LMFDB - Embedded newform 2166.2.a.s.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2166,2,Mod(1,2166)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2166, 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("2166.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2166 = 2 \cdot 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2166.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:	$17.2955970778$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.87939$ of defining polynomial
Character	$\chi$	$=$	2166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.22668 q^{5} -1.00000 q^{6} -2.65270 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.22668 q^{5} -1.00000 q^{6} -2.65270 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.22668 q^{10} +2.22668 q^{11} -1.00000 q^{12} +5.29086 q^{13} -2.65270 q^{14} +2.22668 q^{15} +1.00000 q^{16} -3.41147 q^{17} +1.00000 q^{18} -2.22668 q^{20} +2.65270 q^{21} +2.22668 q^{22} +2.22668 q^{23} -1.00000 q^{24} -0.0418891 q^{25} +5.29086 q^{26} -1.00000 q^{27} -2.65270 q^{28} -4.81521 q^{29} +2.22668 q^{30} -10.3131 q^{31} +1.00000 q^{32} -2.22668 q^{33} -3.41147 q^{34} +5.90673 q^{35} +1.00000 q^{36} -2.30541 q^{37} -5.29086 q^{39} -2.22668 q^{40} +7.23442 q^{41} +2.65270 q^{42} -5.92127 q^{43} +2.22668 q^{44} -2.22668 q^{45} +2.22668 q^{46} +11.0077 q^{47} -1.00000 q^{48} +0.0368366 q^{49} -0.0418891 q^{50} +3.41147 q^{51} +5.29086 q^{52} -9.82295 q^{53} -1.00000 q^{54} -4.95811 q^{55} -2.65270 q^{56} -4.81521 q^{58} -4.95811 q^{59} +2.22668 q^{60} -5.70233 q^{61} -10.3131 q^{62} -2.65270 q^{63} +1.00000 q^{64} -11.7811 q^{65} -2.22668 q^{66} -8.57398 q^{67} -3.41147 q^{68} -2.22668 q^{69} +5.90673 q^{70} -4.40373 q^{71} +1.00000 q^{72} -2.79561 q^{73} -2.30541 q^{74} +0.0418891 q^{75} -5.90673 q^{77} -5.29086 q^{78} -13.8007 q^{79} -2.22668 q^{80} +1.00000 q^{81} +7.23442 q^{82} -10.5030 q^{83} +2.65270 q^{84} +7.59627 q^{85} -5.92127 q^{86} +4.81521 q^{87} +2.22668 q^{88} -7.81521 q^{89} -2.22668 q^{90} -14.0351 q^{91} +2.22668 q^{92} +10.3131 q^{93} +11.0077 q^{94} -1.00000 q^{96} +17.7888 q^{97} +0.0368366 q^{98} +2.22668 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} - 9 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 - 9 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} - 9 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{12} - 9 q^{14} + 3 q^{16} + 3 q^{18} + 9 q^{21} - 3 q^{24} + 3 q^{25} - 3 q^{27} - 9 q^{28} - 18 q^{29} - 9 q^{31} + 3 q^{32} - 9 q^{35} + 3 q^{36} - 9 q^{37} - 9 q^{41} + 9 q^{42} - 9 q^{43} + 9 q^{47} - 3 q^{48} + 12 q^{49} + 3 q^{50} - 9 q^{53} - 3 q^{54} - 18 q^{55} - 9 q^{56} - 18 q^{58} - 18 q^{59} + 9 q^{61} - 9 q^{62} - 9 q^{63} + 3 q^{64} - 18 q^{65} - 18 q^{67} - 9 q^{70} - 27 q^{71} + 3 q^{72} - 9 q^{73} - 9 q^{74} - 3 q^{75} + 9 q^{77} - 27 q^{79} + 3 q^{81} - 9 q^{82} + 9 q^{83} + 9 q^{84} + 9 q^{85} - 9 q^{86} + 18 q^{87} - 27 q^{89} + 3 q^{91} + 9 q^{93} + 9 q^{94} - 3 q^{96} + 12 q^{97} + 12 q^{98}+O(q^{100}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 - 9 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^12 - 9 * q^14 + 3 * q^16 + 3 * q^18 + 9 * q^21 - 3 * q^24 + 3 * q^25 - 3 * q^27 - 9 * q^28 - 18 * q^29 - 9 * q^31 + 3 * q^32 - 9 * q^35 + 3 * q^36 - 9 * q^37 - 9 * q^41 + 9 * q^42 - 9 * q^43 + 9 * q^47 - 3 * q^48 + 12 * q^49 + 3 * q^50 - 9 * q^53 - 3 * q^54 - 18 * q^55 - 9 * q^56 - 18 * q^58 - 18 * q^59 + 9 * q^61 - 9 * q^62 - 9 * q^63 + 3 * q^64 - 18 * q^65 - 18 * q^67 - 9 * q^70 - 27 * q^71 + 3 * q^72 - 9 * q^73 - 9 * q^74 - 3 * q^75 + 9 * q^77 - 27 * q^79 + 3 * q^81 - 9 * q^82 + 9 * q^83 + 9 * q^84 + 9 * q^85 - 9 * q^86 + 18 * q^87 - 27 * q^89 + 3 * q^91 + 9 * q^93 + 9 * q^94 - 3 * q^96 + 12 * q^97 + 12 * q^98

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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−2.22668	−0.995802	−0.497901	−	0.867234i	$-0.665896\pi$
$5$	−2.22668	−0.995802	−0.497901	+	0.867234i	$0.665896\pi$
$6$	−1.00000	−0.408248
$7$	−2.65270	−1.00263	−0.501314	−	0.865266i	$-0.667150\pi$
$7$	−2.65270	−1.00263	−0.501314	+	0.865266i	$0.667150\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.22668	−0.704139
$11$	2.22668	0.671370	0.335685	−	0.941974i	$-0.391032\pi$
$11$	2.22668	0.671370	0.335685	+	0.941974i	$0.391032\pi$
$12$	−1.00000	−0.288675
$13$	5.29086	1.46742	0.733710	−	0.679463i	$-0.237787\pi$
$13$	5.29086	1.46742	0.733710	+	0.679463i	$0.237787\pi$
$14$	−2.65270	−0.708965
$15$	2.22668	0.574927
$16$	1.00000	0.250000
$17$	−3.41147	−0.827404	−0.413702	−	0.910412i	$-0.635764\pi$
$17$	−3.41147	−0.827404	−0.413702	+	0.910412i	$0.635764\pi$
$18$	1.00000	0.235702
$19$	0	0
$19$	0	0
$20$	−2.22668	−0.497901
$21$	2.65270	0.578867
$22$	2.22668	0.474730
$23$	2.22668	0.464295	0.232148	−	0.972681i	$-0.425425\pi$
$23$	2.22668	0.464295	0.232148	+	0.972681i	$0.425425\pi$
$24$	−1.00000	−0.204124
$25$	−0.0418891	−0.00837781
$26$	5.29086	1.03762
$27$	−1.00000	−0.192450
$28$	−2.65270	−0.501314
$29$	−4.81521	−0.894162	−0.447081	−	0.894494i	$-0.647536\pi$
$29$	−4.81521	−0.894162	−0.447081	+	0.894494i	$0.647536\pi$
$30$	2.22668	0.406535
$31$	−10.3131	−1.85230	−0.926148	−	0.377160i	$-0.876901\pi$
$31$	−10.3131	−1.85230	−0.926148	+	0.377160i	$0.876901\pi$
$32$	1.00000	0.176777
$33$	−2.22668	−0.387616
$34$	−3.41147	−0.585063
$35$	5.90673	0.998419
$36$	1.00000	0.166667
$37$	−2.30541	−0.379007	−0.189503	−	0.981880i	$-0.560688\pi$
$37$	−2.30541	−0.379007	−0.189503	+	0.981880i	$0.560688\pi$
$38$	0	0
$39$	−5.29086	−0.847216
$40$	−2.22668	−0.352069
$41$	7.23442	1.12983	0.564913	−	0.825150i	$-0.308910\pi$
$41$	7.23442	1.12983	0.564913	+	0.825150i	$0.308910\pi$
$42$	2.65270	0.409321
$43$	−5.92127	−0.902986	−0.451493	−	0.892275i	$-0.649108\pi$
$43$	−5.92127	−0.902986	−0.451493	+	0.892275i	$0.649108\pi$
$44$	2.22668	0.335685
$45$	−2.22668	−0.331934
$46$	2.22668	0.328306
$47$	11.0077	1.60564	0.802822	−	0.596219i	$-0.203331\pi$
