462153	+	0.886800i	$0.652923\pi$
$998$	−7.08252	−0.224193
$999$	7.72355	0.244362

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.j.1.3		3
7.6	odd	2		8281.2.a.bi.1.3		3
13.5	odd	4		91.2.c.a.64.1	✓	6
13.8	odd	4		91.2.c.a.64.6	yes	6
13.12	even	2		1183.2.a.h.1.1		3
39.5	even	4		819.2.c.b.64.6		6
39.8	even	4		819.2.c.b.64.1		6
52.31	even	4		1456.2.k.c.337.2		6
52.47	even	4		1456.2.k.c.337.1		6
91.5	even	12		637.2.r.d.116.1		12
91.18	odd	12		637.2.r.e.324.6		12
91.31	even	12		637.2.r.d.324.6		12
91.34	even	4		637.2.c.d.246.6		6
91.44	odd	12		637.2.r.e.116.1		12
91.47	even	12		637.2.r.d.116.6		12
91.60	odd	12		637.2.r.e.324.1		12
91.73	even	12		637.2.r.d.324.1		12
91.83	even	4		637.2.c.d.246.1		6
91.86	odd	12		637.2.r.e.116.6		12
91.90	odd	2		8281.2.a.be.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.c.a.64.1	✓	6	13.5	odd	4
91.2.c.a.64.6	yes	6	13.8	odd	4
637.2.c.d.246.1		6	91.83	even	4
637.2.c.d.246.6		6	91.34	even	4
637.2.r.d.116.1		12	91.5	even	12
637.2.r.d.116.6		12	91.47	even	12
637.2.r.d.324.1		12	91.73	even	12
637.2.r.d.324.6		12	91.31	even	12
637.2.r.e.116.1		12	91.44	odd	12
637.2.r.e.116.6		12	91.86	odd	12
637.2.r.e.324.1		12	91.60	odd	12
637.2.r.e.324.6		12	91.18	odd	12
819.2.c.b.64.1		6	39.8	even	4
819.2.c.b.64.6		6	39.5	even	4
1183.2.a.h.1.1		3	13.12	even	2
1183.2.a.j.1.3		3	1.1	even	1	trivial
1456.2.k.c.337.1		6	52.47	even	4
1456.2.k.c.337.2		6	52.31	even	4
8281.2.a.be.1.1		3	91.90	odd	2
8281.2.a.bi.1.3		3	7.6	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)

