LMFDB - Embedded newform 2366.2.a.bh.1.2

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:	$6$
Coefficient field:	6.6.285686784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 10x^{4} + 12x^{3} + 21x^{2} + 2x - 2 $ x^6 - 2x^5 - 10x^4 + 12x^3 + 21x^2 + 2*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
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			1.2
Root			$-0.865515$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.865515 q^{3} +1.00000 q^{4} -3.71131 q^{5} -0.865515 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.25088 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.865515 q^{3} +1.00000 q^{4} -3.71131 q^{5} -0.865515 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.25088 q^{9} -3.71131 q^{10} -5.77486 q^{11} -0.865515 q^{12} +1.00000 q^{14} +3.21220 q^{15} +1.00000 q^{16} -0.212197 q^{17} -2.25088 q^{18} +2.13714 q^{19} -3.71131 q^{20} -0.865515 q^{21} -5.77486 q^{22} +2.47940 q^{23} -0.865515 q^{24} +8.77384 q^{25} +4.54472 q^{27} +1.00000 q^{28} -0.0985660 q^{29} +3.21220 q^{30} +2.31076 q^{31} +1.00000 q^{32} +4.99823 q^{33} -0.212197 q^{34} -3.71131 q^{35} -2.25088 q^{36} +7.87343 q^{37} +2.13714 q^{38} -3.71131 q^{40} -7.52119 q^{41} -0.865515 q^{42} +4.57973 q^{43} -5.77486 q^{44} +8.35373 q^{45} +2.47940 q^{46} -9.15570 q^{47} -0.865515 q^{48} +1.00000 q^{49} +8.77384 q^{50} +0.183660 q^{51} +12.0948 q^{53} +4.54472 q^{54} +21.4323 q^{55} +1.00000 q^{56} -1.84972 q^{57} -0.0985660 q^{58} +0.231914 q^{59} +3.21220 q^{60} +8.03211 q^{61} +2.31076 q^{62} -2.25088 q^{63} +1.00000 q^{64} +4.99823 q^{66} +12.9700 q^{67} -0.212197 q^{68} -2.14596 q^{69} -3.71131 q^{70} +7.36377 q^{71} -2.25088 q^{72} -5.60414 q^{73} +7.87343 q^{74} -7.59389 q^{75} +2.13714 q^{76} -5.77486 q^{77} -9.19749 q^{79} -3.71131 q^{80} +2.81913 q^{81} -7.52119 q^{82} +3.17186 q^{83} -0.865515 q^{84} +0.787529 q^{85} +4.57973 q^{86} +0.0853103 q^{87} -5.77486 q^{88} -11.8167 q^{89} +8.35373 q^{90} +2.47940 q^{92} -2.00000 q^{93} -9.15570 q^{94} -7.93158 q^{95} -0.865515 q^{96} +14.0819 q^{97} +1.00000 q^{98} +12.9985 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	$ 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{12} + 6 q^{14} + 14 q^{15} + 6 q^{16} + 4 q^{17} + 6 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 2 q^{22} - 6 q^{23} + 2 q^{24} + 12 q^{25} + 20 q^{27} + 6 q^{28} + 10 q^{29} + 14 q^{30} - 2 q^{31} + 6 q^{32} + 4 q^{34} - 2 q^{35} + 6 q^{36} - 4 q^{38} - 2 q^{40} + 6 q^{41} + 2 q^{42} + 26 q^{43} + 2 q^{44} - 6 q^{45} - 6 q^{46} - 8 q^{47} + 2 q^{48} + 6 q^{49} + 12 q^{50} + 18 q^{51} + 18 q^{53} + 20 q^{54} + 6 q^{55} + 6 q^{56} - 28 q^{57} + 10 q^{58} + 2 q^{59} + 14 q^{60} + 28 q^{61} - 2 q^{62} + 6 q^{63} + 6 q^{64} + 6 q^{67} + 4 q^{68} + 32 q^{69} - 2 q^{70} + 4 q^{71} + 6 q^{72} - 22 q^{73} - 48 q^{75} - 4 q^{76} + 2 q^{77} + 22 q^{79} - 2 q^{80} + 34 q^{81} + 6 q^{82} - 10 q^{83} + 2 q^{84} + 32 q^{85} + 26 q^{86} - 2 q^{87} + 2 q^{88} - 4 q^{89} - 6 q^{90} - 6 q^{92} - 12 q^{93} - 8 q^{94} + 32 q^{95} + 2 q^{96} - 12 q^{97} + 6 q^{98} - 2 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 - 2 * q^10 + 2 * q^11 + 2 * q^12 + 6 * q^14 + 14 * q^15 + 6 * q^16 + 4 * q^17 + 6 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 2 * q^22 - 6 * q^23 + 2 * q^24 + 12 * q^25 + 20 * q^27 + 6 * q^28 + 10 * q^29 + 14 * q^30 - 2 * q^31 + 6 * q^32 + 4 * q^34 - 2 * q^35 + 6 * q^36 - 4 * q^38 - 2 * q^40 + 6 * q^41 + 2 * q^42 + 26 * q^43 + 2 * q^44 - 6 * q^45 - 6 * q^46 - 8 * q^47 + 2 * q^48 + 6 * q^49 + 12 * q^50 + 18 * q^51 + 18 * q^53 + 20 * q^54 + 6 * q^55 + 6 * q^56 - 28 * q^57 + 10 * q^58 + 2 * q^59 + 14 * q^60 + 28 * q^61 - 2 * q^62 + 6 * q^63 + 6 * q^64 + 6 * q^67 + 4 * q^68 + 32 * q^69 - 2 * q^70 + 4 * q^71 + 6 * q^72 - 22 * q^73 - 48 * q^75 - 4 * q^76 + 2 * q^77 + 22 * q^79 - 2 * q^80 + 34 * q^81 + 6 * q^82 - 10 * q^83 + 2 * q^84 + 32 * q^85 + 26 * q^86 - 2 * q^87 + 2 * q^88 - 4 * q^89 - 6 * q^90 - 6 * q^92 - 12 * q^93 - 8 * q^94 + 32 * q^95 + 2 * q^96 - 12 * q^97 + 6 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.865515	−0.499705	−0.249853	−	0.968284i	$-0.580382\pi$
$3$	−0.865515	−0.499705	−0.249853	+	0.968284i	$0.580382\pi$
$4$	1.00000	0.500000
$5$	−3.71131	−1.65975	−0.829875	−	0.557950i	$-0.811588\pi$
$5$	−3.71131	−1.65975	−0.829875	+	0.557950i	$0.811588\pi$
$6$	−0.865515	−0.353345
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−2.25088	−0.750295
$10$	−3.71131	−1.17362
$11$	−5.77486	−1.74119	−0.870594	−	0.492003i	$-0.836265\pi$
$11$	−5.77486	−1.74119	−0.870594	+	0.492003i	$0.836265\pi$
$12$	−0.865515	−0.249853
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	3.21220	0.829386
$16$	1.00000	0.250000
$17$	−0.212197	−0.0514653	−0.0257327	−	0.999669i	$-0.508192\pi$
$17$	−0.212197	−0.0514653	−0.0257327	+	0.999669i	$0.508192\pi$
$18$	−2.25088	−0.530538
$19$	2.13714	0.490293	0.245146	−	0.969486i	$-0.421164\pi$
$19$	2.13714	0.490293	0.245146	+	0.969486i	$0.421164\pi$
$20$	−3.71131	−0.829875
$21$	−0.865515	−0.188871
$22$	−5.77486	−1.23121
$23$	2.47940	0.516990	0.258495	−	0.966013i	$-0.416773\pi$
$23$	2.47940	0.516990	0.258495	+	0.966013i	$0.416773\pi$
$24$	−0.865515	−0.176673
$25$	8.77384	1.75477
$26$	0	0
$27$	4.54472	0.874632
$28$	1.00000	0.188982
$29$	−0.0985660	−0.0183032	−0.00915162	−	0.999958i	$-0.502913\pi$
$29$	−0.0985660	−0.0183032	−0.00915162	+	0.999958i	$0.502913\pi$
$30$	3.21220	0.586464
$31$	2.31076	0.415025	0.207513	−	0.978232i	$-0.433463\pi$
$31$	2.31076	0.415025	0.207513	+	0.978232i	$0.433463\pi$
$32$	1.00000	0.176777
$33$	4.99823	0.870080
$34$	−0.212197	−0.0363915
$35$	−3.71131	−0.627326
$36$	−2.25088	−0.375147
$37$	7.87343	1.29438	0.647192	−	0.762327i	$-0.275943\pi$
$37$	7.87343	1.29438	0.647192	+	0.762327i	$0.275943\pi$
$38$	2.13714	0.346689
$39$	0	0
$40$	−3.71131	−0.586810
$41$	−7.52119	−1.17461	−0.587306	−	0.809365i	$-0.699812\pi$
$41$	−7.52119	−1.17461	−0.587306	+	0.809365i	$0.699812\pi$
$42$	−0.865515	−0.133552
$43$	4.57973	0.698403	0.349201	−	0.937048i	$-0.386453\pi$