$47$	11.0077	1.60564	0.802822	+	0.596219i	$0.203331\pi$
$48$	−1.00000	−0.144338
$49$	0.0368366	0.00526238
$50$	−0.0418891	−0.00592401
$51$	3.41147	0.477702
$52$	5.29086	0.733710
$53$	−9.82295	−1.34929	−0.674643	−	0.738144i	$-0.735702\pi$
$53$	−9.82295	−1.34929	−0.674643	+	0.738144i	$0.735702\pi$
$54$	−1.00000	−0.136083
$55$	−4.95811	−0.668552
$56$	−2.65270	−0.354482
$57$	0	0
$58$	−4.81521	−0.632268
$59$	−4.95811	−0.645491	−0.322746	−	0.946486i	$-0.604606\pi$
$59$	−4.95811	−0.645491	−0.322746	+	0.946486i	$0.604606\pi$
$60$	2.22668	0.287463
$61$	−5.70233	−0.730109	−0.365054	−	0.930986i	$-0.618950\pi$
$61$	−5.70233	−0.730109	−0.365054	+	0.930986i	$0.618950\pi$
$62$	−10.3131	−1.30977
$63$	−2.65270	−0.334209
$64$	1.00000	0.125000
$65$	−11.7811	−1.46126
$66$	−2.22668	−0.274086
$67$	−8.57398	−1.04748	−0.523739	−	0.851879i	$-0.675463\pi$
$67$	−8.57398	−1.04748	−0.523739	+	0.851879i	$0.675463\pi$
$68$	−3.41147	−0.413702
$69$	−2.22668	−0.268061
$70$	5.90673	0.705989
$71$	−4.40373	−0.522627	−0.261313	−	0.965254i	$-0.584156\pi$
$71$	−4.40373	−0.522627	−0.261313	+	0.965254i	$0.584156\pi$
$72$	1.00000	0.117851
$73$	−2.79561	−0.327201	−0.163601	−	0.986527i	$-0.552311\pi$
$73$	−2.79561	−0.327201	−0.163601	+	0.986527i	$0.552311\pi$
$74$	−2.30541	−0.267998
$75$	0.0418891	0.00483693
$76$	0	0
$77$	−5.90673	−0.673134
$78$	−5.29086	−0.599072
$79$	−13.8007	−1.55270	−0.776348	−	0.630305i	$-0.782930\pi$
$79$	−13.8007	−1.55270	−0.776348	+	0.630305i	$0.782930\pi$
$80$	−2.22668	−0.248951
$81$	1.00000	0.111111
$82$	7.23442	0.798908
$83$	−10.5030	−1.15285	−0.576427	−	0.817149i	$-0.695553\pi$
$83$	−10.5030	−1.15285	−0.576427	+	0.817149i	$0.695553\pi$
$84$	2.65270	0.289434
$85$	7.59627	0.823931
$86$	−5.92127	−0.638507
$87$	4.81521	0.516244
$88$	2.22668	0.237365
$89$	−7.81521	−0.828410	−0.414205	−	0.910184i	$-0.635940\pi$
$89$	−7.81521	−0.828410	−0.414205	+	0.910184i	$0.635940\pi$
$90$	−2.22668	−0.234713
$91$	−14.0351	−1.47128
$92$	2.22668	0.232148
$93$	10.3131	1.06942
$94$	11.0077	1.13536
$95$	0	0
$96$	−1.00000	−0.102062
$97$	17.7888	1.80618	0.903089	−	0.429452i	$-0.141293\pi$
$97$	17.7888	1.80618	0.903089	+	0.429452i	$0.141293\pi$
$98$	0.0368366	0.00372106
$99$	2.22668	0.223790
$100$	−0.0418891	−0.00418891
$101$	17.9067	1.78179	0.890893	−	0.454213i	$-0.150080\pi$
$101$	17.9067	1.78179	0.890893	+	0.454213i	$0.150080\pi$
$102$	3.41147	0.337786
$103$	−4.24628	−0.418399	−0.209199	−	0.977873i	$-0.567086\pi$
$103$	−4.24628	−0.418399	−0.209199	+	0.977873i	$0.567086\pi$
$104$	5.29086	0.518811
$105$	−5.90673	−0.576437
$106$	−9.82295	−0.954089
$107$	−15.6040	−1.50850	−0.754248	−	0.656589i	$-0.771998\pi$
$107$	−15.6040	−1.50850	−0.754248	+	0.656589i	$0.771998\pi$
$108$	−1.00000	−0.0962250
$109$	1.36184	0.130441	0.0652205	−	0.997871i	$-0.479225\pi$
$109$	1.36184	0.130441	0.0652205	+	0.997871i	$0.479225\pi$
$110$	−4.95811	−0.472737
$111$	2.30541	0.218820
$112$	−2.65270	−0.250657
$113$	−17.2003	−1.61807	−0.809033	−	0.587763i	$-0.800009\pi$
$113$	−17.2003	−1.61807	−0.809033	+	0.587763i	$0.800009\pi$
$114$	0	0
$115$	−4.95811	−0.462346
$116$	−4.81521	−0.447081
$117$	5.29086	0.489140
$118$	−4.95811	−0.456431
$119$	9.04963	0.829578
$120$	2.22668	0.203267
$121$	−6.04189	−0.549263
$122$	−5.70233	−0.516265
$123$	−7.23442	−0.652306
$124$	−10.3131	−0.926148
$125$	11.2267	1.00414
$126$	−2.65270	−0.236322
$127$	13.1925	1.17065	0.585324	−	0.810799i	$-0.300967\pi$
$127$	13.1925	1.17065	0.585324	+	0.810799i	$0.300967\pi$
$128$	1.00000	0.0883883
$129$	5.92127	0.521339
$130$	−11.7811	−1.03327
$131$	7.50299	0.655540	0.327770	−	0.944758i	$-0.393703\pi$
$131$	7.50299	0.655540	0.327770	+	0.944758i	$0.393703\pi$
$132$	−2.22668	−0.193808
$133$	0	0
$134$	−8.57398	−0.740679
$135$	2.22668	0.191642
$136$	−3.41147	−0.292531
$137$	6.63041	0.566475	0.283237	−	0.959050i	$-0.408592\pi$
$137$	6.63041	0.566475	0.283237	+	0.959050i	$0.408592\pi$
$138$	−2.22668	−0.189548
$139$	−8.50980	−0.721792	−0.360896	−	0.932606i	$-0.617529\pi$
$139$	−8.50980	−0.721792	−0.360896	+	0.932606i	$0.617529\pi$
$140$	5.90673	0.499209
$141$	−11.0077	−0.927019
$142$	−4.40373	−0.369553
$143$	11.7811	0.985182
$144$	1.00000	0.0833333
$145$	10.7219	0.890408
$146$	−2.79561	−0.231366
$147$	−0.0368366	−0.00303823
$148$	−2.30541	−0.189503
$149$	−3.41147	−0.279479	−0.139739	−	0.990188i	$-0.544626\pi$
$149$	−3.41147	−0.279479	−0.139739	+	0.990188i	$0.544626\pi$
$150$	0.0418891	0.00342023
$151$	−3.04189	−0.247545	−0.123773	−	0.992311i	$-0.539499\pi$
$151$	−3.04189	−0.247545	−0.123773	+	0.992311i	$0.539499\pi$
$152$	0	0
$153$	−3.41147	−0.275801
$154$	−5.90673	−0.475978
$155$	22.9641	1.84452
$156$	−5.29086	−0.423608
$157$	−15.5253	−1.23905	−0.619526	−	0.784976i	$-0.712675\pi$
$157$	−15.5253	−1.23905	−0.619526	+	0.784976i	$0.712675\pi$
$158$	−13.8007	−1.09792
$159$	9.82295	0.779010
$160$	−2.22668	−0.176035
$161$	−5.90673	−0.465515
$162$	1.00000	0.0785674
$163$	4.43882	0.347675	0.173837	−	0.984774i	$-0.444383\pi$
$163$	4.43882	0.347675	0.173837	+	0.984774i	$0.444383\pi$
$164$	7.23442	0.564913
$165$	4.95811	0.385988
$166$	−10.5030	−0.815190
$167$	8.15064	0.630716	0.315358	−	0.948973i	$-0.397875\pi$
$167$	8.15064	0.630716	0.315358	+	0.948973i	$0.397875\pi$
$168$	2.65270	0.204661
$169$	14.9932	1.15332
$170$	7.59627	0.582607
$171$	0	0
$172$	−5.92127	−0.451493
$173$	15.9659	1.21386	0.606931	−	0.794755i	$-0.292401\pi$
$173$	15.9659	1.21386	0.606931	+	0.794755i	$0.292401\pi$
$174$	4.81521	0.365040
$175$	0.111119	0.00839983
$176$	2.22668	0.167842
$177$	4.95811	0.372674
$178$	−7.81521	−0.585775
$179$	−1.45336	−0.108629	−0.0543147	−	0.998524i	$-0.517297\pi$
$179$	−1.45336	−0.108629	−0.0543147	+	0.998524i	$0.517297\pi$
$180$	−2.22668	−0.165967
$181$	1.12567	0.0836702	0.0418351	−	0.999125i	$-0.486680\pi$
$181$	1.12567	0.0836702	0.0418351	+	0.999125i	$0.486680\pi$
$182$	−14.0351	−1.04035
$183$	5.70233	0.421529
$184$	2.22668	0.164153
$185$	5.13341	0.377416
$186$	10.3131	0.756197
