LMFDB - Embedded newform 2366.2.a.x.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2366,2,Mod(1,2366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, 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("2366.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2366.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:	$18.8926051182$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.1384.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 10x + 14 $ x^3 - x^2 - 10*x + 14
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.78567$ of defining polynomial
Character	$\chi$	$=$	2366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.78567 q^{3} +1.00000 q^{4} +2.54561 q^{5} -2.78567 q^{6} -1.00000 q^{7} -1.00000 q^{8} +4.75994 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.78567 q^{3} +1.00000 q^{4} +2.54561 q^{5} -2.78567 q^{6} -1.00000 q^{7} -1.00000 q^{8} +4.75994 q^{9} -2.54561 q^{10} +3.33127 q^{11} +2.78567 q^{12} +1.00000 q^{14} +7.09122 q^{15} +1.00000 q^{16} +7.09122 q^{17} -4.75994 q^{18} -4.54561 q^{19} +2.54561 q^{20} -2.78567 q^{21} -3.33127 q^{22} +1.75994 q^{23} -2.78567 q^{24} +1.48012 q^{25} +4.90261 q^{27} -1.00000 q^{28} +7.57133 q^{29} -7.09122 q^{30} -3.33127 q^{31} -1.00000 q^{32} +9.27982 q^{33} -7.09122 q^{34} -2.54561 q^{35} +4.75994 q^{36} -3.75994 q^{37} +4.54561 q^{38} -2.54561 q^{40} +4.24006 q^{41} +2.78567 q^{42} -9.09122 q^{43} +3.33127 q^{44} +12.1169 q^{45} -1.75994 q^{46} -11.3313 q^{47} +2.78567 q^{48} +1.00000 q^{49} -1.48012 q^{50} +19.7538 q^{51} -6.00000 q^{53} -4.90261 q^{54} +8.48012 q^{55} +1.00000 q^{56} -12.6625 q^{57} -7.57133 q^{58} -8.06549 q^{59} +7.09122 q^{60} -0.785667 q^{61} +3.33127 q^{62} -4.75994 q^{63} +1.00000 q^{64} -9.27982 q^{66} -5.75994 q^{67} +7.09122 q^{68} +4.90261 q^{69} +2.54561 q^{70} +11.1427 q^{71} -4.75994 q^{72} +9.33127 q^{73} +3.75994 q^{74} +4.12312 q^{75} -4.54561 q^{76} -3.33127 q^{77} +4.85116 q^{79} +2.54561 q^{80} -0.622787 q^{81} -4.24006 q^{82} +11.2082 q^{83} -2.78567 q^{84} +18.0515 q^{85} +9.09122 q^{86} +21.0912 q^{87} -3.33127 q^{88} +15.0912 q^{89} -12.1169 q^{90} +1.75994 q^{92} -9.27982 q^{93} +11.3313 q^{94} -11.5713 q^{95} -2.78567 q^{96} +7.75994 q^{97} -1.00000 q^{98} +15.8567 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + q^{3} + 3 q^{4} - 2 q^{5} - q^{6} - 3 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + q^3 + 3 * q^4 - 2 * q^5 - q^6 - 3 * q^7 - 3 * q^8 + 12 * q^9	$ 3 q - 3 q^{2} + q^{3} + 3 q^{4} - 2 q^{5} - q^{6} - 3 q^{7} - 3 q^{8} + 12 q^{9} + 2 q^{10} - 7 q^{11} + q^{12} + 3 q^{14} + 2 q^{15} + 3 q^{16} + 2 q^{17} - 12 q^{18} - 4 q^{19} - 2 q^{20} - q^{21} + 7 q^{22} + 3 q^{23} - q^{24} + 9 q^{25} - 17 q^{27} - 3 q^{28} + 8 q^{29} - 2 q^{30} + 7 q^{31} - 3 q^{32} + 21 q^{33} - 2 q^{34} + 2 q^{35} + 12 q^{36} - 9 q^{37} + 4 q^{38} + 2 q^{40} + 15 q^{41} + q^{42} - 8 q^{43} - 7 q^{44} + 12 q^{45} - 3 q^{46} - 17 q^{47} + q^{48} + 3 q^{49} - 9 q^{50} + 6 q^{51} - 18 q^{53} + 17 q^{54} + 30 q^{55} + 3 q^{56} - 4 q^{57} - 8 q^{58} - 10 q^{59} + 2 q^{60} + 5 q^{61} - 7 q^{62} - 12 q^{63} + 3 q^{64} - 21 q^{66} - 15 q^{67} + 2 q^{68} - 17 q^{69} - 2 q^{70} + 4 q^{71} - 12 q^{72} + 11 q^{73} + 9 q^{74} + 39 q^{75} - 4 q^{76} + 7 q^{77} - 7 q^{79} - 2 q^{80} + 23 q^{81} - 15 q^{82} - 10 q^{83} - q^{84} + 44 q^{85} + 8 q^{86} + 44 q^{87} + 7 q^{88} + 26 q^{89} - 12 q^{90} + 3 q^{92} - 21 q^{93} + 17 q^{94} - 20 q^{95} - q^{96} + 21 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + q^3 + 3 * q^4 - 2 * q^5 - q^6 - 3 * q^7 - 3 * q^8 + 12 * q^9 + 2 * q^10 - 7 * q^11 + q^12 + 3 * q^14 + 2 * q^15 + 3 * q^16 + 2 * q^17 - 12 * q^18 - 4 * q^19 - 2 * q^20 - q^21 + 7 * q^22 + 3 * q^23 - q^24 + 9 * q^25 - 17 * q^27 - 3 * q^28 + 8 * q^29 - 2 * q^30 + 7 * q^31 - 3 * q^32 + 21 * q^33 - 2 * q^34 + 2 * q^35 + 12 * q^36 - 9 * q^37 + 4 * q^38 + 2 * q^40 + 15 * q^41 + q^42 - 8 * q^43 - 7 * q^44 + 12 * q^45 - 3 * q^46 - 17 * q^47 + q^48 + 3 * q^49 - 9 * q^50 + 6 * q^51 - 18 * q^53 + 17 * q^54 + 30 * q^55 + 3 * q^56 - 4 * q^57 - 8 * q^58 - 10 * q^59 + 2 * q^60 + 5 * q^61 - 7 * q^62 - 12 * q^63 + 3 * q^64 - 21 * q^66 - 15 * q^67 + 2 * q^68 - 17 * q^69 - 2 * q^70 + 4 * q^71 - 12 * q^72 + 11 * q^73 + 9 * q^74 + 39 * q^75 - 4 * q^76 + 7 * q^77 - 7 * q^79 - 2 * q^80 + 23 * q^81 - 15 * q^82 - 10 * q^83 - q^84 + 44 * q^85 + 8 * q^86 + 44 * q^87 + 7 * q^88 + 26 * q^89 - 12 * q^90 + 3 * q^92 - 21 * q^93 + 17 * q^94 - 20 * q^95 - q^96 + 21 * q^97 - 3 * q^98 - 26 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.78567	1.60831	0.804153	−	0.594423i	$-0.202619\pi$
$3$	2.78567	1.60831	0.804153	+	0.594423i	$0.202619\pi$
$4$	1.00000	0.500000
$5$	2.54561	1.13843	0.569215	−	0.822189i	$-0.307247\pi$
$5$	2.54561	1.13843	0.569215	+	0.822189i	$0.307247\pi$
$6$	−2.78567	−1.13724
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	4.75994	1.58665
$10$	−2.54561	−0.804992
$11$	3.33127	1.00442	0.502209	−	0.864747i	$-0.332521\pi$
$11$	3.33127	1.00442	0.502209	+	0.864747i	$0.332521\pi$
$12$	2.78567	0.804153
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	7.09122	1.83094
$16$	1.00000	0.250000
$17$	7.09122	1.71987	0.859936	−	0.510402i	$-0.170503\pi$
$17$	7.09122	1.71987	0.859936	+	0.510402i	$0.170503\pi$
$18$	−4.75994	−1.12193
$19$	−4.54561	−1.04283	−0.521417	−	0.853302i	$-0.674596\pi$
$19$	−4.54561	−1.04283	−0.521417	+	0.853302i	$0.674596\pi$
$20$	2.54561	0.569215
$21$	−2.78567	−0.607882
$22$	−3.33127	−0.710230
$23$	1.75994	0.366973	0.183487	−	0.983022i	$-0.441262\pi$
$23$	1.75994	0.366973	0.183487	+	0.983022i	$0.441262\pi$
$24$	−2.78567	−0.568622
$25$	1.48012	0.296024
$26$	0	0
$27$	4.90261	0.943507
$28$	−1.00000	−0.188982
$29$	7.57133	1.40596	0.702981	−	0.711209i	$-0.251852\pi$
$29$	7.57133	1.40596	0.702981	+	0.711209i	$0.251852\pi$
$30$	−7.09122	−1.29467
$31$	−3.33127	−0.598315	−0.299157	−	0.954204i	$-0.596706\pi$
$31$	−3.33127	−0.598315	−0.299157	+	0.954204i	$0.596706\pi$
$32$	−1.00000	−0.176777
$33$	9.27982	1.61541
$34$	−7.09122	−1.21613
$35$	−2.54561	−0.430286
$36$	4.75994	0.793323