$43$	4.57973	0.698403	0.349201	+	0.937048i	$0.386453\pi$
$44$	−5.77486	−0.870594
$45$	8.35373	1.24530
$46$	2.47940	0.365567
$47$	−9.15570	−1.33550	−0.667748	−	0.744388i	$-0.732742\pi$
$47$	−9.15570	−1.33550	−0.667748	+	0.744388i	$0.732742\pi$
$48$	−0.865515	−0.124926
$49$	1.00000	0.142857
$50$	8.77384	1.24081
$51$	0.183660	0.0257175
$52$	0	0
$53$	12.0948	1.66135	0.830674	−	0.556759i	$-0.187955\pi$
$53$	12.0948	1.66135	0.830674	+	0.556759i	$0.187955\pi$
$54$	4.54472	0.618458
$55$	21.4323	2.88993
$56$	1.00000	0.133631
$57$	−1.84972	−0.245002
$58$	−0.0985660	−0.0129423
$59$	0.231914	0.0301926	0.0150963	−	0.999886i	$-0.495195\pi$
$59$	0.231914	0.0301926	0.0150963	+	0.999886i	$0.495195\pi$
$60$	3.21220	0.414693
$61$	8.03211	1.02841	0.514203	−	0.857668i	$-0.328088\pi$
$61$	8.03211	1.02841	0.514203	+	0.857668i	$0.328088\pi$
$62$	2.31076	0.293467
$63$	−2.25088	−0.283585
$64$	1.00000	0.125000
$65$	0	0
$66$	4.99823	0.615240
$67$	12.9700	1.58454	0.792269	−	0.610172i	$-0.208900\pi$
$67$	12.9700	1.58454	0.792269	+	0.610172i	$0.208900\pi$
$68$	−0.212197	−0.0257327
$69$	−2.14596	−0.258343
$70$	−3.71131	−0.443587
$71$	7.36377	0.873918	0.436959	−	0.899481i	$-0.356055\pi$
$71$	7.36377	0.873918	0.436959	+	0.899481i	$0.356055\pi$
$72$	−2.25088	−0.265269
$73$	−5.60414	−0.655915	−0.327958	−	0.944692i	$-0.606360\pi$
$73$	−5.60414	−0.655915	−0.327958	+	0.944692i	$0.606360\pi$
$74$	7.87343	0.915268
$75$	−7.59389	−0.876867
$76$	2.13714	0.245146
$77$	−5.77486	−0.658107
$78$	0	0
$79$	−9.19749	−1.03480	−0.517399	−	0.855744i	$-0.673100\pi$
$79$	−9.19749	−1.03480	−0.517399	+	0.855744i	$0.673100\pi$
$80$	−3.71131	−0.414937
$81$	2.81913	0.313237
$82$	−7.52119	−0.830577
$83$	3.17186	0.348157	0.174078	−	0.984732i	$-0.444305\pi$
$83$	3.17186	0.348157	0.174078	+	0.984732i	$0.444305\pi$
$84$	−0.865515	−0.0944354
$85$	0.787529	0.0854196
$86$	4.57973	0.493845
$87$	0.0853103	0.00914623
$88$	−5.77486	−0.615603
$89$	−11.8167	−1.25256	−0.626282	−	0.779597i	$-0.715424\pi$
$89$	−11.8167	−1.25256	−0.626282	+	0.779597i	$0.715424\pi$
$90$	8.35373	0.880561
$91$	0	0
$92$	2.47940	0.258495
$93$	−2.00000	−0.207390
$94$	−9.15570	−0.944338
$95$	−7.93158	−0.813763
$96$	−0.865515	−0.0883363
$97$	14.0819	1.42980	0.714898	−	0.699229i	$-0.246473\pi$
$97$	14.0819	1.42980	0.714898	+	0.699229i	$0.246473\pi$
$98$	1.00000	0.101015
$99$	12.9985	1.30640
$100$	8.77384	0.877384
$101$	−6.15243	−0.612190	−0.306095	−	0.952001i	$-0.599023\pi$
$101$	−6.15243	−0.612190	−0.306095	+	0.952001i	$0.599023\pi$
$102$	0.183660	0.0181850
$103$	−19.3491	−1.90652	−0.953260	−	0.302152i	$-0.902295\pi$
$103$	−19.3491	−1.90652	−0.953260	+	0.302152i	$0.902295\pi$
$104$	0	0
$105$	3.21220	0.313478
$106$	12.0948	1.17475
$107$	11.6501	1.12626	0.563130	−	0.826368i	$-0.309597\pi$
$107$	11.6501	1.12626	0.563130	+	0.826368i	$0.309597\pi$
$108$	4.54472	0.437316
$109$	−5.73307	−0.549129	−0.274564	−	0.961569i	$-0.588534\pi$
$109$	−5.73307	−0.549129	−0.274564	+	0.961569i	$0.588534\pi$
$110$	21.4323	2.04349
$111$	−6.81457	−0.646811
$112$	1.00000	0.0944911
$113$	16.5194	1.55402	0.777008	−	0.629490i	$-0.216736\pi$
$113$	16.5194	1.55402	0.777008	+	0.629490i	$0.216736\pi$
$114$	−1.84972	−0.173243
$115$	−9.20183	−0.858075
$116$	−0.0985660	−0.00915162
$117$	0	0
$118$	0.231914	0.0213494
$119$	−0.212197	−0.0194521
$120$	3.21220	0.293232
$121$	22.3491	2.03173
$122$	8.03211	0.727193
$123$	6.50970	0.586960
$124$	2.31076	0.207513
$125$	−14.0059	−1.25273
$126$	−2.25088	−0.200525
$127$	−11.7884	−1.04605	−0.523025	−	0.852317i	$-0.675197\pi$
$127$	−11.7884	−1.04605	−0.523025	+	0.852317i	$0.675197\pi$
$128$	1.00000	0.0883883
$129$	−3.96383	−0.348996
$130$	0	0
$131$	−5.12859	−0.448087	−0.224043	−	0.974579i	$-0.571926\pi$
$131$	−5.12859	−0.448087	−0.224043	+	0.974579i	$0.571926\pi$
$132$	4.99823	0.435040
$133$	2.13714	0.185313
$134$	12.9700	1.12044
$135$	−16.8669	−1.45167
$136$	−0.212197	−0.0181957
$137$	9.39328	0.802522	0.401261	−	0.915964i	$-0.368572\pi$
$137$	9.39328	0.802522	0.401261	+	0.915964i	$0.368572\pi$
$138$	−2.14596	−0.182676
$139$	15.1413	1.28427	0.642133	−	0.766594i	$-0.278050\pi$
$139$	15.1413	1.28427	0.642133	+	0.766594i	$0.278050\pi$
$140$	−3.71131	−0.313663
$141$	7.92439	0.667354
$142$	7.36377	0.617954
$143$	0	0
$144$	−2.25088	−0.187574
$145$	0.365809	0.0303788
$146$	−5.60414	−0.463802
$147$	−0.865515	−0.0713865
$148$	7.87343	0.647192
$149$	−20.6027	−1.68784	−0.843919	−	0.536470i	$-0.819757\pi$
$149$	−20.6027	−1.68784	−0.843919	+	0.536470i	$0.819757\pi$
$150$	−7.59389	−0.620039
$151$	−11.9407	−0.971721	−0.485861	−	0.874036i	$-0.661494\pi$
$151$	−11.9407	−0.971721	−0.485861	+	0.874036i	$0.661494\pi$
$152$	2.13714	0.173345
$153$	0.477631	0.0386142
$154$	−5.77486	−0.465352
$155$	−8.57596	−0.688838
$156$	0	0
$157$	9.34022	0.745431	0.372715	−	0.927946i	$-0.378427\pi$
$157$	9.34022	0.745431	0.372715	+	0.927946i	$0.378427\pi$
$158$	−9.19749	−0.731713
$159$	−10.4682	−0.830185
$160$	−3.71131	−0.293405
$161$	2.47940	0.195404
$162$	2.81913	0.221492
$163$	−4.47730	−0.350689	−0.175345	−	0.984507i	$-0.556104\pi$
$163$	−4.47730	−0.350689	−0.175345	+	0.984507i	$0.556104\pi$
$164$	−7.52119	−0.587306
$165$	−18.5500	−1.44412
$166$	3.17186	0.246184
$167$	14.7068	1.13805	0.569025	−	0.822321i	$-0.307321\pi$
$167$	14.7068	1.13805	0.569025	+	0.822321i	$0.307321\pi$
$168$	−0.865515	−0.0667759
$169$	0	0
$170$	0.787529	0.0604008
$171$	−4.81045	−0.367864
$172$	4.57973	0.349201
$173$	13.7657	1.04659	0.523294	−	0.852152i	$-0.324703\pi$
$173$	13.7657	1.04659	0.523294	+	0.852152i	$0.324703\pi$
$174$	0.0853103	0.00646736
$175$	8.77384	0.663240
$176$	−5.77486	−0.435297
$177$	−0.200725	−0.0150874
$178$	−11.8167	−0.885696
$179$	15.2787	1.14198	0.570992	−	0.820955i	$-0.306559\pi$
$179$	15.2787	1.14198	0.570992	+	0.820955i	$0.306559\pi$
$180$	8.35373	0.622651
$181$	1.66748	0.123943	0.0619713	−	0.998078i	$-0.480261\pi$
$181$	1.66748	0.123943	0.0619713	+	0.998078i	$0.480261\pi$
$182$	0	0
$183$	−6.95191	−0.513900
$184$	2.47940	0.182784
$185$	−29.2208	−2.14835
$186$	−2.00000	−0.146647
$187$	1.22541	0.0896108
$188$	−9.15570	−0.667748
$189$	4.54472	0.330580
