LMFDB - Embedded newform 5577.2.a.ba.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5577,2,Mod(1,5577)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5577, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5577.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5577 = 3 \cdot 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5577.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:	$44.5325692073$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 14 x^{10} + 13 x^{9} + 70 x^{8} - 61 x^{7} - 152 x^{6} + 127 x^{5} + 138 x^{4} + \cdots + 1 $ x^12 - x^11 - 14x^10 + 13x^9 + 70x^8 - 61x^7 - 152x^6 + 127x^5 + 138x^4 - 110x^3 - 40x^2 + 29x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.13773$ of defining polynomial
Character	$\chi$	$=$	5577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.13773 q^{2} -1.00000 q^{3} +2.56988 q^{4} +2.55253 q^{5} +2.13773 q^{6} -4.81735 q^{7} -1.21826 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.13773 q^{2} -1.00000 q^{3} +2.56988 q^{4} +2.55253 q^{5} +2.13773 q^{6} -4.81735 q^{7} -1.21826 q^{8} +1.00000 q^{9} -5.45661 q^{10} -1.00000 q^{11} -2.56988 q^{12} +10.2982 q^{14} -2.55253 q^{15} -2.53547 q^{16} -3.27802 q^{17} -2.13773 q^{18} +5.49877 q^{19} +6.55969 q^{20} +4.81735 q^{21} +2.13773 q^{22} -8.25023 q^{23} +1.21826 q^{24} +1.51539 q^{25} -1.00000 q^{27} -12.3800 q^{28} +8.16808 q^{29} +5.45661 q^{30} +3.71249 q^{31} +7.85665 q^{32} +1.00000 q^{33} +7.00753 q^{34} -12.2964 q^{35} +2.56988 q^{36} +7.51419 q^{37} -11.7549 q^{38} -3.10963 q^{40} -9.43022 q^{41} -10.2982 q^{42} -8.82277 q^{43} -2.56988 q^{44} +2.55253 q^{45} +17.6367 q^{46} +3.10277 q^{47} +2.53547 q^{48} +16.2069 q^{49} -3.23948 q^{50} +3.27802 q^{51} +11.6746 q^{53} +2.13773 q^{54} -2.55253 q^{55} +5.86876 q^{56} -5.49877 q^{57} -17.4611 q^{58} -5.33724 q^{59} -6.55969 q^{60} +1.43736 q^{61} -7.93628 q^{62} -4.81735 q^{63} -11.7245 q^{64} -2.13773 q^{66} +9.84979 q^{67} -8.42414 q^{68} +8.25023 q^{69} +26.2864 q^{70} +13.6934 q^{71} -1.21826 q^{72} +5.52024 q^{73} -16.0633 q^{74} -1.51539 q^{75} +14.1312 q^{76} +4.81735 q^{77} -6.92947 q^{79} -6.47184 q^{80} +1.00000 q^{81} +20.1592 q^{82} -1.26264 q^{83} +12.3800 q^{84} -8.36724 q^{85} +18.8607 q^{86} -8.16808 q^{87} +1.21826 q^{88} -1.86082 q^{89} -5.45661 q^{90} -21.2021 q^{92} -3.71249 q^{93} -6.63289 q^{94} +14.0358 q^{95} -7.85665 q^{96} -8.44116 q^{97} -34.6459 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} - 12 q^{3} + 5 q^{4} + 6 q^{5} + q^{6} + q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q - q^2 - 12 * q^3 + 5 * q^4 + 6 * q^5 + q^6 + q^7 + 12 * q^9	$ 12 q - q^{2} - 12 q^{3} + 5 q^{4} + 6 q^{5} + q^{6} + q^{7} + 12 q^{9} - 11 q^{10} - 12 q^{11} - 5 q^{12} + 9 q^{14} - 6 q^{15} - 9 q^{16} + 3 q^{17} - q^{18} - 6 q^{19} + 20 q^{20} - q^{21} + q^{22} - 22 q^{23} - 2 q^{25} - 12 q^{27} + 11 q^{28} + 13 q^{29} + 11 q^{30} - 2 q^{31} - 11 q^{32} + 12 q^{33} - 10 q^{34} - 14 q^{35} + 5 q^{36} - 3 q^{37} - 18 q^{38} - 18 q^{40} - 4 q^{41} - 9 q^{42} - 26 q^{43} - 5 q^{44} + 6 q^{45} + 18 q^{46} + 9 q^{47} + 9 q^{48} - 3 q^{49} - 29 q^{50} - 3 q^{51} - 5 q^{53} + q^{54} - 6 q^{55} + 5 q^{56} + 6 q^{57} - 37 q^{58} + 22 q^{59} - 20 q^{60} - 11 q^{61} - 18 q^{62} + q^{63} - 10 q^{64} - q^{66} + 28 q^{67} + 12 q^{68} + 22 q^{69} + 29 q^{70} - 10 q^{71} + 7 q^{73} - 6 q^{74} + 2 q^{75} - 32 q^{76} - q^{77} - 40 q^{79} - 30 q^{80} + 12 q^{81} + 26 q^{82} - q^{83} - 11 q^{84} + 32 q^{85} + 9 q^{86} - 13 q^{87} - 11 q^{89} - 11 q^{90} - 38 q^{92} + 2 q^{93} - 25 q^{94} - 10 q^{95} + 11 q^{96} - 7 q^{97} - 28 q^{98} - 12 q^{99}+O(q^{100}) $ 12 * q - q^2 - 12 * q^3 + 5 * q^4 + 6 * q^5 + q^6 + q^7 + 12 * q^9 - 11 * q^10 - 12 * q^11 - 5 * q^12 + 9 * q^14 - 6 * q^15 - 9 * q^16 + 3 * q^17 - q^18 - 6 * q^19 + 20 * q^20 - q^21 + q^22 - 22 * q^23 - 2 * q^25 - 12 * q^27 + 11 * q^28 + 13 * q^29 + 11 * q^30 - 2 * q^31 - 11 * q^32 + 12 * q^33 - 10 * q^34 - 14 * q^35 + 5 * q^36 - 3 * q^37 - 18 * q^38 - 18 * q^40 - 4 * q^41 - 9 * q^42 - 26 * q^43 - 5 * q^44 + 6 * q^45 + 18 * q^46 + 9 * q^47 + 9 * q^48 - 3 * q^49 - 29 * q^50 - 3 * q^51 - 5 * q^53 + q^54 - 6 * q^55 + 5 * q^56 + 6 * q^57 - 37 * q^58 + 22 * q^59 - 20 * q^60 - 11 * q^61 - 18 * q^62 + q^63 - 10 * q^64 - q^66 + 28 * q^67 + 12 * q^68 + 22 * q^69 + 29 * q^70 - 10 * q^71 + 7 * q^73 - 6 * q^74 + 2 * q^75 - 32 * q^76 - q^77 - 40 * q^79 - 30 * q^80 + 12 * q^81 + 26 * q^82 - q^83 - 11 * q^84 + 32 * q^85 + 9 * q^86 - 13 * q^87 - 11 * q^89 - 11 * q^90 - 38 * q^92 + 2 * q^93 - 25 * q^94 - 10 * q^95 + 11 * q^96 - 7 * q^97 - 28 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.13773	−1.51160	−0.755801	−	0.654801i	$-0.772752\pi$
$2$	−2.13773	−1.51160	−0.755801	+	0.654801i	$0.772752\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.56988	1.28494
$5$	2.55253	1.14152	0.570762	−	0.821116i	$-0.306648\pi$
$5$	2.55253	1.14152	0.570762	+	0.821116i	$0.306648\pi$
$6$	2.13773	0.872724
$7$	−4.81735	−1.82079	−0.910394	−	0.413742i	$-0.864221\pi$
$7$	−4.81735	−1.82079	−0.910394	+	0.413742i	$0.864221\pi$
$8$	−1.21826	−0.430718
$9$	1.00000	0.333333
$10$	−5.45661	−1.72553
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.56988	−0.741861
$13$	0	0
$13$	0	0
$14$	10.2982	2.75231
$15$	−2.55253	−0.659059
$16$	−2.53547	−0.633867
$17$	−3.27802	−0.795038	−0.397519	−	0.917594i	$-0.630129\pi$
$17$	−3.27802	−0.795038	−0.397519	+	0.917594i	$0.630129\pi$
$18$	−2.13773	−0.503867
$19$	5.49877	1.26150	0.630752	−	0.775984i	$-0.282746\pi$
$19$	5.49877	1.26150	0.630752	+	0.775984i	$0.282746\pi$
$20$	6.55969	1.46679
$21$	4.81735	1.05123
$22$	2.13773	0.455765