$187$	−7.59627	−0.555494
$188$	11.0077	0.802822
$189$	2.65270	0.192956
$190$	0	0
$191$	−1.32770	−0.0960687	−0.0480344	−	0.998846i	$-0.515296\pi$
$191$	−1.32770	−0.0960687	−0.0480344	+	0.998846i	$0.515296\pi$
$192$	−1.00000	−0.0721688
$193$	−14.9855	−1.07868	−0.539338	−	0.842089i	$-0.681326\pi$
$193$	−14.9855	−1.07868	−0.539338	+	0.842089i	$0.681326\pi$
$194$	17.7888	1.27716
$195$	11.7811	0.843659
$196$	0.0368366	0.00263119
$197$	23.0077	1.63923	0.819617	−	0.572912i	$-0.194186\pi$
$197$	23.0077	1.63923	0.819617	+	0.572912i	$0.194186\pi$
$198$	2.22668	0.158243
$199$	9.68273	0.686391	0.343195	−	0.939264i	$-0.388491\pi$
$199$	9.68273	0.686391	0.343195	+	0.939264i	$0.388491\pi$
$200$	−0.0418891	−0.00296200
$201$	8.57398	0.604762
$202$	17.9067	1.25991
$203$	12.7733	0.896511
$204$	3.41147	0.238851
$205$	−16.1088	−1.12508
$206$	−4.24628	−0.295852
$207$	2.22668	0.154765
$208$	5.29086	0.366855
$209$	0	0
$210$	−5.90673	−0.407603
$211$	1.10607	0.0761448	0.0380724	−	0.999275i	$-0.487878\pi$
$211$	1.10607	0.0761448	0.0380724	+	0.999275i	$0.487878\pi$
$212$	−9.82295	−0.674643
$213$	4.40373	0.301739
$214$	−15.6040	−1.06667
$215$	13.1848	0.899195
$216$	−1.00000	−0.0680414
$217$	27.3577	1.85716
$218$	1.36184	0.0922357
$219$	2.79561	0.188910
$220$	−4.95811	−0.334276
$221$	−18.0496	−1.21415
$222$	2.30541	0.154729
$223$	−25.2867	−1.69333	−0.846663	−	0.532130i	$-0.821392\pi$
$223$	−25.2867	−1.69333	−0.846663	+	0.532130i	$0.821392\pi$
$224$	−2.65270	−0.177241
$225$	−0.0418891	−0.00279260
$226$	−17.2003	−1.14415
$227$	−3.42871	−0.227572	−0.113786	−	0.993505i	$-0.536298\pi$
$227$	−3.42871	−0.227572	−0.113786	+	0.993505i	$0.536298\pi$
$228$	0	0
$229$	29.9418	1.97861	0.989305	−	0.145860i	$-0.0465950\pi$
$229$	29.9418	1.97861	0.989305	+	0.145860i	$0.0465950\pi$
$230$	−4.95811	−0.326928
$231$	5.90673	0.388634
$232$	−4.81521	−0.316134
$233$	−10.3773	−0.679841	−0.339921	−	0.940454i	$-0.610400\pi$
$233$	−10.3773	−0.679841	−0.339921	+	0.940454i	$0.610400\pi$
$234$	5.29086	0.345874
$235$	−24.5107	−1.59890
$236$	−4.95811	−0.322746
$237$	13.8007	0.896449
$238$	9.04963	0.586600
$239$	−16.0155	−1.03596	−0.517978	−	0.855394i	$-0.673315\pi$
$239$	−16.0155	−1.03596	−0.517978	+	0.855394i	$0.673315\pi$
$240$	2.22668	0.143732
$241$	−25.5817	−1.64786	−0.823932	−	0.566689i	$-0.808224\pi$
$241$	−25.5817	−1.64786	−0.823932	+	0.566689i	$0.808224\pi$
$242$	−6.04189	−0.388387
$243$	−1.00000	−0.0641500
$244$	−5.70233	−0.365054
$245$	−0.0820234	−0.00524029
$246$	−7.23442	−0.461250
$247$	0	0
$248$	−10.3131	−0.654886
$249$	10.5030	0.665600
$250$	11.2267	0.710038
$251$	10.6895	0.674718	0.337359	−	0.941376i	$-0.390466\pi$
$251$	10.6895	0.674718	0.337359	+	0.941376i	$0.390466\pi$
$252$	−2.65270	−0.167105
$253$	4.95811	0.311714
$254$	13.1925	0.827773
$255$	−7.59627	−0.475697
$256$	1.00000	0.0625000
$257$	30.7793	1.91996	0.959980	−	0.280068i	$-0.0903571\pi$
$257$	30.7793	1.91996	0.959980	+	0.280068i	$0.0903571\pi$
$258$	5.92127	0.368642
$259$	6.11556	0.380003
$260$	−11.7811	−0.730630
$261$	−4.81521	−0.298054
$262$	7.50299	0.463536
$263$	3.14290	0.193800	0.0968999	−	0.995294i	$-0.469107\pi$
$263$	3.14290	0.193800	0.0968999	+	0.995294i	$0.469107\pi$
$264$	−2.22668	−0.137043
$265$	21.8726	1.34362
$266$	0	0
$267$	7.81521	0.478283
$268$	−8.57398	−0.523739
$269$	−14.8803	−0.907269	−0.453635	−	0.891188i	$-0.649873\pi$
$269$	−14.8803	−0.907269	−0.453635	+	0.891188i	$0.649873\pi$
$270$	2.22668	0.135512
$271$	15.2344	0.925425	0.462713	−	0.886508i	$-0.346876\pi$
$271$	15.2344	0.925425	0.462713	+	0.886508i	$0.346876\pi$
$272$	−3.41147	−0.206851
$273$	14.0351	0.849442
$274$	6.63041	0.400558
$275$	−0.0932736	−0.00562461
$276$	−2.22668	−0.134030
$277$	−12.2094	−0.733594	−0.366797	−	0.930301i	$-0.619546\pi$
$277$	−12.2094	−0.733594	−0.366797	+	0.930301i	$0.619546\pi$
$278$	−8.50980	−0.510384
$279$	−10.3131	−0.617432
$280$	5.90673	0.352994
$281$	2.24392	0.133861	0.0669305	−	0.997758i	$-0.478679\pi$
$281$	2.24392	0.133861	0.0669305	+	0.997758i	$0.478679\pi$
$282$	−11.0077	−0.655501
$283$	−14.7888	−0.879103	−0.439551	−	0.898217i	$-0.644863\pi$
$283$	−14.7888	−0.879103	−0.439551	+	0.898217i	$0.644863\pi$
$284$	−4.40373	−0.261313
$285$	0	0
$286$	11.7811	0.696629
$287$	−19.1908	−1.13280
$288$	1.00000	0.0589256
$289$	−5.36184	−0.315403
$290$	10.7219	0.629614
$291$	−17.7888	−1.04280
$292$	−2.79561	−0.163601
$293$	12.0496	0.703947	0.351973	−	0.936010i	$-0.385511\pi$
$293$	12.0496	0.703947	0.351973	+	0.936010i	$0.385511\pi$
$294$	−0.0368366	−0.00214836
$295$	11.0401	0.642781
$296$	−2.30541	−0.133999
$297$	−2.22668	−0.129205
$298$	−3.41147	−0.197621
$299$	11.7811	0.681316
$300$	0.0418891	0.00241847
$301$	15.7074	0.905359
$302$	−3.04189	−0.175041
$303$	−17.9067	−1.02871
$304$	0	0
$305$	12.6973	0.727044
$306$	−3.41147	−0.195021
$307$	−22.5945	−1.28954	−0.644768	−	0.764378i	$-0.723046\pi$
$307$	−22.5945	−1.28954	−0.644768	+	0.764378i	$0.723046\pi$
$308$	−5.90673	−0.336567
$309$	4.24628	0.241563
$310$	22.9641	1.30427
$311$	−11.3259	−0.642235	−0.321118	−	0.947039i	$-0.604058\pi$
$311$	−11.3259	−0.642235	−0.321118	+	0.947039i	$0.604058\pi$
$312$	−5.29086	−0.299536
$313$	−5.95811	−0.336772	−0.168386	−	0.985721i	$-0.553856\pi$
$313$	−5.95811	−0.336772	−0.168386	+	0.985721i	$0.553856\pi$
$314$	−15.5253	−0.876142
$315$	5.90673	0.332806
$316$	−13.8007	−0.776348
$317$	8.92396	0.501220	0.250610	−	0.968088i	$-0.419369\pi$
$317$	8.92396	0.501220	0.250610	+	0.968088i	$0.419369\pi$
$318$	9.82295	0.550844
$319$	−10.7219	−0.600313
$320$	−2.22668	−0.124475
$321$	15.6040	0.870931
$322$	−5.90673	−0.329169
$323$	0	0
$324$	1.00000	0.0555556
$325$	−0.221629	−0.0122938
$326$	4.43882	0.245843
$327$	−1.36184	−0.0753102
$328$	7.23442	0.399454
$329$	−29.2003	−1.60986
$330$	4.95811	0.272935
$331$	−6.65951	−0.366040	−0.183020	−	0.983109i	$-0.558587\pi$
$331$	−6.65951	−0.366040	−0.183020	+	0.983109i	$0.558587\pi$
$332$	−10.5030	−0.576427
$333$	−2.30541	−0.126336