$190$	−7.93158	−0.575418
$191$	0.120976	0.00875351	0.00437676	−	0.999990i	$-0.498607\pi$
$191$	0.120976	0.00875351	0.00437676	+	0.999990i	$0.498607\pi$
$192$	−0.865515	−0.0624632
$193$	−2.75550	−0.198345	−0.0991725	−	0.995070i	$-0.531620\pi$
$193$	−2.75550	−0.198345	−0.0991725	+	0.995070i	$0.531620\pi$
$194$	14.0819	1.01102
$195$	0	0
$196$	1.00000	0.0714286
$197$	15.1253	1.07764	0.538818	−	0.842422i	$-0.318871\pi$
$197$	15.1253	1.07764	0.538818	+	0.842422i	$0.318871\pi$
$198$	12.9985	0.923767
$199$	5.30640	0.376161	0.188080	−	0.982154i	$-0.439773\pi$
$199$	5.30640	0.376161	0.188080	+	0.982154i	$0.439773\pi$
$200$	8.77384	0.620404
$201$	−11.2257	−0.791802
$202$	−6.15243	−0.432884
$203$	−0.0985660	−0.00691798
$204$	0.183660	0.0128587
$205$	27.9135	1.94956
$206$	−19.3491	−1.34811
$207$	−5.58084	−0.387895
$208$	0	0
$209$	−12.3417	−0.853691
$210$	3.21220	0.221663
$211$	17.8982	1.23216	0.616081	−	0.787682i	$-0.288719\pi$
$211$	17.8982	1.23216	0.616081	+	0.787682i	$0.288719\pi$
$212$	12.0948	0.830674
$213$	−6.37345	−0.436702
$214$	11.6501	0.796386
$215$	−16.9968	−1.15917
$216$	4.54472	0.309229
$217$	2.31076	0.156865
$218$	−5.73307	−0.388293
$219$	4.85047	0.327764
$220$	21.4323	1.44497
$221$	0	0
$222$	−6.81457	−0.457364
$223$	16.4385	1.10080	0.550402	−	0.834900i	$-0.314475\pi$
$223$	16.4385	1.10080	0.550402	+	0.834900i	$0.314475\pi$
$224$	1.00000	0.0668153
$225$	−19.7489	−1.31659
$226$	16.5194	1.09886
$227$	−5.63095	−0.373739	−0.186870	−	0.982385i	$-0.559834\pi$
$227$	−5.63095	−0.373739	−0.186870	+	0.982385i	$0.559834\pi$
$228$	−1.84972	−0.122501
$229$	−27.7225	−1.83196	−0.915978	−	0.401228i	$-0.868584\pi$
$229$	−27.7225	−1.83196	−0.915978	+	0.401228i	$0.868584\pi$
$230$	−9.20183	−0.606750
$231$	4.99823	0.328860
$232$	−0.0985660	−0.00647117
$233$	20.1104	1.31747	0.658737	−	0.752374i	$-0.271091\pi$
$233$	20.1104	1.31747	0.658737	+	0.752374i	$0.271091\pi$
$234$	0	0
$235$	33.9797	2.21659
$236$	0.231914	0.0150963
$237$	7.96057	0.517094
$238$	−0.212197	−0.0137547
$239$	6.62968	0.428838	0.214419	−	0.976742i	$-0.431214\pi$
$239$	6.62968	0.428838	0.214419	+	0.976742i	$0.431214\pi$
$240$	3.21220	0.207346
$241$	−1.61687	−0.104151	−0.0520757	−	0.998643i	$-0.516584\pi$
$241$	−1.61687	−0.104151	−0.0520757	+	0.998643i	$0.516584\pi$
$242$	22.3491	1.43665
$243$	−16.0742	−1.03116
$244$	8.03211	0.514203
$245$	−3.71131	−0.237107
$246$	6.50970	0.415044
$247$	0	0
$248$	2.31076	0.146734
$249$	−2.74529	−0.173976
$250$	−14.0059	−0.885812
$251$	0.507011	0.0320023	0.0160011	−	0.999872i	$-0.494906\pi$
$251$	0.507011	0.0320023	0.0160011	+	0.999872i	$0.494906\pi$
$252$	−2.25088	−0.141792
$253$	−14.3182	−0.900177
$254$	−11.7884	−0.739670
$255$	−0.681619	−0.0426846
$256$	1.00000	0.0625000
$257$	−9.64063	−0.601366	−0.300683	−	0.953724i	$-0.597215\pi$
$257$	−9.64063	−0.601366	−0.300683	+	0.953724i	$0.597215\pi$
$258$	−3.96383	−0.246777
$259$	7.87343	0.489231
$260$	0	0
$261$	0.221861	0.0137328
$262$	−5.12859	−0.316845
$263$	−7.34617	−0.452985	−0.226492	−	0.974013i	$-0.572726\pi$
$263$	−7.34617	−0.452985	−0.226492	+	0.974013i	$0.572726\pi$
$264$	4.99823	0.307620
$265$	−44.8876	−2.75742
$266$	2.13714	0.131036
$267$	10.2275	0.625912
$268$	12.9700	0.792269
$269$	22.3541	1.36295	0.681476	−	0.731841i	$-0.261338\pi$
$269$	22.3541	1.36295	0.681476	+	0.731841i	$0.261338\pi$
$270$	−16.8669	−1.02649
$271$	−9.61740	−0.584215	−0.292108	−	0.956385i	$-0.594357\pi$
$271$	−9.61740	−0.584215	−0.292108	+	0.956385i	$0.594357\pi$
$272$	−0.212197	−0.0128663
$273$	0	0
$274$	9.39328	0.567469
$275$	−50.6678	−3.05538
$276$	−2.14596	−0.129171
$277$	10.1789	0.611590	0.305795	−	0.952097i	$-0.401078\pi$
$277$	10.1789	0.611590	0.305795	+	0.952097i	$0.401078\pi$
$278$	15.1413	0.908113
$279$	−5.20126	−0.311391
$280$	−3.71131	−0.221793
$281$	−14.1692	−0.845265	−0.422633	−	0.906301i	$-0.638894\pi$
$281$	−14.1692	−0.845265	−0.422633	+	0.906301i	$0.638894\pi$
$282$	7.92439	0.471891
$283$	18.9326	1.12543	0.562714	−	0.826652i	$-0.309757\pi$
$283$	18.9326	1.12543	0.562714	+	0.826652i	$0.309757\pi$
$284$	7.36377	0.436959
$285$	6.86490	0.406642
$286$	0	0
$287$	−7.52119	−0.443962
$288$	−2.25088	−0.132635
$289$	−16.9550	−0.997351
$290$	0.365809	0.0214811
$291$	−12.1881	−0.714477
$292$	−5.60414	−0.327958
$293$	−3.65982	−0.213809	−0.106905	−	0.994269i	$-0.534094\pi$
$293$	−3.65982	−0.213809	−0.106905	+	0.994269i	$0.534094\pi$
$294$	−0.865515	−0.0504779
$295$	−0.860706	−0.0501122
$296$	7.87343	0.457634
$297$	−26.2451	−1.52290
$298$	−20.6027	−1.19348
$299$	0	0
$300$	−7.59389	−0.438434
$301$	4.57973	0.263971
$302$	−11.9407	−0.687111
$303$	5.32502	0.305915
$304$	2.13714	0.122573
$305$	−29.8097	−1.70690
$306$	0.477631	0.0273043
$307$	19.6987	1.12426	0.562132	−	0.827048i	$-0.309981\pi$
$307$	19.6987	1.12426	0.562132	+	0.827048i	$0.309981\pi$
$308$	−5.77486	−0.329053
$309$	16.7469	0.952698
$310$	−8.57596	−0.487082
$311$	−16.9685	−0.962195	−0.481098	−	0.876667i	$-0.659762\pi$
$311$	−16.9685	−0.962195	−0.481098	+	0.876667i	$0.659762\pi$
$312$	0	0
$313$	−4.53794	−0.256500	−0.128250	−	0.991742i	$-0.540936\pi$
$313$	−4.53794	−0.256500	−0.128250	+	0.991742i	$0.540936\pi$
$314$	9.34022	0.527099
$315$	8.35373	0.470680
$316$	−9.19749	−0.517399
$317$	29.1866	1.63928	0.819641	−	0.572877i	$-0.194173\pi$
$317$	29.1866	1.63928	0.819641	+	0.572877i	$0.194173\pi$
$318$	−10.4682	−0.587029
$319$	0.569205	0.0318694
$320$	−3.71131	−0.207469
$321$	−10.0834	−0.562798
$322$	2.47940	0.138171
$323$	−0.453494	−0.0252331
$324$	2.81913	0.156618
$325$	0	0
$326$	−4.47730	−0.247975
$327$	4.96206	0.274403
$328$	−7.52119	−0.415288
$329$	−9.15570	−0.504770
$330$	−18.5500	−1.02114
$331$	4.80542	0.264130	0.132065	−	0.991241i	$-0.457839\pi$
$331$	4.80542	0.264130	0.132065	+	0.991241i	$0.457839\pi$
$332$	3.17186	0.174078
$333$	−17.7222	−0.971169
$334$	14.7068	0.804722
$335$	−48.1357	−2.62994
$336$	−0.865515	−0.0472177
$337$	−17.7312	−0.965883	−0.482941	−	0.875653i	$-0.660432\pi$
$337$	−17.7312	−0.965883	−0.482941	+	0.875653i	$0.660432\pi$
$338$	0	0
$339$	−14.2978	−0.776550
$340$	0.787529	0.0427098