$23$	−8.25023	−1.72029	−0.860146	−	0.510049i	$-0.829627\pi$
$23$	−8.25023	−1.72029	−0.860146	+	0.510049i	$0.829627\pi$
$24$	1.21826	0.248675
$25$	1.51539	0.303077
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−12.3800	−2.33961
$29$	8.16808	1.51677	0.758387	−	0.651804i	$-0.225988\pi$
$29$	8.16808	1.51677	0.758387	+	0.651804i	$0.225988\pi$
$30$	5.45661	0.996235
$31$	3.71249	0.666782	0.333391	−	0.942789i	$-0.391807\pi$
$31$	3.71249	0.666782	0.333391	+	0.942789i	$0.391807\pi$
$32$	7.85665	1.38887
$33$	1.00000	0.174078
$34$	7.00753	1.20178
$35$	−12.2964	−2.07847
$36$	2.56988	0.428314
$37$	7.51419	1.23532	0.617662	−	0.786443i	$-0.288080\pi$
$37$	7.51419	1.23532	0.617662	+	0.786443i	$0.288080\pi$
$38$	−11.7549	−1.90689
$39$	0	0
$40$	−3.10963	−0.491675
$41$	−9.43022	−1.47275	−0.736376	−	0.676572i	$-0.763465\pi$
$41$	−9.43022	−1.47275	−0.736376	+	0.676572i	$0.763465\pi$
$42$	−10.2982	−1.58905
$43$	−8.82277	−1.34546	−0.672730	−	0.739888i	$-0.734878\pi$
$43$	−8.82277	−1.34546	−0.672730	+	0.739888i	$0.734878\pi$
$44$	−2.56988	−0.387424
$45$	2.55253	0.380508
$46$	17.6367	2.60040
$47$	3.10277	0.452586	0.226293	−	0.974059i	$-0.427339\pi$
$47$	3.10277	0.452586	0.226293	+	0.974059i	$0.427339\pi$
$48$	2.53547	0.365963
$49$	16.2069	2.31527
$50$	−3.23948	−0.458132
$51$	3.27802	0.459015
$52$	0	0
$53$	11.6746	1.60363	0.801816	−	0.597571i	$-0.203867\pi$
$53$	11.6746	1.60363	0.801816	+	0.597571i	$0.203867\pi$
$54$	2.13773	0.290908
$55$	−2.55253	−0.344182
$56$	5.86876	0.784247
$57$	−5.49877	−0.728330
$58$	−17.4611	−2.29276
$59$	−5.33724	−0.694850	−0.347425	−	0.937708i	$-0.612944\pi$
$59$	−5.33724	−0.694850	−0.347425	+	0.937708i	$0.612944\pi$
$60$	−6.55969	−0.846853
$61$	1.43736	0.184035	0.0920177	−	0.995757i	$-0.470668\pi$
$61$	1.43736	0.184035	0.0920177	+	0.995757i	$0.470668\pi$
$62$	−7.93628	−1.00791
$63$	−4.81735	−0.606929
$64$	−11.7245	−1.46556
$65$	0	0
$66$	−2.13773	−0.263136
$67$	9.84979	1.20334	0.601672	−	0.798744i	$-0.294502\pi$
$67$	9.84979	1.20334	0.601672	+	0.798744i	$0.294502\pi$
$68$	−8.42414	−1.02158
$69$	8.25023	0.993211
$70$	26.2864	3.14182
$71$	13.6934	1.62511	0.812556	−	0.582883i	$-0.198075\pi$
$71$	13.6934	1.62511	0.812556	+	0.582883i	$0.198075\pi$
$72$	−1.21826	−0.143573
$73$	5.52024	0.646095	0.323048	−	0.946383i	$-0.395293\pi$
$73$	5.52024	0.646095	0.323048	+	0.946383i	$0.395293\pi$
$74$	−16.0633	−1.86732
$75$	−1.51539	−0.174982
$76$	14.1312	1.62096
$77$	4.81735	0.548988
$78$	0	0
$79$	−6.92947	−0.779626	−0.389813	−	0.920894i	$-0.627460\pi$
$79$	−6.92947	−0.779626	−0.389813	+	0.920894i	$0.627460\pi$
$80$	−6.47184	−0.723574
$81$	1.00000	0.111111
$82$	20.1592	2.22622
$83$	−1.26264	−0.138593	−0.0692964	−	0.997596i	$-0.522075\pi$
$83$	−1.26264	−0.138593	−0.0692964	+	0.997596i	$0.522075\pi$
$84$	12.3800	1.35077
$85$	−8.36724	−0.907555
$86$	18.8607	2.03380
$87$	−8.16808	−0.875710
$88$	1.21826	0.129866
$89$	−1.86082	−0.197246	−0.0986230	−	0.995125i	$-0.531444\pi$
$89$	−1.86082	−0.197246	−0.0986230	+	0.995125i	$0.531444\pi$
$90$	−5.45661	−0.575177
$91$	0	0
$92$	−21.2021	−2.21047
$93$	−3.71249	−0.384967
$94$	−6.63289	−0.684130
$95$	14.0358	1.44004
$96$	−7.85665	−0.801866
$97$	−8.44116	−0.857070	−0.428535	−	0.903525i	$-0.640970\pi$
$97$	−8.44116	−0.857070	−0.428535	+	0.903525i	$0.640970\pi$
$98$	−34.6459	−3.49977
$99$	−1.00000	−0.100504
$100$	3.89436	0.389436
$101$	4.99744	0.497264	0.248632	−	0.968598i	$-0.420019\pi$
$101$	4.99744	0.497264	0.248632	+	0.968598i	$0.420019\pi$
$102$	−7.00753	−0.693848
$103$	−13.9990	−1.37937	−0.689683	−	0.724112i	$-0.742250\pi$
$103$	−13.9990	−1.37937	−0.689683	+	0.724112i	$0.742250\pi$
$104$	0	0
$105$	12.2964	1.20001
$106$	−24.9572	−2.42405
$107$	−10.6410	−1.02871	−0.514354	−	0.857578i	$-0.671968\pi$
$107$	−10.6410	−1.02871	−0.514354	+	0.857578i	$0.671968\pi$
$108$	−2.56988	−0.247287
$109$	1.85521	0.177697	0.0888485	−	0.996045i	$-0.471681\pi$
$109$	1.85521	0.177697	0.0888485	+	0.996045i	$0.471681\pi$
$110$	5.45661	0.520267
$111$	−7.51419	−0.713215
$112$	12.2142	1.15414
$113$	−3.99736	−0.376040	−0.188020	−	0.982165i	$-0.560207\pi$
$113$	−3.99736	−0.376040	−0.188020	+	0.982165i	$0.560207\pi$
$114$	11.7549	1.10095
$115$	−21.0589	−1.96375
$116$	20.9910	1.94897
$117$	0	0
$118$	11.4096	1.05034
$119$	15.7914	1.44759
$120$	3.10963	0.283869
$121$	1.00000	0.0909091
$122$	−3.07269	−0.278188
$123$	9.43022	0.850294
$124$	9.54065	0.856776
$125$	−8.89457	−0.795554
$126$	10.2982	0.917436
$127$	−19.8339	−1.75998	−0.879989	−	0.474994i	$-0.842450\pi$
$127$	−19.8339	−1.75998	−0.879989	+	0.474994i	$0.842450\pi$
$128$	9.35039	0.826466
$129$	8.82277	0.776802
$130$	0	0
$131$	9.22553	0.806038	0.403019	−	0.915192i	$-0.367961\pi$
$131$	9.22553	0.806038	0.403019	+	0.915192i	$0.367961\pi$
$132$	2.56988	0.223680
$133$	−26.4895	−2.29693
$134$	−21.0562	−1.81898
$135$	−2.55253	−0.219686
$136$	3.99347	0.342437
$137$	16.4001	1.40116	0.700579	−	0.713575i	$-0.252925\pi$
$137$	16.4001	1.40116	0.700579	+	0.713575i	$0.252925\pi$
$138$	−17.6367	−1.50134
$139$	2.24114	0.190091	0.0950456	−	0.995473i	$-0.469700\pi$
$139$	2.24114	0.190091	0.0950456	+	0.995473i	$0.469700\pi$
$140$	−31.6003	−2.67072
$141$	−3.10277	−0.261301
$142$	−29.2729	−2.45652
$143$	0	0
$144$	−2.53547	−0.211289
$145$	20.8492	1.73143
$146$	−11.8008	−0.976639
$147$	−16.2069	−1.33672
$148$	19.3106	1.58732
$149$	−1.56598	−0.128290	−0.0641450	−	0.997941i	$-0.520432\pi$
$149$	−1.56598	−0.128290	−0.0641450	+	0.997941i	$0.520432\pi$
$150$	3.23948	0.264503
$151$	−14.5560	−1.18455	−0.592277	−	0.805734i	$-0.701771\pi$
$151$	−14.5560	−1.18455	−0.592277	+	0.805734i	$0.701771\pi$
$152$	−6.69891	−0.543353
$153$	−3.27802	−0.265013
$154$	−10.2982	−0.829852
$155$	9.47621	0.761148