$334$	8.15064	0.445983
$335$	19.0915	1.04308
$336$	2.65270	0.144717
$337$	10.8298	0.589934	0.294967	−	0.955507i	$-0.404691\pi$
$337$	10.8298	0.589934	0.294967	+	0.955507i	$0.404691\pi$
$338$	14.9932	0.815522
$339$	17.2003	0.934191
$340$	7.59627	0.411965
$341$	−22.9641	−1.24358
$342$	0	0
$343$	18.4712	0.997352
$344$	−5.92127	−0.319254
$345$	4.95811	0.266936
$346$	15.9659	0.858330
$347$	20.6614	1.10916	0.554580	−	0.832130i	$-0.312879\pi$
$347$	20.6614	1.10916	0.554580	+	0.832130i	$0.312879\pi$
$348$	4.81521	0.258122
$349$	−2.03952	−0.109173	−0.0545866	−	0.998509i	$-0.517384\pi$
$349$	−2.03952	−0.109173	−0.0545866	+	0.998509i	$0.517384\pi$
$350$	0.111119	0.00593958
$351$	−5.29086	−0.282405
$352$	2.22668	0.118683
$353$	31.3013	1.66600	0.833000	−	0.553273i	$-0.186622\pi$
$353$	31.3013	1.66600	0.833000	+	0.553273i	$0.186622\pi$
$354$	4.95811	0.263521
$355$	9.80571	0.520433
$356$	−7.81521	−0.414205
$357$	−9.04963	−0.478957
$358$	−1.45336	−0.0768126
$359$	−8.90673	−0.470079	−0.235040	−	0.971986i	$-0.575522\pi$
$359$	−8.90673	−0.470079	−0.235040	+	0.971986i	$0.575522\pi$
$360$	−2.22668	−0.117356
$361$	0	0
$362$	1.12567	0.0591638
$363$	6.04189	0.317117
$364$	−14.0351	−0.735638
$365$	6.22493	0.325828
$366$	5.70233	0.298066
$367$	3.44057	0.179596	0.0897981	−	0.995960i	$-0.471378\pi$
$367$	3.44057	0.179596	0.0897981	+	0.995960i	$0.471378\pi$
$368$	2.22668	0.116074
$369$	7.23442	0.376609
$370$	5.13341	0.266873
$371$	26.0574	1.35283
$372$	10.3131	0.534712
$373$	6.31996	0.327235	0.163617	−	0.986524i	$-0.447684\pi$
$373$	6.31996	0.327235	0.163617	+	0.986524i	$0.447684\pi$
$374$	−7.59627	−0.392794
$375$	−11.2267	−0.579743
$376$	11.0077	0.567681
$377$	−25.4766	−1.31211
$378$	2.65270	0.136440
$379$	14.4074	0.740056	0.370028	−	0.929021i	$-0.379348\pi$
$379$	14.4074	0.740056	0.370028	+	0.929021i	$0.379348\pi$
$380$	0	0
$381$	−13.1925	−0.675874
$382$	−1.32770	−0.0679308
$383$	1.89124	0.0966381	0.0483190	−	0.998832i	$-0.484614\pi$
$383$	1.89124	0.0966381	0.0483190	+	0.998832i	$0.484614\pi$
$384$	−1.00000	−0.0510310
$385$	13.1524	0.670308
$386$	−14.9855	−0.762739
$387$	−5.92127	−0.300995
$388$	17.7888	0.903089
$389$	−7.37733	−0.374045	−0.187023	−	0.982356i	$-0.559884\pi$
$389$	−7.37733	−0.374045	−0.187023	+	0.982356i	$0.559884\pi$
$390$	11.7811	0.596557
$391$	−7.59627	−0.384160
$392$	0.0368366	0.00186053
$393$	−7.50299	−0.378476
$394$	23.0077	1.15911
$395$	30.7297	1.54618
$396$	2.22668	0.111895
$397$	−11.5767	−0.581016	−0.290508	−	0.956873i	$-0.593824\pi$
$397$	−11.5767	−0.581016	−0.290508	+	0.956873i	$0.593824\pi$
$398$	9.68273	0.485352
$399$	0	0
$400$	−0.0418891	−0.00209445
$401$	−15.2098	−0.759540	−0.379770	−	0.925081i	$-0.623997\pi$
$401$	−15.2098	−0.759540	−0.379770	+	0.925081i	$0.623997\pi$
$402$	8.57398	0.427631
$403$	−54.5654	−2.71810
$404$	17.9067	0.890893
$405$	−2.22668	−0.110645
$406$	12.7733	0.633929
$407$	−5.13341	−0.254454
$408$	3.41147	0.168893
$409$	1.53116	0.0757108	0.0378554	−	0.999283i	$-0.487947\pi$
$409$	1.53116	0.0757108	0.0378554	+	0.999283i	$0.487947\pi$
$410$	−16.1088	−0.795555
$411$	−6.63041	−0.327054
$412$	−4.24628	−0.209199
$413$	13.1524	0.647187
$414$	2.22668	0.109435
$415$	23.3868	1.14801
$416$	5.29086	0.259406
$417$	8.50980	0.416727
$418$	0	0
$419$	−26.7374	−1.30621	−0.653104	−	0.757268i	$-0.726534\pi$
$419$	−26.7374	−1.30621	−0.653104	+	0.757268i	$0.726534\pi$
$420$	−5.90673	−0.288219
$421$	−23.8726	−1.16348	−0.581739	−	0.813375i	$-0.697628\pi$
$421$	−23.8726	−1.16348	−0.581739	+	0.813375i	$0.697628\pi$
$422$	1.10607	0.0538425
$423$	11.0077	0.535215
$424$	−9.82295	−0.477045
$425$	0.142903	0.00693184
$426$	4.40373	0.213362
$427$	15.1266	0.732028
$428$	−15.6040	−0.754248
$429$	−11.7811	−0.568795
$430$	13.1848	0.635827
$431$	−15.7793	−0.760062	−0.380031	−	0.924974i	$-0.624087\pi$
$431$	−15.7793	−0.760062	−0.380031	+	0.924974i	$0.624087\pi$
$432$	−1.00000	−0.0481125
$433$	13.4183	0.644841	0.322421	−	0.946596i	$-0.395503\pi$
$433$	13.4183	0.644841	0.322421	+	0.946596i	$0.395503\pi$
$434$	27.3577	1.31321
$435$	−10.7219	−0.514077
$436$	1.36184	0.0652205
$437$	0	0
$438$	2.79561	0.133579
$439$	−18.9017	−0.902128	−0.451064	−	0.892492i	$-0.648955\pi$
$439$	−18.9017	−0.902128	−0.451064	+	0.892492i	$0.648955\pi$
$440$	−4.95811	−0.236369
$441$	0.0368366	0.00175413
$442$	−18.0496	−0.858533
$443$	−11.2935	−0.536573	−0.268286	−	0.963339i	$-0.586457\pi$
$443$	−11.2935	−0.536573	−0.268286	+	0.963339i	$0.586457\pi$
$444$	2.30541	0.109410
$445$	17.4020	0.824933
$446$	−25.2867	−1.19736
$447$	3.41147	0.161357
$448$	−2.65270	−0.125328
$449$	8.75465	0.413158	0.206579	−	0.978430i	$-0.433767\pi$
$449$	8.75465	0.413158	0.206579	+	0.978430i	$0.433767\pi$
$450$	−0.0418891	−0.00197467
$451$	16.1088	0.758532
$452$	−17.2003	−0.809033
$453$	3.04189	0.142920
$454$	−3.42871	−0.160917
$455$	31.2517	1.46510
$456$	0	0
$457$	23.8334	1.11488	0.557439	−	0.830218i	$-0.311784\pi$
$457$	23.8334	1.11488	0.557439	+	0.830218i	$0.311784\pi$
$458$	29.9418	1.39909
$459$	3.41147	0.159234
$460$	−4.95811	−0.231173
$461$	15.7469	0.733407	0.366703	−	0.930338i	$-0.380486\pi$
$461$	15.7469	0.733407	0.366703	+	0.930338i	$0.380486\pi$
$462$	5.90673	0.274806
$463$	−4.37464	−0.203307	−0.101653	−	0.994820i	$-0.532413\pi$
$463$	−4.37464	−0.203307	−0.101653	+	0.994820i	$0.532413\pi$
$464$	−4.81521	−0.223540
$465$	−22.9641	−1.06493
$466$	−10.3773	−0.480720
$467$	26.1070	1.20809	0.604044	−	0.796951i	$-0.293555\pi$
$467$	26.1070	1.20809	0.604044	+	0.796951i	$0.293555\pi$
$468$	5.29086	0.244570
$469$	22.7442	1.05023
$470$	−24.5107	−1.13060
$471$	15.5253	0.715367
$472$	−4.95811	−0.228216
$473$	−13.1848	−0.606237
$474$	13.8007	0.633885
$475$	0	0
$476$	9.04963	0.414789
$477$	−9.82295	−0.449762
$478$	−16.0155	−0.732531
$479$	−34.1239	−1.55916	−0.779581	−	0.626302i	$-0.784568\pi$
$479$	−34.1239	−1.55916	−0.779581	+	0.626302i	$0.784568\pi$
$480$	2.22668	0.101634
$481$	−12.1976	−0.556162
$482$	−25.5817	−1.16522