$341$	−13.3443	−0.722637
$342$	−4.81045	−0.260119
$343$	1.00000	0.0539949
$344$	4.57973	0.246923
$345$	7.96432	0.428784
$346$	13.7657	0.740049
$347$	−16.7048	−0.896760	−0.448380	−	0.893843i	$-0.647999\pi$
$347$	−16.7048	−0.896760	−0.448380	+	0.893843i	$0.647999\pi$
$348$	0.0853103	0.00457311
$349$	0.0200475	0.00107312	0.000536559	−	1.00000i	$-0.499829\pi$
$349$	0.0200475	0.00107312	0.000536559		1.00000i	$0.499829\pi$
$350$	8.77384	0.468982
$351$	0	0
$352$	−5.77486	−0.307801
$353$	−29.8258	−1.58747	−0.793734	−	0.608265i	$-0.791866\pi$
$353$	−29.8258	−1.58747	−0.793734	+	0.608265i	$0.791866\pi$
$354$	−0.200725	−0.0106684
$355$	−27.3292	−1.45049
$356$	−11.8167	−0.626282
$357$	0.183660	0.00972030
$358$	15.2787	0.807505
$359$	18.3351	0.967687	0.483844	−	0.875154i	$-0.339240\pi$
$359$	18.3351	0.967687	0.483844	+	0.875154i	$0.339240\pi$
$360$	8.35373	0.440280
$361$	−14.4326	−0.759613
$362$	1.66748	0.0876407
$363$	−19.3434	−1.01527
$364$	0	0
$365$	20.7987	1.08866
$366$	−6.95191	−0.363382
$367$	1.34485	0.0702007	0.0351004	−	0.999384i	$-0.488825\pi$
$367$	1.34485	0.0702007	0.0351004	+	0.999384i	$0.488825\pi$
$368$	2.47940	0.129248
$369$	16.9293	0.881306
$370$	−29.2208	−1.51912
$371$	12.0948	0.627931
$372$	−2.00000	−0.103695
$373$	−11.0715	−0.573261	−0.286630	−	0.958041i	$-0.592535\pi$
$373$	−11.0715	−0.573261	−0.286630	+	0.958041i	$0.592535\pi$
$374$	1.22541	0.0633644
$375$	12.1223	0.625994
$376$	−9.15570	−0.472169
$377$	0	0
$378$	4.54472	0.233755
$379$	−16.8105	−0.863495	−0.431747	−	0.901995i	$-0.642103\pi$
$379$	−16.8105	−0.863495	−0.431747	+	0.901995i	$0.642103\pi$
$380$	−7.93158	−0.406882
$381$	10.2030	0.522717
$382$	0.120976	0.00618967
$383$	16.5771	0.847051	0.423525	−	0.905884i	$-0.360792\pi$
$383$	16.5771	0.847051	0.423525	+	0.905884i	$0.360792\pi$
$384$	−0.865515	−0.0441681
$385$	21.4323	1.09229
$386$	−2.75550	−0.140251
$387$	−10.3084	−0.524008
$388$	14.0819	0.714898
$389$	1.17013	0.0593280	0.0296640	−	0.999560i	$-0.490556\pi$
$389$	1.17013	0.0593280	0.0296640	+	0.999560i	$0.490556\pi$
$390$	0	0
$391$	−0.526121	−0.0266071
$392$	1.00000	0.0505076
$393$	4.43887	0.223911
$394$	15.1253	0.762003
$395$	34.1348	1.71751
$396$	12.9985	0.653202
$397$	−26.1975	−1.31481	−0.657406	−	0.753536i	$-0.728346\pi$
$397$	−26.1975	−1.31481	−0.657406	+	0.753536i	$0.728346\pi$
$398$	5.30640	0.265986
$399$	−1.84972	−0.0926020
$400$	8.77384	0.438692
$401$	−11.3687	−0.567726	−0.283863	−	0.958865i	$-0.591616\pi$
$401$	−11.3687	−0.567726	−0.283863	+	0.958865i	$0.591616\pi$
$402$	−11.2257	−0.559888
$403$	0	0
$404$	−6.15243	−0.306095
$405$	−10.4627	−0.519894
$406$	−0.0985660	−0.00489175
$407$	−45.4680	−2.25376
$408$	0.183660	0.00909251
$409$	−23.3314	−1.15366	−0.576832	−	0.816863i	$-0.695711\pi$
$409$	−23.3314	−1.15366	−0.576832	+	0.816863i	$0.695711\pi$
$410$	27.9135	1.37855
$411$	−8.13003	−0.401025
$412$	−19.3491	−0.953260
$413$	0.231914	0.0114117
$414$	−5.58084	−0.274283
$415$	−11.7718	−0.577853
$416$	0	0
$417$	−13.1050	−0.641754
$418$	−12.3417	−0.603651
$419$	−12.6680	−0.618875	−0.309437	−	0.950920i	$-0.600141\pi$
$419$	−12.6680	−0.618875	−0.309437	+	0.950920i	$0.600141\pi$
$420$	3.21220	0.156739
$421$	27.6625	1.34819	0.674094	−	0.738646i	$-0.264534\pi$
$421$	27.6625	1.34819	0.674094	+	0.738646i	$0.264534\pi$
$422$	17.8982	0.871271
$423$	20.6084	1.00202
$424$	12.0948	0.587375
$425$	−1.86178	−0.0903098
$426$	−6.37345	−0.308795
$427$	8.03211	0.388701
$428$	11.6501	0.563130
$429$	0	0
$430$	−16.9968	−0.819660
$431$	−6.41393	−0.308948	−0.154474	−	0.987997i	$-0.549368\pi$
$431$	−6.41393	−0.308948	−0.154474	+	0.987997i	$0.549368\pi$
$432$	4.54472	0.218658
$433$	−0.0650270	−0.00312500	−0.00156250	−	0.999999i	$-0.500497\pi$
$433$	−0.0650270	−0.00312500	−0.00156250	+	0.999999i	$0.500497\pi$
$434$	2.31076	0.110920
$435$	−0.316613	−0.0151804
$436$	−5.73307	−0.274564
$437$	5.29881	0.253477
$438$	4.85047	0.231764
$439$	36.7778	1.75531	0.877655	−	0.479294i	$-0.159107\pi$
$439$	36.7778	1.75531	0.877655	+	0.479294i	$0.159107\pi$
$440$	21.4323	1.02175
$441$	−2.25088	−0.107185
$442$	0	0
$443$	−8.46383	−0.402129	−0.201064	−	0.979578i	$-0.564440\pi$
$443$	−8.46383	−0.402129	−0.201064	+	0.979578i	$0.564440\pi$
$444$	−6.81457	−0.323405
$445$	43.8553	2.07894
$446$	16.4385	0.778385
$447$	17.8319	0.843422
$448$	1.00000	0.0472456
$449$	22.6303	1.06799	0.533995	−	0.845488i	$-0.320690\pi$
$449$	22.6303	1.06799	0.533995	+	0.845488i	$0.320690\pi$
$450$	−19.7489	−0.930972
$451$	43.4339	2.04522
$452$	16.5194	0.777008
$453$	10.3349	0.485574
$454$	−5.63095	−0.264274
$455$	0	0
$456$	−1.84972	−0.0866213
$457$	16.3170	0.763278	0.381639	−	0.924311i	$-0.375360\pi$
$457$	16.3170	0.763278	0.381639	+	0.924311i	$0.375360\pi$
$458$	−27.7225	−1.29539
$459$	−0.964376	−0.0450132
$460$	−9.20183	−0.429037
$461$	19.2778	0.897858	0.448929	−	0.893567i	$-0.351806\pi$
$461$	19.2778	0.897858	0.448929	+	0.893567i	$0.351806\pi$
$462$	4.99823	0.232539
$463$	2.70218	0.125581	0.0627904	−	0.998027i	$-0.480000\pi$
$463$	2.70218	0.125581	0.0627904	+	0.998027i	$0.480000\pi$
$464$	−0.0985660	−0.00457581
$465$	7.42263	0.344216
$466$	20.1104	0.931594
$467$	18.3906	0.851014	0.425507	−	0.904955i	$-0.360096\pi$
$467$	18.3906	0.851014	0.425507	+	0.904955i	$0.360096\pi$
$468$	0	0
$469$	12.9700	0.598899
$470$	33.9797	1.56736
$471$	−8.08410	−0.372496
$472$	0.231914	0.0106747
$473$	−26.4473	−1.21605
$474$	7.96057	0.365641
$475$	18.7509	0.860350
$476$	−0.212197	−0.00972603
$477$	−27.2240	−1.24650
$478$	6.62968	0.303234
$479$	40.8708	1.86743	0.933717	−	0.358012i	$-0.116545\pi$
$479$	40.8708	1.86743	0.933717	+	0.358012i	$0.116545\pi$
$480$	3.21220	0.146616
$481$	0	0
$482$	−1.61687	−0.0736462
$483$	−2.14596	−0.0976444
$484$	22.3491	1.01587
$485$	−52.2622	−2.37310
$486$	−16.0742	−0.729138
$487$	17.6293	0.798861	0.399430	−	0.916764i	$-0.369208\pi$
$487$	17.6293	0.798861	0.399430	+	0.916764i	$0.369208\pi$
$488$	8.03211	0.363597
$489$	3.87517	0.175241
$490$	−3.71131	−0.167660
$491$	−18.8599	−0.851137	−0.425569	−	0.904926i	$-0.639926\pi$
$491$	−18.8599	−0.851137	−0.425569	+	0.904926i	$0.639926\pi$