$156$	0	0
$157$	−9.05041	−0.722301	−0.361151	−	0.932507i	$-0.617616\pi$
$157$	−9.05041	−0.722301	−0.361151	+	0.932507i	$0.617616\pi$
$158$	14.8133	1.17848
$159$	−11.6746	−0.925857
$160$	20.0543	1.58543
$161$	39.7442	3.13229
$162$	−2.13773	−0.167956
$163$	12.3992	0.971179	0.485590	−	0.874187i	$-0.338605\pi$
$163$	12.3992	0.971179	0.485590	+	0.874187i	$0.338605\pi$
$164$	−24.2346	−1.89240
$165$	2.55253	0.198714
$166$	2.69918	0.209497
$167$	2.38012	0.184179	0.0920895	−	0.995751i	$-0.470645\pi$
$167$	2.38012	0.184179	0.0920895	+	0.995751i	$0.470645\pi$
$168$	−5.86876	−0.452785
$169$	0	0
$170$	17.8869	1.37186
$171$	5.49877	0.420502
$172$	−22.6735	−1.72884
$173$	0.886459	0.0673963	0.0336981	−	0.999432i	$-0.489272\pi$
$173$	0.886459	0.0673963	0.0336981	+	0.999432i	$0.489272\pi$
$174$	17.4611	1.32373
$175$	−7.30014	−0.551839
$176$	2.53547	0.191118
$177$	5.33724	0.401172
$178$	3.97792	0.298158
$179$	−9.04240	−0.675861	−0.337930	−	0.941171i	$-0.609727\pi$
$179$	−9.04240	−0.675861	−0.337930	+	0.941171i	$0.609727\pi$
$180$	6.55969	0.488931
$181$	2.79225	0.207546	0.103773	−	0.994601i	$-0.466908\pi$
$181$	2.79225	0.207546	0.103773	+	0.994601i	$0.466908\pi$
$182$	0	0
$183$	−1.43736	−0.106253
$184$	10.0509	0.740961
$185$	19.1802	1.41015
$186$	7.93628	0.581917
$187$	3.27802	0.239713
$188$	7.97376	0.581547
$189$	4.81735	0.350411
$190$	−30.0046	−2.17676
$191$	3.70287	0.267930	0.133965	−	0.990986i	$-0.457229\pi$
$191$	3.70287	0.267930	0.133965	+	0.990986i	$0.457229\pi$
$192$	11.7245	0.846139
$193$	−17.8144	−1.28231	−0.641155	−	0.767411i	$-0.721544\pi$
$193$	−17.8144	−1.28231	−0.641155	+	0.767411i	$0.721544\pi$
$194$	18.0449	1.29555
$195$	0	0
$196$	41.6498	2.97499
$197$	20.0238	1.42664	0.713319	−	0.700840i	$-0.247191\pi$
$197$	20.0238	1.42664	0.713319	+	0.700840i	$0.247191\pi$
$198$	2.13773	0.151922
$199$	−8.41861	−0.596780	−0.298390	−	0.954444i	$-0.596450\pi$
$199$	−8.41861	−0.596780	−0.298390	+	0.954444i	$0.596450\pi$
$200$	−1.84613	−0.130541
$201$	−9.84979	−0.694750
$202$	−10.6832	−0.751665
$203$	−39.3485	−2.76173
$204$	8.42414	0.589808
$205$	−24.0709	−1.68118
$206$	29.9261	2.08505
$207$	−8.25023	−0.573430
$208$	0	0
$209$	−5.49877	−0.380358
$210$	−26.2864	−1.81393
$211$	−1.97756	−0.136141	−0.0680705	−	0.997681i	$-0.521684\pi$
$211$	−1.97756	−0.136141	−0.0680705	+	0.997681i	$0.521684\pi$
$212$	30.0024	2.06057
$213$	−13.6934	−0.938259
$214$	22.7476	1.55500
$215$	−22.5203	−1.53587
$216$	1.21826	0.0828918
$217$	−17.8843	−1.21407
$218$	−3.96594	−0.268607
$219$	−5.52024	−0.373023
$220$	−6.55969	−0.442254
$221$	0	0
$222$	16.0633	1.07810
$223$	15.7098	1.05200	0.526001	−	0.850484i	$-0.323691\pi$
$223$	15.7098	1.05200	0.526001	+	0.850484i	$0.323691\pi$
$224$	−37.8483	−2.52884
$225$	1.51539	0.101026
$226$	8.54528	0.568423
$227$	−11.4466	−0.759737	−0.379869	−	0.925040i	$-0.624031\pi$
$227$	−11.4466	−0.759737	−0.379869	+	0.925040i	$0.624031\pi$
$228$	−14.1312	−0.935861
$229$	−9.92293	−0.655726	−0.327863	−	0.944725i	$-0.606328\pi$
$229$	−9.92293	−0.655726	−0.327863	+	0.944725i	$0.606328\pi$
$230$	45.0182	2.96841
$231$	−4.81735	−0.316959
$232$	−9.95081	−0.653303
$233$	−4.56061	−0.298776	−0.149388	−	0.988779i	$-0.547730\pi$
$233$	−4.56061	−0.298776	−0.149388	+	0.988779i	$0.547730\pi$
$234$	0	0
$235$	7.91991	0.516638
$236$	−13.7161	−0.892841
$237$	6.92947	0.450117
$238$	−33.7577	−2.18819
$239$	−3.34883	−0.216618	−0.108309	−	0.994117i	$-0.534544\pi$
$239$	−3.34883	−0.216618	−0.108309	+	0.994117i	$0.534544\pi$
$240$	6.47184	0.417756
$241$	7.51405	0.484023	0.242011	−	0.970273i	$-0.422193\pi$
$241$	7.51405	0.484023	0.242011	+	0.970273i	$0.422193\pi$
$242$	−2.13773	−0.137418
$243$	−1.00000	−0.0641500
$244$	3.69385	0.236475
$245$	41.3685	2.64293
$246$	−20.1592	−1.28531
$247$	0	0
$248$	−4.52275	−0.287195
$249$	1.26264	0.0800166
$250$	19.0142	1.20256
$251$	23.9749	1.51328	0.756642	−	0.653830i	$-0.226839\pi$
$251$	23.9749	1.51328	0.756642	+	0.653830i	$0.226839\pi$
$252$	−12.3800	−0.779869
$253$	8.25023	0.518687
$254$	42.3996	2.66039
$255$	8.36724	0.523977
$256$	3.46030	0.216269
$257$	1.28396	0.0800914	0.0400457	−	0.999198i	$-0.487250\pi$
$257$	1.28396	0.0800914	0.0400457	+	0.999198i	$0.487250\pi$
$258$	−18.8607	−1.17422
$259$	−36.1985	−2.24926
$260$	0	0
$261$	8.16808	0.505592
$262$	−19.7217	−1.21841
$263$	4.16995	0.257130	0.128565	−	0.991701i	$-0.458963\pi$
$263$	4.16995	0.257130	0.128565	+	0.991701i	$0.458963\pi$
$264$	−1.21826	−0.0749784
$265$	29.7997	1.83058
$266$	56.6274	3.47205
$267$	1.86082	0.113880
$268$	25.3128	1.54623
$269$	12.4232	0.757457	0.378728	−	0.925508i	$-0.376361\pi$
$269$	12.4232	0.757457	0.378728	+	0.925508i	$0.376361\pi$
$270$	5.45661	0.332078
$271$	19.9796	1.21367	0.606836	−	0.794827i	$-0.292438\pi$
$271$	19.9796	1.21367	0.606836	+	0.794827i	$0.292438\pi$
$272$	8.31132	0.503948
$273$	0	0
$274$	−35.0590	−2.11799
$275$	−1.51539	−0.0913812
$276$	21.2021	1.27622
$277$	−13.4804	−0.809956	−0.404978	−	0.914326i	$-0.632721\pi$
$277$	−13.4804	−0.809956	−0.404978	+	0.914326i	$0.632721\pi$
$278$	−4.79095	−0.287342
$279$	3.71249	0.222261
$280$	14.9802	0.895236
$281$	−7.83400	−0.467337	−0.233669	−	0.972316i	$-0.575073\pi$
$281$	−7.83400	−0.467337	−0.233669	+	0.972316i	$0.575073\pi$
$282$	6.63289	0.394983
$283$	1.47959	0.0879525	0.0439762	−	0.999033i	$-0.485997\pi$
$283$	1.47959	0.0879525	0.0439762	+	0.999033i	$0.485997\pi$
$284$	35.1905	2.08817
$285$	−14.0358	−0.831406
$286$	0	0
$287$	45.4287	2.68157
$288$	7.85665	0.462958
$289$	−6.25456	−0.367915
$290$	−44.5700	−2.61724
$291$	8.44116	0.494830
$292$	14.1864	0.830194
$293$	−19.8817	−1.16150	−0.580752	−	0.814081i	$-0.697241\pi$
$293$	−19.8817	−1.16150	−0.580752	+	0.814081i	$0.697241\pi$