$483$	5.90673	0.268765
$484$	−6.04189	−0.274631
$485$	−39.6100	−1.79860
$486$	−1.00000	−0.0453609
$487$	15.7638	0.714327	0.357164	−	0.934042i	$-0.383744\pi$
$487$	15.7638	0.714327	0.357164	+	0.934042i	$0.383744\pi$
$488$	−5.70233	−0.258133
$489$	−4.43882	−0.200730
$490$	−0.0820234	−0.00370544
$491$	13.8384	0.624520	0.312260	−	0.949997i	$-0.398914\pi$
$491$	13.8384	0.624520	0.312260	+	0.949997i	$0.398914\pi$
$492$	−7.23442	−0.326153
$493$	16.4270	0.739833
$494$	0	0
$495$	−4.95811	−0.222851
$496$	−10.3131	−0.463074
$497$	11.6818	0.524000
$498$	10.5030	0.470650
$499$	−19.9290	−0.892145	−0.446073	−	0.894997i	$-0.647178\pi$
$499$	−19.9290	−0.892145	−0.446073	+	0.894997i	$0.647178\pi$
$500$	11.2267	0.502072
$501$	−8.15064	−0.364144
$502$	10.6895	0.477098
$503$	−14.8803	−0.663481	−0.331740	−	0.943371i	$-0.607636\pi$
$503$	−14.8803	−0.663481	−0.331740	+	0.943371i	$0.607636\pi$
$504$	−2.65270	−0.118161
$505$	−39.8726	−1.77431
$506$	4.95811	0.220415
$507$	−14.9932	−0.665871
$508$	13.1925	0.585324
$509$	36.6860	1.62608	0.813040	−	0.582208i	$-0.197811\pi$
$509$	36.6860	1.62608	0.813040	+	0.582208i	$0.197811\pi$
$510$	−7.59627	−0.336368
$511$	7.41592	0.328061
$512$	1.00000	0.0441942
$513$	0	0
$514$	30.7793	1.35762
$515$	9.45512	0.416642
$516$	5.92127	0.260670
$517$	24.5107	1.07798
$518$	6.11556	0.268702
$519$	−15.9659	−0.700823
$520$	−11.7811	−0.516634
$521$	37.5354	1.64446	0.822228	−	0.569159i	$-0.192731\pi$
$521$	37.5354	1.64446	0.822228	+	0.569159i	$0.192731\pi$
$522$	−4.81521	−0.210756
$523$	−0.396926	−0.0173564	−0.00867819	−	0.999962i	$-0.502762\pi$
$523$	−0.396926	−0.0173564	−0.00867819	+	0.999962i	$0.502762\pi$
$524$	7.50299	0.327770
$525$	−0.111119	−0.00484964
$526$	3.14290	0.137037
$527$	35.1830	1.53260
$528$	−2.22668	−0.0969039
$529$	−18.0419	−0.784430
$530$	21.8726	0.950084
$531$	−4.95811	−0.215164
$532$	0	0
$533$	38.2763	1.65793
$534$	7.81521	0.338197
$535$	34.7452	1.50216
$536$	−8.57398	−0.370339
$537$	1.45336	0.0627173
$538$	−14.8803	−0.641536
$539$	0.0820234	0.00353300
$540$	2.22668	0.0958211
$541$	−20.8512	−0.896464	−0.448232	−	0.893917i	$-0.647946\pi$
$541$	−20.8512	−0.896464	−0.448232	+	0.893917i	$0.647946\pi$
$542$	15.2344	0.654374
$543$	−1.12567	−0.0483070
$544$	−3.41147	−0.146266
$545$	−3.03239	−0.129893
$546$	14.0351	0.600646
$547$	5.16519	0.220848	0.110424	−	0.993885i	$-0.464779\pi$
$547$	5.16519	0.220848	0.110424	+	0.993885i	$0.464779\pi$
$548$	6.63041	0.283237
$549$	−5.70233	−0.243370
$550$	−0.0932736	−0.00397720
$551$	0	0
$552$	−2.22668	−0.0947739
$553$	36.6091	1.55678
$554$	−12.2094	−0.518730
$555$	−5.13341	−0.217901
$556$	−8.50980	−0.360896
$557$	28.9641	1.22725	0.613624	−	0.789598i	$-0.289711\pi$
$557$	28.9641	1.22725	0.613624	+	0.789598i	$0.289711\pi$
$558$	−10.3131	−0.436590
$559$	−31.3286	−1.32506
$560$	5.90673	0.249605
$561$	7.59627	0.320715
$562$	2.24392	0.0946540
$563$	8.75784	0.369099	0.184549	−	0.982823i	$-0.440917\pi$
$563$	8.75784	0.369099	0.184549	+	0.982823i	$0.440917\pi$
$564$	−11.0077	−0.463510
$565$	38.2995	1.61127
$566$	−14.7888	−0.621620
$567$	−2.65270	−0.111403
$568$	−4.40373	−0.184777
$569$	−11.3696	−0.476638	−0.238319	−	0.971187i	$-0.576596\pi$
$569$	−11.3696	−0.476638	−0.238319	+	0.971187i	$0.576596\pi$
$570$	0	0
$571$	2.98545	0.124937	0.0624686	−	0.998047i	$-0.480103\pi$
$571$	2.98545	0.124937	0.0624686	+	0.998047i	$0.480103\pi$
$572$	11.7811	0.492591
$573$	1.32770	0.0554653
$574$	−19.1908	−0.801008
$575$	−0.0932736	−0.00388978
$576$	1.00000	0.0416667
$577$	−22.7469	−0.946966	−0.473483	−	0.880803i	$-0.657004\pi$
$577$	−22.7469	−0.946966	−0.473483	+	0.880803i	$0.657004\pi$
$578$	−5.36184	−0.223023
$579$	14.9855	0.622774
$580$	10.7219	0.445204
$581$	27.8613	1.15588
$582$	−17.7888	−0.737369
$583$	−21.8726	−0.905870
$584$	−2.79561	−0.115683
$585$	−11.7811	−0.487087
$586$	12.0496	0.497766
$587$	−16.5202	−0.681863	−0.340931	−	0.940088i	$-0.610742\pi$
$587$	−16.5202	−0.681863	−0.340931	+	0.940088i	$0.610742\pi$
$588$	−0.0368366	−0.00151912
$589$	0	0
$590$	11.0401	0.454515
$591$	−23.0077	−0.946412
$592$	−2.30541	−0.0947517
$593$	15.1084	0.620429	0.310214	−	0.950667i	$-0.399599\pi$
$593$	15.1084	0.620429	0.310214	+	0.950667i	$0.399599\pi$
$594$	−2.22668	−0.0913619
$595$	−20.1506	−0.826096
$596$	−3.41147	−0.139739
$597$	−9.68273	−0.396288
$598$	11.7811	0.481763
$599$	18.3182	0.748461	0.374231	−	0.927336i	$-0.377907\pi$
$599$	18.3182	0.748461	0.374231	+	0.927336i	$0.377907\pi$
$600$	0.0418891	0.00171011
$601$	3.57491	0.145824	0.0729118	−	0.997338i	$-0.476771\pi$
$601$	3.57491	0.145824	0.0729118	+	0.997338i	$0.476771\pi$
$602$	15.7074	0.640185
$603$	−8.57398	−0.349159
$604$	−3.04189	−0.123773
$605$	13.4534	0.546957
$606$	−17.9067	−0.727411
$607$	−10.9436	−0.444186	−0.222093	−	0.975026i	$-0.571289\pi$
$607$	−10.9436	−0.444186	−0.222093	+	0.975026i	$0.571289\pi$
$608$	0	0
$609$	−12.7733	−0.517601
$610$	12.6973	0.514098
$611$	58.2404	2.35615
$612$	−3.41147	−0.137901
$613$	44.5928	1.80108	0.900542	−	0.434769i	$-0.143170\pi$
$613$	44.5928	1.80108	0.900542	+	0.434769i	$0.143170\pi$
$614$	−22.5945	−0.911840
$615$	16.1088	0.649568
$616$	−5.90673	−0.237989
$617$	−1.44738	−0.0582692	−0.0291346	−	0.999575i	$-0.509275\pi$
$617$	−1.44738	−0.0582692	−0.0291346	+	0.999575i	$0.509275\pi$
$618$	4.24628	0.170811
$619$	−47.2472	−1.89903	−0.949513	−	0.313728i	$-0.898422\pi$
$619$	−47.2472	−1.89903	−0.949513	+	0.313728i	$0.898422\pi$
$620$	22.9641	0.922260
$621$	−2.22668	−0.0893537
$622$	−11.3259	−0.454129
$623$	20.7314	0.830587
$624$	−5.29086	−0.211804
$625$	−24.7888	−0.991552
$626$	−5.95811	−0.238134
$627$	0	0
$628$	−15.5253	−0.619526
$629$	7.86484	0.313592
$630$	5.90673	0.235330
$631$	34.8411	1.38700	0.693502	−	0.720455i	$-0.256067\pi$
$631$	34.8411	1.38700	0.693502	+	0.720455i	$0.256067\pi$
$632$	−13.8007	−0.548961
$633$	−1.10607	−0.0439622
$634$	8.92396	0.354416
$635$	−29.3756	−1.16573
$636$	9.82295	0.389505
$637$	0.194897	0.00772212