$37$	−3.75994	−0.618130	−0.309065	−	0.951041i	$-0.600016\pi$
$37$	−3.75994	−0.618130	−0.309065	+	0.951041i	$0.600016\pi$
$38$	4.54561	0.737395
$39$	0	0
$40$	−2.54561	−0.402496
$41$	4.24006	0.662186	0.331093	−	0.943598i	$-0.392583\pi$
$41$	4.24006	0.662186	0.331093	+	0.943598i	$0.392583\pi$
$42$	2.78567	0.429838
$43$	−9.09122	−1.38640	−0.693199	−	0.720747i	$-0.743799\pi$
$43$	−9.09122	−1.38640	−0.693199	+	0.720747i	$0.743799\pi$
$44$	3.33127	0.502209
$45$	12.1169	1.80629
$46$	−1.75994	−0.259489
$47$	−11.3313	−1.65284	−0.826418	−	0.563057i	$-0.809625\pi$
$47$	−11.3313	−1.65284	−0.826418	+	0.563057i	$0.809625\pi$
$48$	2.78567	0.402076
$49$	1.00000	0.142857
$50$	−1.48012	−0.209320
$51$	19.7538	2.76608
$52$	0	0
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	−4.90261	−0.667161
$55$	8.48012	1.14346
$56$	1.00000	0.133631
$57$	−12.6625	−1.67720
$58$	−7.57133	−0.994165
$59$	−8.06549	−1.05004	−0.525019	−	0.851091i	$-0.675942\pi$
$59$	−8.06549	−1.05004	−0.525019	+	0.851091i	$0.675942\pi$
$60$	7.09122	0.915472
$61$	−0.785667	−0.100594	−0.0502972	−	0.998734i	$-0.516017\pi$
$61$	−0.785667	−0.100594	−0.0502972	+	0.998734i	$0.516017\pi$
$62$	3.33127	0.423072
$63$	−4.75994	−0.599696
$64$	1.00000	0.125000
$65$	0	0
$66$	−9.27982	−1.14227
$67$	−5.75994	−0.703689	−0.351844	−	0.936059i	$-0.614445\pi$
$67$	−5.75994	−0.703689	−0.351844	+	0.936059i	$0.614445\pi$
$68$	7.09122	0.859936
$69$	4.90261	0.590205
$70$	2.54561	0.304258
$71$	11.1427	1.32239	0.661196	−	0.750213i	$-0.270049\pi$
$71$	11.1427	1.32239	0.661196	+	0.750213i	$0.270049\pi$
$72$	−4.75994	−0.560964
$73$	9.33127	1.09214	0.546072	−	0.837739i	$-0.316123\pi$
$73$	9.33127	1.09214	0.546072	+	0.837739i	$0.316123\pi$
$74$	3.75994	0.437084
$75$	4.12312	0.476097
$76$	−4.54561	−0.521417
$77$	−3.33127	−0.379634
$78$	0	0
$79$	4.85116	0.545798	0.272899	−	0.962043i	$-0.412018\pi$
$79$	4.85116	0.545798	0.272899	+	0.962043i	$0.412018\pi$
$80$	2.54561	0.284608
$81$	−0.622787	−0.0691985
$82$	−4.24006	−0.468236
$83$	11.2082	1.23026	0.615128	−	0.788428i	$-0.289105\pi$
$83$	11.2082	1.23026	0.615128	+	0.788428i	$0.289105\pi$
$84$	−2.78567	−0.303941
$85$	18.0515	1.95795
$86$	9.09122	0.980331
$87$	21.0912	2.26122
$88$	−3.33127	−0.355115
$89$	15.0912	1.59967	0.799833	−	0.600223i	$-0.204921\pi$
$89$	15.0912	1.59967	0.799833	+	0.600223i	$0.204921\pi$
$90$	−12.1169	−1.27724
$91$	0	0
$92$	1.75994	0.183487
$93$	−9.27982	−0.962273
$94$	11.3313	1.16873
$95$	−11.5713	−1.18719
$96$	−2.78567	−0.284311
$97$	7.75994	0.787903	0.393951	−	0.919131i	$-0.371108\pi$
$97$	7.75994	0.787903	0.393951	+	0.919131i	$0.371108\pi$
$98$	−1.00000	−0.101015
$99$	15.8567	1.59366
$100$	1.48012	0.148012
$101$	3.69445	0.367612	0.183806	−	0.982963i	$-0.441158\pi$
$101$	3.69445	0.367612	0.183806	+	0.982963i	$0.441158\pi$
$102$	−19.7538	−1.95591
$103$	−13.0912	−1.28992	−0.644958	−	0.764218i	$-0.723125\pi$
$103$	−13.0912	−1.28992	−0.644958	+	0.764218i	$0.723125\pi$
$104$	0	0
$105$	−7.09122	−0.692032
$106$	6.00000	0.582772
$107$	−3.51988	−0.340280	−0.170140	−	0.985420i	$-0.554422\pi$
$107$	−3.51988	−0.340280	−0.170140	+	0.985420i	$0.554422\pi$
$108$	4.90261	0.471754
$109$	−13.1427	−1.25884	−0.629420	−	0.777066i	$-0.716707\pi$
$109$	−13.1427	−1.25884	−0.629420	+	0.777066i	$0.716707\pi$
$110$	−8.48012	−0.808548
$111$	−10.4739	−0.994143
$112$	−1.00000	−0.0944911
$113$	−1.75994	−0.165561	−0.0827806	−	0.996568i	$-0.526380\pi$
$113$	−1.75994	−0.165561	−0.0827806	+	0.996568i	$0.526380\pi$
$114$	12.6625	1.18596
$115$	4.48012	0.417773
$116$	7.57133	0.702981
$117$	0	0
$118$	8.06549	0.742488
$119$	−7.09122	−0.650051
$120$	−7.09122	−0.647336
$121$	0.0973913	0.00885375
$122$	0.785667	0.0711309
$123$	11.8114	1.06500
$124$	−3.33127	−0.299157
$125$	−8.96024	−0.801428
$126$	4.75994	0.424049
$127$	12.9026	1.14492	0.572461	−	0.819932i	$-0.305989\pi$
$127$	12.9026	1.14492	0.572461	+	0.819932i	$0.305989\pi$
$128$	−1.00000	−0.0883883
$129$	−25.3251	−2.22975
$130$	0	0
$131$	−16.7795	−1.46603	−0.733015	−	0.680212i	$-0.761888\pi$
$131$	−16.7795	−1.46603	−0.733015	+	0.680212i	$0.761888\pi$
$132$	9.27982	0.807705
$133$	4.54561	0.394154
$134$	5.75994	0.497583
$135$	12.4801	1.07412
$136$	−7.09122	−0.608067
$137$	11.1427	0.951982	0.475991	−	0.879450i	$-0.342089\pi$
$137$	11.1427	0.951982	0.475991	+	0.879450i	$0.342089\pi$
$138$	−4.90261	−0.417338
$139$	4.54561	0.385553	0.192777	−	0.981243i	$-0.438251\pi$
$139$	4.54561	0.385553	0.192777	+	0.981243i	$0.438251\pi$
$140$	−2.54561	−0.215143
$141$	−31.5652	−2.65827
$142$	−11.1427	−0.935072
$143$	0	0
$144$	4.75994	0.396662
$145$	19.2736	1.60059
$146$	−9.33127	−0.772262
$147$	2.78567	0.229758
$148$	−3.75994	−0.309065
$149$	−5.81139	−0.476088	−0.238044	−	0.971254i	$-0.576506\pi$
$149$	−5.81139	−0.476088	−0.238044	+	0.971254i	$0.576506\pi$
$150$	−4.12312	−0.336651
$151$	−3.09122	−0.251560	−0.125780	−	0.992058i	$-0.540143\pi$
$151$	−3.09122	−0.251560	−0.125780	+	0.992058i	$0.540143\pi$
$152$	4.54561	0.368697
$153$	33.7538	2.72883
$154$	3.33127	0.268442
$155$	−8.48012	−0.681140
$156$	0	0
$157$	−7.92834	−0.632750	−0.316375	−	0.948634i	$-0.602466\pi$
$157$	−7.92834	−0.632750	−0.316375	+	0.948634i	$0.602466\pi$
$158$	−4.85116	−0.385937
$159$	−16.7140	−1.32551
$160$	−2.54561	−0.201248
$161$	−1.75994	−0.138703
$162$	0.622787	0.0489307
$163$	−10.0515	−0.787291	−0.393645	−	0.919262i	$-0.628786\pi$
$163$	−10.0515	−0.787291	−0.393645	+	0.919262i	$0.628786\pi$
$164$	4.24006	0.331093
$165$	23.6228	1.83903
$166$	−11.2082	−0.869922
$167$	24.2339	1.87527	0.937637	−	0.347616i	$-0.113009\pi$
$167$	24.2339	1.87527	0.937637	+	0.347616i	$0.113009\pi$
$168$	2.78567	0.214919
$169$	0	0
$170$	−18.0515	−1.38448
$171$	−21.6368	−1.65461
$172$	−9.09122	−0.693199
$173$	−20.5971	−1.56597	−0.782983	−	0.622043i	$-0.786303\pi$
$173$	−20.5971	−1.56597	−0.782983	+	0.622043i	$0.786303\pi$
$174$	−21.0912	−1.59892
$175$	−1.48012	−0.111886
$176$	3.33127	0.251104
$177$	−22.4678	−1.68878
$178$	−15.0912	−1.13113
$179$	−17.3251	−1.29494	−0.647469	−	0.762091i	$-0.724173\pi$
$179$	−17.3251	−1.29494	−0.647469	+	0.762091i	$0.724173\pi$
$180$	12.1169	0.903144
$181$	16.9166	1.25740	0.628702	−	0.777646i	$-0.283586\pi$