$492$	6.50970	0.293480
$493$	0.0209154	0.000941982 0
$494$	0	0
$495$	−48.2417	−2.16830
$496$	2.31076	0.103756
$497$	7.36377	0.330310
$498$	−2.74529	−0.123019
$499$	2.10742	0.0943410	0.0471705	−	0.998887i	$-0.484980\pi$
$499$	2.10742	0.0943410	0.0471705	+	0.998887i	$0.484980\pi$
$500$	−14.0059	−0.626364
$501$	−12.7290	−0.568689
$502$	0.507011	0.0226290
$503$	21.7884	0.971498	0.485749	−	0.874098i	$-0.338547\pi$
$503$	21.7884	0.971498	0.485749	+	0.874098i	$0.338547\pi$
$504$	−2.25088	−0.100262
$505$	22.8336	1.01608
$506$	−14.3182	−0.636521
$507$	0	0
$508$	−11.7884	−0.523025
$509$	12.1977	0.540655	0.270328	−	0.962768i	$-0.412868\pi$
$509$	12.1977	0.540655	0.270328	+	0.962768i	$0.412868\pi$
$510$	−0.681619	−0.0301826
$511$	−5.60414	−0.247913
$512$	1.00000	0.0441942
$513$	9.71268	0.428826
$514$	−9.64063	−0.425230
$515$	71.8104	3.16435
$516$	−3.96383	−0.174498
$517$	52.8729	2.32535
$518$	7.87343	0.345939
$519$	−11.9144	−0.522986
$520$	0	0
$521$	−26.9765	−1.18186	−0.590932	−	0.806722i	$-0.701240\pi$
$521$	−26.9765	−1.18186	−0.590932	+	0.806722i	$0.701240\pi$
$522$	0.221861	0.00971057
$523$	−3.75365	−0.164136	−0.0820679	−	0.996627i	$-0.526152\pi$
$523$	−3.75365	−0.164136	−0.0820679	+	0.996627i	$0.526152\pi$
$524$	−5.12859	−0.224043
$525$	−7.59389	−0.331425
$526$	−7.34617	−0.320308
$527$	−0.490337	−0.0213594
$528$	4.99823	0.217520
$529$	−16.8526	−0.732721
$530$	−44.8876	−1.94979
$531$	−0.522012	−0.0226534
$532$	2.13714	0.0926566
$533$	0	0
$534$	10.2275	0.442587
$535$	−43.2372	−1.86931
$536$	12.9700	0.560219
$537$	−13.2240	−0.570656
$538$	22.3541	0.963752
$539$	−5.77486	−0.248741
$540$	−16.8669	−0.725835
$541$	0.0135705	0.000583440 0	0.000291720	−	1.00000i	$-0.499907\pi$
$541$	0.0135705	0.000583440 0	0.000291720		1.00000i	$0.499907\pi$
$542$	−9.61740	−0.413103
$543$	−1.44323	−0.0619348
$544$	−0.212197	−0.00909787
$545$	21.2772	0.911416
$546$	0	0
$547$	−9.66115	−0.413081	−0.206540	−	0.978438i	$-0.566220\pi$
$547$	−9.66115	−0.413081	−0.206540	+	0.978438i	$0.566220\pi$
$548$	9.39328	0.401261
$549$	−18.0793	−0.771608
$550$	−50.6678	−2.16048
$551$	−0.210649	−0.00897395
$552$	−2.14596	−0.0913380
$553$	−9.19749	−0.391117
$554$	10.1789	0.432460
$555$	25.2910	1.07354
$556$	15.1413	0.642133
$557$	−24.9582	−1.05751	−0.528757	−	0.848773i	$-0.677342\pi$
$557$	−24.9582	−1.05751	−0.528757	+	0.848773i	$0.677342\pi$
$558$	−5.20126	−0.220187
$559$	0	0
$560$	−3.71131	−0.156832
$561$	−1.06061	−0.0447790
$562$	−14.1692	−0.597693
$563$	15.8994	0.670080	0.335040	−	0.942204i	$-0.391250\pi$
$563$	15.8994	0.670080	0.335040	+	0.942204i	$0.391250\pi$
$564$	7.92439	0.333677
$565$	−61.3088	−2.57928
$566$	18.9326	0.795798
$567$	2.81913	0.118392
$568$	7.36377	0.308977
$569$	−17.9093	−0.750797	−0.375398	−	0.926864i	$-0.622494\pi$
$569$	−17.9093	−0.750797	−0.375398	+	0.926864i	$0.622494\pi$
$570$	6.86490	0.287539
$571$	12.5123	0.523623	0.261812	−	0.965119i	$-0.415680\pi$
$571$	12.5123	0.523623	0.261812	+	0.965119i	$0.415680\pi$
$572$	0	0
$573$	−0.104707	−0.00437418
$574$	−7.52119	−0.313928
$575$	21.7539	0.907199
$576$	−2.25088	−0.0937868
$577$	22.0910	0.919662	0.459831	−	0.888007i	$-0.347910\pi$
$577$	22.0910	0.919662	0.459831	+	0.888007i	$0.347910\pi$
$578$	−16.9550	−0.705234
$579$	2.38492	0.0991141
$580$	0.365809	0.0151894
$581$	3.17186	0.131591
$582$	−12.1881	−0.505211
$583$	−69.8458	−2.89272
$584$	−5.60414	−0.231901
$585$	0	0
$586$	−3.65982	−0.151186
$587$	21.1319	0.872205	0.436102	−	0.899897i	$-0.356359\pi$
$587$	21.1319	0.872205	0.436102	+	0.899897i	$0.356359\pi$
$588$	−0.865515	−0.0356932
$589$	4.93842	0.203484
$590$	−0.860706	−0.0354347
$591$	−13.0912	−0.538500
$592$	7.87343	0.323596
$593$	8.95493	0.367735	0.183867	−	0.982951i	$-0.441138\pi$
$593$	8.95493	0.367735	0.183867	+	0.982951i	$0.441138\pi$
$594$	−26.2451	−1.07685
$595$	0.787529	0.0322856
$596$	−20.6027	−0.843919
$597$	−4.59277	−0.187970
$598$	0	0
$599$	41.7996	1.70788	0.853942	−	0.520368i	$-0.174205\pi$
$599$	41.7996	1.70788	0.853942	+	0.520368i	$0.174205\pi$
$600$	−7.59389	−0.310019
$601$	15.2896	0.623676	0.311838	−	0.950135i	$-0.399055\pi$
$601$	15.2896	0.623676	0.311838	+	0.950135i	$0.399055\pi$
$602$	4.57973	0.186656
$603$	−29.1940	−1.18887
$604$	−11.9407	−0.485861
$605$	−82.9444	−3.37217
$606$	5.32502	0.216314
$607$	14.6087	0.592948	0.296474	−	0.955041i	$-0.404189\pi$
$607$	14.6087	0.592948	0.296474	+	0.955041i	$0.404189\pi$
$608$	2.13714	0.0866723
$609$	0.0853103	0.00345695
$610$	−29.8097	−1.20696
$611$	0	0
$612$	0.477631	0.0193071
$613$	39.2163	1.58393	0.791965	−	0.610566i	$-0.209058\pi$
$613$	39.2163	1.58393	0.791965	+	0.610566i	$0.209058\pi$
$614$	19.6987	0.794975
$615$	−24.1595	−0.974207
$616$	−5.77486	−0.232676
$617$	9.35868	0.376766	0.188383	−	0.982096i	$-0.439675\pi$
$617$	9.35868	0.376766	0.188383	+	0.982096i	$0.439675\pi$
$618$	16.7469	0.673659
$619$	−43.7075	−1.75675	−0.878376	−	0.477970i	$-0.841373\pi$
$619$	−43.7075	−1.75675	−0.878376	+	0.477970i	$0.841373\pi$
$620$	−8.57596	−0.344419
$621$	11.2682	0.452176
$622$	−16.9685	−0.680375
$623$	−11.8167	−0.473424
$624$	0	0
$625$	8.11112	0.324445
$626$	−4.53794	−0.181373
$627$	10.6819	0.426594
$628$	9.34022	0.372715
$629$	−1.67072	−0.0666159
$630$	8.35373	0.332821
$631$	20.7957	0.827864	0.413932	−	0.910308i	$-0.364155\pi$
$631$	20.7957	0.827864	0.413932	+	0.910308i	$0.364155\pi$
$632$	−9.19749	−0.365857
$633$	−15.4912	−0.615718
$634$	29.1866	1.15915
$635$	43.7504	1.73618
$636$	−10.4682	−0.415092
$637$	0	0
$638$	0.569205	0.0225350
$639$	−16.5750	−0.655696
$640$	−3.71131	−0.146703
$641$	−7.23795	−0.285882	−0.142941	−	0.989731i	$-0.545656\pi$
$641$	−7.23795	−0.285882	−0.142941	+	0.989731i	$0.545656\pi$
$642$	−10.0834	−0.397958
$643$	40.1718	1.58422	0.792111	−	0.610377i	$-0.208982\pi$
$643$	40.1718	1.58422	0.792111	+	0.610377i	$0.208982\pi$
$644$	2.47940	0.0977020
$645$	14.7110	0.579245
$646$	−0.453494	−0.0178425
$647$	14.5512	0.572068	0.286034	−	0.958220i	$-0.407663\pi$
$647$	14.5512	0.572068	0.286034	+	0.958220i	$0.407663\pi$
$648$	2.81913	0.110746
$649$	−1.33927	−0.0525710
$650$	0	0
$651$	−2.00000	−0.0783862