$294$	34.6459	2.02059
$295$	−13.6234	−0.793188
$296$	−9.15420	−0.532077
$297$	1.00000	0.0580259
$298$	3.34764	0.193924
$299$	0	0
$300$	−3.89436	−0.224841
$301$	42.5024	2.44980
$302$	31.1169	1.79057
$303$	−4.99744	−0.287095
$304$	−13.9420	−0.799626
$305$	3.66890	0.210081
$306$	7.00753	0.400594
$307$	10.1023	0.576569	0.288285	−	0.957545i	$-0.406915\pi$
$307$	10.1023	0.576569	0.288285	+	0.957545i	$0.406915\pi$
$308$	12.3800	0.705418
$309$	13.9990	0.796377
$310$	−20.2576	−1.15055
$311$	18.2710	1.03605	0.518026	−	0.855365i	$-0.326667\pi$
$311$	18.2710	1.03605	0.518026	+	0.855365i	$0.326667\pi$
$312$	0	0
$313$	−27.3128	−1.54381	−0.771906	−	0.635737i	$-0.780696\pi$
$313$	−27.3128	−1.54381	−0.771906	+	0.635737i	$0.780696\pi$
$314$	19.3473	1.09183
$315$	−12.2964	−0.692824
$316$	−17.8079	−1.00177
$317$	2.96809	0.166705	0.0833523	−	0.996520i	$-0.473437\pi$
$317$	2.96809	0.166705	0.0833523	+	0.996520i	$0.473437\pi$
$318$	24.9572	1.39953
$319$	−8.16808	−0.457325
$320$	−29.9270	−1.67297
$321$	10.6410	0.593925
$322$	−84.9624	−4.73477
$323$	−18.0251	−1.00294
$324$	2.56988	0.142771
$325$	0	0
$326$	−26.5061	−1.46804
$327$	−1.85521	−0.102593
$328$	11.4884	0.634341
$329$	−14.9472	−0.824063
$330$	−5.45661	−0.300376
$331$	−28.3400	−1.55771	−0.778854	−	0.627206i	$-0.784199\pi$
$331$	−28.3400	−1.55771	−0.778854	+	0.627206i	$0.784199\pi$
$332$	−3.24484	−0.178084
$333$	7.51419	0.411775
$334$	−5.08804	−0.278405
$335$	25.1418	1.37365
$336$	−12.2142	−0.666341
$337$	0.180147	0.00981322	0.00490661	−	0.999988i	$-0.498438\pi$
$337$	0.180147	0.00981322	0.00490661	+	0.999988i	$0.498438\pi$
$338$	0	0
$339$	3.99736	0.217107
$340$	−21.5028	−1.16615
$341$	−3.71249	−0.201042
$342$	−11.7549	−0.635631
$343$	−44.3528	−2.39483
$344$	10.7484	0.579514
$345$	21.0589	1.13377
$346$	−1.89501	−0.101876
$347$	−34.1440	−1.83295	−0.916473	−	0.400097i	$-0.868976\pi$
$347$	−34.1440	−1.83295	−0.916473	+	0.400097i	$0.868976\pi$
$348$	−20.9910	−1.12524
$349$	−2.81278	−0.150565	−0.0752823	−	0.997162i	$-0.523986\pi$
$349$	−2.81278	−0.150565	−0.0752823	+	0.997162i	$0.523986\pi$
$350$	15.6057	0.834161
$351$	0	0
$352$	−7.85665	−0.418761
$353$	2.56377	0.136456	0.0682278	−	0.997670i	$-0.478266\pi$
$353$	2.56377	0.136456	0.0682278	+	0.997670i	$0.478266\pi$
$354$	−11.4096	−0.606412
$355$	34.9529	1.85511
$356$	−4.78208	−0.253450
$357$	−15.7914	−0.835769
$358$	19.3302	1.02163
$359$	3.46652	0.182956	0.0914778	−	0.995807i	$-0.470841\pi$
$359$	3.46652	0.182956	0.0914778	+	0.995807i	$0.470841\pi$
$360$	−3.10963	−0.163892
$361$	11.2365	0.591394
$362$	−5.96907	−0.313727
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	14.0905	0.737533
$366$	3.07269	0.160612
$367$	−21.6358	−1.12938	−0.564690	−	0.825303i	$-0.691004\pi$
$367$	−21.6358	−1.12938	−0.564690	+	0.825303i	$0.691004\pi$
$368$	20.9182	1.09044
$369$	−9.43022	−0.490917
$370$	−41.0020	−2.13159
$371$	−56.2407	−2.91987
$372$	−9.54065	−0.494660
$373$	8.27083	0.428247	0.214124	−	0.976807i	$-0.431310\pi$
$373$	8.27083	0.428247	0.214124	+	0.976807i	$0.431310\pi$
$374$	−7.00753	−0.362351
$375$	8.89457	0.459313
$376$	−3.77997	−0.194937
$377$	0	0
$378$	−10.2982	−0.529682
$379$	7.14055	0.366786	0.183393	−	0.983040i	$-0.441292\pi$
$379$	7.14055	0.366786	0.183393	+	0.983040i	$0.441292\pi$
$380$	36.0702	1.85036
$381$	19.8339	1.01612
$382$	−7.91572	−0.405004
$383$	−0.814848	−0.0416368	−0.0208184	−	0.999783i	$-0.506627\pi$
$383$	−0.814848	−0.0416368	−0.0208184	+	0.999783i	$0.506627\pi$
$384$	−9.35039	−0.477160
$385$	12.2964	0.626683
$386$	38.0824	1.93834
$387$	−8.82277	−0.448487
$388$	−21.6928	−1.10129
$389$	3.60775	0.182920	0.0914600	−	0.995809i	$-0.470847\pi$
$389$	3.60775	0.182920	0.0914600	+	0.995809i	$0.470847\pi$
$390$	0	0
$391$	27.0444	1.36770
$392$	−19.7441	−0.997229
$393$	−9.22553	−0.465366
$394$	−42.8055	−2.15651
$395$	−17.6876	−0.889962
$396$	−2.56988	−0.129141
$397$	24.4209	1.22565	0.612824	−	0.790219i	$-0.290033\pi$
$397$	24.4209	1.22565	0.612824	+	0.790219i	$0.290033\pi$
$398$	17.9967	0.902094
$399$	26.4895	1.32613
$400$	−3.84221	−0.192110
$401$	10.8213	0.540391	0.270195	−	0.962806i	$-0.412912\pi$
$401$	10.8213	0.540391	0.270195	+	0.962806i	$0.412912\pi$
$402$	21.0562	1.05019
$403$	0	0
$404$	12.8428	0.638955
$405$	2.55253	0.126836
$406$	84.1165	4.17463
$407$	−7.51419	−0.372464
$408$	−3.99347	−0.197706
$409$	−37.7393	−1.86609	−0.933043	−	0.359764i	$-0.882857\pi$
$409$	−37.7393	−1.86609	−0.933043	+	0.359764i	$0.882857\pi$
$410$	51.4570	2.54128
$411$	−16.4001	−0.808959
$412$	−35.9759	−1.77240
$413$	25.7114	1.26517
$414$	17.6367	0.866799
$415$	−3.22292	−0.158207
$416$	0	0
$417$	−2.24114	−0.109749
$418$	11.7549	0.574950
$419$	37.6290	1.83829	0.919147	−	0.393914i	$-0.128879\pi$
$419$	37.6290	1.83829	0.919147	+	0.393914i	$0.128879\pi$
$420$	31.6003	1.54194
$421$	−24.3109	−1.18484	−0.592420	−	0.805629i	$-0.701827\pi$
$421$	−24.3109	−1.18484	−0.592420	+	0.805629i	$0.701827\pi$
$422$	4.22749	0.205791
$423$	3.10277	0.150862
$424$	−14.2227	−0.690713
$425$	−4.96747	−0.240958
$426$	29.2729	1.41827
$427$	−6.92428	−0.335090
$428$	−27.3462	−1.32183
$429$	0	0
$430$	48.1424	2.32163
$431$	−14.1227	−0.680265	−0.340133	−	0.940377i	$-0.610472\pi$
$431$	−14.1227	−0.680265	−0.340133	+	0.940377i	$0.610472\pi$
$432$	2.53547	0.121988
$433$	15.4483	0.742399	0.371200	−	0.928553i	$-0.378947\pi$
$433$	15.4483	0.742399	0.371200	+	0.928553i	$0.378947\pi$
$434$	38.2319	1.83519
$435$	−20.8492	−0.999644
$436$	4.76768	0.228330
$437$	−45.3661	−2.17016
$438$	11.8008	0.563863
$439$	12.5035	0.596761	0.298380	−	0.954447i	$-0.403554\pi$
$439$	12.5035	0.596761	0.298380	+	0.954447i	$0.403554\pi$
$440$	3.10963	0.148246