$181$	16.9166	1.25740	0.628702	+	0.777646i	$0.283586\pi$
$182$	0	0
$183$	−2.18861	−0.161786
$184$	−1.75994	−0.129745
$185$	−9.57133	−0.703698
$186$	9.27982	0.680430
$187$	23.6228	1.72747
$188$	−11.3313	−0.826418
$189$	−4.90261	−0.356612
$190$	11.5713	0.839473
$191$	4.42867	0.320447	0.160224	−	0.987081i	$-0.448779\pi$
$191$	4.42867	0.320447	0.160224	+	0.987081i	$0.448779\pi$
$192$	2.78567	0.201038
$193$	−2.48012	−0.178523	−0.0892614	−	0.996008i	$-0.528451\pi$
$193$	−2.48012	−0.178523	−0.0892614	+	0.996008i	$0.528451\pi$
$194$	−7.75994	−0.557131
$195$	0	0
$196$	1.00000	0.0714286
$197$	−8.85116	−0.630619	−0.315309	−	0.948989i	$-0.602108\pi$
$197$	−8.85116	−0.630619	−0.315309	+	0.948989i	$0.602108\pi$
$198$	−15.8567	−1.12688
$199$	−1.09122	−0.0773542	−0.0386771	−	0.999252i	$-0.512314\pi$
$199$	−1.09122	−0.0773542	−0.0386771	+	0.999252i	$0.512314\pi$
$200$	−1.48012	−0.104660
$201$	−16.0453	−1.13175
$202$	−3.69445	−0.259941
$203$	−7.57133	−0.531403
$204$	19.7538	1.38304
$205$	10.7935	0.753853
$206$	13.0912	0.912108
$207$	8.37721	0.582257
$208$	0	0
$209$	−15.1427	−1.04744
$210$	7.09122	0.489340
$211$	15.0398	1.03538	0.517690	−	0.855568i	$-0.326792\pi$
$211$	15.0398	1.03538	0.517690	+	0.855568i	$0.326792\pi$
$212$	−6.00000	−0.412082
$213$	31.0398	2.12681
$214$	3.51988	0.240614
$215$	−23.1427	−1.57832
$216$	−4.90261	−0.333580
$217$	3.33127	0.226142
$218$	13.1427	0.890134
$219$	25.9938	1.75650
$220$	8.48012	0.571729
$221$	0	0
$222$	10.4739	0.702965
$223$	−12.9026	−0.864023	−0.432011	−	0.901868i	$-0.642196\pi$
$223$	−12.9026	−0.864023	−0.432011	+	0.901868i	$0.642196\pi$
$224$	1.00000	0.0668153
$225$	7.04528	0.469685
$226$	1.75994	0.117070
$227$	9.02573	0.599058	0.299529	−	0.954087i	$-0.403170\pi$
$227$	9.02573	0.599058	0.299529	+	0.954087i	$0.403170\pi$
$228$	−12.6625	−0.838598
$229$	−14.1684	−0.936274	−0.468137	−	0.883656i	$-0.655075\pi$
$229$	−14.1684	−0.936274	−0.468137	+	0.883656i	$0.655075\pi$
$230$	−4.48012	−0.295410
$231$	−9.27982	−0.610567
$232$	−7.57133	−0.497082
$233$	7.38273	0.483659	0.241829	−	0.970319i	$-0.422253\pi$
$233$	7.38273	0.483659	0.241829	+	0.970319i	$0.422253\pi$
$234$	0	0
$235$	−28.8450	−1.88164
$236$	−8.06549	−0.525019
$237$	13.5137	0.877810
$238$	7.09122	0.459655
$239$	6.13098	0.396580	0.198290	−	0.980143i	$-0.436461\pi$
$239$	6.13098	0.396580	0.198290	+	0.980143i	$0.436461\pi$
$240$	7.09122	0.457736
$241$	27.3251	1.76016	0.880082	−	0.474821i	$-0.157487\pi$
$241$	27.3251	1.76016	0.880082	+	0.474821i	$0.157487\pi$
$242$	−0.0973913	−0.00626055
$243$	−16.4427	−1.05480
$244$	−0.785667	−0.0502972
$245$	2.54561	0.162633
$246$	−11.8114	−0.753067
$247$	0	0
$248$	3.33127	0.211536
$249$	31.2222	1.97863
$250$	8.96024	0.566695
$251$	−16.4880	−1.04071	−0.520356	−	0.853949i	$-0.674201\pi$
$251$	−16.4880	−1.04071	−0.520356	+	0.853949i	$0.674201\pi$
$252$	−4.75994	−0.299848
$253$	5.86285	0.368594
$254$	−12.9026	−0.809582
$255$	50.2853	3.14899
$256$	1.00000	0.0625000
$257$	1.14267	0.0712777	0.0356388	−	0.999365i	$-0.488653\pi$
$257$	1.14267	0.0712777	0.0356388	+	0.999365i	$0.488653\pi$
$258$	25.3251	1.57667
$259$	3.75994	0.233631
$260$	0	0
$261$	36.0391	2.23076
$262$	16.7795	1.03664
$263$	−10.6111	−0.654308	−0.327154	−	0.944971i	$-0.606090\pi$
$263$	−10.6111	−0.654308	−0.327154	+	0.944971i	$0.606090\pi$
$264$	−9.27982	−0.571134
$265$	−15.2736	−0.938253
$266$	−4.54561	−0.278709
$267$	42.0391	2.57275
$268$	−5.75994	−0.351844
$269$	−12.0593	−0.735269	−0.367635	−	0.929970i	$-0.619832\pi$
$269$	−12.0593	−0.735269	−0.367635	+	0.929970i	$0.619832\pi$
$270$	−12.4801	−0.759516
$271$	1.38273	0.0839947	0.0419974	−	0.999118i	$-0.486628\pi$
$271$	1.38273	0.0839947	0.0419974	+	0.999118i	$0.486628\pi$
$272$	7.09122	0.429968
$273$	0	0
$274$	−11.1427	−0.673153
$275$	4.93068	0.297331
$276$	4.90261	0.295102
$277$	−1.14267	−0.0686563	−0.0343281	−	0.999411i	$-0.510929\pi$
$277$	−1.14267	−0.0686563	−0.0343281	+	0.999411i	$0.510929\pi$
$278$	−4.54561	−0.272627
$279$	−15.8567	−0.949314
$280$	2.54561	0.152129
$281$	7.14267	0.426096	0.213048	−	0.977042i	$-0.431661\pi$
$281$	7.14267	0.426096	0.213048	+	0.977042i	$0.431661\pi$
$282$	31.5652	1.87968
$283$	4.83712	0.287537	0.143768	−	0.989611i	$-0.454078\pi$
$283$	4.83712	0.287537	0.143768	+	0.989611i	$0.454078\pi$
$284$	11.1427	0.661196
$285$	−32.2339	−1.90937
$286$	0	0
$287$	−4.24006	−0.250283
$288$	−4.75994	−0.280482
$289$	33.2853	1.95796
$290$	−19.2736	−1.13179
$291$	21.6166	1.26719
$292$	9.33127	0.546072
$293$	−7.63682	−0.446148	−0.223074	−	0.974802i	$-0.571609\pi$
$293$	−7.63682	−0.446148	−0.223074	+	0.974802i	$0.571609\pi$
$294$	−2.78567	−0.162463
$295$	−20.5316	−1.19539
$296$	3.75994	0.218542
$297$	16.3319	0.947675
$298$	5.81139	0.336645
$299$	0	0
$300$	4.12312	0.238048
$301$	9.09122	0.524009
$302$	3.09122	0.177879
$303$	10.2915	0.591232
$304$	−4.54561	−0.260708
$305$	−2.00000	−0.114520
$306$	−33.7538	−1.92957
$307$	−14.3508	−0.819045	−0.409522	−	0.912300i	$-0.634305\pi$
$307$	−14.3508	−0.819045	−0.409522	+	0.912300i	$0.634305\pi$
$308$	−3.33127	−0.189817
$309$	−36.4678	−2.07458
$310$	8.48012	0.481638
$311$	−2.18243	−0.123754	−0.0618771	−	0.998084i	$-0.519709\pi$
$311$	−2.18243	−0.123754	−0.0618771	+	0.998084i	$0.519709\pi$
$312$	0	0
$313$	15.5713	0.880144	0.440072	−	0.897963i	$-0.354953\pi$
$313$	15.5713	0.880144	0.440072	+	0.897963i	$0.354953\pi$
$314$	7.92834	0.447422
$315$	−12.1169	−0.682712
$316$	4.85116	0.272899
$317$	14.1886	0.796912	0.398456	−	0.917188i	$-0.369546\pi$
$317$	14.1886	0.796912	0.398456	+	0.917188i	$0.369546\pi$
$318$	16.7140	0.937275
$319$	25.2222	1.41217
$320$	2.54561	0.142304
$321$	−9.80522	−0.547274
$322$	1.75994	0.0980777
$323$	−32.2339	−1.79354
$324$	−0.622787	−0.0345993
$325$	0	0
$326$	10.0515	0.556698
$327$	−36.6111	−2.02460
$328$	−4.24006	−0.234118
$329$	11.3313	0.624713
$330$	−23.6228	−1.30039
$331$	−2.85116	−0.156714	−0.0783569	−	0.996925i	$-0.524967\pi$
$331$	−2.85116	−0.156714	−0.0783569	+	0.996925i	$0.524967\pi$
$332$	11.2082	0.615128
$333$	−17.8971	−0.980755
$334$	−24.2339	−1.32602
$335$	−14.6625	−0.801101
$336$	−2.78567	−0.151971