$652$	−4.47730	−0.175345
$653$	−49.7267	−1.94596	−0.972978	−	0.230896i	$-0.925834\pi$
$653$	−49.7267	−1.94596	−0.972978	+	0.230896i	$0.925834\pi$
$654$	4.96206	0.194032
$655$	19.0338	0.743712
$656$	−7.52119	−0.293653
$657$	12.6143	0.492130
$658$	−9.15570	−0.356926
$659$	−31.5977	−1.23087	−0.615436	−	0.788187i	$-0.711020\pi$
$659$	−31.5977	−1.23087	−0.615436	+	0.788187i	$0.711020\pi$
$660$	−18.5500	−0.722058
$661$	−24.8712	−0.967379	−0.483689	−	0.875240i	$-0.660704\pi$
$661$	−24.8712	−0.967379	−0.483689	+	0.875240i	$0.660704\pi$
$662$	4.80542	0.186768
$663$	0	0
$664$	3.17186	0.123092
$665$	−7.93158	−0.307574
$666$	−17.7222	−0.686720
$667$	−0.244384	−0.00946260
$668$	14.7068	0.569025
$669$	−14.2278	−0.550077
$670$	−48.1357	−1.85964
$671$	−46.3843	−1.79065
$672$	−0.865515	−0.0333880
$673$	−21.6490	−0.834508	−0.417254	−	0.908790i	$-0.637007\pi$
$673$	−21.6490	−0.834508	−0.417254	+	0.908790i	$0.637007\pi$
$674$	−17.7312	−0.682982
$675$	39.8747	1.53478
$676$	0	0
$677$	14.3935	0.553187	0.276594	−	0.960987i	$-0.410794\pi$
$677$	14.3935	0.553187	0.276594	+	0.960987i	$0.410794\pi$
$678$	−14.2978	−0.549104
$679$	14.0819	0.540412
$680$	0.787529	0.0302004
$681$	4.87367	0.186759
$682$	−13.3443	−0.510981
$683$	42.3738	1.62139	0.810694	−	0.585471i	$-0.199090\pi$
$683$	42.3738	1.62139	0.810694	+	0.585471i	$0.199090\pi$
$684$	−4.81045	−0.183932
$685$	−34.8614	−1.33199
$686$	1.00000	0.0381802
$687$	23.9943	0.915438
$688$	4.57973	0.174601
$689$	0	0
$690$	7.96432	0.303196
$691$	22.9382	0.872610	0.436305	−	0.899799i	$-0.356287\pi$
$691$	22.9382	0.872610	0.436305	+	0.899799i	$0.356287\pi$
$692$	13.7657	0.523294
$693$	12.9985	0.493774
$694$	−16.7048	−0.634105
$695$	−56.1940	−2.13156
$696$	0.0853103	0.00323368
$697$	1.59597	0.0604518
$698$	0.0200475	0.000758808 0
$699$	−17.4058	−0.658348
$700$	8.77384	0.331620
$701$	−1.70699	−0.0644723	−0.0322361	−	0.999480i	$-0.510263\pi$
$701$	−1.70699	−0.0644723	−0.0322361	+	0.999480i	$0.510263\pi$
$702$	0	0
$703$	16.8266	0.634627
$704$	−5.77486	−0.217648
$705$	−29.4099	−1.10764
$706$	−29.8258	−1.12251
$707$	−6.15243	−0.231386
$708$	−0.200725	−0.00754371
$709$	18.2131	0.684009	0.342005	−	0.939698i	$-0.388894\pi$
$709$	18.2131	0.684009	0.342005	+	0.939698i	$0.388894\pi$
$710$	−27.3292	−1.02565
$711$	20.7025	0.776404
$712$	−11.8167	−0.442848
$713$	5.72930	0.214564
$714$	0.183660	0.00687329
$715$	0	0
$716$	15.2787	0.570992
$717$	−5.73808	−0.214293
$718$	18.3351	0.684258
$719$	3.58214	0.133591	0.0667956	−	0.997767i	$-0.478722\pi$
$719$	3.58214	0.133591	0.0667956	+	0.997767i	$0.478722\pi$
$720$	8.35373	0.311325
$721$	−19.3491	−0.720597
$722$	−14.4326	−0.537128
$723$	1.39942	0.0520450
$724$	1.66748	0.0619713
$725$	−0.864802	−0.0321180
$726$	−19.3434	−0.717903
$727$	−3.21747	−0.119329	−0.0596647	−	0.998218i	$-0.519003\pi$
$727$	−3.21747	−0.119329	−0.0596647	+	0.998218i	$0.519003\pi$
$728$	0	0
$729$	5.45503	0.202038
$730$	20.7987	0.769796
$731$	−0.971806	−0.0359435
$732$	−6.95191	−0.256950
$733$	−4.79233	−0.177009	−0.0885043	−	0.996076i	$-0.528209\pi$
$733$	−4.79233	−0.177009	−0.0885043	+	0.996076i	$0.528209\pi$
$734$	1.34485	0.0496394
$735$	3.21220	0.118484
$736$	2.47940	0.0913919
$737$	−74.9000	−2.75898
$738$	16.9293	0.623177
$739$	11.1989	0.411958	0.205979	−	0.978556i	$-0.433962\pi$
$739$	11.1989	0.411958	0.205979	+	0.978556i	$0.433962\pi$
$740$	−29.2208	−1.07418
$741$	0	0
$742$	12.0948	0.444014
$743$	38.2570	1.40351	0.701757	−	0.712417i	$-0.252399\pi$
$743$	38.2570	1.40351	0.701757	+	0.712417i	$0.252399\pi$
$744$	−2.00000	−0.0733236
$745$	76.4630	2.80139
$746$	−11.0715	−0.405357
$747$	−7.13948	−0.261220
$748$	1.22541	0.0448054
$749$	11.6501	0.425686
$750$	12.1223	0.442645
$751$	−1.84025	−0.0671517	−0.0335758	−	0.999436i	$-0.510690\pi$
$751$	−1.84025	−0.0671517	−0.0335758	+	0.999436i	$0.510690\pi$
$752$	−9.15570	−0.333874
$753$	−0.438826	−0.0159917
$754$	0	0
$755$	44.3157	1.61281
$756$	4.54472	0.165290
$757$	−21.1921	−0.770241	−0.385120	−	0.922866i	$-0.625840\pi$
$757$	−21.1921	−0.770241	−0.385120	+	0.922866i	$0.625840\pi$
$758$	−16.8105	−0.610583
$759$	12.3926	0.449823
$760$	−7.93158	−0.287709
$761$	14.1313	0.512260	0.256130	−	0.966642i	$-0.417553\pi$
$761$	14.1313	0.512260	0.256130	+	0.966642i	$0.417553\pi$
$762$	10.2030	0.369617
$763$	−5.73307	−0.207551
$764$	0.120976	0.00437676
$765$	−1.77264	−0.0640898
$766$	16.5771	0.598955
$767$	0	0
$768$	−0.865515	−0.0312316
$769$	30.6249	1.10436	0.552181	−	0.833725i	$-0.313796\pi$
$769$	30.6249	1.10436	0.552181	+	0.833725i	$0.313796\pi$
$770$	21.4323	0.772368
$771$	8.34411	0.300506
$772$	−2.75550	−0.0991725
$773$	−9.79479	−0.352294	−0.176147	−	0.984364i	$-0.556363\pi$
$773$	−9.79479	−0.352294	−0.176147	+	0.984364i	$0.556363\pi$
$774$	−10.3084	−0.370529
$775$	20.2743	0.728273
$776$	14.0819	0.505509
$777$	−6.81457	−0.244471
$778$	1.17013	0.0419512
$779$	−16.0738	−0.575904
$780$	0	0
$781$	−42.5248	−1.52166
$782$	−0.526121	−0.0188140
$783$	−0.447955	−0.0160086
$784$	1.00000	0.0357143
$785$	−34.6645	−1.23723
$786$	4.43887	0.158329
$787$	−20.6305	−0.735397	−0.367699	−	0.929945i	$-0.619854\pi$
$787$	−20.6305	−0.735397	−0.367699	+	0.929945i	$0.619854\pi$
$788$	15.1253	0.538818
$789$	6.35822	0.226359
$790$	34.1348	1.21446
$791$	16.5194	0.587363
$792$	12.9985	0.461883
$793$	0	0
$794$	−26.1975	−0.929713
$795$	38.8509	1.37790
$796$	5.30640	0.188080
$797$	7.77168	0.275287	0.137643	−	0.990482i	$-0.456047\pi$
$797$	7.77168	0.275287	0.137643	+	0.990482i	$0.456047\pi$
$798$	−1.84972	−0.0654795
$799$	1.94281	0.0687317
$800$	8.77384	0.310202
$801$	26.5979	0.939791
$802$	−11.3687	−0.401443
$803$	32.3632	1.14207
$804$	−11.2257	−0.395901
$805$	−9.20183	−0.324322
$806$	0	0
$807$	−19.3478	−0.681074
$808$	−6.15243	−0.216442
$809$	42.5430	1.49573	0.747866	−	0.663850i	$-0.231078\pi$
$809$	42.5430	1.49573	0.747866	+	0.663850i	$0.231078\pi$
$810$	−10.4627	−0.367621
$811$	22.1131	0.776494	0.388247	−	0.921555i	$-0.373081\pi$
$811$	22.1131	0.776494	0.388247	+	0.921555i	$0.373081\pi$
$812$	−0.0985660	−0.00345899
$813$	8.32400	0.291936
$814$	−45.4680	−1.59365