$441$	16.2069	0.771756
$442$	0	0
$443$	−38.2342	−1.81656	−0.908281	−	0.418360i	$-0.862605\pi$
$443$	−38.2342	−1.81656	−0.908281	+	0.418360i	$0.862605\pi$
$444$	−19.3106	−0.916440
$445$	−4.74978	−0.225161
$446$	−33.5832	−1.59021
$447$	1.56598	0.0740683
$448$	56.4808	2.66847
$449$	−24.2023	−1.14218	−0.571089	−	0.820888i	$-0.693479\pi$
$449$	−24.2023	−1.14218	−0.571089	+	0.820888i	$0.693479\pi$
$450$	−3.23948	−0.152711
$451$	9.43022	0.444052
$452$	−10.2728	−0.483190
$453$	14.5560	0.683903
$454$	24.4697	1.14842
$455$	0	0
$456$	6.69891	0.313705
$457$	−1.36549	−0.0638749	−0.0319375	−	0.999490i	$-0.510168\pi$
$457$	−1.36549	−0.0638749	−0.0319375	+	0.999490i	$0.510168\pi$
$458$	21.2125	0.991197
$459$	3.27802	0.153005
$460$	−54.1189	−2.52331
$461$	−35.1576	−1.63745	−0.818727	−	0.574183i	$-0.805320\pi$
$461$	−35.1576	−1.63745	−0.818727	+	0.574183i	$0.805320\pi$
$462$	10.2982	0.479115
$463$	11.3585	0.527874	0.263937	−	0.964540i	$-0.414979\pi$
$463$	11.3585	0.527874	0.263937	+	0.964540i	$0.414979\pi$
$464$	−20.7099	−0.961433
$465$	−9.47621	−0.439449
$466$	9.74935	0.451630
$467$	11.6803	0.540500	0.270250	−	0.962790i	$-0.412894\pi$
$467$	11.6803	0.540500	0.270250	+	0.962790i	$0.412894\pi$
$468$	0	0
$469$	−47.4499	−2.19103
$470$	−16.9306	−0.780951
$471$	9.05041	0.417021
$472$	6.50212	0.299284
$473$	8.82277	0.405671
$474$	−14.8133	−0.680398
$475$	8.33276	0.382333
$476$	40.5820	1.86007
$477$	11.6746	0.534544
$478$	7.15888	0.327440
$479$	17.0868	0.780717	0.390358	−	0.920663i	$-0.372351\pi$
$479$	17.0868	0.780717	0.390358	+	0.920663i	$0.372351\pi$
$480$	−20.0543	−0.915349
$481$	0	0
$482$	−16.0630	−0.731650
$483$	−39.7442	−1.80843
$484$	2.56988	0.116813
$485$	−21.5463	−0.978366
$486$	2.13773	0.0969693
$487$	12.4106	0.562378	0.281189	−	0.959652i	$-0.409271\pi$
$487$	12.4106	0.562378	0.281189	+	0.959652i	$0.409271\pi$
$488$	−1.75107	−0.0792674
$489$	−12.3992	−0.560711
$490$	−88.4346	−3.99507
$491$	−8.62585	−0.389279	−0.194639	−	0.980875i	$-0.562354\pi$
$491$	−8.62585	−0.389279	−0.194639	+	0.980875i	$0.562354\pi$
$492$	24.2346	1.09258
$493$	−26.7752	−1.20589
$494$	0	0
$495$	−2.55253	−0.114727
$496$	−9.41288	−0.422651
$497$	−65.9661	−2.95899
$498$	−2.69918	−0.120953
$499$	−28.5260	−1.27700	−0.638499	−	0.769623i	$-0.720444\pi$
$499$	−28.5260	−1.27700	−0.638499	+	0.769623i	$0.720444\pi$
$500$	−22.8580	−1.02224
$501$	−2.38012	−0.106336
$502$	−51.2519	−2.28748
$503$	26.7221	1.19148	0.595740	−	0.803178i	$-0.296859\pi$
$503$	26.7221	1.19148	0.595740	+	0.803178i	$0.296859\pi$
$504$	5.86876	0.261416
$505$	12.7561	0.567638
$506$	−17.6367	−0.784049
$507$	0	0
$508$	−50.9709	−2.26147
$509$	28.3102	1.25483	0.627414	−	0.778686i	$-0.284114\pi$
$509$	28.3102	1.25483	0.627414	+	0.778686i	$0.284114\pi$
$510$	−17.8869	−0.792045
$511$	−26.5929	−1.17640
$512$	−26.0980	−1.15338
$513$	−5.49877	−0.242777
$514$	−2.74477	−0.121066
$515$	−35.7329	−1.57458
$516$	22.6735	0.998145
$517$	−3.10277	−0.136460
$518$	77.3825	3.39999
$519$	−0.886459	−0.0389113
$520$	0	0
$521$	−38.9662	−1.70714	−0.853570	−	0.520977i	$-0.825568\pi$
$521$	−38.9662	−1.70714	−0.853570	+	0.520977i	$0.825568\pi$
$522$	−17.4611	−0.764253
$523$	−44.6350	−1.95175	−0.975877	−	0.218322i	$-0.929942\pi$
$523$	−44.6350	−1.95175	−0.975877	+	0.218322i	$0.929942\pi$
$524$	23.7085	1.03571
$525$	7.30014	0.318604
$526$	−8.91423	−0.388679
$527$	−12.1696	−0.530117
$528$	−2.53547	−0.110342
$529$	45.0662	1.95940
$530$	−63.7038	−2.76712
$531$	−5.33724	−0.231617
$532$	−68.0750	−2.95142
$533$	0	0
$534$	−3.97792	−0.172141
$535$	−27.1615	−1.17429
$536$	−11.9996	−0.518302
$537$	9.04240	0.390208
$538$	−26.5575	−1.14497
$539$	−16.2069	−0.698080
$540$	−6.55969	−0.282284
$541$	−35.4667	−1.52483	−0.762416	−	0.647087i	$-0.775987\pi$
$541$	−35.4667	−1.52483	−0.762416	+	0.647087i	$0.775987\pi$
$542$	−42.7109	−1.83459
$543$	−2.79225	−0.119827
$544$	−25.7543	−1.10421
$545$	4.73547	0.202845
$546$	0	0
$547$	13.7288	0.587001	0.293500	−	0.955959i	$-0.405180\pi$
$547$	13.7288	0.587001	0.293500	+	0.955959i	$0.405180\pi$
$548$	42.1464	1.80041
$549$	1.43736	0.0613451
$550$	3.23948	0.138132
$551$	44.9144	1.91342
$552$	−10.0509	−0.427794
$553$	33.3817	1.41953
$554$	28.8173	1.22433
$555$	−19.1802	−0.814152
$556$	5.75947	0.244256
$557$	−37.1223	−1.57292	−0.786460	−	0.617641i	$-0.788089\pi$
$557$	−37.1223	−1.57292	−0.786460	+	0.617641i	$0.788089\pi$
$558$	−7.93628	−0.335970
$559$	0	0
$560$	31.1772	1.31748
$561$	−3.27802	−0.138398
$562$	16.7470	0.706428
$563$	34.1253	1.43821	0.719105	−	0.694901i	$-0.244552\pi$
$563$	34.1253	1.43821	0.719105	+	0.694901i	$0.244552\pi$
$564$	−7.97376	−0.335756
$565$	−10.2034	−0.429259
$566$	−3.16296	−0.132949
$567$	−4.81735	−0.202310
$568$	−16.6821	−0.699966
$569$	−4.24345	−0.177894	−0.0889472	−	0.996036i	$-0.528350\pi$
$569$	−4.24345	−0.177894	−0.0889472	+	0.996036i	$0.528350\pi$
$570$	30.0046	1.25676
$571$	−29.0063	−1.21388	−0.606938	−	0.794749i	$-0.707602\pi$
$571$	−29.0063	−1.21388	−0.606938	+	0.794749i	$0.707602\pi$
$572$	0	0
$573$	−3.70287	−0.154689
$574$	−97.1142	−4.05347
$575$	−12.5023	−0.521381
$576$	−11.7245	−0.488519
$577$	−36.6975	−1.52774	−0.763868	−	0.645372i	$-0.776702\pi$
$577$	−36.6975	−1.52774	−0.763868	+	0.645372i	$0.776702\pi$
$578$	13.3705	0.556141
$579$	17.8144	0.740342
$580$	53.5801	2.22479
$581$	6.08258	0.252348
$582$	−18.0449	−0.747986
$583$	−11.6746	−0.483513
$584$	−6.72506	−0.278285
$585$	0	0
$586$	42.5017	1.75573
$587$	3.96933	0.163832	0.0819159	−	0.996639i	$-0.473896\pi$
$587$	3.96933	0.163832	0.0819159	+	0.996639i	$0.473896\pi$
$588$	−41.6498	−1.71761
$589$	20.4141	0.841149
$590$	29.1232	1.19898
$591$	−20.0238	−0.823670
$592$	−19.0520	−0.783031
