LMFDB - Embedded newform 2366.2.a.bf.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:	$6$
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			1.3
Root			$-0.466545$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.466545 q^{3} +1.00000 q^{4} -3.38938 q^{5} +0.466545 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.78234 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.466545 q^{3} +1.00000 q^{4} -3.38938 q^{5} +0.466545 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.78234 q^{9} +3.38938 q^{10} +0.822730 q^{11} -0.466545 q^{12} +1.00000 q^{14} +1.58130 q^{15} +1.00000 q^{16} +4.58130 q^{17} +2.78234 q^{18} -5.90621 q^{19} -3.38938 q^{20} +0.466545 q^{21} -0.822730 q^{22} -6.13055 q^{23} +0.466545 q^{24} +6.48787 q^{25} +2.69772 q^{27} -1.00000 q^{28} -6.86813 q^{29} -1.58130 q^{30} -4.28683 q^{31} -1.00000 q^{32} -0.383841 q^{33} -4.58130 q^{34} +3.38938 q^{35} -2.78234 q^{36} -9.69086 q^{37} +5.90621 q^{38} +3.38938 q^{40} +0.0893760 q^{41} -0.466545 q^{42} +7.35374 q^{43} +0.822730 q^{44} +9.43038 q^{45} +6.13055 q^{46} -11.1759 q^{47} -0.466545 q^{48} +1.00000 q^{49} -6.48787 q^{50} -2.13738 q^{51} -7.01530 q^{53} -2.69772 q^{54} -2.78854 q^{55} +1.00000 q^{56} +2.75551 q^{57} +6.86813 q^{58} -1.74117 q^{59} +1.58130 q^{60} +2.37945 q^{61} +4.28683 q^{62} +2.78234 q^{63} +1.00000 q^{64} +0.383841 q^{66} -0.291719 q^{67} +4.58130 q^{68} +2.86018 q^{69} -3.38938 q^{70} +10.9484 q^{71} +2.78234 q^{72} +12.7187 q^{73} +9.69086 q^{74} -3.02688 q^{75} -5.90621 q^{76} -0.822730 q^{77} +9.95602 q^{79} -3.38938 q^{80} +7.08840 q^{81} -0.0893760 q^{82} +3.23553 q^{83} +0.466545 q^{84} -15.5277 q^{85} -7.35374 q^{86} +3.20429 q^{87} -0.822730 q^{88} +8.04265 q^{89} -9.43038 q^{90} -6.13055 q^{92} +2.00000 q^{93} +11.1759 q^{94} +20.0184 q^{95} +0.466545 q^{96} +14.7739 q^{97} -1.00000 q^{98} -2.28911 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.466545	−0.269360	−0.134680	−	0.990889i	$-0.543001\pi$
$3$	−0.466545	−0.269360	−0.134680	+	0.990889i	$0.543001\pi$
$4$	1.00000	0.500000
$5$	−3.38938	−1.51578	−0.757888	−	0.652385i	$-0.773768\pi$
$5$	−3.38938	−1.51578	−0.757888	+	0.652385i	$0.773768\pi$
$6$	0.466545	0.190466
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.78234	−0.927445
$10$	3.38938	1.07181
$11$	0.822730	0.248063	0.124031	−	0.992278i	$-0.460418\pi$
$11$	0.822730	0.248063	0.124031	+	0.992278i	$0.460418\pi$
$12$	−0.466545	−0.134680
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	1.58130	0.408289
$16$	1.00000	0.250000
$17$	4.58130	1.11113	0.555564	−	0.831474i	$-0.312502\pi$
$17$	4.58130	1.11113	0.555564	+	0.831474i	$0.312502\pi$
$18$	2.78234	0.655803
$19$	−5.90621	−1.35498	−0.677488	−	0.735534i	$-0.736932\pi$
$19$	−5.90621	−1.35498	−0.677488	+	0.735534i	$0.736932\pi$
$20$	−3.38938	−0.757888
$21$	0.466545	0.101808
$22$	−0.822730	−0.175407
$23$	−6.13055	−1.27831	−0.639154	−	0.769079i	$-0.720715\pi$
$23$	−6.13055	−1.27831	−0.639154	+	0.769079i	$0.720715\pi$
$24$	0.466545	0.0952331
$25$	6.48787	1.29757
$26$	0	0
$27$	2.69772	0.519176
$28$	−1.00000	−0.188982
$29$	−6.86813	−1.27538	−0.637690	−	0.770293i	$-0.720110\pi$
$29$	−6.86813	−1.27538	−0.637690	+	0.770293i	$0.720110\pi$
$30$	−1.58130	−0.288704
$31$	−4.28683	−0.769938	−0.384969	−	0.922930i	$-0.625788\pi$
$31$	−4.28683	−0.769938	−0.384969	+	0.922930i	$0.625788\pi$
$32$	−1.00000	−0.176777
$33$	−0.383841	−0.0668181
$34$	−4.58130	−0.785686
$35$	3.38938	0.572909
$36$	−2.78234	−0.463723
$37$	−9.69086	−1.59317	−0.796584	−	0.604528i	$-0.793362\pi$
$37$	−9.69086	−1.59317	−0.796584	+	0.604528i	$0.793362\pi$
$38$	5.90621	0.958113
$39$	0	0
$40$	3.38938	0.535907
$41$	0.0893760	0.0139582	0.00697909	−	0.999976i	$-0.497778\pi$
$41$	0.0893760	0.0139582	0.00697909	+	0.999976i	$0.497778\pi$
$42$	−0.466545	−0.0719895
$43$	7.35374	1.12144	0.560718	−	0.828007i	$-0.310525\pi$
$43$	7.35374	1.12144	0.560718	+	0.828007i	$0.310525\pi$
$44$	0.822730	0.124031
$45$	9.43038	1.40580
$46$	6.13055	0.903900
$47$	−11.1759	−1.63018	−0.815089	−	0.579335i	$-0.803312\pi$
$47$	−11.1759	−1.63018	−0.815089	+	0.579335i	$0.803312\pi$
$48$	−0.466545	−0.0673400
$49$	1.00000	0.142857
$50$	−6.48787	−0.917524
$51$	−2.13738	−0.299293
$52$	0	0
$53$	−7.01530	−0.963625	−0.481813	−	0.876274i	$-0.660021\pi$
$53$	−7.01530	−0.963625	−0.481813	+	0.876274i	$0.660021\pi$
$54$	−2.69772	−0.367113
$55$	−2.78854	−0.376007
$56$	1.00000	0.133631
$57$	2.75551	0.364976
$58$	6.86813	0.901829
$59$	−1.74117	−0.226681	−0.113340	−	0.993556i	$-0.536155\pi$
$59$	−1.74117	−0.226681	−0.113340	+	0.993556i	$0.536155\pi$
$60$	1.58130	0.204145
$61$	2.37945	0.304657	0.152329	−	0.988330i	$-0.451323\pi$
$61$	2.37945	0.304657	0.152329	+	0.988330i	$0.451323\pi$
$62$	4.28683	0.544428
$63$	2.78234	0.350541
$64$	1.00000	0.125000
$65$	0	0
$66$	0.383841	0.0472475
$67$	−0.291719	−0.0356391	−0.0178196	−	0.999841i	$-0.505672\pi$
$67$	−0.291719	−0.0356391	−0.0178196	+	0.999841i	$0.505672\pi$
$68$	4.58130	0.555564
$69$	2.86018	0.344325
$70$	−3.38938	−0.405108
$71$	10.9484	1.29933	0.649667	−	0.760219i	$-0.274908\pi$
$71$	10.9484	1.29933	0.649667	+	0.760219i	$0.274908\pi$
$72$	2.78234	0.327901
$73$	12.7187	1.48861	0.744304	−	0.667841i	$-0.232781\pi$
$73$	12.7187	1.48861	0.744304	+	0.667841i	$0.232781\pi$
$74$	9.69086	1.12654
$75$	−3.02688	−0.349514
$76$	−5.90621	−0.677488
$77$	−0.822730	−0.0937588
$78$	0	0
$79$	9.95602	1.12014	0.560070	−	0.828445i	$-0.310774\pi$
$79$	9.95602	1.12014	0.560070	+	0.828445i	$0.310774\pi$
$80$	−3.38938	−0.378944
$81$	7.08840	0.787600
$82$	−0.0893760	−0.00986993