\(f(q)\)	\(=\)	\(q+2.48119 q^{2} +1.67513 q^{3} +4.15633 q^{4} -0.675131 q^{5} +4.15633 q^{6} -1.00000 q^{7} +5.35026 q^{8} -0.193937 q^{9} +O(q^{10})\)	\(q+2.48119 q^{2} +1.67513 q^{3} +4.15633 q^{4} -0.675131 q^{5} +4.15633 q^{6} -1.00000 q^{7} +5.35026 q^{8} -0.193937 q^{9} -1.67513 q^{10} +4.48119 q^{11} +6.96239 q^{12} -2.48119 q^{14} -1.13093 q^{15} +4.96239 q^{16} +3.28726 q^{17} -0.481194 q^{18} +5.21933 q^{19} -2.80606 q^{20} -1.67513 q^{21} +11.1187 q^{22} -4.76845 q^{23} +8.96239 q^{24} -4.54420 q^{25} -5.35026 q^{27} -4.15633 q^{28} -9.31265 q^{29} -2.80606 q^{30} -1.63752 q^{31} +1.61213 q^{32} +7.50659 q^{33} +8.15633 q^{34} +0.675131 q^{35} -0.806063 q^{36} -1.44358 q^{37} +12.9502 q^{38} -3.61213 q^{40} +7.92478 q^{41} -4.15633 q^{42} +4.61213 q^{43} +18.6253 q^{44} +0.130933 q^{45} -11.8315 q^{46} +7.86907 q^{47} +8.31265 q^{48} +1.00000 q^{49} -11.2750 q^{50} +5.50659 q^{51} -3.15633 q^{53} -13.2750 q^{54} -3.02539 q^{55} -5.35026 q^{56} +8.74306 q^{57} -23.1065 q^{58} -2.54420 q^{59} -4.70052 q^{60} -2.31265 q^{61} -4.06300 q^{62} +0.193937 q^{63} -5.92478 q^{64} +18.6253 q^{66} -7.35026 q^{67} +13.6629 q^{68} -7.98778 q^{69} +1.67513 q^{70} -7.75623 q^{71} -1.03761 q^{72} -15.1441 q^{73} -3.58181 q^{74} -7.61213 q^{75} +21.6932 q^{76} -4.48119 q^{77} +14.6629 q^{79} -3.35026 q^{80} -8.38058 q^{81} +19.6629 q^{82} +1.45088 q^{83} -6.96239 q^{84} -2.21933 q^{85} +11.4436 q^{86} -15.5999 q^{87} +23.9756 q^{88} -7.79384 q^{89} +0.324869 q^{90} -19.8192 q^{92} -2.74306 q^{93} +19.5247 q^{94} -3.52373 q^{95} +2.70052 q^{96} +17.9805 q^{97} +2.48119 q^{98} -0.869067 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} + 2 q^{4} + 3 q^{5} + 2 q^{6} - 3 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 + 2 * q^4 + 3 * q^5 + 2 * q^6 - 3 * q^7 + 6 * q^8 - q^9	\( 3 q + 2 q^{2} + 2 q^{4} + 3 q^{5} + 2 q^{6} - 3 q^{7} + 6 q^{8} - q^{9} + 8 q^{11} + 10 q^{12} - 2 q^{14} - 8 q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} + q^{19} - 8 q^{20} + 12 q^{22} - 3 q^{23} + 16 q^{24} - 4 q^{25} - 6 q^{27} - 2 q^{28} - 7 q^{29} - 8 q^{30} + 11 q^{31} + 4 q^{32} + 2 q^{33} + 14 q^{34} - 3 q^{35} - 2 q^{36} + 12 q^{37} + 2 q^{38} - 10 q^{40} + 2 q^{41} - 2 q^{42} + 13 q^{43} + 14 q^{44} + 5 q^{45} - 20 q^{46} + 19 q^{47} + 4 q^{48} + 3 q^{49} - 2 q^{50} - 4 q^{51} + q^{53} - 8 q^{54} + 6 q^{55} - 6 q^{56} + 30 q^{57} - 22 q^{58} + 2 q^{59} + 6 q^{60} + 14 q^{61} - 8 q^{62} + q^{63} + 4 q^{64} + 14 q^{66} - 12 q^{67} + 10 q^{68} + 2 q^{69} + 14 q^{71} - 14 q^{72} - 9 q^{73} - 12 q^{74} - 22 q^{75} + 32 q^{76} - 8 q^{77} + 13 q^{79} - 13 q^{81} + 28 q^{82} + q^{83} - 10 q^{84} + 8 q^{85} + 18 q^{86} - 20 q^{87} + 20 q^{88} + 3 q^{89} + 6 q^{90} - 18 q^{92} - 12 q^{93} + 10 q^{94} - 29 q^{95} - 12 q^{96} + 15 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 + 2 * q^4 + 3 * q^5 + 2 * q^6 - 3 * q^7 + 6 * q^8 - q^9 + 8 * q^11 + 10 * q^12 - 2 * q^14 - 8 * q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 + q^19 - 8 * q^20 + 12 * q^22 - 3 * q^23 + 16 * q^24 - 4 * q^25 - 6 * q^27 - 2 * q^28 - 7 * q^29 - 8 * q^30 + 11 * q^31 + 4 * q^32 + 2 * q^33 + 14 * q^34 - 3 * q^35 - 2 * q^36 + 12 * q^37 + 2 * q^38 - 10 * q^40 + 2 * q^41 - 2 * q^42 + 13 * q^43 + 14 * q^44 + 5 * q^45 - 20 * q^46 + 19 * q^47 + 4 * q^48 + 3 * q^49 - 2 * q^50 - 4 * q^51 + q^53 - 8 * q^54 + 6 * q^55 - 6 * q^56 + 30 * q^57 - 22 * q^58 + 2 * q^59 + 6 * q^60 + 14 * q^61 - 8 * q^62 + q^63 + 4 * q^64 + 14 * q^66 - 12 * q^67 + 10 * q^68 + 2 * q^69 + 14 * q^71 - 14 * q^72 - 9 * q^73 - 12 * q^74 - 22 * q^75 + 32 * q^76 - 8 * q^77 + 13 * q^79 - 13 * q^81 + 28 * q^82 + q^83 - 10 * q^84 + 8 * q^85 + 18 * q^86 - 20 * q^87 + 20 * q^88 + 3 * q^89 + 6 * q^90 - 18 * q^92 - 12 * q^93 + 10 * q^94 - 29 * q^95 - 12 * q^96 + 15 * q^97 + 2 * q^98 + 2 * q^99

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