$638$	−10.7219	−0.424485
$639$	−4.40373	−0.174209
$640$	−2.22668	−0.0880173
$641$	−10.9581	−0.432819	−0.216410	−	0.976303i	$-0.569435\pi$
$641$	−10.9581	−0.432819	−0.216410	+	0.976303i	$0.569435\pi$
$642$	15.6040	0.615841
$643$	3.69997	0.145913	0.0729563	−	0.997335i	$-0.476757\pi$
$643$	3.69997	0.145913	0.0729563	+	0.997335i	$0.476757\pi$
$644$	−5.90673	−0.232758
$645$	−13.1848	−0.519151
$646$	0	0
$647$	26.2671	1.03267	0.516334	−	0.856387i	$-0.327296\pi$
$647$	26.2671	1.03267	0.516334	+	0.856387i	$0.327296\pi$
$648$	1.00000	0.0392837
$649$	−11.0401	−0.433363
$650$	−0.221629	−0.00869301
$651$	−27.3577	−1.07223
$652$	4.43882	0.173837
$653$	26.1566	1.02359	0.511794	−	0.859108i	$-0.328981\pi$
$653$	26.1566	1.02359	0.511794	+	0.859108i	$0.328981\pi$
$654$	−1.36184	−0.0532523
$655$	−16.7068	−0.652788
$656$	7.23442	0.282457
$657$	−2.79561	−0.109067
$658$	−29.2003	−1.13835
$659$	−26.8803	−1.04711	−0.523554	−	0.851992i	$-0.675394\pi$
$659$	−26.8803	−1.04711	−0.523554	+	0.851992i	$0.675394\pi$
$660$	4.95811	0.192994
$661$	−5.59802	−0.217738	−0.108869	−	0.994056i	$-0.534723\pi$
$661$	−5.59802	−0.217738	−0.108869	+	0.994056i	$0.534723\pi$
$662$	−6.65951	−0.258829
$663$	18.0496	0.700990
$664$	−10.5030	−0.407595
$665$	0	0
$666$	−2.30541	−0.0893327
$667$	−10.7219	−0.415155
$668$	8.15064	0.315358
$669$	25.2867	0.977642
$670$	19.0915	0.737570
$671$	−12.6973	−0.490173
$672$	2.65270	0.102330
$673$	−22.9932	−0.886322	−0.443161	−	0.896442i	$-0.646143\pi$
$673$	−22.9932	−0.886322	−0.443161	+	0.896442i	$0.646143\pi$
$674$	10.8298	0.417147
$675$	0.0418891	0.00161231
$676$	14.9932	0.576661
$677$	−15.3354	−0.589389	−0.294694	−	0.955592i	$-0.595218\pi$
$677$	−15.3354	−0.589389	−0.294694	+	0.955592i	$0.595218\pi$
$678$	17.2003	0.660573
$679$	−47.1884	−1.81093
$680$	7.59627	0.291304
$681$	3.42871	0.131388
$682$	−22.9641	−0.879341
$683$	19.6459	0.751729	0.375865	−	0.926675i	$-0.377346\pi$
$683$	19.6459	0.751729	0.375865	+	0.926675i	$0.377346\pi$
$684$	0	0
$685$	−14.7638	−0.564097
$686$	18.4712	0.705234
$687$	−29.9418	−1.14235
$688$	−5.92127	−0.225746
$689$	−51.9718	−1.97997
$690$	4.95811	0.188752
$691$	19.4688	0.740630	0.370315	−	0.928906i	$-0.379250\pi$
$691$	19.4688	0.740630	0.370315	+	0.928906i	$0.379250\pi$
$692$	15.9659	0.606931
$693$	−5.90673	−0.224378
$694$	20.6614	0.784295
$695$	18.9486	0.718762
$696$	4.81521	0.182520
$697$	−24.6800	−0.934823
$698$	−2.03952	−0.0771972
$699$	10.3773	0.392507
$700$	0.111119	0.00419991
$701$	22.1179	0.835383	0.417691	−	0.908589i	$-0.362839\pi$
$701$	22.1179	0.835383	0.417691	+	0.908589i	$0.362839\pi$
$702$	−5.29086	−0.199691
$703$	0	0
$704$	2.22668	0.0839212
$705$	24.5107	0.923128
$706$	31.3013	1.17804
$707$	−47.5012	−1.78647
$708$	4.95811	0.186337
$709$	9.53983	0.358276	0.179138	−	0.983824i	$-0.442669\pi$
$709$	9.53983	0.358276	0.179138	+	0.983824i	$0.442669\pi$
$710$	9.80571	0.368002
$711$	−13.8007	−0.517565
$712$	−7.81521	−0.292887
$713$	−22.9641	−0.860012
$714$	−9.04963	−0.338674
$715$	−26.2327	−0.981046
$716$	−1.45336	−0.0543147
$717$	16.0155	0.598109
$718$	−8.90673	−0.332396
$719$	−38.7870	−1.44651	−0.723256	−	0.690580i	$-0.757355\pi$
$719$	−38.7870	−1.44651	−0.723256	+	0.690580i	$0.757355\pi$
$720$	−2.22668	−0.0829835
$721$	11.2641	0.419498
$722$	0	0
$723$	25.5817	0.951394
$724$	1.12567	0.0418351
$725$	0.201705	0.00749112
$726$	6.04189	0.224236
$727$	−35.8452	−1.32943	−0.664713	−	0.747099i	$-0.731446\pi$
$727$	−35.8452	−1.32943	−0.664713	+	0.747099i	$0.731446\pi$
$728$	−14.0351	−0.520175
$729$	1.00000	0.0370370
$730$	6.22493	0.230395
$731$	20.2003	0.747134
$732$	5.70233	0.210764
$733$	0.403733	0.0149122	0.00745612	−	0.999972i	$-0.497627\pi$
$733$	0.403733	0.0149122	0.00745612	+	0.999972i	$0.497627\pi$
$734$	3.44057	0.126994
$735$	0.0820234	0.00302548
$736$	2.22668	0.0820766
$737$	−19.0915	−0.703245
$738$	7.23442	0.266303
$739$	−0.595333	−0.0218997	−0.0109498	−	0.999940i	$-0.503486\pi$
$739$	−0.595333	−0.0218997	−0.0109498	+	0.999940i	$0.503486\pi$
$740$	5.13341	0.188708
$741$	0	0
$742$	26.0574	0.956596
$743$	−11.8743	−0.435627	−0.217814	−	0.975990i	$-0.569892\pi$
$743$	−11.8743	−0.435627	−0.217814	+	0.975990i	$0.569892\pi$
$744$	10.3131	0.378098
$745$	7.59627	0.278306
$746$	6.31996	0.231390
$747$	−10.5030	−0.384284
$748$	−7.59627	−0.277747
$749$	41.3928	1.51246
$750$	−11.2267	−0.409940
$751$	−5.45748	−0.199146	−0.0995732	−	0.995030i	$-0.531748\pi$
$751$	−5.45748	−0.199146	−0.0995732	+	0.995030i	$0.531748\pi$
$752$	11.0077	0.401411
$753$	−10.6895	−0.389549
$754$	−25.4766	−0.927803
$755$	6.77332	0.246506
$756$	2.65270	0.0964779
$757$	12.0939	0.439560	0.219780	−	0.975550i	$-0.429466\pi$
$757$	12.0939	0.439560	0.219780	+	0.975550i	$0.429466\pi$
$758$	14.4074	0.523299
$759$	−4.95811	−0.179968
$760$	0	0
$761$	−18.8726	−0.684130	−0.342065	−	0.939676i	$-0.611126\pi$
$761$	−18.8726	−0.684130	−0.342065	+	0.939676i	$0.611126\pi$
$762$	−13.1925	−0.477915
$763$	−3.61257	−0.130784
$764$	−1.32770	−0.0480344
$765$	7.59627	0.274644
$766$	1.89124	0.0683335
$767$	−26.2327	−0.947207
$768$	−1.00000	−0.0360844
$769$	−50.2704	−1.81280	−0.906399	−	0.422422i	$-0.861180\pi$
$769$	−50.2704	−1.81280	−0.906399	+	0.422422i	$0.861180\pi$
$770$	13.1524	0.473980
$771$	−30.7793	−1.10849
$772$	−14.9855	−0.539338
$773$	21.4843	0.772738	0.386369	−	0.922344i	$-0.373729\pi$
$773$	21.4843	0.772738	0.386369	+	0.922344i	$0.373729\pi$
$774$	−5.92127	−0.212836
$775$	0.432008	0.0155182
$776$	17.7888	0.638581
$777$	−6.11556	−0.219395
$778$	−7.37733	−0.264490
$779$	0	0
$780$	11.7811	0.421830
$781$	−9.80571	−0.350876
$782$	−7.59627	−0.271642
$783$	4.81521	0.172081
$784$	0.0368366	0.00131559
$785$	34.5699	1.23385
$786$	−7.50299	−0.267623
$787$	22.5499	0.803818	0.401909	−	0.915680i	$-0.368347\pi$
$787$	22.5499	0.803818	0.401909	+	0.915680i	$0.368347\pi$
$788$	23.0077	0.819617
$789$	−3.14290	−0.111890
$790$	30.7297	1.09331
$791$	45.6272	1.62232
$792$	2.22668	0.0791217
$793$	−30.1702	−1.07138