$337$	32.5254	1.77177	0.885886	−	0.463904i	$-0.153552\pi$
$337$	32.5254	1.77177	0.885886	+	0.463904i	$0.153552\pi$
$338$	0	0
$339$	−4.90261	−0.266273
$340$	18.0515	0.978977
$341$	−11.0974	−0.600957
$342$	21.6368	1.16999
$343$	−1.00000	−0.0539949
$344$	9.09122	0.490165
$345$	12.4801	0.671907
$346$	20.5971	1.10730
$347$	5.94855	0.319335	0.159667	−	0.987171i	$-0.448958\pi$
$347$	5.94855	0.319335	0.159667	+	0.987171i	$0.448958\pi$
$348$	21.0912	1.13061
$349$	−32.9619	−1.76441	−0.882206	−	0.470864i	$-0.843942\pi$
$349$	−32.9619	−1.76441	−0.882206	+	0.470864i	$0.843942\pi$
$350$	1.48012	0.0791157
$351$	0	0
$352$	−3.33127	−0.177558
$353$	−0.851156	−0.0453025	−0.0226512	−	0.999743i	$-0.507211\pi$
$353$	−0.851156	−0.0453025	−0.0226512	+	0.999743i	$0.507211\pi$
$354$	22.4678	1.19415
$355$	28.3649	1.50545
$356$	15.0912	0.799833
$357$	−19.7538	−1.04548
$358$	17.3251	0.915660
$359$	27.9362	1.47442	0.737208	−	0.675666i	$-0.236144\pi$
$359$	27.9362	1.47442	0.737208	+	0.675666i	$0.236144\pi$
$360$	−12.1169	−0.638619
$361$	1.66255	0.0875026
$362$	−16.9166	−0.889119
$363$	0.271300	0.0142395
$364$	0	0
$365$	23.7538	1.24333
$366$	2.18861	0.114400
$367$	−7.14267	−0.372844	−0.186422	−	0.982470i	$-0.559689\pi$
$367$	−7.14267	−0.372844	−0.186422	+	0.982470i	$0.559689\pi$
$368$	1.75994	0.0917433
$369$	20.1824	1.05066
$370$	9.57133	0.497590
$371$	6.00000	0.311504
$372$	−9.27982	−0.481136
$373$	−33.1427	−1.71606	−0.858031	−	0.513598i	$-0.828312\pi$
$373$	−33.1427	−1.71606	−0.858031	+	0.513598i	$0.828312\pi$
$374$	−23.6228	−1.22151
$375$	−24.9602	−1.28894
$376$	11.3313	0.584366
$377$	0	0
$378$	4.90261	0.252163
$379$	−35.2736	−1.81189	−0.905943	−	0.423400i	$-0.860836\pi$
$379$	−35.2736	−1.81189	−0.905943	+	0.423400i	$0.860836\pi$
$380$	−11.5713	−0.593597
$381$	35.9424	1.84138
$382$	−4.42867	−0.226590
$383$	−6.95406	−0.355336	−0.177668	−	0.984090i	$-0.556855\pi$
$383$	−6.95406	−0.355336	−0.177668	+	0.984090i	$0.556855\pi$
$384$	−2.78567	−0.142155
$385$	−8.48012	−0.432187
$386$	2.48012	0.126235
$387$	−43.2736	−2.19972
$388$	7.75994	0.393951
$389$	5.27365	0.267384	0.133692	−	0.991023i	$-0.457317\pi$
$389$	5.27365	0.267384	0.133692	+	0.991023i	$0.457317\pi$
$390$	0	0
$391$	12.4801	0.631147
$392$	−1.00000	−0.0505076
$393$	−46.7421	−2.35783
$394$	8.85116	0.445915
$395$	12.3491	0.621353
$396$	15.8567	0.796828
$397$	−18.6766	−0.937351	−0.468675	−	0.883370i	$-0.655269\pi$
$397$	−18.6766	−0.937351	−0.468675	+	0.883370i	$0.655269\pi$
$398$	1.09122	0.0546977
$399$	12.6625	0.633920
$400$	1.48012	0.0740059
$401$	21.5199	1.07465	0.537326	−	0.843375i	$-0.319435\pi$
$401$	21.5199	1.07465	0.537326	+	0.843375i	$0.319435\pi$
$402$	16.0453	0.800266
$403$	0	0
$404$	3.69445	0.183806
$405$	−1.58537	−0.0787777
$406$	7.57133	0.375759
$407$	−12.5254	−0.620861
$408$	−19.7538	−0.977957
$409$	19.3251	0.955565	0.477782	−	0.878478i	$-0.341441\pi$
$409$	19.3251	0.955565	0.477782	+	0.878478i	$0.341441\pi$
$410$	−10.7935	−0.533054
$411$	31.0398	1.53108
$412$	−13.0912	−0.644958
$413$	8.06549	0.396877
$414$	−8.37721	−0.411718
$415$	28.5316	1.40056
$416$	0	0
$417$	12.6625	0.620088
$418$	15.1427	0.740652
$419$	12.8371	0.627134	0.313567	−	0.949566i	$-0.398476\pi$
$419$	12.8371	0.627134	0.313567	+	0.949566i	$0.398476\pi$
$420$	−7.09122	−0.346016
$421$	−21.3313	−1.03962	−0.519811	−	0.854281i	$-0.673998\pi$
$421$	−21.3313	−1.03962	−0.519811	+	0.854281i	$0.673998\pi$
$422$	−15.0398	−0.732124
$423$	−53.9362	−2.62247
$424$	6.00000	0.291386
$425$	10.4958	0.509123
$426$	−31.0398	−1.50388
$427$	0.785667	0.0380211
$428$	−3.51988	−0.170140
$429$	0	0
$430$	23.1427	1.11604
$431$	11.5713	0.557372	0.278686	−	0.960382i	$-0.410101\pi$
$431$	11.5713	0.557372	0.278686	+	0.960382i	$0.410101\pi$
$432$	4.90261	0.235877
$433$	−29.3766	−1.41175	−0.705873	−	0.708338i	$-0.749445\pi$
$433$	−29.3766	−1.41175	−0.705873	+	0.708338i	$0.749445\pi$
$434$	−3.33127	−0.159906
$435$	53.6900	2.57424
$436$	−13.1427	−0.629420
$437$	−8.00000	−0.382692
$438$	−25.9938	−1.24203
$439$	−0.102905	−0.00491140	−0.00245570	−	0.999997i	$-0.500782\pi$
$439$	−0.102905	−0.00491140	−0.00245570	+	0.999997i	$0.500782\pi$
$440$	−8.48012	−0.404274
$441$	4.75994	0.226664
$442$	0	0
$443$	27.1427	1.28959	0.644794	−	0.764357i	$-0.276943\pi$
$443$	27.1427	1.28959	0.644794	+	0.764357i	$0.276943\pi$
$444$	−10.4739	−0.497071
$445$	38.4163	1.82111
$446$	12.9026	0.610956
$447$	−16.1886	−0.765695
$448$	−1.00000	−0.0472456
$449$	−9.70231	−0.457880	−0.228940	−	0.973440i	$-0.573526\pi$
$449$	−9.70231	−0.457880	−0.228940	+	0.973440i	$0.573526\pi$
$450$	−7.04528	−0.332118
$451$	14.1248	0.665111
$452$	−1.75994	−0.0827806
$453$	−8.61110	−0.404585
$454$	−9.02573	−0.423598
$455$	0	0
$456$	12.6625	0.592978
$457$	−36.1701	−1.69196	−0.845982	−	0.533211i	$-0.820985\pi$
$457$	−36.1701	−1.69196	−0.845982	+	0.533211i	$0.820985\pi$
$458$	14.1684	0.662046
$459$	34.7655	1.62271
$460$	4.48012	0.208887
$461$	−20.9743	−0.976869	−0.488435	−	0.872600i	$-0.662432\pi$
$461$	−20.9743	−0.976869	−0.488435	+	0.872600i	$0.662432\pi$
$462$	9.27982	0.431736
$463$	24.8450	1.15464	0.577322	−	0.816517i	$-0.304098\pi$
$463$	24.8450	1.15464	0.577322	+	0.816517i	$0.304098\pi$
$464$	7.57133	0.351490
$465$	−23.6228	−1.09548
$466$	−7.38273	−0.341998
$467$	−1.27196	−0.0588594	−0.0294297	−	0.999567i	$-0.509369\pi$
$467$	−1.27196	−0.0588594	−0.0294297	+	0.999567i	$0.509369\pi$
$468$	0	0
$469$	5.75994	0.265969
$470$	28.8450	1.33052
$471$	−22.0857	−1.01766
$472$	8.06549	0.371244
$473$	−30.2853	−1.39252
$474$	−13.5137	−0.620705
$475$	−6.72804	−0.308704
$476$	−7.09122	−0.325025
$477$	−28.5596	−1.30766
$478$	−6.13098	−0.280424
$479$	22.0515	1.00756	0.503778	−	0.863833i	$-0.331943\pi$
$479$	22.0515	1.00756	0.503778	+	0.863833i	$0.331943\pi$
$480$	−7.09122	−0.323668
$481$	0	0
$482$	−27.3251	−1.24462
$483$	−4.90261	−0.223076
$484$	0.0973913	0.00442688
$485$	19.7538	0.896972
$486$	16.4427	0.745856
$487$	4.42867	0.200682	0.100341	−	0.994953i	$-0.468007\pi$
$487$	4.42867	0.200682	0.100341	+	0.994953i	$0.468007\pi$
$488$	0.785667	0.0355655
$489$	−28.0000	−1.26620
$490$	−2.54561	−0.114999