$593$	−28.3903	−1.16585	−0.582925	−	0.812526i	$-0.698092\pi$
$593$	−28.3903	−1.16585	−0.582925	+	0.812526i	$0.698092\pi$
$594$	−2.13773	−0.0877121
$595$	40.3079	1.65246
$596$	−4.02439	−0.164845
$597$	8.41861	0.344551
$598$	0	0
$599$	−10.7536	−0.439379	−0.219689	−	0.975570i	$-0.570504\pi$
$599$	−10.7536	−0.439379	−0.219689	+	0.975570i	$0.570504\pi$
$600$	1.84613	0.0753678
$601$	−25.1457	−1.02572	−0.512858	−	0.858473i	$-0.671413\pi$
$601$	−25.1457	−1.02572	−0.512858	+	0.858473i	$0.671413\pi$
$602$	−90.8586	−3.70312
$603$	9.84979	0.401114
$604$	−37.4073	−1.52208
$605$	2.55253	0.103775
$606$	10.6832	0.433974
$607$	−21.2856	−0.863957	−0.431979	−	0.901884i	$-0.642184\pi$
$607$	−21.2856	−0.863957	−0.431979	+	0.901884i	$0.642184\pi$
$608$	43.2019	1.75207
$609$	39.3485	1.59448
$610$	−7.84312	−0.317559
$611$	0	0
$612$	−8.42414	−0.340526
$613$	−29.1936	−1.17912	−0.589559	−	0.807725i	$-0.700698\pi$
$613$	−29.1936	−1.17912	−0.589559	+	0.807725i	$0.700698\pi$
$614$	−21.5960	−0.871544
$615$	24.0709	0.970631
$616$	−5.86876	−0.236459
$617$	11.6111	0.467445	0.233722	−	0.972303i	$-0.424909\pi$
$617$	11.6111	0.467445	0.233722	+	0.972303i	$0.424909\pi$
$618$	−29.9261	−1.20381
$619$	−36.0498	−1.44897	−0.724483	−	0.689293i	$-0.757921\pi$
$619$	−36.0498	−1.44897	−0.724483	+	0.689293i	$0.757921\pi$
$620$	24.3528	0.978030
$621$	8.25023	0.331070
$622$	−39.0584	−1.56610
$623$	8.96420	0.359143
$624$	0	0
$625$	−30.2805	−1.21122
$626$	58.3874	2.33363
$627$	5.49877	0.219600
$628$	−23.2585	−0.928115
$629$	−24.6317	−0.982130
$630$	26.2864	1.04727
$631$	−7.42370	−0.295533	−0.147766	−	0.989022i	$-0.547208\pi$
$631$	−7.42370	−0.295533	−0.147766	+	0.989022i	$0.547208\pi$
$632$	8.44186	0.335799
$633$	1.97756	0.0786010
$634$	−6.34497	−0.251991
$635$	−50.6266	−2.00906
$636$	−30.0024	−1.18967
$637$	0	0
$638$	17.4611	0.691293
$639$	13.6934	0.541704
$640$	23.8671	0.943431
$641$	−25.2982	−0.999220	−0.499610	−	0.866250i	$-0.666523\pi$
$641$	−25.2982	−0.999220	−0.499610	+	0.866250i	$0.666523\pi$
$642$	−22.7476	−0.897778
$643$	−42.2378	−1.66570	−0.832849	−	0.553500i	$-0.813292\pi$
$643$	−42.2378	−1.66570	−0.832849	+	0.553500i	$0.813292\pi$
$644$	102.138	4.02480
$645$	22.5203	0.886738
$646$	38.5328	1.51605
$647$	−34.0105	−1.33709	−0.668546	−	0.743671i	$-0.733083\pi$
$647$	−34.0105	−1.33709	−0.668546	+	0.743671i	$0.733083\pi$
$648$	−1.21826	−0.0478576
$649$	5.33724	0.209505
$650$	0	0
$651$	17.8843	0.700943
$652$	31.8645	1.24791
$653$	20.0036	0.782802	0.391401	−	0.920220i	$-0.371991\pi$
$653$	20.0036	0.782802	0.391401	+	0.920220i	$0.371991\pi$
$654$	3.96594	0.155080
$655$	23.5484	0.920112
$656$	23.9100	0.933529
$657$	5.52024	0.215365
$658$	31.9530	1.24566
$659$	−37.7205	−1.46938	−0.734691	−	0.678402i	$-0.762673\pi$
$659$	−37.7205	−1.46938	−0.734691	+	0.678402i	$0.762673\pi$
$660$	6.55969	0.255336
$661$	−5.23216	−0.203507	−0.101754	−	0.994810i	$-0.532445\pi$
$661$	−5.23216	−0.203507	−0.101754	+	0.994810i	$0.532445\pi$
$662$	60.5832	2.35463
$663$	0	0
$664$	1.53822	0.0596945
$665$	−67.6152	−2.62200
$666$	−16.0633	−0.622440
$667$	−67.3885	−2.60929
$668$	6.11662	0.236659
$669$	−15.7098	−0.607374
$670$	−53.7464	−2.07640
$671$	−1.43736	−0.0554888
$672$	37.8483	1.46003
$673$	19.0761	0.735330	0.367665	−	0.929958i	$-0.380157\pi$
$673$	19.0761	0.735330	0.367665	+	0.929958i	$0.380157\pi$
$674$	−0.385105	−0.0148337
$675$	−1.51539	−0.0583272
$676$	0	0
$677$	−4.99378	−0.191927	−0.0959633	−	0.995385i	$-0.530593\pi$
$677$	−4.99378	−0.191927	−0.0959633	+	0.995385i	$0.530593\pi$
$678$	−8.54528	−0.328179
$679$	40.6641	1.56054
$680$	10.1934	0.390900
$681$	11.4466	0.438634
$682$	7.93628	0.303896
$683$	30.9657	1.18487	0.592436	−	0.805618i	$-0.298166\pi$
$683$	30.9657	1.18487	0.592436	+	0.805618i	$0.298166\pi$
$684$	14.1312	0.540320
$685$	41.8617	1.59946
$686$	94.8142	3.62002
$687$	9.92293	0.378584
$688$	22.3698	0.852842
$689$	0	0
$690$	−45.0182	−1.71381
$691$	−38.2139	−1.45373	−0.726863	−	0.686783i	$-0.759022\pi$
$691$	−38.2139	−1.45373	−0.726863	+	0.686783i	$0.759022\pi$
$692$	2.27810	0.0866003
$693$	4.81735	0.182996
$694$	72.9906	2.77068
$695$	5.72057	0.216994
$696$	9.95081	0.377184
$697$	30.9125	1.17089
$698$	6.01296	0.227594
$699$	4.56061	0.172498
$700$	−18.7605	−0.709081
$701$	−3.16956	−0.119713	−0.0598563	−	0.998207i	$-0.519064\pi$
$701$	−3.16956	−0.119713	−0.0598563	+	0.998207i	$0.519064\pi$
$702$	0	0
$703$	41.3188	1.55837
$704$	11.7245	0.441882
$705$	−7.91991	−0.298281
$706$	−5.48064	−0.206266
$707$	−24.0744	−0.905412
$708$	13.7161	0.515482
$709$	−51.9985	−1.95285	−0.976423	−	0.215866i	$-0.930743\pi$
$709$	−51.9985	−1.95285	−0.976423	+	0.215866i	$0.930743\pi$
$710$	−74.7197	−2.80418
$711$	−6.92947	−0.259875
$712$	2.26695	0.0849575
$713$	−30.6288	−1.14706
$714$	33.7577	1.26335
$715$	0	0
$716$	−23.2379	−0.868441
$717$	3.34883	0.125064
$718$	−7.41047	−0.276556
$719$	−28.0481	−1.04602	−0.523009	−	0.852327i	$-0.675190\pi$
$719$	−28.0481	−1.04602	−0.523009	+	0.852327i	$0.675190\pi$
$720$	−6.47184	−0.241191
$721$	67.4383	2.51153
$722$	−24.0205	−0.893952
$723$	−7.51405	−0.279451
$724$	7.17575	0.266685
$725$	12.3778	0.459700
$726$	2.13773	0.0793385
$727$	11.5828	0.429581	0.214790	−	0.976660i	$-0.431093\pi$
$727$	11.5828	0.429581	0.214790	+	0.976660i	$0.431093\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−30.1218	−1.11486
$731$	28.9213	1.06969
$732$	−3.69385	−0.136529
$733$	44.3661	1.63870	0.819351	−	0.573293i	$-0.194334\pi$
$733$	44.3661	1.63870	0.819351	+	0.573293i	$0.194334\pi$
$734$	46.2515	1.70717
$735$	−41.3685	−1.52590
$736$	−64.8192	−2.38927
$737$	−9.84979	−0.362822
$738$	20.1592	0.742072
$739$	−6.82052	−0.250897	−0.125448	−	0.992100i	$-0.540037\pi$