$794$	−11.5767	−0.410841
$795$	−21.8726	−0.775740
$796$	9.68273	0.343195
$797$	27.2098	0.963819	0.481910	−	0.876221i	$-0.339943\pi$
$797$	27.2098	0.963819	0.481910	+	0.876221i	$0.339943\pi$
$798$	0	0
$799$	−37.5526	−1.32852
$800$	−0.0418891	−0.00148100
$801$	−7.81521	−0.276137
$802$	−15.2098	−0.537076
$803$	−6.22493	−0.219673
$804$	8.57398	0.302381
$805$	13.1524	0.463561
$806$	−54.5654	−1.92198
$807$	14.8803	0.523812
$808$	17.9067	0.629956
$809$	−29.3523	−1.03197	−0.515987	−	0.856597i	$-0.672575\pi$
$809$	−29.3523	−1.03197	−0.515987	+	0.856597i	$0.672575\pi$
$810$	−2.22668	−0.0782376
$811$	−19.1070	−0.670938	−0.335469	−	0.942051i	$-0.608895\pi$
$811$	−19.1070	−0.670938	−0.335469	+	0.942051i	$0.608895\pi$
$812$	12.7733	0.448256
$813$	−15.2344	−0.534295
$814$	−5.13341	−0.179926
$815$	−9.88383	−0.346215
$816$	3.41147	0.119425
$817$	0	0
$818$	1.53116	0.0535356
$819$	−14.0351	−0.490425
$820$	−16.1088	−0.562542
$821$	0.420645	0.0146806	0.00734031	−	0.999973i	$-0.497663\pi$
$821$	0.420645	0.0146806	0.00734031	+	0.999973i	$0.497663\pi$
$822$	−6.63041	−0.231262
$823$	−36.6382	−1.27713	−0.638563	−	0.769570i	$-0.720471\pi$
$823$	−36.6382	−1.27713	−0.638563	+	0.769570i	$0.720471\pi$
$824$	−4.24628	−0.147926
$825$	0.0932736	0.00324737
$826$	13.1524	0.457630
$827$	−29.4861	−1.02533	−0.512666	−	0.858588i	$-0.671342\pi$
$827$	−29.4861	−1.02533	−0.512666	+	0.858588i	$0.671342\pi$
$828$	2.22668	0.0773825
$829$	5.62630	0.195409	0.0977047	−	0.995215i	$-0.468850\pi$
$829$	5.62630	0.195409	0.0977047	+	0.995215i	$0.468850\pi$
$830$	23.3868	0.811768
$831$	12.2094	0.423541
$832$	5.29086	0.183428
$833$	−0.125667	−0.00435411
$834$	8.50980	0.294670
$835$	−18.1489	−0.628068
$836$	0	0
$837$	10.3131	0.356475
$838$	−26.7374	−0.923629
$839$	−43.0155	−1.48506	−0.742530	−	0.669813i	$-0.766374\pi$
$839$	−43.0155	−1.48506	−0.742530	+	0.669813i	$0.766374\pi$
$840$	−5.90673	−0.203801
$841$	−5.81378	−0.200475
$842$	−23.8726	−0.822703
$843$	−2.24392	−0.0772846
$844$	1.10607	0.0380724
$845$	−33.3851	−1.14848
$846$	11.0077	0.378454
$847$	16.0273	0.550706
$848$	−9.82295	−0.337321
$849$	14.7888	0.507550
$850$	0.142903	0.00490155
$851$	−5.13341	−0.175971
$852$	4.40373	0.150869
$853$	23.6905	0.811146	0.405573	−	0.914063i	$-0.367072\pi$
$853$	23.6905	0.811146	0.405573	+	0.914063i	$0.367072\pi$
$854$	15.1266	0.517622
$855$	0	0
$856$	−15.6040	−0.533334
$857$	−50.5012	−1.72509	−0.862545	−	0.505981i	$-0.831131\pi$
$857$	−50.5012	−1.72509	−0.862545	+	0.505981i	$0.831131\pi$
$858$	−11.7811	−0.402199
$859$	4.97596	0.169777	0.0848887	−	0.996390i	$-0.472947\pi$
$859$	4.97596	0.169777	0.0848887	+	0.996390i	$0.472947\pi$
$860$	13.1848	0.449598
$861$	19.1908	0.654020
$862$	−15.7793	−0.537445
$863$	7.90848	0.269208	0.134604	−	0.990899i	$-0.457024\pi$
$863$	7.90848	0.269208	0.134604	+	0.990899i	$0.457024\pi$
$864$	−1.00000	−0.0340207
$865$	−35.5509	−1.20877
$866$	13.4183	0.455972
$867$	5.36184	0.182098
$868$	27.3577	0.928582
$869$	−30.7297	−1.04243
$870$	−10.7219	−0.363508
$871$	−45.3637	−1.53709
$872$	1.36184	0.0461179
$873$	17.7888	0.602060
$874$	0	0
$875$	−29.7811	−1.00678
$876$	2.79561	0.0944548
$877$	7.63722	0.257891	0.128945	−	0.991652i	$-0.458841\pi$
$877$	7.63722	0.257891	0.128945	+	0.991652i	$0.458841\pi$
$878$	−18.9017	−0.637901
$879$	−12.0496	−0.406424
$880$	−4.95811	−0.167138
$881$	18.8898	0.636414	0.318207	−	0.948021i	$-0.396919\pi$
$881$	18.8898	0.636414	0.318207	+	0.948021i	$0.396919\pi$
$882$	0.0368366	0.00124035
$883$	53.6965	1.80703	0.903515	−	0.428557i	$-0.140978\pi$
$883$	53.6965	1.80703	0.903515	+	0.428557i	$0.140978\pi$
$884$	−18.0496	−0.607075
$885$	−11.0401	−0.371110
$886$	−11.2935	−0.379414
$887$	48.8117	1.63894	0.819468	−	0.573125i	$-0.194269\pi$
$887$	48.8117	1.63894	0.819468	+	0.573125i	$0.194269\pi$
$888$	2.30541	0.0773644
$889$	−34.9959	−1.17372
$890$	17.4020	0.583316
$891$	2.22668	0.0745966
$892$	−25.2867	−0.846663
$893$	0	0
$894$	3.41147	0.114097
$895$	3.23618	0.108173
$896$	−2.65270	−0.0886206
$897$	−11.7811	−0.393358
$898$	8.75465	0.292147
$899$	49.6599	1.65625
$900$	−0.0418891	−0.00139630
$901$	33.5107	1.11640
$902$	16.1088	0.536363
$903$	−15.7074	−0.522709
$904$	−17.2003	−0.572073
$905$	−2.50650	−0.0833190
$906$	3.04189	0.101060
$907$	40.5776	1.34736	0.673679	−	0.739025i	$-0.264713\pi$
$907$	40.5776	1.34736	0.673679	+	0.739025i	$0.264713\pi$
$908$	−3.42871	−0.113786
$909$	17.9067	0.593929
$910$	31.2517	1.03598
$911$	−36.0384	−1.19400	−0.597002	−	0.802239i	$-0.703642\pi$
$911$	−36.0384	−1.19400	−0.597002	+	0.802239i	$0.703642\pi$
$912$	0	0
$913$	−23.3868	−0.773991
$914$	23.8334	0.788338
$915$	−12.6973	−0.419759
$916$	29.9418	0.989305
$917$	−19.9032	−0.657262
$918$	3.41147	0.112595
$919$	26.1917	0.863985	0.431992	−	0.901877i	$-0.357811\pi$
$919$	26.1917	0.863985	0.431992	+	0.901877i	$0.357811\pi$
$920$	−4.95811	−0.163464
$921$	22.5945	0.744514
$922$	15.7469	0.518597
$923$	−23.2995	−0.766913
$924$	5.90673	0.194317
$925$	0.0965714	0.00317525
$926$	−4.37464	−0.143760
$927$	−4.24628	−0.139466
$928$	−4.81521	−0.158067
$929$	48.3242	1.58547	0.792733	−	0.609570i	$-0.208658\pi$
$929$	48.3242	1.58547	0.792733	+	0.609570i	$0.208658\pi$
$930$	−22.9641	−0.753022
$931$	0	0
$932$	−10.3773	−0.339921
$933$	11.3259	0.370795
$934$	26.1070	0.854247
$935$	16.9145	0.553162
$936$	5.29086	0.172937
$937$	59.1917	1.93371	0.966854	−	0.255328i	$-0.0821835\pi$
$937$	59.1917	1.93371	0.966854	+	0.255328i	$0.0821835\pi$
$938$	22.7442	0.742625
$939$	5.95811	0.194436
$940$	−24.5107	−0.799452
$941$	−5.79023	−0.188756	−0.0943781	−	0.995536i	$-0.530086\pi$
$941$	−5.79023	−0.188756	−0.0943781	+	0.995536i	$0.530086\pi$
$942$	15.5253	0.505841
$943$	16.1088	0.524573
$944$	−4.95811	−0.161373
$945$	−5.90673	−0.192146
$946$	−13.1848	−0.428675
$947$	−45.9130	−1.49197	−0.745987	−	0.665961i	$-0.768022\pi$
$947$	−45.9130	−1.49197	−0.745987	+	0.665961i	$0.768022\pi$
$948$	13.8007	0.448225
$949$	−14.7912	−0.480142
$950$	0	0