$491$	31.0274	1.40025	0.700124	−	0.714022i	$-0.253128\pi$
$491$	31.0274	1.40025	0.700124	+	0.714022i	$0.253128\pi$
$492$	11.8114	0.532499
$493$	53.6900	2.41807
$494$	0	0
$495$	40.3649	1.81427
$496$	−3.33127	−0.149579
$497$	−11.1427	−0.499817
$498$	−31.2222	−1.39910
$499$	23.0850	1.03343	0.516714	−	0.856158i	$-0.327155\pi$
$499$	23.0850	1.03343	0.516714	+	0.856158i	$0.327155\pi$
$500$	−8.96024	−0.400714
$501$	67.5075	3.01601
$502$	16.4880	0.735895
$503$	−17.7023	−0.789307	−0.394654	−	0.918830i	$-0.629135\pi$
$503$	−17.7023	−0.789307	−0.394654	+	0.918830i	$0.629135\pi$
$504$	4.75994	0.212025
$505$	9.40462	0.418500
$506$	−5.86285	−0.260635
$507$	0	0
$508$	12.9026	0.572461
$509$	−24.7280	−1.09605	−0.548026	−	0.836462i	$-0.684620\pi$
$509$	−24.7280	−1.09605	−0.548026	+	0.836462i	$0.684620\pi$
$510$	−50.2853	−2.22667
$511$	−9.33127	−0.412791
$512$	−1.00000	−0.0441942
$513$	−22.2853	−0.983922
$514$	−1.14267	−0.0504009
$515$	−33.3251	−1.46848
$516$	−25.3251	−1.11488
$517$	−37.7476	−1.66014
$518$	−3.75994	−0.165202
$519$	−57.3766	−2.51855
$520$	0	0
$521$	−20.4287	−0.894996	−0.447498	−	0.894285i	$-0.647685\pi$
$521$	−20.4287	−0.894996	−0.447498	+	0.894285i	$0.647685\pi$
$522$	−36.0391	−1.57739
$523$	25.8254	1.12927	0.564634	−	0.825342i	$-0.309017\pi$
$523$	25.8254	1.12927	0.564634	+	0.825342i	$0.309017\pi$
$524$	−16.7795	−0.733015
$525$	−4.12312	−0.179948
$526$	10.6111	0.462666
$527$	−23.6228	−1.02902
$528$	9.27982	0.403852
$529$	−19.9026	−0.865331
$530$	15.2736	0.663445
$531$	−38.3912	−1.66604
$532$	4.54561	0.197077
$533$	0	0
$534$	−42.0391	−1.81921
$535$	−8.96024	−0.387385
$536$	5.75994	0.248792
$537$	−48.2620	−2.08266
$538$	12.0593	0.519914
$539$	3.33127	0.143488
$540$	12.4801	0.537059
$541$	−28.3134	−1.21729	−0.608644	−	0.793443i	$-0.708286\pi$
$541$	−28.3134	−1.21729	−0.608644	+	0.793443i	$0.708286\pi$
$542$	−1.38273	−0.0593932
$543$	47.1241	2.02229
$544$	−7.09122	−0.304033
$545$	−33.4561	−1.43310
$546$	0	0
$547$	25.5713	1.09335	0.546676	−	0.837344i	$-0.315893\pi$
$547$	25.5713	1.09335	0.546676	+	0.837344i	$0.315893\pi$
$548$	11.1427	0.475991
$549$	−3.73973	−0.159608
$550$	−4.93068	−0.210245
$551$	−34.4163	−1.46618
$552$	−4.90261	−0.208669
$553$	−4.85116	−0.206292
$554$	1.14267	0.0485473
$555$	−26.6625	−1.13176
$556$	4.54561	0.192777
$557$	−3.99382	−0.169224	−0.0846119	−	0.996414i	$-0.526965\pi$
$557$	−3.99382	−0.169224	−0.0846119	+	0.996414i	$0.526965\pi$
$558$	15.8567	0.671266
$559$	0	0
$560$	−2.54561	−0.107572
$561$	65.8052	2.77830
$562$	−7.14267	−0.301295
$563$	−43.4997	−1.83329	−0.916646	−	0.399699i	$-0.869114\pi$
$563$	−43.4997	−1.83329	−0.916646	+	0.399699i	$0.869114\pi$
$564$	−31.5652	−1.32913
$565$	−4.48012	−0.188480
$566$	−4.83712	−0.203319
$567$	0.622787	0.0261546
$568$	−11.1427	−0.467536
$569$	−41.2675	−1.73002	−0.865011	−	0.501753i	$-0.832689\pi$
$569$	−41.2675	−1.73002	−0.865011	+	0.501753i	$0.832689\pi$
$570$	32.2339	1.35013
$571$	−13.9362	−0.583212	−0.291606	−	0.956539i	$-0.594190\pi$
$571$	−13.9362	−0.583212	−0.291606	+	0.956539i	$0.594190\pi$
$572$	0	0
$573$	12.3368	0.515377
$574$	4.24006	0.176977
$575$	2.60492	0.108633
$576$	4.75994	0.198331
$577$	32.4163	1.34951	0.674754	−	0.738042i	$-0.264250\pi$
$577$	32.4163	1.34951	0.674754	+	0.738042i	$0.264250\pi$
$578$	−33.2853	−1.38449
$579$	−6.90878	−0.287119
$580$	19.2736	0.800295
$581$	−11.2082	−0.464993
$582$	−21.6166	−0.896037
$583$	−19.9876	−0.827804
$584$	−9.33127	−0.386131
$585$	0	0
$586$	7.63682	0.315474
$587$	−4.03742	−0.166642	−0.0833210	−	0.996523i	$-0.526553\pi$
$587$	−4.03742	−0.166642	−0.0833210	+	0.996523i	$0.526553\pi$
$588$	2.78567	0.114879
$589$	15.1427	0.623943
$590$	20.5316	0.845271
$591$	−24.6564	−1.01423
$592$	−3.75994	−0.154533
$593$	−20.4163	−0.838398	−0.419199	−	0.907894i	$-0.637689\pi$
$593$	−20.4163	−0.838398	−0.419199	+	0.907894i	$0.637689\pi$
$594$	−16.3319	−0.670107
$595$	−18.0515	−0.740037
$596$	−5.81139	−0.238044
$597$	−3.03976	−0.124409
$598$	0	0
$599$	−8.10908	−0.331328	−0.165664	−	0.986182i	$-0.552977\pi$
$599$	−8.10908	−0.331328	−0.165664	+	0.986182i	$0.552977\pi$
$600$	−4.12312	−0.168326
$601$	−7.70231	−0.314184	−0.157092	−	0.987584i	$-0.550212\pi$
$601$	−7.70231	−0.314184	−0.157092	+	0.987584i	$0.550212\pi$
$602$	−9.09122	−0.370530
$603$	−27.4170	−1.11651
$604$	−3.09122	−0.125780
$605$	0.247920	0.0100794
$606$	−10.2915	−0.418064
$607$	−33.7023	−1.36793	−0.683967	−	0.729513i	$-0.739747\pi$
$607$	−33.7023	−1.36793	−0.683967	+	0.729513i	$0.739747\pi$
$608$	4.54561	0.184349
$609$	−21.0912	−0.854659
$610$	2.00000	0.0809776
$611$	0	0
$612$	33.7538	1.36442
$613$	23.2675	0.939764	0.469882	−	0.882729i	$-0.344296\pi$
$613$	23.2675	0.939764	0.469882	+	0.882729i	$0.344296\pi$
$614$	14.3508	0.579152
$615$	30.0672	1.21243
$616$	3.33127	0.134221
$617$	−1.51988	−0.0611881	−0.0305941	−	0.999532i	$-0.509740\pi$
$617$	−1.51988	−0.0611881	−0.0305941	+	0.999532i	$0.509740\pi$
$618$	36.4678	1.46695
$619$	−0.779491	−0.0313304	−0.0156652	−	0.999877i	$-0.504987\pi$
$619$	−0.779491	−0.0313304	−0.0156652	+	0.999877i	$0.504987\pi$
$620$	−8.48012	−0.340570
$621$	8.62830	0.346242
$622$	2.18243	0.0875075
$623$	−15.0912	−0.604617
$624$	0	0
$625$	−30.2098	−1.20839
$626$	−15.5713	−0.622356
$627$	−42.1824	−1.68460
$628$	−7.92834	−0.316375
$629$	−26.6625	−1.06311
$630$	12.1169	0.482751
$631$	−32.4678	−1.29252	−0.646261	−	0.763117i	$-0.723668\pi$
$631$	−32.4678	−1.29252	−0.646261	+	0.763117i	$0.723668\pi$
$632$	−4.85116	−0.192969
$633$	41.8958	1.66521
$634$	−14.1886	−0.563502
$635$	32.8450	1.30341
$636$	−16.7140	−0.662753
$637$	0	0
$638$	−25.2222	−0.998556
$639$	53.0384	2.09817
$640$	−2.54561	−0.100624
$641$	42.2277	1.66789	0.833947	−	0.551844i	$-0.186076\pi$
$641$	42.2277	1.66789	0.833947	+	0.551844i	$0.186076\pi$
$642$	9.80522	0.386981
$643$	6.84330	0.269873	0.134937	−	0.990854i	$-0.456917\pi$
$643$	6.84330	0.269873	0.134937	+	0.990854i	$0.456917\pi$
$644$	−1.75994	−0.0693514
$645$	−64.4678	−2.53842
$646$	32.2339	1.26823
$647$	3.75376	0.147576	0.0737879	−	0.997274i	$-0.476491\pi$
$647$	3.75376	0.147576	0.0737879	+	0.997274i	$0.476491\pi$
$648$	0.622787	0.0244654