$83$	3.23553	0.355146	0.177573	−	0.984108i	$-0.443175\pi$
$83$	3.23553	0.355146	0.177573	+	0.984108i	$0.443175\pi$
$84$	0.466545	0.0509042
$85$	−15.5277	−1.68422
$86$	−7.35374	−0.792974
$87$	3.20429	0.343536
$88$	−0.822730	−0.0877033
$89$	8.04265	0.852519	0.426260	−	0.904601i	$-0.359831\pi$
$89$	8.04265	0.852519	0.426260	+	0.904601i	$0.359831\pi$
$90$	−9.43038	−0.994050
$91$	0	0
$92$	−6.13055	−0.639154
$93$	2.00000	0.207390
$94$	11.1759	1.15271
$95$	20.0184	2.05384
$96$	0.466545	0.0476166
$97$	14.7739	1.50006	0.750029	−	0.661405i	$-0.230039\pi$
$97$	14.7739	1.50006	0.750029	+	0.661405i	$0.230039\pi$
$98$	−1.00000	−0.101015
$99$	−2.28911	−0.230064
$100$	6.48787	0.648787
$101$	−8.23976	−0.819887	−0.409943	−	0.912111i	$-0.634452\pi$
$101$	−8.23976	−0.819887	−0.409943	+	0.912111i	$0.634452\pi$
$102$	2.13738	0.211632
$103$	13.3231	1.31277	0.656383	−	0.754428i	$-0.272086\pi$
$103$	13.3231	1.31277	0.656383	+	0.754428i	$0.272086\pi$
$104$	0	0
$105$	−1.58130	−0.154319
$106$	7.01530	0.681386
$107$	−9.02649	−0.872624	−0.436312	−	0.899795i	$-0.643716\pi$
$107$	−9.02649	−0.872624	−0.436312	+	0.899795i	$0.643716\pi$
$108$	2.69772	0.259588
$109$	−0.397192	−0.0380441	−0.0190220	−	0.999819i	$-0.506055\pi$
$109$	−0.397192	−0.0380441	−0.0190220	+	0.999819i	$0.506055\pi$
$110$	2.78854	0.265877
$111$	4.52122	0.429135
$112$	−1.00000	−0.0944911
$113$	4.47322	0.420805	0.210402	−	0.977615i	$-0.432523\pi$
$113$	4.47322	0.420805	0.210402	+	0.977615i	$0.432523\pi$
$114$	−2.75551	−0.258077
$115$	20.7787	1.93763
$116$	−6.86813	−0.637690
$117$	0	0
$118$	1.74117	0.160288
$119$	−4.58130	−0.419967
$120$	−1.58130	−0.144352
$121$	−10.3231	−0.938465
$122$	−2.37945	−0.215425
$123$	−0.0416979	−0.00375978
$124$	−4.28683	−0.384969
$125$	−5.04295	−0.451056
$126$	−2.78234	−0.247870
$127$	−0.540127	−0.0479285	−0.0239642	−	0.999713i	$-0.507629\pi$
$127$	−0.540127	−0.0479285	−0.0239642	+	0.999713i	$0.507629\pi$
$128$	−1.00000	−0.0883883
$129$	−3.43085	−0.302070
$130$	0	0
$131$	−7.72615	−0.675037	−0.337518	−	0.941319i	$-0.609587\pi$
$131$	−7.72615	−0.675037	−0.337518	+	0.941319i	$0.609587\pi$
$132$	−0.383841	−0.0334090
$133$	5.90621	0.512133
$134$	0.291719	0.0252007
$135$	−9.14359	−0.786955
$136$	−4.58130	−0.392843
$137$	−12.5401	−1.07137	−0.535687	−	0.844417i	$-0.679947\pi$
$137$	−12.5401	−1.07137	−0.535687	+	0.844417i	$0.679947\pi$
$138$	−2.86018	−0.243474
$139$	12.0974	1.02608	0.513042	−	0.858363i	$-0.328518\pi$
$139$	12.0974	1.02608	0.513042	+	0.858363i	$0.328518\pi$
$140$	3.38938	0.286455
$141$	5.21408	0.439105
$142$	−10.9484	−0.918768
$143$	0	0
$144$	−2.78234	−0.231861
$145$	23.2787	1.93319
$146$	−12.7187	−1.05261
$147$	−0.466545	−0.0384800
$148$	−9.69086	−0.796584
$149$	17.0078	1.39333	0.696666	−	0.717395i	$-0.254666\pi$
$149$	17.0078	1.39333	0.696666	+	0.717395i	$0.254666\pi$
$150$	3.02688	0.247144
$151$	−5.54567	−0.451300	−0.225650	−	0.974208i	$-0.572451\pi$
$151$	−5.54567	−0.451300	−0.225650	+	0.974208i	$0.572451\pi$
$152$	5.90621	0.479057
$153$	−12.7467	−1.03051
$154$	0.822730	0.0662975
$155$	14.5297	1.16705
$156$	0	0
$157$	2.29353	0.183044	0.0915218	−	0.995803i	$-0.470827\pi$
$157$	2.29353	0.183044	0.0915218	+	0.995803i	$0.470827\pi$
$158$	−9.95602	−0.792059
$159$	3.27295	0.259562
$160$	3.38938	0.267954
$161$	6.13055	0.483155
$162$	−7.08840	−0.556917
$163$	23.3560	1.82938	0.914691	−	0.404155i	$-0.132434\pi$
$163$	23.3560	1.82938	0.914691	+	0.404155i	$0.132434\pi$
$164$	0.0893760	0.00697909
$165$	1.30098	0.101281
$166$	−3.23553	−0.251126
$167$	−21.7780	−1.68523	−0.842614	−	0.538517i	$-0.818985\pi$
$167$	−21.7780	−1.68523	−0.842614	+	0.538517i	$0.818985\pi$
$168$	−0.466545	−0.0359947
$169$	0	0
$170$	15.5277	1.19092
$171$	16.4330	1.25667
$172$	7.35374	0.560718
$173$	8.09733	0.615629	0.307814	−	0.951446i	$-0.400402\pi$
$173$	8.09733	0.615629	0.307814	+	0.951446i	$0.400402\pi$
$174$	−3.20429	−0.242917
$175$	−6.48787	−0.490437
$176$	0.822730	0.0620156
$177$	0.812334	0.0610588
$178$	−8.04265	−0.602822
$179$	9.90883	0.740621	0.370310	−	0.928908i	$-0.379251\pi$
$179$	9.90883	0.740621	0.370310	+	0.928908i	$0.379251\pi$
$180$	9.43038	0.702899
$181$	−1.27902	−0.0950685	−0.0475343	−	0.998870i	$-0.515136\pi$
$181$	−1.27902	−0.0950685	−0.0475343	+	0.998870i	$0.515136\pi$
$182$	0	0
$183$	−1.11012	−0.0820624
$184$	6.13055	0.451950
$185$	32.8460	2.41488
$186$	−2.00000	−0.146647
$187$	3.76917	0.275629
$188$	−11.1759	−0.815089
$189$	−2.69772	−0.196230
$190$	−20.0184	−1.45228
$191$	−10.0342	−0.726050	−0.363025	−	0.931779i	$-0.618256\pi$
$191$	−10.0342	−0.726050	−0.363025	+	0.931779i	$0.618256\pi$
$192$	−0.466545	−0.0336700
$193$	−15.8582	−1.14150	−0.570750	−	0.821124i	$-0.693347\pi$
$193$	−15.8582	−1.14150	−0.570750	+	0.821124i	$0.693347\pi$
$194$	−14.7739	−1.06070
$195$	0	0
$196$	1.00000	0.0714286
$197$	−14.8081	−1.05503	−0.527515	−	0.849546i	$-0.676876\pi$
$197$	−14.8081	−1.05503	−0.527515	+	0.849546i	$0.676876\pi$
$198$	2.28911	0.162680
$199$	−2.55543	−0.181149	−0.0905747	−	0.995890i	$-0.528870\pi$
$199$	−2.55543	−0.181149	−0.0905747	+	0.995890i	$0.528870\pi$
$200$	−6.48787	−0.458762
$201$	0.136100	0.00959974
$202$	8.23976	0.579748
$203$	6.86813	0.482048
$204$	−2.13738	−0.149647
$205$	−0.302929	−0.0211575
$206$	−13.3231	−0.928265
$207$	17.0572	1.18556
$208$	0	0
$209$	−4.85921	−0.336119
$210$	1.58130	0.109120
$211$	−8.63648	−0.594560	−0.297280	−	0.954790i	$-0.596080\pi$
$211$	−8.63648	−0.594560	−0.297280	+	0.954790i	$0.596080\pi$
$212$	−7.01530	−0.481813
$213$	−5.10792	−0.349989
$214$	9.02649	0.617038
$215$	−24.9246	−1.69984
$216$	−2.69772	−0.183557