$739$	−6.82052	−0.250897	−0.125448	+	0.992100i	$0.540037\pi$
$740$	49.2907	1.81196
$741$	0	0
$742$	120.227	4.41369
$743$	26.9874	0.990072	0.495036	−	0.868872i	$-0.335155\pi$
$743$	26.9874	0.990072	0.495036	+	0.868872i	$0.335155\pi$
$744$	4.52275	0.165812
$745$	−3.99720	−0.146446
$746$	−17.6808	−0.647340
$747$	−1.26264	−0.0461976
$748$	8.42414	0.308017
$749$	51.2616	1.87306
$750$	−19.0142	−0.694299
$751$	20.6729	0.754363	0.377182	−	0.926139i	$-0.376893\pi$
$751$	20.6729	0.754363	0.377182	+	0.926139i	$0.376893\pi$
$752$	−7.86698	−0.286879
$753$	−23.9749	−0.873695
$754$	0	0
$755$	−37.1547	−1.35220
$756$	12.3800	0.450257
$757$	27.1298	0.986048	0.493024	−	0.870016i	$-0.335891\pi$
$757$	27.1298	0.986048	0.493024	+	0.870016i	$0.335891\pi$
$758$	−15.2646	−0.554434
$759$	−8.25023	−0.299464
$760$	−17.0991	−0.620251
$761$	47.6634	1.72780	0.863899	−	0.503666i	$-0.168016\pi$
$761$	47.6634	1.72780	0.863899	+	0.503666i	$0.168016\pi$
$762$	−42.3996	−1.53598
$763$	−8.93721	−0.323549
$764$	9.51593	0.344274
$765$	−8.36724	−0.302518
$766$	1.74192	0.0629383
$767$	0	0
$768$	−3.46030	−0.124863
$769$	20.6964	0.746330	0.373165	−	0.927765i	$-0.378272\pi$
$769$	20.6964	0.746330	0.373165	+	0.927765i	$0.378272\pi$
$770$	−26.2864	−0.947296
$771$	−1.28396	−0.0462408
$772$	−45.7810	−1.64769
$773$	−30.5232	−1.09784	−0.548922	−	0.835874i	$-0.684962\pi$
$773$	−30.5232	−1.09784	−0.548922	+	0.835874i	$0.684962\pi$
$774$	18.8607	0.677933
$775$	5.62584	0.202086
$776$	10.2835	0.369156
$777$	36.1985	1.29861
$778$	−7.71238	−0.276502
$779$	−51.8546	−1.85788
$780$	0	0
$781$	−13.6934	−0.489990
$782$	−57.8137	−2.06741
$783$	−8.16808	−0.291903
$784$	−41.0920	−1.46757
$785$	−23.1014	−0.824524
$786$	19.7217	0.703449
$787$	−24.7816	−0.883369	−0.441685	−	0.897170i	$-0.645619\pi$
$787$	−24.7816	−0.883369	−0.441685	+	0.897170i	$0.645619\pi$
$788$	51.4589	1.83315
$789$	−4.16995	−0.148454
$790$	37.8114	1.34527
$791$	19.2567	0.684690
$792$	1.21826	0.0432888
$793$	0	0
$794$	−52.2052	−1.85269
$795$	−29.7997	−1.05689
$796$	−21.6349	−0.766827
$797$	−16.3140	−0.577872	−0.288936	−	0.957348i	$-0.593301\pi$
$797$	−16.3140	−0.577872	−0.288936	+	0.957348i	$0.593301\pi$
$798$	−56.6274	−2.00459
$799$	−10.1710	−0.359823
$800$	11.9059	0.420935
$801$	−1.86082	−0.0657487
$802$	−23.1330	−0.816856
$803$	−5.52024	−0.194805
$804$	−25.3128	−0.892714
$805$	101.448	3.57558
$806$	0	0
$807$	−12.4232	−0.437318
$808$	−6.08816	−0.214181
$809$	−11.1504	−0.392026	−0.196013	−	0.980601i	$-0.562799\pi$
$809$	−11.1504	−0.392026	−0.196013	+	0.980601i	$0.562799\pi$
$810$	−5.45661	−0.191726
$811$	−17.6093	−0.618347	−0.309174	−	0.951006i	$-0.600052\pi$
$811$	−17.6093	−0.618347	−0.309174	+	0.951006i	$0.600052\pi$
$812$	−101.121	−3.54866
$813$	−19.9796	−0.700714
$814$	16.0633	0.563018
$815$	31.6492	1.10862
$816$	−8.31132	−0.290954
$817$	−48.5144	−1.69730
$818$	80.6763	2.82078
$819$	0	0
$820$	−61.8593	−2.16022
$821$	−19.5763	−0.683218	−0.341609	−	0.939842i	$-0.610972\pi$
$821$	−19.5763	−0.683218	−0.341609	+	0.939842i	$0.610972\pi$
$822$	35.0590	1.22282
$823$	−14.0616	−0.490158	−0.245079	−	0.969503i	$-0.578814\pi$
$823$	−14.0616	−0.490158	−0.245079	+	0.969503i	$0.578814\pi$
$824$	17.0544	0.594118
$825$	1.51539	0.0527589
$826$	−54.9639	−1.91244
$827$	−15.1016	−0.525134	−0.262567	−	0.964914i	$-0.584569\pi$
$827$	−15.1016	−0.525134	−0.262567	+	0.964914i	$0.584569\pi$
$828$	−21.2021	−0.736825
$829$	−36.7082	−1.27493	−0.637464	−	0.770480i	$-0.720017\pi$
$829$	−36.7082	−1.27493	−0.637464	+	0.770480i	$0.720017\pi$
$830$	6.88973	0.239146
$831$	13.4804	0.467628
$832$	0	0
$833$	−53.1266	−1.84073
$834$	4.79095	0.165897
$835$	6.07531	0.210245
$836$	−14.1312	−0.488738
$837$	−3.71249	−0.128322
$838$	−80.4405	−2.77877
$839$	−12.3191	−0.425303	−0.212652	−	0.977128i	$-0.568210\pi$
$839$	−12.3191	−0.425303	−0.212652	+	0.977128i	$0.568210\pi$
$840$	−14.9802	−0.516865
$841$	37.7176	1.30061
$842$	51.9701	1.79101
$843$	7.83400	0.269817
$844$	−5.08210	−0.174933
$845$	0	0
$846$	−6.63289	−0.228043
$847$	−4.81735	−0.165526
$848$	−29.6006	−1.01649
$849$	−1.47959	−0.0507794
$850$	10.6191	0.364232
$851$	−61.9937	−2.12512
$852$	−35.1905	−1.20561
$853$	28.9348	0.990708	0.495354	−	0.868691i	$-0.335038\pi$
$853$	28.9348	0.990708	0.495354	+	0.868691i	$0.335038\pi$
$854$	14.8022	0.506522
$855$	14.0358	0.480013
$856$	12.9635	0.443083
$857$	24.1469	0.824841	0.412420	−	0.910994i	$-0.364683\pi$
$857$	24.1469	0.824841	0.412420	+	0.910994i	$0.364683\pi$
$858$	0	0
$859$	−2.01217	−0.0686543	−0.0343271	−	0.999411i	$-0.510929\pi$
$859$	−2.01217	−0.0686543	−0.0343271	+	0.999411i	$0.510929\pi$
$860$	−57.8747	−1.97351
$861$	−45.4287	−1.54821
$862$	30.1904	1.02829
$863$	−26.5071	−0.902314	−0.451157	−	0.892445i	$-0.648988\pi$
$863$	−26.5071	−0.902314	−0.451157	+	0.892445i	$0.648988\pi$
$864$	−7.85665	−0.267289
$865$	2.26271	0.0769345
$866$	−33.0243	−1.12221
$867$	6.25456	0.212416
$868$	−45.9607	−1.56001
$869$	6.92947	0.235066
$870$	44.5700	1.51106
$871$	0	0
$872$	−2.26012	−0.0765374
$873$	−8.44116	−0.285690
$874$	96.9804	3.28041
$875$	42.8483	1.44854
$876$	−14.1864	−0.479313
$877$	39.5002	1.33383	0.666913	−	0.745136i	$-0.267615\pi$
$877$	39.5002	1.33383	0.666913	+	0.745136i	$0.267615\pi$
$878$	−26.7292	−0.902065
$879$	19.8817	0.670594
$880$	6.47184	0.218166
$881$	37.5282	1.26436	0.632178	−	0.774823i	$-0.282161\pi$
$881$	37.5282	1.26436	0.632178	+	0.774823i	$0.282161\pi$
$882$	−34.6459	−1.16659
$883$	27.6458	0.930356	0.465178	−	0.885217i	$-0.345990\pi$
$883$	27.6458	0.930356	0.465178	+	0.885217i	$0.345990\pi$
$884$	0	0
$885$	13.6234	0.457947
$886$	81.7344	2.74592
$887$	−11.6222	−0.390236	−0.195118	−	0.980780i	$-0.562509\pi$