$649$	−26.8684	−1.05468
$650$	0	0
$651$	9.27982	0.363705
$652$	−10.0515	−0.393645
$653$	23.8333	0.932669	0.466334	−	0.884609i	$-0.345574\pi$
$653$	23.8333	0.932669	0.466334	+	0.884609i	$0.345574\pi$
$654$	36.6111	1.43161
$655$	−42.7140	−1.66897
$656$	4.24006	0.165547
$657$	44.4163	1.73285
$658$	−11.3313	−0.441739
$659$	−21.0912	−0.821597	−0.410799	−	0.911726i	$-0.634750\pi$
$659$	−21.0912	−0.821597	−0.410799	+	0.911726i	$0.634750\pi$
$660$	23.6228	0.919516
$661$	34.4023	1.33809	0.669047	−	0.743220i	$-0.266703\pi$
$661$	34.4023	1.33809	0.669047	+	0.743220i	$0.266703\pi$
$662$	2.85116	0.110813
$663$	0	0
$664$	−11.2082	−0.434961
$665$	11.5713	0.448717
$666$	17.8971	0.693498
$667$	13.3251	0.515950
$668$	24.2339	0.937637
$669$	−35.9424	−1.38961
$670$	14.6625	0.566464
$671$	−2.61727	−0.101039
$672$	2.78567	0.107459
$673$	−10.7997	−0.416298	−0.208149	−	0.978097i	$-0.566744\pi$
$673$	−10.7997	−0.416298	−0.208149	+	0.978097i	$0.566744\pi$
$674$	−32.5254	−1.25283
$675$	7.25644	0.279301
$676$	0	0
$677$	−33.7336	−1.29649	−0.648243	−	0.761434i	$-0.724496\pi$
$677$	−33.7336	−1.29649	−0.648243	+	0.761434i	$0.724496\pi$
$678$	4.90261	0.188284
$679$	−7.75994	−0.297799
$680$	−18.0515	−0.692242
$681$	25.1427	0.963469
$682$	11.0974	0.424941
$683$	−21.8628	−0.836559	−0.418279	−	0.908318i	$-0.637367\pi$
$683$	−21.8628	−0.836559	−0.418279	+	0.908318i	$0.637367\pi$
$684$	−21.6368	−0.827305
$685$	28.3649	1.08377
$686$	1.00000	0.0381802
$687$	−39.4684	−1.50581
$688$	−9.09122	−0.346599
$689$	0	0
$690$	−12.4801	−0.475110
$691$	10.7404	0.408584	0.204292	−	0.978910i	$-0.434511\pi$
$691$	10.7404	0.408584	0.204292	+	0.978910i	$0.434511\pi$
$692$	−20.5971	−0.782983
$693$	−15.8567	−0.602345
$694$	−5.94855	−0.225804
$695$	11.5713	0.438926
$696$	−21.0912	−0.799460
$697$	30.0672	1.13888
$698$	32.9619	1.24763
$699$	20.5658	0.777871
$700$	−1.48012	−0.0559432
$701$	11.1941	0.422796	0.211398	−	0.977400i	$-0.432198\pi$
$701$	11.1941	0.422796	0.211398	+	0.977400i	$0.432198\pi$
$702$	0	0
$703$	17.0912	0.644607
$704$	3.33127	0.125552
$705$	−80.3525	−3.02625
$706$	0.851156	0.0320337
$707$	−3.69445	−0.138944
$708$	−22.4678	−0.844390
$709$	−5.20030	−0.195301	−0.0976506	−	0.995221i	$-0.531133\pi$
$709$	−5.20030	−0.195301	−0.0976506	+	0.995221i	$0.531133\pi$
$710$	−28.3649	−1.06451
$711$	23.0912	0.865988
$712$	−15.0912	−0.565567
$713$	−5.86285	−0.219565
$714$	19.7538	0.739266
$715$	0	0
$716$	−17.3251	−0.647469
$717$	17.0789	0.637822
$718$	−27.9362	−1.04257
$719$	38.0515	1.41908	0.709540	−	0.704665i	$-0.248903\pi$
$719$	38.0515	1.41908	0.709540	+	0.704665i	$0.248903\pi$
$720$	12.1169	0.451572
$721$	13.0912	0.487542
$722$	−1.66255	−0.0618737
$723$	76.1186	2.83088
$724$	16.9166	0.628702
$725$	11.2065	0.416198
$726$	−0.271300	−0.0100689
$727$	28.6111	1.06113	0.530563	−	0.847645i	$-0.321980\pi$
$727$	28.6111	1.06113	0.530563	+	0.847645i	$0.321980\pi$
$728$	0	0
$729$	−43.9355	−1.62724
$730$	−23.7538	−0.879166
$731$	−64.4678	−2.38443
$732$	−2.18861	−0.0808932
$733$	−8.21985	−0.303607	−0.151803	−	0.988411i	$-0.548508\pi$
$733$	−8.21985	−0.303607	−0.151803	+	0.988411i	$0.548508\pi$
$734$	7.14267	0.263641
$735$	7.09122	0.261563
$736$	−1.75994	−0.0648723
$737$	−19.1879	−0.706797
$738$	−20.1824	−0.742926
$739$	−1.58369	−0.0582568	−0.0291284	−	0.999576i	$-0.509273\pi$
$739$	−1.58369	−0.0582568	−0.0291284	+	0.999576i	$0.509273\pi$
$740$	−9.57133	−0.351849
$741$	0	0
$742$	−6.00000	−0.220267
$743$	11.9485	0.438350	0.219175	−	0.975686i	$-0.429663\pi$
$743$	11.9485	0.438350	0.219175	+	0.975686i	$0.429663\pi$
$744$	9.27982	0.340215
$745$	−14.7935	−0.541993
$746$	33.1427	1.21344
$747$	53.3502	1.95198
$748$	23.6228	0.863735
$749$	3.51988	0.128614
$750$	24.9602	0.911419
$751$	−27.5652	−1.00587	−0.502933	−	0.864325i	$-0.667746\pi$
$751$	−27.5652	−1.00587	−0.502933	+	0.864325i	$0.667746\pi$
$752$	−11.3313	−0.413209
$753$	−45.9300	−1.67378
$754$	0	0
$755$	−7.86902	−0.286383
$756$	−4.90261	−0.178306
$757$	−38.2339	−1.38963	−0.694817	−	0.719187i	$-0.744515\pi$
$757$	−38.2339	−1.38963	−0.694817	+	0.719187i	$0.744515\pi$
$758$	35.2736	1.28120
$759$	16.3319	0.592812
$760$	11.5713	0.419736
$761$	51.7476	1.87585	0.937924	−	0.346840i	$-0.112745\pi$
$761$	51.7476	1.87585	0.937924	+	0.346840i	$0.112745\pi$
$762$	−35.9424	−1.30205
$763$	13.1427	0.475797
$764$	4.42867	0.160224
$765$	85.9238	3.10658
$766$	6.95406	0.251260
$767$	0	0
$768$	2.78567	0.100519
$769$	24.2401	0.874119	0.437059	−	0.899433i	$-0.356020\pi$
$769$	24.2401	0.874119	0.437059	+	0.899433i	$0.356020\pi$
$770$	8.48012	0.305602
$771$	3.18309	0.114636
$772$	−2.48012	−0.0892614
$773$	16.5971	0.596955	0.298477	−	0.954417i	$-0.403521\pi$
$773$	16.5971	0.596955	0.298477	+	0.954417i	$0.403521\pi$
$774$	43.2736	1.55544
$775$	−4.93068	−0.177115
$776$	−7.75994	−0.278566
$777$	10.4739	0.375751
$778$	−5.27365	−0.189069
$779$	−19.2736	−0.690550
$780$	0	0
$781$	37.1193	1.32823
$782$	−12.4801	−0.446288
$783$	37.1193	1.32654
$784$	1.00000	0.0357143
$785$	−20.1824	−0.720342
$786$	46.7421	1.66723
$787$	−8.31172	−0.296281	−0.148140	−	0.988966i	$-0.547329\pi$
$787$	−8.31172	−0.296281	−0.148140	+	0.988966i	$0.547329\pi$
$788$	−8.85116	−0.315309
$789$	−29.5590	−1.05233
$790$	−12.3491	−0.439363
$791$	1.75994	0.0625763
$792$	−15.8567	−0.563442
$793$	0	0
$794$	18.6766	0.662807
$795$	−42.5473	−1.50900
$796$	−1.09122	−0.0386771
$797$	−24.3055	−0.860947	−0.430473	−	0.902603i	$-0.641653\pi$
$797$	−24.3055	−0.860947	−0.430473	+	0.902603i	$0.641653\pi$
$798$	−12.6625	−0.448249
$799$	−80.3525	−2.84267
$800$	−1.48012	−0.0523301
$801$	71.8333	2.53810
$802$	−21.5199	−0.759893
$803$	31.0850	1.09697
$804$	−16.0453	−0.565873
$805$	−4.48012	−0.157903
$806$	0	0
$807$	−33.5932	−1.18254
$808$	−3.69445	−0.129970
$809$	−15.9876	−0.562096	−0.281048	−	0.959694i	$-0.590682\pi$
$809$	−15.9876	−0.562096	−0.281048	+	0.959694i	$0.590682\pi$
$810$	1.58537	0.0557042
$811$	19.7163	0.692335	0.346167	−	0.938173i	$-0.387483\pi$
$811$	19.7163	0.692335	0.346167	+	0.938173i	$0.387483\pi$
$812$	−7.57133	−0.265702
$813$	3.85182	0.135089
$814$	12.5254	0.439015
$815$	−25.5871	−0.896275