$217$	4.28683	0.291009
$218$	0.397192	0.0269012
$219$	−5.93384	−0.400971
$220$	−2.78854	−0.188003
$221$	0	0
$222$	−4.52122	−0.303445
$223$	19.9277	1.33446	0.667228	−	0.744854i	$-0.267481\pi$
$223$	19.9277	1.33446	0.667228	+	0.744854i	$0.267481\pi$
$224$	1.00000	0.0668153
$225$	−18.0514	−1.20343
$226$	−4.47322	−0.297554
$227$	0.352624	0.0234045	0.0117022	−	0.999932i	$-0.496275\pi$
$227$	0.352624	0.0234045	0.0117022	+	0.999932i	$0.496275\pi$
$228$	2.75551	0.182488
$229$	8.31317	0.549350	0.274675	−	0.961537i	$-0.411430\pi$
$229$	8.31317	0.549350	0.274675	+	0.961537i	$0.411430\pi$
$230$	−20.7787	−1.37011
$231$	0.383841	0.0252549
$232$	6.86813	0.450915
$233$	15.3798	1.00756	0.503781	−	0.863831i	$-0.331942\pi$
$233$	15.3798	1.00756	0.503781	+	0.863831i	$0.331942\pi$
$234$	0	0
$235$	37.8795	2.47098
$236$	−1.74117	−0.113340
$237$	−4.64493	−0.301721
$238$	4.58130	0.296961
$239$	2.88606	0.186684	0.0933418	−	0.995634i	$-0.470245\pi$
$239$	2.88606	0.186684	0.0933418	+	0.995634i	$0.470245\pi$
$240$	1.58130	0.102072
$241$	6.26744	0.403722	0.201861	−	0.979414i	$-0.435301\pi$
$241$	6.26744	0.403722	0.201861	+	0.979414i	$0.435301\pi$
$242$	10.3231	0.663595
$243$	−11.4002	−0.731324
$244$	2.37945	0.152329
$245$	−3.38938	−0.216539
$246$	0.0416979	0.00265856
$247$	0	0
$248$	4.28683	0.272214
$249$	−1.50952	−0.0956621
$250$	5.04295	0.318944
$251$	17.2665	1.08985	0.544926	−	0.838484i	$-0.316558\pi$
$251$	17.2665	1.08985	0.544926	+	0.838484i	$0.316558\pi$
$252$	2.78234	0.175271
$253$	−5.04379	−0.317100
$254$	0.540127	0.0338906
$255$	7.24439	0.453661
$256$	1.00000	0.0625000
$257$	−11.1931	−0.698206	−0.349103	−	0.937084i	$-0.613514\pi$
$257$	−11.1931	−0.698206	−0.349103	+	0.937084i	$0.613514\pi$
$258$	3.43085	0.213595
$259$	9.69086	0.602161
$260$	0	0
$261$	19.1094	1.18284
$262$	7.72615	0.477323
$263$	−28.5826	−1.76248	−0.881240	−	0.472668i	$-0.843291\pi$
$263$	−28.5826	−1.76248	−0.881240	+	0.472668i	$0.843291\pi$
$264$	0.383841	0.0236238
$265$	23.7775	1.46064
$266$	−5.90621	−0.362133
$267$	−3.75226	−0.229635
$268$	−0.291719	−0.0178196
$269$	−18.3754	−1.12037	−0.560183	−	0.828369i	$-0.689269\pi$
$269$	−18.3754	−1.12037	−0.560183	+	0.828369i	$0.689269\pi$
$270$	9.14359	0.556461
$271$	20.3825	1.23815	0.619075	−	0.785332i	$-0.287508\pi$
$271$	20.3825	1.23815	0.619075	+	0.785332i	$0.287508\pi$
$272$	4.58130	0.277782
$273$	0	0
$274$	12.5401	0.757575
$275$	5.33777	0.321880
$276$	2.86018	0.172162
$277$	7.23219	0.434540	0.217270	−	0.976112i	$-0.430285\pi$
$277$	7.23219	0.434540	0.217270	+	0.976112i	$0.430285\pi$
$278$	−12.0974	−0.725551
$279$	11.9274	0.714075
$280$	−3.38938	−0.202554
$281$	−12.4585	−0.743215	−0.371607	−	0.928390i	$-0.621193\pi$
$281$	−12.4585	−0.743215	−0.371607	+	0.928390i	$0.621193\pi$
$282$	−5.21408	−0.310494
$283$	13.0607	0.776378	0.388189	−	0.921580i	$-0.373101\pi$
$283$	13.0607	0.776378	0.388189	+	0.921580i	$0.373101\pi$
$284$	10.9484	0.649667
$285$	−9.33946	−0.553222
$286$	0	0
$287$	−0.0893760	−0.00527570
$288$	2.78234	0.163951
$289$	3.98828	0.234605
$290$	−23.2787	−1.36697
$291$	−6.89267	−0.404056
$292$	12.7187	0.744304
$293$	14.5582	0.850498	0.425249	−	0.905076i	$-0.360187\pi$
$293$	14.5582	0.850498	0.425249	+	0.905076i	$0.360187\pi$
$294$	0.466545	0.0272095
$295$	5.90148	0.343597
$296$	9.69086	0.563270
$297$	2.21950	0.128788
$298$	−17.0078	−0.985235
$299$	0	0
$300$	−3.02688	−0.174757
$301$	−7.35374	−0.423863
$302$	5.54567	0.319117
$303$	3.84422	0.220845
$304$	−5.90621	−0.338744
$305$	−8.06485	−0.461792
$306$	12.7467	0.728681
$307$	3.24267	0.185069	0.0925345	−	0.995709i	$-0.470503\pi$
$307$	3.24267	0.185069	0.0925345	+	0.995709i	$0.470503\pi$
$308$	−0.822730	−0.0468794
$309$	−6.21583	−0.353606
$310$	−14.5297	−0.825231
$311$	10.2709	0.582408	0.291204	−	0.956661i	$-0.405944\pi$
$311$	10.2709	0.582408	0.291204	+	0.956661i	$0.405944\pi$
$312$	0	0
$313$	−6.13382	−0.346704	−0.173352	−	0.984860i	$-0.555460\pi$
$313$	−6.13382	−0.346704	−0.173352	+	0.984860i	$0.555460\pi$
$314$	−2.29353	−0.129431
$315$	−9.43038	−0.531342
$316$	9.95602	0.560070
$317$	5.04487	0.283348	0.141674	−	0.989913i	$-0.454752\pi$
$317$	5.04487	0.283348	0.141674	+	0.989913i	$0.454752\pi$
$318$	−3.27295	−0.183538
$319$	−5.65062	−0.316374
$320$	−3.38938	−0.189472
$321$	4.21127	0.235050
$322$	−6.13055	−0.341642
$323$	−27.0581	−1.50555
$324$	7.08840	0.393800
$325$	0	0
$326$	−23.3560	−1.29357
$327$	0.185308	0.0102475
$328$	−0.0893760	−0.00493496
$329$	11.1759	0.616150
$330$	−1.30098	−0.0716166
$331$	−23.0874	−1.26900	−0.634499	−	0.772924i	$-0.718793\pi$
$331$	−23.0874	−1.26900	−0.634499	+	0.772924i	$0.718793\pi$
$332$	3.23553	0.177573
$333$	26.9632	1.47758
$334$	21.7780	1.19164
$335$	0.988744	0.0540209
$336$	0.466545	0.0254521
$337$	−29.1429	−1.58751	−0.793757	−	0.608235i	$-0.791878\pi$
$337$	−29.1429	−1.58751	−0.793757	+	0.608235i	$0.791878\pi$
$338$	0	0
$339$	−2.08696	−0.113348
$340$	−15.5277	−0.842110
$341$	−3.52691	−0.190993
$342$	−16.4330	−0.888597
$343$	−1.00000	−0.0539949
$344$	−7.35374	−0.396487
$345$	−9.69421	−0.521919
$346$	−8.09733	−0.435315
$347$	−29.1082	−1.56261	−0.781306	−	0.624148i	$-0.785446\pi$
$347$	−29.1082	−1.56261	−0.781306	+	0.624148i	$0.785446\pi$
$348$	3.20429	0.171768
$349$	25.7802	1.37998	0.689992	−	0.723817i	$-0.257614\pi$
$349$	25.7802	1.37998	0.689992	+	0.723817i	$0.257614\pi$
$350$	6.48787	0.346791
$351$	0	0
$352$	−0.822730	−0.0438517
$353$	9.91779	0.527871	0.263935	−	0.964540i	$-0.414979\pi$
$353$	9.91779	0.527871	0.263935	+	0.964540i	$0.414979\pi$
$354$	−0.812334	−0.0431751
$355$	−37.1082	−1.96950
$356$	8.04265	0.426260