$951$	−8.92396	−0.289379
$952$	9.04963	0.293300
$953$	−28.5526	−0.924910	−0.462455	−	0.886643i	$-0.653031\pi$
$953$	−28.5526	−0.924910	−0.462455	+	0.886643i	$0.653031\pi$
$954$	−9.82295	−0.318030
$955$	2.95636	0.0956654
$956$	−16.0155	−0.517978
$957$	10.7219	0.346591
$958$	−34.1239	−1.10249
$959$	−17.5885	−0.567963
$960$	2.22668	0.0718658
$961$	75.3610	2.43100
$962$	−12.1976	−0.393266
$963$	−15.6040	−0.502832
$964$	−25.5817	−0.823932
$965$	33.3678	1.07415
$966$	5.90673	0.190046
$967$	−22.0797	−0.710034	−0.355017	−	0.934860i	$-0.615525\pi$
$967$	−22.0797	−0.710034	−0.355017	+	0.934860i	$0.615525\pi$
$968$	−6.04189	−0.194194
$969$	0	0
$970$	−39.6100	−1.27180
$971$	12.6709	0.406628	0.203314	−	0.979114i	$-0.434829\pi$
$971$	12.6709	0.406628	0.203314	+	0.979114i	$0.434829\pi$
$972$	−1.00000	−0.0320750
$973$	22.5740	0.723689
$974$	15.7638	0.505105
$975$	0.221629	0.00709781
$976$	−5.70233	−0.182527
$977$	17.2499	0.551873	0.275937	−	0.961176i	$-0.411012\pi$
$977$	17.2499	0.551873	0.275937	+	0.961176i	$0.411012\pi$
$978$	−4.43882	−0.141938
$979$	−17.4020	−0.556170
$980$	−0.0820234	−0.00262014
$981$	1.36184	0.0434803
$982$	13.8384	0.441602
$983$	6.07604	0.193795	0.0968977	−	0.995294i	$-0.469108\pi$
$983$	6.07604	0.193795	0.0968977	+	0.995294i	$0.469108\pi$
$984$	−7.23442	−0.230625
$985$	−51.2309	−1.63235
$986$	16.4270	0.523141
$987$	29.2003	0.929455
$988$	0	0
$989$	−13.1848	−0.419252
$990$	−4.95811	−0.157579
$991$	9.98040	0.317038	0.158519	−	0.987356i	$-0.449328\pi$
$991$	9.98040	0.317038	0.158519	+	0.987356i	$0.449328\pi$
$992$	−10.3131	−0.327443
$993$	6.65951	0.211333
$994$	11.6818	0.370524
$995$	−21.5604	−0.683509
$996$	10.5030	0.332800
$997$	25.3040	0.801385	0.400692	−	0.916213i	$-0.368770\pi$
$997$	25.3040	0.801385	0.400692	+	0.916213i	$0.368770\pi$
$998$	−19.9290	−0.630842
$999$	2.30541	0.0729399

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.2.a.s.1.1		3
3.2	odd	2		6498.2.a.bm.1.3		3
19.14	odd	18		114.2.i.a.25.1	✓	6
19.15	odd	18		114.2.i.a.73.1	yes	6
19.18	odd	2		2166.2.a.q.1.1		3
57.14	even	18		342.2.u.e.253.1		6
57.53	even	18		342.2.u.e.73.1		6
57.56	even	2		6498.2.a.br.1.3		3
76.15	even	18		912.2.bo.a.529.1		6
76.71	even	18		912.2.bo.a.481.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.a.25.1	✓	6	19.14	odd	18
114.2.i.a.73.1	yes	6	19.15	odd	18
342.2.u.e.73.1		6	57.53	even	18
342.2.u.e.253.1		6	57.14	even	18
912.2.bo.a.481.1		6	76.71	even	18
912.2.bo.a.529.1		6	76.15	even	18
2166.2.a.q.1.1		3	19.18	odd	2
2166.2.a.s.1.1		3	1.1	even	1	trivial
6498.2.a.bm.1.3		3	3.2	odd	2
6498.2.a.br.1.3		3	57.56	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2166.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.22668 q^{5} -1.00000 q^{6} -2.65270 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.22668 q^{5} -1.00000 q^{6} -2.65270 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.22668 q^{10} +2.22668 q^{11} -1.00000 q^{12} +5.29086 q^{13} -2.65270 q^{14} +2.22668 q^{15} +1.00000 q^{16} -3.41147 q^{17} +1.00000 q^{18} -2.22668 q^{20} +2.65270 q^{21} +2.22668 q^{22} +2.22668 q^{23} -1.00000 q^{24} -0.0418891 q^{25} +5.29086 q^{26} -1.00000 q^{27} -2.65270 q^{28} -4.81521 q^{29} +2.22668 q^{30} -10.3131 q^{31} +1.00000 q^{32} -2.22668 q^{33} -3.41147 q^{34} +5.90673 q^{35} +1.00000 q^{36} -2.30541 q^{37} -5.29086 q^{39} -2.22668 q^{40} +7.23442 q^{41} +2.65270 q^{42} -5.92127 q^{43} +2.22668 q^{44} -2.22668 q^{45} +2.22668 q^{46} +11.0077 q^{47} -1.00000 q^{48} +0.0368366 q^{49} -0.0418891 q^{50} +3.41147 q^{51} +5.29086 q^{52} -9.82295 q^{53} -1.00000 q^{54} -4.95811 q^{55} -2.65270 q^{56} -4.81521 q^{58} -4.95811 q^{59} +2.22668 q^{60} -5.70233 q^{61} -10.3131 q^{62} -2.65270 q^{63} +1.00000 q^{64} -11.7811 q^{65} -2.22668 q^{66} -8.57398 q^{67} -3.41147 q^{68} -2.22668 q^{69} +5.90673 q^{70} -4.40373 q^{71} +1.00000 q^{72} -2.79561 q^{73} -2.30541 q^{74} +0.0418891 q^{75} -5.90673 q^{77} -5.29086 q^{78} -13.8007 q^{79} -2.22668 q^{80} +1.00000 q^{81} +7.23442 q^{82} -10.5030 q^{83} +2.65270 q^{84} +7.59627 q^{85} -5.92127 q^{86} +4.81521 q^{87} +2.22668 q^{88} -7.81521 q^{89} -2.22668 q^{90} -14.0351 q^{91} +2.22668 q^{92} +10.3131 q^{93} +11.0077 q^{94} -1.00000 q^{96} +17.7888 q^{97} +0.0368366 q^{98} +2.22668 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} - 9 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 - 9 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} - 9 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{12} - 9 q^{14} + 3 q^{16} + 3 q^{18} + 9 q^{21} - 3 q^{24} + 3 q^{25} - 3 q^{27} - 9 q^{28} - 18 q^{29} - 9 q^{31} + 3 q^{32} - 9 q^{35} + 3 q^{36} - 9 q^{37} - 9 q^{41} + 9 q^{42} - 9 q^{43} + 9 q^{47} - 3 q^{48} + 12 q^{49} + 3 q^{50} - 9 q^{53} - 3 q^{54} - 18 q^{55} - 9 q^{56} - 18 q^{58} - 18 q^{59} + 9 q^{61} - 9 q^{62} - 9 q^{63} + 3 q^{64} - 18 q^{65} - 18 q^{67} - 9 q^{70} - 27 q^{71} + 3 q^{72} - 9 q^{73} - 9 q^{74} - 3 q^{75} + 9 q^{77} - 27 q^{79} + 3 q^{81} - 9 q^{82} + 9 q^{83} + 9 q^{84} + 9 q^{85} - 9 q^{86} + 18 q^{87} - 27 q^{89} + 3 q^{91} + 9 q^{93} + 9 q^{94} - 3 q^{96} + 12 q^{97} + 12 q^{98}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 - 9 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^12 - 9 * q^14 + 3 * q^16 + 3 * q^18 + 9 * q^21 - 3 * q^24 + 3 * q^25 - 3 * q^27 - 9 * q^28 - 18 * q^29 - 9 * q^31 + 3 * q^32 - 9 * q^35 + 3 * q^36 - 9 * q^37 - 9 * q^41 + 9 * q^42 - 9 * q^43 + 9 * q^47 - 3 * q^48 + 12 * q^49 + 3 * q^50 - 9 * q^53 - 3 * q^54 - 18 * q^55 - 9 * q^56 - 18 * q^58 - 18 * q^59 + 9 * q^61 - 9 * q^62 - 9 * q^63 + 3 * q^64 - 18 * q^65 - 18 * q^67 - 9 * q^70 - 27 * q^71 + 3 * q^72 - 9 * q^73 - 9 * q^74 - 3 * q^75 + 9 * q^77 - 27 * q^79 + 3 * q^81 - 9 * q^82 + 9 * q^83 + 9 * q^84 + 9 * q^85 - 9 * q^86 + 18 * q^87 - 27 * q^89 + 3 * q^91 + 9 * q^93 + 9 * q^94 - 3 * q^96 + 12 * q^97 + 12 * q^98

Introduction

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