$816$	19.7538	0.691520
$817$	41.3251	1.44578
$818$	−19.3251	−0.675686
$819$	0	0
$820$	10.7935	0.376926
$821$	15.9485	0.556608	0.278304	−	0.960493i	$-0.410228\pi$
$821$	15.9485	0.556608	0.278304	+	0.960493i	$0.410228\pi$
$822$	−31.0398	−1.08264
$823$	−23.9938	−0.836372	−0.418186	−	0.908361i	$-0.637334\pi$
$823$	−23.9938	−0.836372	−0.418186	+	0.908361i	$0.637334\pi$
$824$	13.0912	0.456054
$825$	13.7352	0.478200
$826$	−8.06549	−0.280634
$827$	−49.4280	−1.71878	−0.859390	−	0.511321i	$-0.829156\pi$
$827$	−49.4280	−1.71878	−0.859390	+	0.511321i	$0.829156\pi$
$828$	8.37721	0.291128
$829$	11.7678	0.408713	0.204356	−	0.978897i	$-0.434490\pi$
$829$	11.7678	0.408713	0.204356	+	0.978897i	$0.434490\pi$
$830$	−28.5316	−0.990345
$831$	−3.18309	−0.110420
$832$	0	0
$833$	7.09122	0.245696
$834$	−12.6625	−0.438468
$835$	61.6900	2.13487
$836$	−15.1427	−0.523720
$837$	−16.3319	−0.564514
$838$	−12.8371	−0.443451
$839$	−16.6687	−0.575468	−0.287734	−	0.957710i	$-0.592902\pi$
$839$	−16.6687	−0.575468	−0.287734	+	0.957710i	$0.592902\pi$
$840$	7.09122	0.244670
$841$	28.3251	0.976728
$842$	21.3313	0.735124
$843$	19.8971	0.685292
$844$	15.0398	0.517690
$845$	0	0
$846$	53.9362	1.85436
$847$	−0.0973913	−0.00334640
$848$	−6.00000	−0.206041
$849$	13.4746	0.462447
$850$	−10.4958	−0.360004
$851$	−6.61727	−0.226837
$852$	31.0398	1.06340
$853$	23.1286	0.791909	0.395955	−	0.918270i	$-0.370414\pi$
$853$	23.1286	0.791909	0.395955	+	0.918270i	$0.370414\pi$
$854$	−0.785667	−0.0268850
$855$	−55.0789	−1.88366
$856$	3.51988	0.120307
$857$	−13.6509	−0.466304	−0.233152	−	0.972440i	$-0.574904\pi$
$857$	−13.6509	−0.466304	−0.233152	+	0.972440i	$0.574904\pi$
$858$	0	0
$859$	−12.8371	−0.437997	−0.218998	−	0.975725i	$-0.570279\pi$
$859$	−12.8371	−0.437997	−0.218998	+	0.975725i	$0.570279\pi$
$860$	−23.1427	−0.789158
$861$	−11.8114	−0.402531
$862$	−11.5713	−0.394121
$863$	−39.6228	−1.34878	−0.674388	−	0.738377i	$-0.735592\pi$
$863$	−39.6228	−1.34878	−0.674388	+	0.738377i	$0.735592\pi$
$864$	−4.90261	−0.166790
$865$	−52.4320	−1.78274
$866$	29.3766	0.998256
$867$	92.7219	3.14900
$868$	3.33127	0.113071
$869$	16.1605	0.548209
$870$	−53.6900	−1.82026
$871$	0	0
$872$	13.1427	0.445067
$873$	36.9369	1.25012
$874$	8.00000	0.270604
$875$	8.96024	0.302911
$876$	25.9938	0.878250
$877$	47.3704	1.59958	0.799792	−	0.600277i	$-0.204943\pi$
$877$	47.3704	1.59958	0.799792	+	0.600277i	$0.204943\pi$
$878$	0.102905	0.00347288
$879$	−21.2736	−0.717542
$880$	8.48012	0.285865
$881$	43.8052	1.47584	0.737918	−	0.674891i	$-0.235809\pi$
$881$	43.8052	1.47584	0.737918	+	0.674891i	$0.235809\pi$
$882$	−4.75994	−0.160276
$883$	1.81757	0.0611661	0.0305830	−	0.999532i	$-0.490264\pi$
$883$	1.81757	0.0611661	0.0305830	+	0.999532i	$0.490264\pi$
$884$	0	0
$885$	−57.1941	−1.92256
$886$	−27.1427	−0.911876
$887$	7.27365	0.244225	0.122113	−	0.992516i	$-0.461033\pi$
$887$	7.27365	0.244225	0.122113	+	0.992516i	$0.461033\pi$
$888$	10.4739	0.351483
$889$	−12.9026	−0.432740
$890$	−38.4163	−1.28772
$891$	−2.07467	−0.0695042
$892$	−12.9026	−0.432011
$893$	51.5075	1.72363
$894$	16.1886	0.541428
$895$	−44.1029	−1.47420
$896$	1.00000	0.0334077
$897$	0	0
$898$	9.70231	0.323770
$899$	−25.2222	−0.841207
$900$	7.04528	0.234843
$901$	−42.5473	−1.41746
$902$	−14.1248	−0.470304
$903$	25.3251	0.842767
$904$	1.75994	0.0585348
$905$	43.0631	1.43147
$906$	8.61110	0.286085
$907$	12.4678	0.413985	0.206993	−	0.978342i	$-0.433632\pi$
$907$	12.4678	0.413985	0.206993	+	0.978342i	$0.433632\pi$
$908$	9.02573	0.299529
$909$	17.5854	0.583270
$910$	0	0
$911$	1.92047	0.0636282	0.0318141	−	0.999494i	$-0.489872\pi$
$911$	1.92047	0.0636282	0.0318141	+	0.999494i	$0.489872\pi$
$912$	−12.6625	−0.419299
$913$	37.3375	1.23569
$914$	36.1701	1.19640
$915$	−5.57133	−0.184183
$916$	−14.1684	−0.468137
$917$	16.7795	0.554108
$918$	−34.7655	−1.14743
$919$	−13.2284	−0.436364	−0.218182	−	0.975908i	$-0.570013\pi$
$919$	−13.2284	−0.436364	−0.218182	+	0.975908i	$0.570013\pi$
$920$	−4.48012	−0.147705
$921$	−39.9766	−1.31727
$922$	20.9743	0.690751
$923$	0	0
$924$	−9.27982	−0.305284
$925$	−5.56516	−0.182981
$926$	−24.8450	−0.816457
$927$	−62.3134	−2.04664
$928$	−7.57133	−0.248541
$929$	1.30320	0.0427567	0.0213783	−	0.999771i	$-0.493195\pi$
$929$	1.30320	0.0427567	0.0213783	+	0.999771i	$0.493195\pi$
$930$	23.6228	0.774622
$931$	−4.54561	−0.148976
$932$	7.38273	0.241829
$933$	−6.07953	−0.199035
$934$	1.27196	0.0416199
$935$	60.1343	1.96660
$936$	0	0
$937$	14.9602	0.488730	0.244365	−	0.969683i	$-0.421421\pi$
$937$	14.9602	0.488730	0.244365	+	0.969683i	$0.421421\pi$
$938$	−5.75994	−0.188069
$939$	43.3766	1.41554
$940$	−28.8450	−0.940820
$941$	9.93451	0.323856	0.161928	−	0.986803i	$-0.448229\pi$
$941$	9.93451	0.323856	0.161928	+	0.986803i	$0.448229\pi$
$942$	22.0857	0.719591
$943$	7.46225	0.243004
$944$	−8.06549	−0.262509
$945$	−12.4801	−0.405978
$946$	30.2853	0.984661
$947$	−40.4958	−1.31594	−0.657969	−	0.753045i	$-0.728584\pi$
$947$	−40.4958	−1.31594	−0.657969	+	0.753045i	$0.728584\pi$
$948$	13.5137	0.438905
$949$	0	0
$950$	6.72804	0.218286
$951$	39.5247	1.28168
$952$	7.09122	0.229828
$953$	18.9602	0.614182	0.307091	−	0.951680i	$-0.400644\pi$
$953$	18.9602	0.614182	0.307091	+	0.951680i	$0.400644\pi$
$954$	28.5596	0.924653
$955$	11.2736	0.364807
$956$	6.13098	0.198290
$957$	70.2606	2.27120
$958$	−22.0515	−0.712450
$959$	−11.1427	−0.359816
$960$	7.09122	0.228868
$961$	−19.9026	−0.642020
$962$	0	0
$963$	−16.7544	−0.539904
$964$	27.3251	0.880082
$965$	−6.31341	−0.203236
$966$	4.90261	0.157739
$967$	−4.63448	−0.149035	−0.0745174	−	0.997220i	$-0.523742\pi$
$967$	−4.63448	−0.149035	−0.0745174	+	0.997220i	$0.523742\pi$
$968$	−0.0973913	−0.00313027
$969$	−89.7929	−2.88456
$970$	−19.7538	−0.634255
$971$	23.7336	0.761646	0.380823	−	0.924648i	$-0.375641\pi$
$971$	23.7336	0.761646	0.380823	+	0.924648i	$0.375641\pi$
$972$	−16.4427	−0.527400
$973$	−4.54561	−0.145725
$974$	−4.42867	−0.141904
$975$	0	0
$976$	−0.785667	−0.0251486
$977$	−4.74208	−0.151712	−0.0758562	−	0.997119i	$-0.524169\pi$
$977$	−4.74208	−0.151712	−0.0758562	+	0.997119i	$0.524169\pi$
$978$	28.0000	0.895341
$979$	50.2730	1.60673