$357$	2.13738	0.113122
$358$	−9.90883	−0.523698
$359$	25.2683	1.33361	0.666804	−	0.745233i	$-0.267662\pi$
$359$	25.2683	1.33361	0.666804	+	0.745233i	$0.267662\pi$
$360$	−9.43038	−0.497025
$361$	15.8833	0.835962
$362$	1.27902	0.0672236
$363$	4.81620	0.252785
$364$	0	0
$365$	−43.1084	−2.25640
$366$	1.11012	0.0580269
$367$	35.7838	1.86790	0.933950	−	0.357404i	$-0.116338\pi$
$367$	35.7838	1.86790	0.933950	+	0.357404i	$0.116338\pi$
$368$	−6.13055	−0.319577
$369$	−0.248674	−0.0129455
$370$	−32.8460	−1.70758
$371$	7.01530	0.364216
$372$	2.00000	0.103695
$373$	−23.3304	−1.20800	−0.604000	−	0.796984i	$-0.706427\pi$
$373$	−23.3304	−1.20800	−0.604000	+	0.796984i	$0.706427\pi$
$374$	−3.76917	−0.194899
$375$	2.35277	0.121496
$376$	11.1759	0.576355
$377$	0	0
$378$	2.69772	0.138756
$379$	−24.3066	−1.24855	−0.624274	−	0.781206i	$-0.714605\pi$
$379$	−24.3066	−1.24855	−0.624274	+	0.781206i	$0.714605\pi$
$380$	20.0184	1.02692
$381$	0.251993	0.0129100
$382$	10.0342	0.513395
$383$	4.91150	0.250966	0.125483	−	0.992096i	$-0.459952\pi$
$383$	4.91150	0.250966	0.125483	+	0.992096i	$0.459952\pi$
$384$	0.466545	0.0238083
$385$	2.78854	0.142117
$386$	15.8582	0.807162
$387$	−20.4606	−1.04007
$388$	14.7739	0.750029
$389$	5.14522	0.260873	0.130437	−	0.991457i	$-0.458362\pi$
$389$	5.14522	0.260873	0.130437	+	0.991457i	$0.458362\pi$
$390$	0	0
$391$	−28.0858	−1.42036
$392$	−1.00000	−0.0505076
$393$	3.60460	0.181828
$394$	14.8081	0.746019
$395$	−33.7447	−1.69788
$396$	−2.28911	−0.115032
$397$	12.3500	0.619827	0.309913	−	0.950765i	$-0.399700\pi$
$397$	12.3500	0.619827	0.309913	+	0.950765i	$0.399700\pi$
$398$	2.55543	0.128092
$399$	−2.75551	−0.137948
$400$	6.48787	0.324394
$401$	32.4894	1.62244	0.811221	−	0.584739i	$-0.198803\pi$
$401$	32.4894	1.62244	0.811221	+	0.584739i	$0.198803\pi$
$402$	−0.136100	−0.00678804
$403$	0	0
$404$	−8.23976	−0.409943
$405$	−24.0253	−1.19382
$406$	−6.86813	−0.340859
$407$	−7.97296	−0.395205
$408$	2.13738	0.105816
$409$	3.76834	0.186332	0.0931662	−	0.995651i	$-0.470301\pi$
$409$	3.76834	0.186332	0.0931662	+	0.995651i	$0.470301\pi$
$410$	0.302929	0.0149606
$411$	5.85052	0.288585
$412$	13.3231	0.656383
$413$	1.74117	0.0856774
$414$	−17.0572	−0.838317
$415$	−10.9664	−0.538321
$416$	0	0
$417$	−5.64396	−0.276386
$418$	4.85921	0.237672
$419$	−10.5301	−0.514428	−0.257214	−	0.966354i	$-0.582805\pi$
$419$	−10.5301	−0.514428	−0.257214	+	0.966354i	$0.582805\pi$
$420$	−1.58130	−0.0771594
$421$	24.9973	1.21830	0.609148	−	0.793057i	$-0.291512\pi$
$421$	24.9973	1.21830	0.609148	+	0.793057i	$0.291512\pi$
$422$	8.63648	0.420417
$423$	31.0952	1.51190
$424$	7.01530	0.340693
$425$	29.7229	1.44177
$426$	5.10792	0.247479
$427$	−2.37945	−0.115150
$428$	−9.02649	−0.436312
$429$	0	0
$430$	24.9246	1.20197
$431$	−11.9784	−0.576979	−0.288489	−	0.957483i	$-0.593153\pi$
$431$	−11.9784	−0.576979	−0.288489	+	0.957483i	$0.593153\pi$
$432$	2.69772	0.129794
$433$	7.96950	0.382990	0.191495	−	0.981494i	$-0.438666\pi$
$433$	7.96950	0.382990	0.191495	+	0.981494i	$0.438666\pi$
$434$	−4.28683	−0.205775
$435$	−10.8605	−0.520723
$436$	−0.397192	−0.0190220
$437$	36.2083	1.73208
$438$	5.93384	0.283530
$439$	4.35655	0.207927	0.103963	−	0.994581i	$-0.466848\pi$
$439$	4.35655	0.207927	0.103963	+	0.994581i	$0.466848\pi$
$440$	2.78854	0.132939
$441$	−2.78234	−0.132492
$442$	0	0
$443$	−11.4823	−0.545542	−0.272771	−	0.962079i	$-0.587940\pi$
$443$	−11.4823	−0.545542	−0.272771	+	0.962079i	$0.587940\pi$
$444$	4.52122	0.214568
$445$	−27.2596	−1.29223
$446$	−19.9277	−0.943603
$447$	−7.93490	−0.375308
$448$	−1.00000	−0.0472456
$449$	29.5248	1.39336	0.696680	−	0.717382i	$-0.254660\pi$
$449$	29.5248	1.39336	0.696680	+	0.717382i	$0.254660\pi$
$450$	18.0514	0.850953
$451$	0.0735323	0.00346250
$452$	4.47322	0.210402
$453$	2.58730	0.121562
$454$	−0.352624	−0.0165495
$455$	0	0
$456$	−2.75551	−0.129039
$457$	16.5981	0.776428	0.388214	−	0.921569i	$-0.373092\pi$
$457$	16.5981	0.776428	0.388214	+	0.921569i	$0.373092\pi$
$458$	−8.31317	−0.388449
$459$	12.3591	0.576871
$460$	20.7787	0.968813
$461$	26.4422	1.23154	0.615769	−	0.787927i	$-0.288846\pi$
$461$	26.4422	1.23154	0.615769	+	0.787927i	$0.288846\pi$
$462$	−0.383841	−0.0178579
$463$	−10.4717	−0.486663	−0.243331	−	0.969943i	$-0.578240\pi$
$463$	−10.4717	−0.486663	−0.243331	+	0.969943i	$0.578240\pi$
$464$	−6.86813	−0.318845
$465$	−6.77875	−0.314357
$466$	−15.3798	−0.712454
$467$	−27.9010	−1.29110	−0.645551	−	0.763717i	$-0.723372\pi$
$467$	−27.9010	−1.29110	−0.645551	+	0.763717i	$0.723372\pi$
$468$	0	0
$469$	0.291719	0.0134703
$470$	−37.8795	−1.74725
$471$	−1.07003	−0.0493046
$472$	1.74117	0.0801438
$473$	6.05015	0.278186
$474$	4.64493	0.213349
$475$	−38.3187	−1.75818
$476$	−4.58130	−0.209983
$477$	19.5189	0.893710
$478$	−2.88606	−0.132005
$479$	−6.88133	−0.314416	−0.157208	−	0.987566i	$-0.550249\pi$
$479$	−6.88133	−0.314416	−0.157208	+	0.987566i	$0.550249\pi$
$480$	−1.58130	−0.0721760
$481$	0	0
$482$	−6.26744	−0.285474
$483$	−2.86018	−0.130142
$484$	−10.3231	−0.469232
$485$	−50.0742	−2.27375
$486$	11.4002	0.517124
$487$	−40.8062	−1.84911	−0.924553	−	0.381053i	$-0.875562\pi$
$487$	−40.8062	−1.84911	−0.924553	+	0.381053i	$0.875562\pi$
$488$	−2.37945	−0.107713
$489$	−10.8966	−0.492762
$490$	3.38938	0.153116
$491$	6.72706	0.303588	0.151794	−	0.988412i	$-0.451495\pi$
$491$	6.72706	0.303588	0.151794	+	0.988412i	$0.451495\pi$
$492$	−0.0416979	−0.00187989
$493$	−31.4649	−1.41711
$494$	0	0
$495$	7.75866	0.348726
$496$	−4.28683	−0.192484
$497$	−10.9484	−0.491102
$498$	1.50952	0.0676433
$499$	1.16200	0.0520184	0.0260092	−	0.999662i	$-0.491720\pi$