$815$	16.6167	0.582056
$816$	0.183660	0.00642937
$817$	9.78752	0.342422
$818$	−23.3314	−0.815763
$819$	0	0
$820$	27.9135	0.974782
$821$	−24.3549	−0.849992	−0.424996	−	0.905195i	$-0.639725\pi$
$821$	−24.3549	−0.849992	−0.424996	+	0.905195i	$0.639725\pi$
$822$	−8.13003	−0.283567
$823$	−4.75914	−0.165893	−0.0829465	−	0.996554i	$-0.526433\pi$
$823$	−4.75914	−0.165893	−0.0829465	+	0.996554i	$0.526433\pi$
$824$	−19.3491	−0.674056
$825$	43.8537	1.52679
$826$	0.231914	0.00806932
$827$	7.00333	0.243530	0.121765	−	0.992559i	$-0.461145\pi$
$827$	7.00333	0.243530	0.121765	+	0.992559i	$0.461145\pi$
$828$	−5.58084	−0.193948
$829$	−5.75238	−0.199788	−0.0998941	−	0.994998i	$-0.531850\pi$
$829$	−5.75238	−0.199788	−0.0998941	+	0.994998i	$0.531850\pi$
$830$	−11.7718	−0.408604
$831$	−8.80998	−0.305615
$832$	0	0
$833$	−0.212197	−0.00735219
$834$	−13.1050	−0.453789
$835$	−54.5817	−1.88888
$836$	−12.3417	−0.426846
$837$	10.5018	0.362994
$838$	−12.6680	−0.437610
$839$	41.2070	1.42262	0.711311	−	0.702877i	$-0.248102\pi$
$839$	41.2070	1.42262	0.711311	+	0.702877i	$0.248102\pi$
$840$	3.21220	0.110831
$841$	−28.9903	−0.999665
$842$	27.6625	0.953312
$843$	12.2637	0.422384
$844$	17.8982	0.616081
$845$	0	0
$846$	20.6084	0.708532
$847$	22.3491	0.767923
$848$	12.0948	0.415337
$849$	−16.3865	−0.562382
$850$	−1.86178	−0.0638586
$851$	19.5214	0.669184
$852$	−6.37345	−0.218351
$853$	−2.38939	−0.0818113	−0.0409056	−	0.999163i	$-0.513024\pi$
$853$	−2.38939	−0.0818113	−0.0409056	+	0.999163i	$0.513024\pi$
$854$	8.03211	0.274853
$855$	17.8531	0.610562
$856$	11.6501	0.398193
$857$	13.8037	0.471526	0.235763	−	0.971811i	$-0.424241\pi$
$857$	13.8037	0.471526	0.235763	+	0.971811i	$0.424241\pi$
$858$	0	0
$859$	−37.7276	−1.28725	−0.643624	−	0.765342i	$-0.722570\pi$
$859$	−37.7276	−1.28725	−0.643624	+	0.765342i	$0.722570\pi$
$860$	−16.9968	−0.579587
$861$	6.50970	0.221850
$862$	−6.41393	−0.218459
$863$	−25.5180	−0.868643	−0.434322	−	0.900758i	$-0.643012\pi$
$863$	−25.5180	−0.868643	−0.434322	+	0.900758i	$0.643012\pi$
$864$	4.54472	0.154614
$865$	−51.0889	−1.73707
$866$	−0.0650270	−0.00220971
$867$	14.6748	0.498382
$868$	2.31076	0.0784324
$869$	53.1143	1.80178
$870$	−0.316613	−0.0107342
$871$	0	0
$872$	−5.73307	−0.194146
$873$	−31.6966	−1.07277
$874$	5.29881	0.179235
$875$	−14.0059	−0.473486
$876$	4.85047	0.163882
$877$	12.4391	0.420039	0.210019	−	0.977697i	$-0.432647\pi$
$877$	12.4391	0.420039	0.210019	+	0.977697i	$0.432647\pi$
$878$	36.7778	1.24119
$879$	3.16763	0.106842
$880$	21.4323	0.722484
$881$	−22.5419	−0.759457	−0.379728	−	0.925098i	$-0.623983\pi$
$881$	−22.5419	−0.759457	−0.379728	+	0.925098i	$0.623983\pi$
$882$	−2.25088	−0.0757912
$883$	15.1548	0.509998	0.254999	−	0.966941i	$-0.417925\pi$
$883$	15.1548	0.509998	0.254999	+	0.966941i	$0.417925\pi$
$884$	0	0
$885$	0.744954	0.0250413
$886$	−8.46383	−0.284348
$887$	41.7749	1.40266	0.701332	−	0.712835i	$-0.252589\pi$
$887$	41.7749	1.40266	0.701332	+	0.712835i	$0.252589\pi$
$888$	−6.81457	−0.228682
$889$	−11.7884	−0.395370
$890$	43.8553	1.47003
$891$	−16.2801	−0.545404
$892$	16.4385	0.550402
$893$	−19.5670	−0.654784
$894$	17.8319	0.596389
$895$	−56.7041	−1.89541
$896$	1.00000	0.0334077
$897$	0	0
$898$	22.6303	0.755183
$899$	−0.227763	−0.00759631
$900$	−19.7489	−0.658297
$901$	−2.56648	−0.0855018
$902$	43.4339	1.44619
$903$	−3.96383	−0.131908
$904$	16.5194	0.549428
$905$	−6.18853	−0.205714
$906$	10.3349	0.343353
$907$	4.28751	0.142365	0.0711823	−	0.997463i	$-0.477323\pi$
$907$	4.28751	0.142365	0.0711823	+	0.997463i	$0.477323\pi$
$908$	−5.63095	−0.186870
$909$	13.8484	0.459323
$910$	0	0
$911$	−3.87618	−0.128423	−0.0642117	−	0.997936i	$-0.520453\pi$
$911$	−3.87618	−0.128423	−0.0642117	+	0.997936i	$0.520453\pi$
$912$	−1.84972	−0.0612505
$913$	−18.3171	−0.606206
$914$	16.3170	0.539719
$915$	25.8007	0.852945
$916$	−27.7225	−0.915978
$917$	−5.12859	−0.169361
$918$	−0.964376	−0.0318291
$919$	45.9047	1.51426	0.757129	−	0.653266i	$-0.226601\pi$
$919$	45.9047	1.51426	0.757129	+	0.653266i	$0.226601\pi$
$920$	−9.20183	−0.303375
$921$	−17.0495	−0.561801
$922$	19.2778	0.634882
$923$	0	0
$924$	4.99823	0.164430
$925$	69.0802	2.27134
$926$	2.70218	0.0887990
$927$	43.5525	1.43045
$928$	−0.0985660	−0.00323559
$929$	9.83612	0.322713	0.161356	−	0.986896i	$-0.448413\pi$
$929$	9.83612	0.322713	0.161356	+	0.986896i	$0.448413\pi$
$930$	7.42263	0.243397
$931$	2.13714	0.0700418
$932$	20.1104	0.658737
$933$	14.6865	0.480814
$934$	18.3906	0.601758
$935$	−4.54788	−0.148731
$936$	0	0
$937$	21.5135	0.702815	0.351407	−	0.936223i	$-0.385703\pi$
$937$	21.5135	0.702815	0.351407	+	0.936223i	$0.385703\pi$
$938$	12.9700	0.423485
$939$	3.92766	0.128174
$940$	33.9797	1.10829
$941$	−6.41845	−0.209236	−0.104618	−	0.994513i	$-0.533362\pi$
$941$	−6.41845	−0.209236	−0.104618	+	0.994513i	$0.533362\pi$
$942$	−8.08410	−0.263394
$943$	−18.6480	−0.607264
$944$	0.231914	0.00754816
$945$	−16.8669	−0.548679
$946$	−26.4473	−0.859877
$947$	7.57266	0.246078	0.123039	−	0.992402i	$-0.460736\pi$
$947$	7.57266	0.246078	0.123039	+	0.992402i	$0.460736\pi$
$948$	7.96057	0.258547
$949$	0	0
$950$	18.7509	0.608360
$951$	−25.2614	−0.819158
$952$	−0.212197	−0.00687734
$953$	−35.8044	−1.15982	−0.579909	−	0.814681i	$-0.696912\pi$
$953$	−35.8044	−1.15982	−0.579909	+	0.814681i	$0.696912\pi$
$954$	−27.2240	−0.881409
$955$	−0.448980	−0.0145286
$956$	6.62968	0.214419
$957$	−0.492656	−0.0159253
$958$	40.8708	1.32048
$959$	9.39328	0.303325
$960$	3.21220	0.103673
$961$	−25.6604	−0.827754
$962$	0	0
$963$	−26.2231	−0.845027
$964$	−1.61687	−0.0520757
$965$	10.2265	0.329203
$966$	−2.14596	−0.0690450
$967$	32.3876	1.04152	0.520758	−	0.853704i	$-0.325649\pi$
$967$	32.3876	1.04152	0.520758	+	0.853704i	$0.325649\pi$
$968$	22.3491	0.718326
$969$	0.392506	0.0126091
$970$	−52.2622	−1.67804
$971$	34.4065	1.10416	0.552079	−	0.833792i	$-0.313835\pi$
$971$	34.4065	1.10416	0.552079	+	0.833792i	$0.313835\pi$
$972$	−16.0742	−0.515579
$973$	15.1413	0.485407
$974$	17.6293	0.564880
$975$	0	0
$976$	8.03211	0.257102
$977$	−23.1484	−0.740583	−0.370291	−	0.928916i	$-0.620742\pi$