$980$	2.54561	0.0813165
$981$	−62.5583	−1.99733
$982$	−31.0274	−0.990124
$983$	−23.7414	−0.757233	−0.378617	−	0.925554i	$-0.623600\pi$
$983$	−23.7414	−0.757233	−0.378617	+	0.925554i	$0.623600\pi$
$984$	−11.8114	−0.376533
$985$	−22.5316	−0.717916
$986$	−53.6900	−1.70984
$987$	31.5652	1.00473
$988$	0	0
$989$	−16.0000	−0.508770
$990$	−40.3649	−1.28288
$991$	40.8512	1.29768	0.648840	−	0.760925i	$-0.275254\pi$
$991$	40.8512	1.29768	0.648840	+	0.760925i	$0.275254\pi$
$992$	3.33127	0.105768
$993$	−7.94237	−0.252044
$994$	11.1427	0.353424
$995$	−2.77781	−0.0880624
$996$	31.2222	0.989313
$997$	−5.87688	−0.186123	−0.0930614	−	0.995660i	$-0.529665\pi$
$997$	−5.87688	−0.186123	−0.0930614	+	0.995660i	$0.529665\pi$
$998$	−23.0850	−0.730744
$999$	−18.4335	−0.583211

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.a.x.1.3		3
13.5	odd	4		182.2.d.b.155.6	yes	6
13.8	odd	4		182.2.d.b.155.3	✓	6
13.12	even	2		2366.2.a.bc.1.3		3
39.5	even	4		1638.2.c.i.883.3		6
39.8	even	4		1638.2.c.i.883.4		6
52.31	even	4		1456.2.k.b.337.1		6
52.47	even	4		1456.2.k.b.337.2		6
91.5	even	12		1274.2.n.n.753.6		12
91.18	odd	12		1274.2.n.m.961.1		12
91.31	even	12		1274.2.n.n.961.3		12
91.34	even	4		1274.2.d.l.883.1		6
91.44	odd	12		1274.2.n.m.753.4		12
91.47	even	12		1274.2.n.n.753.3		12
91.60	odd	12		1274.2.n.m.961.4		12
91.73	even	12		1274.2.n.n.961.6		12
91.83	even	4		1274.2.d.l.883.4		6
91.86	odd	12		1274.2.n.m.753.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.d.b.155.3	✓	6	13.8	odd	4
182.2.d.b.155.6	yes	6	13.5	odd	4
1274.2.d.l.883.1		6	91.34	even	4
1274.2.d.l.883.4		6	91.83	even	4
1274.2.n.m.753.1		12	91.86	odd	12
1274.2.n.m.753.4		12	91.44	odd	12
1274.2.n.m.961.1		12	91.18	odd	12
1274.2.n.m.961.4		12	91.60	odd	12
1274.2.n.n.753.3		12	91.47	even	12
1274.2.n.n.753.6		12	91.5	even	12
1274.2.n.n.961.3		12	91.31	even	12
1274.2.n.n.961.6		12	91.73	even	12
1456.2.k.b.337.1		6	52.31	even	4
1456.2.k.b.337.2		6	52.47	even	4
1638.2.c.i.883.3		6	39.5	even	4
1638.2.c.i.883.4		6	39.8	even	4
2366.2.a.x.1.3		3	1.1	even	1	trivial
2366.2.a.bc.1.3		3	13.12	even	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:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.78567 q^{3} +1.00000 q^{4} +2.54561 q^{5} -2.78567 q^{6} -1.00000 q^{7} -1.00000 q^{8} +4.75994 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.78567 q^{3} +1.00000 q^{4} +2.54561 q^{5} -2.78567 q^{6} -1.00000 q^{7} -1.00000 q^{8} +4.75994 q^{9} -2.54561 q^{10} +3.33127 q^{11} +2.78567 q^{12} +1.00000 q^{14} +7.09122 q^{15} +1.00000 q^{16} +7.09122 q^{17} -4.75994 q^{18} -4.54561 q^{19} +2.54561 q^{20} -2.78567 q^{21} -3.33127 q^{22} +1.75994 q^{23} -2.78567 q^{24} +1.48012 q^{25} +4.90261 q^{27} -1.00000 q^{28} +7.57133 q^{29} -7.09122 q^{30} -3.33127 q^{31} -1.00000 q^{32} +9.27982 q^{33} -7.09122 q^{34} -2.54561 q^{35} +4.75994 q^{36} -3.75994 q^{37} +4.54561 q^{38} -2.54561 q^{40} +4.24006 q^{41} +2.78567 q^{42} -9.09122 q^{43} +3.33127 q^{44} +12.1169 q^{45} -1.75994 q^{46} -11.3313 q^{47} +2.78567 q^{48} +1.00000 q^{49} -1.48012 q^{50} +19.7538 q^{51} -6.00000 q^{53} -4.90261 q^{54} +8.48012 q^{55} +1.00000 q^{56} -12.6625 q^{57} -7.57133 q^{58} -8.06549 q^{59} +7.09122 q^{60} -0.785667 q^{61} +3.33127 q^{62} -4.75994 q^{63} +1.00000 q^{64} -9.27982 q^{66} -5.75994 q^{67} +7.09122 q^{68} +4.90261 q^{69} +2.54561 q^{70} +11.1427 q^{71} -4.75994 q^{72} +9.33127 q^{73} +3.75994 q^{74} +4.12312 q^{75} -4.54561 q^{76} -3.33127 q^{77} +4.85116 q^{79} +2.54561 q^{80} -0.622787 q^{81} -4.24006 q^{82} +11.2082 q^{83} -2.78567 q^{84} +18.0515 q^{85} +9.09122 q^{86} +21.0912 q^{87} -3.33127 q^{88} +15.0912 q^{89} -12.1169 q^{90} +1.75994 q^{92} -9.27982 q^{93} +11.3313 q^{94} -11.5713 q^{95} -2.78567 q^{96} +7.75994 q^{97} -1.00000 q^{98} +15.8567 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + q^{3} + 3 q^{4} - 2 q^{5} - q^{6} - 3 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + q^3 + 3 * q^4 - 2 * q^5 - q^6 - 3 * q^7 - 3 * q^8 + 12 * q^9	\( 3 q - 3 q^{2} + q^{3} + 3 q^{4} - 2 q^{5} - q^{6} - 3 q^{7} - 3 q^{8} + 12 q^{9} + 2 q^{10} - 7 q^{11} + q^{12} + 3 q^{14} + 2 q^{15} + 3 q^{16} + 2 q^{17} - 12 q^{18} - 4 q^{19} - 2 q^{20} - q^{21} + 7 q^{22} + 3 q^{23} - q^{24} + 9 q^{25} - 17 q^{27} - 3 q^{28} + 8 q^{29} - 2 q^{30} + 7 q^{31} - 3 q^{32} + 21 q^{33} - 2 q^{34} + 2 q^{35} + 12 q^{36} - 9 q^{37} + 4 q^{38} + 2 q^{40} + 15 q^{41} + q^{42} - 8 q^{43} - 7 q^{44} + 12 q^{45} - 3 q^{46} - 17 q^{47} + q^{48} + 3 q^{49} - 9 q^{50} + 6 q^{51} - 18 q^{53} + 17 q^{54} + 30 q^{55} + 3 q^{56} - 4 q^{57} - 8 q^{58} - 10 q^{59} + 2 q^{60} + 5 q^{61} - 7 q^{62} - 12 q^{63} + 3 q^{64} - 21 q^{66} - 15 q^{67} + 2 q^{68} - 17 q^{69} - 2 q^{70} + 4 q^{71} - 12 q^{72} + 11 q^{73} + 9 q^{74} + 39 q^{75} - 4 q^{76} + 7 q^{77} - 7 q^{79} - 2 q^{80} + 23 q^{81} - 15 q^{82} - 10 q^{83} - q^{84} + 44 q^{85} + 8 q^{86} + 44 q^{87} + 7 q^{88} + 26 q^{89} - 12 q^{90} + 3 q^{92} - 21 q^{93} + 17 q^{94} - 20 q^{95} - q^{96} + 21 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + q^3 + 3 * q^4 - 2 * q^5 - q^6 - 3 * q^7 - 3 * q^8 + 12 * q^9 + 2 * q^10 - 7 * q^11 + q^12 + 3 * q^14 + 2 * q^15 + 3 * q^16 + 2 * q^17 - 12 * q^18 - 4 * q^19 - 2 * q^20 - q^21 + 7 * q^22 + 3 * q^23 - q^24 + 9 * q^25 - 17 * q^27 - 3 * q^28 + 8 * q^29 - 2 * q^30 + 7 * q^31 - 3 * q^32 + 21 * q^33 - 2 * q^34 + 2 * q^35 + 12 * q^36 - 9 * q^37 + 4 * q^38 + 2 * q^40 + 15 * q^41 + q^42 - 8 * q^43 - 7 * q^44 + 12 * q^45 - 3 * q^46 - 17 * q^47 + q^48 + 3 * q^49 - 9 * q^50 + 6 * q^51 - 18 * q^53 + 17 * q^54 + 30 * q^55 + 3 * q^56 - 4 * q^57 - 8 * q^58 - 10 * q^59 + 2 * q^60 + 5 * q^61 - 7 * q^62 - 12 * q^63 + 3 * q^64 - 21 * q^66 - 15 * q^67 + 2 * q^68 - 17 * q^69 - 2 * q^70 + 4 * q^71 - 12 * q^72 + 11 * q^73 + 9 * q^74 + 39 * q^75 - 4 * q^76 + 7 * q^77 - 7 * q^79 - 2 * q^80 + 23 * q^81 - 15 * q^82 - 10 * q^83 - q^84 + 44 * q^85 + 8 * q^86 + 44 * q^87 + 7 * q^88 + 26 * q^89 - 12 * q^90 + 3 * q^92 - 21 * q^93 + 17 * q^94 - 20 * q^95 - q^96 + 21 * q^97 - 3 * q^98 - 26 * q^99

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