$499$	1.16200	0.0520184	0.0260092	+	0.999662i	$0.491720\pi$
$500$	−5.04295	−0.225528
$501$	10.1604	0.453933
$502$	−17.2665	−0.770641
$503$	9.95053	0.443672	0.221836	−	0.975084i	$-0.428795\pi$
$503$	9.95053	0.443672	0.221836	+	0.975084i	$0.428795\pi$
$504$	−2.78234	−0.123935
$505$	27.9277	1.24276
$506$	5.04379	0.224224
$507$	0	0
$508$	−0.540127	−0.0239642
$509$	0.0522003	0.00231374	0.00115687	−	0.999999i	$-0.499632\pi$
$509$	0.0522003	0.00231374	0.00115687	+	0.999999i	$0.499632\pi$
$510$	−7.24439	−0.320787
$511$	−12.7187	−0.562641
$512$	−1.00000	−0.0441942
$513$	−15.9333	−0.703472
$514$	11.1931	0.493706
$515$	−45.1570	−1.98986
$516$	−3.43085	−0.151035
$517$	−9.19479	−0.404386
$518$	−9.69086	−0.425792
$519$	−3.77777	−0.165826
$520$	0	0
$521$	26.0984	1.14339	0.571695	−	0.820466i	$-0.306286\pi$
$521$	26.0984	1.14339	0.571695	+	0.820466i	$0.306286\pi$
$522$	−19.1094	−0.836397
$523$	−19.5321	−0.854080	−0.427040	−	0.904233i	$-0.640444\pi$
$523$	−19.5321	−0.854080	−0.427040	+	0.904233i	$0.640444\pi$
$524$	−7.72615	−0.337518
$525$	3.02688	0.132104
$526$	28.5826	1.24626
$527$	−19.6392	−0.855499
$528$	−0.383841	−0.0167045
$529$	14.5836	0.634069
$530$	−23.7775	−1.03283
$531$	4.84452	0.210234
$532$	5.90621	0.256067
$533$	0	0
$534$	3.75226	0.162376
$535$	30.5942	1.32270
$536$	0.291719	0.0126003
$537$	−4.62292	−0.199494
$538$	18.3754	0.792219
$539$	0.822730	0.0354375
$540$	−9.14359	−0.393477
$541$	32.8802	1.41363	0.706814	−	0.707399i	$-0.250132\pi$
$541$	32.8802	1.41363	0.706814	+	0.707399i	$0.250132\pi$
$542$	−20.3825	−0.875504
$543$	0.596719	0.0256077
$544$	−4.58130	−0.196421
$545$	1.34623	0.0576662
$546$	0	0
$547$	−39.0180	−1.66829	−0.834144	−	0.551546i	$-0.814038\pi$
$547$	−39.0180	−1.66829	−0.834144	+	0.551546i	$0.814038\pi$
$548$	−12.5401	−0.535687
$549$	−6.62043	−0.282553
$550$	−5.33777	−0.227603
$551$	40.5646	1.72811
$552$	−2.86018	−0.121737
$553$	−9.95602	−0.423373
$554$	−7.23219	−0.307266
$555$	−15.3241	−0.650473
$556$	12.0974	0.513042
$557$	−29.5492	−1.25204	−0.626020	−	0.779807i	$-0.715317\pi$
$557$	−29.5492	−1.25204	−0.626020	+	0.779807i	$0.715317\pi$
$558$	−11.9274	−0.504927
$559$	0	0
$560$	3.38938	0.143227
$561$	−1.75849	−0.0742434
$562$	12.4585	0.525532
$563$	−27.1323	−1.14349	−0.571745	−	0.820431i	$-0.693733\pi$
$563$	−27.1323	−1.14349	−0.571745	+	0.820431i	$0.693733\pi$
$564$	5.21408	0.219552
$565$	−15.1614	−0.637845
$566$	−13.0607	−0.548982
$567$	−7.08840	−0.297685
$568$	−10.9484	−0.459384
$569$	42.4594	1.77999	0.889996	−	0.455969i	$-0.150707\pi$
$569$	42.4594	1.77999	0.889996	+	0.455969i	$0.150707\pi$
$570$	9.33946	0.391187
$571$	11.2678	0.471543	0.235771	−	0.971809i	$-0.424238\pi$
$571$	11.2678	0.471543	0.235771	+	0.971809i	$0.424238\pi$
$572$	0	0
$573$	4.68141	0.195569
$574$	0.0893760	0.00373048
$575$	−39.7742	−1.65870
$576$	−2.78234	−0.115931
$577$	22.8987	0.953286	0.476643	−	0.879097i	$-0.341853\pi$
$577$	22.8987	0.953286	0.476643	+	0.879097i	$0.341853\pi$
$578$	−3.98828	−0.165890
$579$	7.39857	0.307474
$580$	23.2787	0.966594
$581$	−3.23553	−0.134233
$582$	6.89267	0.285710
$583$	−5.77170	−0.239039
$584$	−12.7187	−0.526303
$585$	0	0
$586$	−14.5582	−0.601393
$587$	−35.8019	−1.47770	−0.738852	−	0.673868i	$-0.764632\pi$
$587$	−35.8019	−1.47770	−0.738852	+	0.673868i	$0.764632\pi$
$588$	−0.466545	−0.0192400
$589$	25.3189	1.04325
$590$	−5.90148	−0.242960
$591$	6.90862	0.284183
$592$	−9.69086	−0.398292
$593$	−14.6093	−0.599931	−0.299965	−	0.953950i	$-0.596975\pi$
$593$	−14.6093	−0.599931	−0.299965	+	0.953950i	$0.596975\pi$
$594$	−2.21950	−0.0910670
$595$	15.5277	0.636575
$596$	17.0078	0.696666
$597$	1.19222	0.0487944
$598$	0	0
$599$	−37.5729	−1.53519	−0.767594	−	0.640936i	$-0.778546\pi$
$599$	−37.5729	−1.53519	−0.767594	+	0.640936i	$0.778546\pi$
$600$	3.02688	0.123572
$601$	−5.45158	−0.222375	−0.111187	−	0.993799i	$-0.535465\pi$
$601$	−5.45158	−0.222375	−0.111187	+	0.993799i	$0.535465\pi$
$602$	7.35374	0.299716
$603$	0.811659	0.0330533
$604$	−5.54567	−0.225650
$605$	34.9889	1.42250
$606$	−3.84422	−0.156161
$607$	−39.9387	−1.62106	−0.810531	−	0.585696i	$-0.800821\pi$
$607$	−39.9387	−1.62106	−0.810531	+	0.585696i	$0.800821\pi$
$608$	5.90621	0.239528
$609$	−3.20429	−0.129844
$610$	8.06485	0.326536
$611$	0	0
$612$	−12.7467	−0.515255
$613$	−16.6552	−0.672696	−0.336348	−	0.941738i	$-0.609192\pi$
$613$	−16.6552	−0.672696	−0.336348	+	0.941738i	$0.609192\pi$
$614$	−3.24267	−0.130864
$615$	0.141330	0.00569897
$616$	0.822730	0.0331487
$617$	−26.9652	−1.08558	−0.542788	−	0.839869i	$-0.682631\pi$
$617$	−26.9652	−1.08558	−0.542788	+	0.839869i	$0.682631\pi$
$618$	6.21583	0.250037
$619$	−12.7533	−0.512597	−0.256298	−	0.966598i	$-0.582503\pi$
$619$	−12.7533	−0.512597	−0.256298	+	0.966598i	$0.582503\pi$
$620$	14.5297	0.583526
$621$	−16.5385	−0.663667
$622$	−10.2709	−0.411825
$623$	−8.04265	−0.322222
$624$	0	0
$625$	−15.3469	−0.613875
$626$	6.13382	0.245157
$627$	2.26704	0.0905369
$628$	2.29353	0.0915218
$629$	−44.3967	−1.77021
$630$	9.43038	0.375715
$631$	−37.5529	−1.49496	−0.747479	−	0.664286i	$-0.768736\pi$
$631$	−37.5529	−1.49496	−0.747479	+	0.664286i	$0.768736\pi$
$632$	−9.95602	−0.396029
$633$	4.02931	0.160151
$634$	−5.04487	−0.200357
$635$	1.83069	0.0726488
$636$	3.27295	0.129781
$637$	0	0
$638$	5.65062	0.223710
$639$	−30.4621	−1.20506
$640$	3.38938	0.133977
$641$	1.97623	0.0780564	0.0390282	−	0.999238i	$-0.487574\pi$
$641$	1.97623	0.0780564	0.0390282	+	0.999238i	$0.487574\pi$
$642$	−4.21127	−0.166205
$643$	−39.0704	−1.54079	−0.770394	−	0.637568i	$-0.779940\pi$
$643$	−39.0704	−1.54079	−0.770394	+	0.637568i	$0.779940\pi$