$977$	−23.1484	−0.740583	−0.370291	+	0.928916i	$0.620742\pi$
$978$	3.87517	0.123914
$979$	68.2396	2.18095
$980$	−3.71131	−0.118554
$981$	12.9045	0.412008
$982$	−18.8599	−0.601845
$983$	47.0579	1.50092	0.750458	−	0.660919i	$-0.229833\pi$
$983$	47.0579	1.50092	0.750458	+	0.660919i	$0.229833\pi$
$984$	6.50970	0.207522
$985$	−56.1349	−1.78861
$986$	0.0209154	0.000666082 0
$987$	7.92439	0.252236
$988$	0	0
$989$	11.3550	0.361068
$990$	−48.2417	−1.53322
$991$	−11.9010	−0.378049	−0.189025	−	0.981972i	$-0.560533\pi$
$991$	−11.9010	−0.378049	−0.189025	+	0.981972i	$0.560533\pi$
$992$	2.31076	0.0733668
$993$	−4.15916	−0.131987
$994$	7.36377	0.233565
$995$	−19.6937	−0.624333
$996$	−2.74529	−0.0869879
$997$	13.0143	0.412166	0.206083	−	0.978534i	$-0.433928\pi$
$997$	13.0143	0.412166	0.206083	+	0.978534i	$0.433928\pi$
$998$	2.10742	0.0667092
$999$	35.7825	1.13211

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.a.bh.1.2		6
13.5	odd	4		2366.2.d.r.337.2		12
13.6	odd	12		182.2.m.b.127.3	yes	12
13.8	odd	4		2366.2.d.r.337.8		12
13.11	odd	12		182.2.m.b.43.3	✓	12
13.12	even	2		2366.2.a.bf.1.2		6
39.11	even	12		1638.2.bj.g.1135.6		12
39.32	even	12		1638.2.bj.g.127.4		12
52.11	even	12		1456.2.cc.d.225.2		12
52.19	even	12		1456.2.cc.d.673.2		12
91.6	even	12		1274.2.m.c.491.1		12
91.11	odd	12		1274.2.v.e.667.4		12
91.19	even	12		1274.2.v.d.361.6		12
91.24	even	12		1274.2.v.d.667.6		12
91.32	odd	12		1274.2.o.d.569.3		12
91.37	odd	12		1274.2.o.d.459.6		12
91.45	even	12		1274.2.o.e.569.1		12
91.58	odd	12		1274.2.v.e.361.4		12
91.76	even	12		1274.2.m.c.589.1		12
91.89	even	12		1274.2.o.e.459.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.3	✓	12	13.11	odd	12
182.2.m.b.127.3	yes	12	13.6	odd	12
1274.2.m.c.491.1		12	91.6	even	12
1274.2.m.c.589.1		12	91.76	even	12
1274.2.o.d.459.6		12	91.37	odd	12
1274.2.o.d.569.3		12	91.32	odd	12
1274.2.o.e.459.4		12	91.89	even	12
1274.2.o.e.569.1		12	91.45	even	12
1274.2.v.d.361.6		12	91.19	even	12
1274.2.v.d.667.6		12	91.24	even	12
1274.2.v.e.361.4		12	91.58	odd	12
1274.2.v.e.667.4		12	91.11	odd	12
1456.2.cc.d.225.2		12	52.11	even	12
1456.2.cc.d.673.2		12	52.19	even	12
1638.2.bj.g.127.4		12	39.32	even	12
1638.2.bj.g.1135.6		12	39.11	even	12
2366.2.a.bf.1.2		6	13.12	even	2
2366.2.a.bh.1.2		6	1.1	even	1	trivial
2366.2.d.r.337.2		12	13.5	odd	4
2366.2.d.r.337.8		12	13.8	odd	4

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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.865515 q^{3} +1.00000 q^{4} -3.71131 q^{5} -0.865515 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.25088 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.865515 q^{3} +1.00000 q^{4} -3.71131 q^{5} -0.865515 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.25088 q^{9} -3.71131 q^{10} -5.77486 q^{11} -0.865515 q^{12} +1.00000 q^{14} +3.21220 q^{15} +1.00000 q^{16} -0.212197 q^{17} -2.25088 q^{18} +2.13714 q^{19} -3.71131 q^{20} -0.865515 q^{21} -5.77486 q^{22} +2.47940 q^{23} -0.865515 q^{24} +8.77384 q^{25} +4.54472 q^{27} +1.00000 q^{28} -0.0985660 q^{29} +3.21220 q^{30} +2.31076 q^{31} +1.00000 q^{32} +4.99823 q^{33} -0.212197 q^{34} -3.71131 q^{35} -2.25088 q^{36} +7.87343 q^{37} +2.13714 q^{38} -3.71131 q^{40} -7.52119 q^{41} -0.865515 q^{42} +4.57973 q^{43} -5.77486 q^{44} +8.35373 q^{45} +2.47940 q^{46} -9.15570 q^{47} -0.865515 q^{48} +1.00000 q^{49} +8.77384 q^{50} +0.183660 q^{51} +12.0948 q^{53} +4.54472 q^{54} +21.4323 q^{55} +1.00000 q^{56} -1.84972 q^{57} -0.0985660 q^{58} +0.231914 q^{59} +3.21220 q^{60} +8.03211 q^{61} +2.31076 q^{62} -2.25088 q^{63} +1.00000 q^{64} +4.99823 q^{66} +12.9700 q^{67} -0.212197 q^{68} -2.14596 q^{69} -3.71131 q^{70} +7.36377 q^{71} -2.25088 q^{72} -5.60414 q^{73} +7.87343 q^{74} -7.59389 q^{75} +2.13714 q^{76} -5.77486 q^{77} -9.19749 q^{79} -3.71131 q^{80} +2.81913 q^{81} -7.52119 q^{82} +3.17186 q^{83} -0.865515 q^{84} +0.787529 q^{85} +4.57973 q^{86} +0.0853103 q^{87} -5.77486 q^{88} -11.8167 q^{89} +8.35373 q^{90} +2.47940 q^{92} -2.00000 q^{93} -9.15570 q^{94} -7.93158 q^{95} -0.865515 q^{96} +14.0819 q^{97} +1.00000 q^{98} +12.9985 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{12} + 6 q^{14} + 14 q^{15} + 6 q^{16} + 4 q^{17} + 6 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 2 q^{22} - 6 q^{23} + 2 q^{24} + 12 q^{25} + 20 q^{27} + 6 q^{28} + 10 q^{29} + 14 q^{30} - 2 q^{31} + 6 q^{32} + 4 q^{34} - 2 q^{35} + 6 q^{36} - 4 q^{38} - 2 q^{40} + 6 q^{41} + 2 q^{42} + 26 q^{43} + 2 q^{44} - 6 q^{45} - 6 q^{46} - 8 q^{47} + 2 q^{48} + 6 q^{49} + 12 q^{50} + 18 q^{51} + 18 q^{53} + 20 q^{54} + 6 q^{55} + 6 q^{56} - 28 q^{57} + 10 q^{58} + 2 q^{59} + 14 q^{60} + 28 q^{61} - 2 q^{62} + 6 q^{63} + 6 q^{64} + 6 q^{67} + 4 q^{68} + 32 q^{69} - 2 q^{70} + 4 q^{71} + 6 q^{72} - 22 q^{73} - 48 q^{75} - 4 q^{76} + 2 q^{77} + 22 q^{79} - 2 q^{80} + 34 q^{81} + 6 q^{82} - 10 q^{83} + 2 q^{84} + 32 q^{85} + 26 q^{86} - 2 q^{87} + 2 q^{88} - 4 q^{89} - 6 q^{90} - 6 q^{92} - 12 q^{93} - 8 q^{94} + 32 q^{95} + 2 q^{96} - 12 q^{97} + 6 q^{98} - 2 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 - 2 * q^10 + 2 * q^11 + 2 * q^12 + 6 * q^14 + 14 * q^15 + 6 * q^16 + 4 * q^17 + 6 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 2 * q^22 - 6 * q^23 + 2 * q^24 + 12 * q^25 + 20 * q^27 + 6 * q^28 + 10 * q^29 + 14 * q^30 - 2 * q^31 + 6 * q^32 + 4 * q^34 - 2 * q^35 + 6 * q^36 - 4 * q^38 - 2 * q^40 + 6 * q^41 + 2 * q^42 + 26 * q^43 + 2 * q^44 - 6 * q^45 - 6 * q^46 - 8 * q^47 + 2 * q^48 + 6 * q^49 + 12 * q^50 + 18 * q^51 + 18 * q^53 + 20 * q^54 + 6 * q^55 + 6 * q^56 - 28 * q^57 + 10 * q^58 + 2 * q^59 + 14 * q^60 + 28 * q^61 - 2 * q^62 + 6 * q^63 + 6 * q^64 + 6 * q^67 + 4 * q^68 + 32 * q^69 - 2 * q^70 + 4 * q^71 + 6 * q^72 - 22 * q^73 - 48 * q^75 - 4 * q^76 + 2 * q^77 + 22 * q^79 - 2 * q^80 + 34 * q^81 + 6 * q^82 - 10 * q^83 + 2 * q^84 + 32 * q^85 + 26 * q^86 - 2 * q^87 + 2 * q^88 - 4 * q^89 - 6 * q^90 - 6 * q^92 - 12 * q^93 - 8 * q^94 + 32 * q^95 + 2 * q^96 - 12 * q^97 + 6 * q^98 - 2 * q^99

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