$644$	6.13055	0.241577
$645$	11.6284	0.457870
$646$	27.0581	1.06459
$647$	12.1051	0.475900	0.237950	−	0.971277i	$-0.423525\pi$
$647$	12.1051	0.475900	0.237950	+	0.971277i	$0.423525\pi$
$648$	−7.08840	−0.278459
$649$	−1.43251	−0.0562311
$650$	0	0
$651$	−2.00000	−0.0783862
$652$	23.3560	0.914691
$653$	40.2464	1.57496	0.787481	−	0.616338i	$-0.211385\pi$
$653$	40.2464	1.57496	0.787481	+	0.616338i	$0.211385\pi$
$654$	−0.185308	−0.00724611
$655$	26.1868	1.02320
$656$	0.0893760	0.00348955
$657$	−35.3876	−1.38060
$658$	−11.1759	−0.435684
$659$	−3.62327	−0.141143	−0.0705714	−	0.997507i	$-0.522482\pi$
$659$	−3.62327	−0.141143	−0.0705714	+	0.997507i	$0.522482\pi$
$660$	1.30098	0.0506406
$661$	−23.6365	−0.919352	−0.459676	−	0.888087i	$-0.652035\pi$
$661$	−23.6365	−0.919352	−0.459676	+	0.888087i	$0.652035\pi$
$662$	23.0874	0.897317
$663$	0	0
$664$	−3.23553	−0.125563
$665$	−20.0184	−0.776278
$666$	−26.9632	−1.04480
$667$	42.1054	1.63033
$668$	−21.7780	−0.842614
$669$	−9.29716	−0.359449
$670$	−0.988744	−0.0381985
$671$	1.95764	0.0755740
$672$	−0.466545	−0.0179974
$673$	46.8710	1.80674	0.903372	−	0.428859i	$-0.141084\pi$
$673$	46.8710	1.80674	0.903372	+	0.428859i	$0.141084\pi$
$674$	29.1429	1.12254
$675$	17.5025	0.673670
$676$	0	0
$677$	−13.7304	−0.527704	−0.263852	−	0.964563i	$-0.584993\pi$
$677$	−13.7304	−0.527704	−0.263852	+	0.964563i	$0.584993\pi$
$678$	2.08696	0.0801491
$679$	−14.7739	−0.566969
$680$	15.5277	0.595462
$681$	−0.164515	−0.00630423
$682$	3.52691	0.135052
$683$	−3.50578	−0.134145	−0.0670725	−	0.997748i	$-0.521366\pi$
$683$	−3.50578	−0.134145	−0.0670725	+	0.997748i	$0.521366\pi$
$684$	16.4330	0.628333
$685$	42.5031	1.62396
$686$	1.00000	0.0381802
$687$	−3.87847	−0.147973
$688$	7.35374	0.280359
$689$	0	0
$690$	9.69421	0.369052
$691$	31.7769	1.20885	0.604426	−	0.796662i	$-0.293403\pi$
$691$	31.7769	1.20885	0.604426	+	0.796662i	$0.293403\pi$
$692$	8.09733	0.307814
$693$	2.28911	0.0869562
$694$	29.1082	1.10493
$695$	−41.0025	−1.55531
$696$	−3.20429	−0.121458
$697$	0.409458	0.0155093
$698$	−25.7802	−0.975796
$699$	−7.17535	−0.271397
$700$	−6.48787	−0.245218
$701$	31.6828	1.19664	0.598322	−	0.801256i	$-0.295834\pi$
$701$	31.6828	1.19664	0.598322	+	0.801256i	$0.295834\pi$
$702$	0	0
$703$	57.2362	2.15870
$704$	0.822730	0.0310078
$705$	−17.6725	−0.665584
$706$	−9.91779	−0.373261
$707$	8.23976	0.309888
$708$	0.812334	0.0305294
$709$	35.3147	1.32627	0.663137	−	0.748498i	$-0.269225\pi$
$709$	35.3147	1.32627	0.663137	+	0.748498i	$0.269225\pi$
$710$	37.1082	1.39265
$711$	−27.7010	−1.03887
$712$	−8.04265	−0.301411
$713$	26.2806	0.984217
$714$	−2.13738	−0.0799895
$715$	0	0
$716$	9.90883	0.370310
$717$	−1.34648	−0.0502850
$718$	−25.2683	−0.943003
$719$	−1.21956	−0.0454818	−0.0227409	−	0.999741i	$-0.507239\pi$
$719$	−1.21956	−0.0454818	−0.0227409	+	0.999741i	$0.507239\pi$
$720$	9.43038	0.351450
$721$	−13.3231	−0.496179
$722$	−15.8833	−0.591114
$723$	−2.92404	−0.108746
$724$	−1.27902	−0.0475343
$725$	−44.5595	−1.65490
$726$	−4.81620	−0.178746
$727$	−5.75380	−0.213397	−0.106698	−	0.994291i	$-0.534028\pi$
$727$	−5.75380	−0.213397	−0.106698	+	0.994291i	$0.534028\pi$
$728$	0	0
$729$	−15.9465	−0.590611
$730$	43.1084	1.59551
$731$	33.6897	1.24606
$732$	−1.11012	−0.0410312
$733$	−35.2258	−1.30110	−0.650548	−	0.759466i	$-0.725461\pi$
$733$	−35.2258	−1.30110	−0.650548	+	0.759466i	$0.725461\pi$
$734$	−35.7838	−1.32080
$735$	1.58130	0.0583270
$736$	6.13055	0.225975
$737$	−0.240006	−0.00884073
$738$	0.248674	0.00915382
$739$	−29.3524	−1.07975	−0.539873	−	0.841746i	$-0.681528\pi$
$739$	−29.3524	−1.07975	−0.539873	+	0.841746i	$0.681528\pi$
$740$	32.8460	1.20744
$741$	0	0
$742$	−7.01530	−0.257540
$743$	14.9838	0.549702	0.274851	−	0.961487i	$-0.411371\pi$
$743$	14.9838	0.549702	0.274851	+	0.961487i	$0.411371\pi$
$744$	−2.00000	−0.0733236
$745$	−57.6458	−2.11198
$746$	23.3304	0.854185
$747$	−9.00234	−0.329378
$748$	3.76917	0.137815
$749$	9.02649	0.329821
$750$	−2.35277	−0.0859108
$751$	43.8390	1.59971	0.799855	−	0.600194i	$-0.204910\pi$
$751$	43.8390	1.59971	0.799855	+	0.600194i	$0.204910\pi$
$752$	−11.1759	−0.407545
$753$	−8.05560	−0.293562
$754$	0	0
$755$	18.7963	0.684069
$756$	−2.69772	−0.0981151
$757$	−36.3597	−1.32152	−0.660758	−	0.750599i	$-0.729765\pi$
$757$	−36.3597	−1.32152	−0.660758	+	0.750599i	$0.729765\pi$
$758$	24.3066	0.882856
$759$	2.35315	0.0854140
$760$	−20.0184	−0.726142
$761$	18.2335	0.660962	0.330481	−	0.943813i	$-0.392789\pi$
$761$	18.2335	0.660962	0.330481	+	0.943813i	$0.392789\pi$
$762$	−0.251993	−0.00912876
$763$	0.397192	0.0143793
$764$	−10.0342	−0.363025
$765$	43.2034	1.56202
$766$	−4.91150	−0.177460
$767$	0	0
$768$	−0.466545	−0.0168350
$769$	6.54565	0.236042	0.118021	−	0.993011i	$-0.462345\pi$
$769$	6.54565	0.236042	0.118021	+	0.993011i	$0.462345\pi$
$770$	−2.78854	−0.100492
$771$	5.22208	0.188069
$772$	−15.8582	−0.570750
$773$	44.6466	1.60583	0.802913	−	0.596097i	$-0.203282\pi$
$773$	44.6466	1.60583	0.802913	+	0.596097i	$0.203282\pi$
$774$	20.4606	0.735440
$775$	−27.8124	−0.999051
$776$	−14.7739	−0.530351
$777$	−4.52122	−0.162198
$778$	−5.14522	−0.184465
$779$	−0.527873	−0.0189130
$780$	0	0
$781$	9.00757	0.322316
$782$	28.0858	1.00435
$783$	−18.5283	−0.662147
$784$	1.00000	0.0357143
$785$	−7.77363	−0.277453
$786$	−3.60460	−0.128572
$787$	−25.0526	−0.893028	−0.446514	−	0.894777i	$-0.647335\pi$
$787$	−25.0526	−0.893028	−0.446514	+	0.894777i	$0.647335\pi$
$788$	−14.8081	−0.527515
$789$	13.3351	0.474742
$790$	33.7447	1.20058
$791$	−4.47322	−0.159049
$792$	2.28911	0.0813400
$793$	0	0
$794$	−12.3500	−0.438284
$795$	−11.0933	−0.393438
$796$	−2.55543	−0.0905747
$797$	27.8264	0.985662	0.492831	−	0.870125i	$-0.335962\pi$
$797$	27.8264	0.985662	0.492831	+	0.870125i	$0.335962\pi$
$798$	2.75551	0.0975440
$799$	−51.2003	−1.81134
$800$	−6.48787	−0.229381
$801$	−22.3774	−0.790665
$802$	−32.4894	−1.14724
$803$	10.4640	0.369268
$804$	0.136100	0.00479987
$805$	−20.7787	−0.732354
$806$	0	0
$807$	8.57294	0.301782
$808$	8.23976	0.289874
$809$	7.49650	0.263563	0.131781	−	0.991279i	$-0.457930\pi$
$809$	7.49650	0.263563	0.131781	+	0.991279i	$0.457930\pi$
$810$	24.0253	0.844161
$811$	9.88726	0.347189	0.173594	−	0.984817i	$-0.444462\pi$
$811$	9.88726	0.347189	0.173594	+	0.984817i	$0.444462\pi$
$812$	6.86813	0.241024
$813$	−9.50936	−0.333508
$814$	7.97296	0.279452
$815$	−79.1622	−2.77293
$816$	−2.13738	−0.0748233
$817$	−43.4327	−1.51952
$818$	−3.76834	−0.131757
$819$	0	0
$820$	−0.302929	−0.0105787
$821$	−14.3675	−0.501430	−0.250715	−	0.968061i	$-0.580666\pi$
$821$	−14.3675	−0.501430	−0.250715	+	0.968061i	$0.580666\pi$
$822$	−5.85052	−0.204060
$823$	11.8869	0.414350	0.207175	−	0.978304i	$-0.433573\pi$
$823$	11.8869	0.414350	0.207175	+	0.978304i	$0.433573\pi$
$824$	−13.3231	−0.464133
$825$	−2.49031	−0.0867014
$826$	−1.74117	−0.0605830
$827$	29.0884	1.01150	0.505752	−	0.862679i	$-0.331215\pi$
$827$	29.0884	1.01150	0.505752	+	0.862679i	$0.331215\pi$
$828$	17.0572	0.592780
$829$	−49.6286	−1.72367	−0.861836	−	0.507187i	$-0.830685\pi$
$829$	−49.6286	−1.72367	−0.861836	+	0.507187i	$0.830685\pi$
$830$	10.9664	0.380651
$831$	−3.37414	−0.117048
$832$	0	0
$833$	4.58130	0.158733
$834$	5.64396	0.195434
$835$	73.8137	2.55443
$836$	−4.85921	−0.168059
$837$	−11.5647	−0.399734
$838$	10.5301	0.363755
$839$	4.61692	0.159394	0.0796969	−	0.996819i	$-0.474605\pi$
$839$	4.61692	0.159394	0.0796969	+	0.996819i	$0.474605\pi$
$840$	1.58130	0.0545599
$841$	18.1712	0.626593
$842$	−24.9973	−0.861465
$843$	5.81247	0.200192
$844$	−8.63648	−0.297280
$845$	0	0
$846$	−31.0952	−1.06908
$847$	10.3231	0.354706
$848$	−7.01530	−0.240906
$849$	−6.09341	−0.209125
$850$	−29.7229	−1.01949
$851$	59.4103	2.03656
$852$	−5.10792	−0.174994
$853$	−37.8266	−1.29516	−0.647579	−	0.761999i	$-0.724218\pi$
$853$	−37.8266	−1.29516	−0.647579	+	0.761999i	$0.724218\pi$
$854$	2.37945	0.0814231
$855$	−55.6978	−1.90482
$856$	9.02649	0.308519
$857$	−30.1652	−1.03042	−0.515211	−	0.857063i	$-0.672287\pi$
$857$	−30.1652	−1.03042	−0.515211	+	0.857063i	$0.672287\pi$
$858$	0	0
$859$	10.6316	0.362745	0.181372	−	0.983414i	$-0.441946\pi$
$859$	10.6316	0.362745	0.181372	+	0.983414i	$0.441946\pi$
$860$	−24.9246	−0.849922
$861$	0.0416979	0.00142106
$862$	11.9784	0.407986
$863$	−23.8352	−0.811360	−0.405680	−	0.914015i	$-0.632965\pi$
$863$	−23.8352	−0.811360	−0.405680	+	0.914015i	$0.632965\pi$
$864$	−2.69772	−0.0917783
$865$	−27.4449	−0.933154
$866$	−7.96950	−0.270814
$867$	−1.86071	−0.0631931
$868$	4.28683	0.145505
$869$	8.19112	0.277865
$870$	10.8605	0.368207
$871$	0	0
$872$	0.397192	0.0134506
$873$	−41.1059	−1.39122
$874$	−36.2083	−1.22476
$875$	5.04295	0.170483
$876$	−5.93384	−0.200486
$877$	28.4246	0.959829	0.479915	−	0.877315i	$-0.340668\pi$
$877$	28.4246	0.959829	0.479915	+	0.877315i	$0.340668\pi$
$878$	−4.35655	−0.147026
$879$	−6.79205	−0.229090
$880$	−2.78854	−0.0940017
$881$	55.1829	1.85916	0.929580	−	0.368621i	$-0.120170\pi$
$881$	55.1829	1.85916	0.929580	+	0.368621i	$0.120170\pi$
$882$	2.78234	0.0936861
$883$	−9.18216	−0.309004	−0.154502	−	0.987992i	$-0.549377\pi$
$883$	−9.18216	−0.309004	−0.154502	+	0.987992i	$0.549377\pi$
$884$	0	0
$885$	−2.75331	−0.0925514
$886$	11.4823	0.385757
$887$	33.5715	1.12722	0.563610	−	0.826041i	$-0.309412\pi$
$887$	33.5715	1.12722	0.563610	+	0.826041i	$0.309412\pi$
$888$	−4.52122	−0.151722
$889$	0.540127	0.0181153
$890$	27.2596	0.913743
$891$	5.83184	0.195374
$892$	19.9277	0.667228
$893$	66.0074	2.20885
$894$	7.93490	0.265383
$895$	−33.5848	−1.12261
$896$	1.00000	0.0334077
$897$	0	0
$898$	−29.5248	−0.985255
$899$	29.4425	0.981963
$900$	−18.0514	−0.601715
$901$	−32.1392	−1.07071
$902$	−0.0735323	−0.00244836
$903$	3.43085	0.114172
$904$	−4.47322	−0.148777
$905$	4.33507	0.144103
$906$	−2.58730	−0.0859574
$907$	11.0349	0.366409	0.183205	−	0.983075i	$-0.441353\pi$
$907$	11.0349	0.366409	0.183205	+	0.983075i	$0.441353\pi$
$908$	0.352624	0.0117022
$909$	22.9258	0.760400
$910$	0	0
$911$	59.9931	1.98766	0.993830	−	0.110917i	$-0.0353789\pi$
$911$	59.9931	1.98766	0.993830	+	0.110917i	$0.0353789\pi$
$912$	2.75551	0.0912441
$913$	2.66197	0.0880984
$914$	−16.5981	−0.549018
$915$	3.76261	0.124388
$916$	8.31317	0.274675
$917$	7.72615	0.255140
$918$	−12.3591	−0.407910
$919$	35.6537	1.17611	0.588053	−	0.808822i	$-0.299895\pi$
$919$	35.6537	1.17611	0.588053	+	0.808822i	$0.299895\pi$
$920$	−20.7787	−0.685054
$921$	−1.51285	−0.0498502
$922$	−26.4422	−0.870828
$923$	0	0
$924$	0.383841	0.0126274
$925$	−62.8730	−2.06725
$926$	10.4717	0.344123
$927$	−37.0694	−1.21752
$928$	6.86813	0.225457
$929$	29.0302	0.952450	0.476225	−	0.879324i	$-0.342005\pi$
$929$	29.0302	0.952450	0.476225	+	0.879324i	$0.342005\pi$
$930$	6.77875	0.222284
$931$	−5.90621	−0.193568
$932$	15.3798	0.503781
$933$	−4.79183	−0.156877
$934$	27.9010	0.912947
$935$	−12.7751	−0.417792
$936$	0	0
$937$	38.2635	1.25001	0.625006	−	0.780620i	$-0.285096\pi$
$937$	38.2635	1.25001	0.625006	+	0.780620i	$0.285096\pi$
$938$	−0.291719	−0.00952495
$939$	2.86170	0.0933882
$940$	37.8795	1.23549
$941$	−4.14746	−0.135203	−0.0676017	−	0.997712i	$-0.521535\pi$
$941$	−4.14746	−0.135203	−0.0676017	+	0.997712i	$0.521535\pi$
$942$	1.07003	0.0348636
$943$	−0.547924	−0.0178428
$944$	−1.74117	−0.0566702
$945$	9.14359	0.297441
$946$	−6.05015	−0.196707
$947$	1.00792	0.0327530	0.0163765	−	0.999866i	$-0.494787\pi$
$947$	1.00792	0.0327530	0.0163765	+	0.999866i	$0.494787\pi$
$948$	−4.64493	−0.150860
$949$	0	0
$950$	38.3187	1.24322
$951$	−2.35366	−0.0763226
$952$	4.58130	0.148481
$953$	16.5029	0.534582	0.267291	−	0.963616i	$-0.413871\pi$
$953$	16.5029	0.534582	0.267291	+	0.963616i	$0.413871\pi$
$954$	−19.5189	−0.631948
$955$	34.0097	1.10053
$956$	2.88606	0.0933418
$957$	2.63627	0.0852184
$958$	6.88133	0.222326
$959$	12.5401	0.404941
$960$	1.58130	0.0510361
$961$	−12.6231	−0.407196
$962$	0	0
$963$	25.1147	0.809311
$964$	6.26744	0.201861
$965$	53.7495	1.73026
$966$	2.86018	0.0920246
$967$	37.7765	1.21481	0.607406	−	0.794392i	$-0.292210\pi$
$967$	37.7765	1.21481	0.607406	+	0.794392i	$0.292210\pi$
$968$	10.3231	0.331797
$969$	12.6238	0.405535
$970$	50.0742	1.60779
$971$	−48.3122	−1.55041	−0.775206	−	0.631709i	$-0.782354\pi$
$971$	−48.3122	−1.55041	−0.775206	+	0.631709i	$0.782354\pi$
$972$	−11.4002	−0.365662
$973$	−12.0974	−0.387823
$974$	40.8062	1.30752
$975$	0	0
$976$	2.37945	0.0761643
$977$	16.3041	0.521615	0.260807	−	0.965391i	$-0.416011\pi$
$977$	16.3041	0.521615	0.260807	+	0.965391i	$0.416011\pi$
$978$	10.8966	0.348435
$979$	6.61693	0.211478
$980$	−3.38938	−0.108270
$981$	1.10512	0.0352838
$982$	−6.72706	−0.214669
$983$	29.5121	0.941291	0.470645	−	0.882322i	$-0.344021\pi$
$983$	29.5121	0.941291	0.470645	+	0.882322i	$0.344021\pi$
$984$	0.0416979	0.00132928
$985$	50.1901	1.59919
$986$	31.4649	1.00205
$987$	−5.21408	−0.165966
$988$	0	0
$989$	−45.0825	−1.43354
$990$	−7.75866	−0.246586
$991$	4.39245	0.139531	0.0697653	−	0.997563i	$-0.477775\pi$
$991$	4.39245	0.139531	0.0697653	+	0.997563i	$0.477775\pi$
$992$	4.28683	0.136107
$993$	10.7713	0.341817
$994$	10.9484	0.347262
$995$	8.66130	0.274582
$996$	−1.50952	−0.0478310
$997$	46.3338	1.46741	0.733704	−	0.679470i	$-0.237790\pi$
$997$	46.3338	1.46741	0.733704	+	0.679470i	$0.237790\pi$
$998$	−1.16200	−0.0367826
$999$	−26.1432	−0.827135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.a.bf.1.3		6
13.5	odd	4		2366.2.d.r.337.9		12
13.6	odd	12		182.2.m.b.127.5	yes	12
13.8	odd	4		2366.2.d.r.337.3		12
13.11	odd	12		182.2.m.b.43.5	✓	12
13.12	even	2		2366.2.a.bh.1.3		6
39.11	even	12		1638.2.bj.g.1135.3		12
39.32	even	12		1638.2.bj.g.127.1		12
52.11	even	12		1456.2.cc.d.225.3		12
52.19	even	12		1456.2.cc.d.673.3		12
91.6	even	12		1274.2.m.c.491.5		12
91.11	odd	12		1274.2.v.e.667.2		12
91.19	even	12		1274.2.v.d.361.2		12
91.24	even	12		1274.2.v.d.667.2		12
91.32	odd	12		1274.2.o.d.569.5		12
91.37	odd	12		1274.2.o.d.459.2		12
91.45	even	12		1274.2.o.e.569.5		12
91.58	odd	12		1274.2.v.e.361.2		12
91.76	even	12		1274.2.m.c.589.5		12
91.89	even	12		1274.2.o.e.459.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.5	✓	12	13.11	odd	12
182.2.m.b.127.5	yes	12	13.6	odd	12
1274.2.m.c.491.5		12	91.6	even	12
1274.2.m.c.589.5		12	91.76	even	12
1274.2.o.d.459.2		12	91.37	odd	12
1274.2.o.d.569.5		12	91.32	odd	12
1274.2.o.e.459.2		12	91.89	even	12
1274.2.o.e.569.5		12	91.45	even	12
1274.2.v.d.361.2		12	91.19	even	12
1274.2.v.d.667.2		12	91.24	even	12
1274.2.v.e.361.2		12	91.58	odd	12
1274.2.v.e.667.2		12	91.11	odd	12
1456.2.cc.d.225.3		12	52.11	even	12
1456.2.cc.d.673.3		12	52.19	even	12
1638.2.bj.g.127.1		12	39.32	even	12
1638.2.bj.g.1135.3		12	39.11	even	12
2366.2.a.bf.1.3		6	1.1	even	1	trivial
2366.2.a.bh.1.3		6	13.12	even	2
2366.2.d.r.337.3		12	13.8	odd	4
2366.2.d.r.337.9		12	13.5	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.466545 q^{3} +1.00000 q^{4} -3.38938 q^{5} +0.466545 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.78234 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.466545 q^{3} +1.00000 q^{4} -3.38938 q^{5} +0.466545 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.78234 q^{9} +3.38938 q^{10} +0.822730 q^{11} -0.466545 q^{12} +1.00000 q^{14} +1.58130 q^{15} +1.00000 q^{16} +4.58130 q^{17} +2.78234 q^{18} -5.90621 q^{19} -3.38938 q^{20} +0.466545 q^{21} -0.822730 q^{22} -6.13055 q^{23} +0.466545 q^{24} +6.48787 q^{25} +2.69772 q^{27} -1.00000 q^{28} -6.86813 q^{29} -1.58130 q^{30} -4.28683 q^{31} -1.00000 q^{32} -0.383841 q^{33} -4.58130 q^{34} +3.38938 q^{35} -2.78234 q^{36} -9.69086 q^{37} +5.90621 q^{38} +3.38938 q^{40} +0.0893760 q^{41} -0.466545 q^{42} +7.35374 q^{43} +0.822730 q^{44} +9.43038 q^{45} +6.13055 q^{46} -11.1759 q^{47} -0.466545 q^{48} +1.00000 q^{49} -6.48787 q^{50} -2.13738 q^{51} -7.01530 q^{53} -2.69772 q^{54} -2.78854 q^{55} +1.00000 q^{56} +2.75551 q^{57} +6.86813 q^{58} -1.74117 q^{59} +1.58130 q^{60} +2.37945 q^{61} +4.28683 q^{62} +2.78234 q^{63} +1.00000 q^{64} +0.383841 q^{66} -0.291719 q^{67} +4.58130 q^{68} +2.86018 q^{69} -3.38938 q^{70} +10.9484 q^{71} +2.78234 q^{72} +12.7187 q^{73} +9.69086 q^{74} -3.02688 q^{75} -5.90621 q^{76} -0.822730 q^{77} +9.95602 q^{79} -3.38938 q^{80} +7.08840 q^{81} -0.0893760 q^{82} +3.23553 q^{83} +0.466545 q^{84} -15.5277 q^{85} -7.35374 q^{86} +3.20429 q^{87} -0.822730 q^{88} +8.04265 q^{89} -9.43038 q^{90} -6.13055 q^{92} +2.00000 q^{93} +11.1759 q^{94} +20.0184 q^{95} +0.466545 q^{96} +14.7739 q^{97} -1.00000 q^{98} -2.28911 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 2 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} - 6 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 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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