$887$	−11.6222	−0.390236	−0.195118	+	0.980780i	$0.562509\pi$
$888$	9.15420	0.307195
$889$	95.5471	3.20455
$890$	10.1537	0.340354
$891$	−1.00000	−0.0335013
$892$	40.3722	1.35176
$893$	17.0614	0.570939
$894$	−3.34764	−0.111962
$895$	−23.0809	−0.771511
$896$	−45.0441	−1.50482
$897$	0	0
$898$	51.7380	1.72652
$899$	30.3239	1.01136
$900$	3.89436	0.129812
$901$	−38.2697	−1.27495
$902$	−20.1592	−0.671229
$903$	−42.5024	−1.41439
$904$	4.86981	0.161967
$905$	7.12728	0.236919
$906$	−31.1169	−1.03379
$907$	−14.4750	−0.480634	−0.240317	−	0.970694i	$-0.577251\pi$
$907$	−14.4750	−0.480634	−0.240317	+	0.970694i	$0.577251\pi$
$908$	−29.4164	−0.976218
$909$	4.99744	0.165755
$910$	0	0
$911$	20.1346	0.667088	0.333544	−	0.942735i	$-0.391755\pi$
$911$	20.1346	0.667088	0.333544	+	0.942735i	$0.391755\pi$
$912$	13.9420	0.461664
$913$	1.26264	0.0417873
$914$	2.91905	0.0965535
$915$	−3.66890	−0.121290
$916$	−25.5008	−0.842570
$917$	−44.4426	−1.46762
$918$	−7.00753	−0.231283
$919$	−29.6007	−0.976438	−0.488219	−	0.872721i	$-0.662353\pi$
$919$	−29.6007	−0.976438	−0.488219	+	0.872721i	$0.662353\pi$
$920$	25.6551	0.845825
$921$	−10.1023	−0.332883
$922$	75.1575	2.47518
$923$	0	0
$924$	−12.3800	−0.407273
$925$	11.3869	0.374399
$926$	−24.2814	−0.797936
$927$	−13.9990	−0.459788
$928$	64.1738	2.10661
$929$	41.3223	1.35574	0.677871	−	0.735181i	$-0.262903\pi$
$929$	41.3223	1.35574	0.677871	+	0.735181i	$0.262903\pi$
$930$	20.2576	0.664272
$931$	89.1179	2.92072
$932$	−11.7202	−0.383909
$933$	−18.2710	−0.598165
$934$	−24.9693	−0.817021
$935$	8.36724	0.273638
$936$	0	0
$937$	37.9242	1.23893	0.619464	−	0.785025i	$-0.287350\pi$
$937$	37.9242	1.23893	0.619464	+	0.785025i	$0.287350\pi$
$938$	101.435	3.31197
$939$	27.3128	0.891320
$940$	20.3532	0.663849
$941$	−24.4126	−0.795829	−0.397914	−	0.917423i	$-0.630266\pi$
$941$	−24.4126	−0.795829	−0.397914	+	0.917423i	$0.630266\pi$
$942$	−19.3473	−0.630370
$943$	77.8014	2.53356
$944$	13.5324	0.440442
$945$	12.2964	0.400002
$946$	−18.8607	−0.613214
$947$	7.90361	0.256833	0.128416	−	0.991720i	$-0.459011\pi$
$947$	7.90361	0.256833	0.128416	+	0.991720i	$0.459011\pi$
$948$	17.8079	0.578375
$949$	0	0
$950$	−17.8132	−0.577935
$951$	−2.96809	−0.0962470
$952$	−19.2380	−0.623506
$953$	−8.40220	−0.272174	−0.136087	−	0.990697i	$-0.543453\pi$
$953$	−8.40220	−0.272174	−0.136087	+	0.990697i	$0.543453\pi$
$954$	−24.9572	−0.808018
$955$	9.45166	0.305848
$956$	−8.60610	−0.278341
$957$	8.16808	0.264037
$958$	−36.5270	−1.18013
$959$	−79.0052	−2.55121
$960$	29.9270	0.965888
$961$	−17.2175	−0.555402
$962$	0	0
$963$	−10.6410	−0.342903
$964$	19.3102	0.621941
$965$	−45.4718	−1.46379
$966$	84.9624	2.73362
$967$	9.34621	0.300554	0.150277	−	0.988644i	$-0.451983\pi$
$967$	9.34621	0.300554	0.150277	+	0.988644i	$0.451983\pi$
$968$	−1.21826	−0.0391562
$969$	18.0251	0.579050
$970$	46.0601	1.47890
$971$	−22.6040	−0.725397	−0.362699	−	0.931906i	$-0.618145\pi$
$971$	−22.6040	−0.725397	−0.362699	+	0.931906i	$0.618145\pi$
$972$	−2.56988	−0.0824290
$973$	−10.7964	−0.346116
$974$	−26.5305	−0.850092
$975$	0	0
$976$	−3.64439	−0.116654
$977$	22.9895	0.735500	0.367750	−	0.929925i	$-0.380128\pi$
$977$	22.9895	0.735500	0.367750	+	0.929925i	$0.380128\pi$
$978$	26.5061	0.847572
$979$	1.86082	0.0594719
$980$	106.312	3.39602
$981$	1.85521	0.0592324
$982$	18.4397	0.588435
$983$	−2.54754	−0.0812539	−0.0406269	−	0.999174i	$-0.512936\pi$
$983$	−2.54754	−0.0812539	−0.0406269	+	0.999174i	$0.512936\pi$
$984$	−11.4884	−0.366237
$985$	51.1113	1.62854
$986$	57.2380	1.82283
$987$	14.9472	0.475773
$988$	0	0
$989$	72.7899	2.31458
$990$	5.45661	0.173422
$991$	23.8118	0.756408	0.378204	−	0.925722i	$-0.376542\pi$
$991$	23.8118	0.756408	0.378204	+	0.925722i	$0.376542\pi$
$992$	29.1677	0.926075
$993$	28.3400	0.899343
$994$	141.018	4.47281
$995$	−21.4887	−0.681238
$996$	3.24484	0.102817
$997$	−9.89112	−0.313255	−0.156627	−	0.987658i	$-0.550062\pi$
$997$	−9.89112	−0.313255	−0.156627	+	0.987658i	$0.550062\pi$
$998$	60.9808	1.93031
$999$	−7.51419	−0.237738

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5577.2.a.ba.1.2	✓	12
13.12	even	2		5577.2.a.bc.1.11	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5577.2.a.ba.1.2	✓	12	1.1	even	1	trivial
5577.2.a.bc.1.11	yes	12	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5577.a (trivial)

\(f(q)\)	\(=\)	\(q-2.13773 q^{2} -1.00000 q^{3} +2.56988 q^{4} +2.55253 q^{5} +2.13773 q^{6} -4.81735 q^{7} -1.21826 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.13773 q^{2} -1.00000 q^{3} +2.56988 q^{4} +2.55253 q^{5} +2.13773 q^{6} -4.81735 q^{7} -1.21826 q^{8} +1.00000 q^{9} -5.45661 q^{10} -1.00000 q^{11} -2.56988 q^{12} +10.2982 q^{14} -2.55253 q^{15} -2.53547 q^{16} -3.27802 q^{17} -2.13773 q^{18} +5.49877 q^{19} +6.55969 q^{20} +4.81735 q^{21} +2.13773 q^{22} -8.25023 q^{23} +1.21826 q^{24} +1.51539 q^{25} -1.00000 q^{27} -12.3800 q^{28} +8.16808 q^{29} +5.45661 q^{30} +3.71249 q^{31} +7.85665 q^{32} +1.00000 q^{33} +7.00753 q^{34} -12.2964 q^{35} +2.56988 q^{36} +7.51419 q^{37} -11.7549 q^{38} -3.10963 q^{40} -9.43022 q^{41} -10.2982 q^{42} -8.82277 q^{43} -2.56988 q^{44} +2.55253 q^{45} +17.6367 q^{46} +3.10277 q^{47} +2.53547 q^{48} +16.2069 q^{49} -3.23948 q^{50} +3.27802 q^{51} +11.6746 q^{53} +2.13773 q^{54} -2.55253 q^{55} +5.86876 q^{56} -5.49877 q^{57} -17.4611 q^{58} -5.33724 q^{59} -6.55969 q^{60} +1.43736 q^{61} -7.93628 q^{62} -4.81735 q^{63} -11.7245 q^{64} -2.13773 q^{66} +9.84979 q^{67} -8.42414 q^{68} +8.25023 q^{69} +26.2864 q^{70} +13.6934 q^{71} -1.21826 q^{72} +5.52024 q^{73} -16.0633 q^{74} -1.51539 q^{75} +14.1312 q^{76} +4.81735 q^{77} -6.92947 q^{79} -6.47184 q^{80} +1.00000 q^{81} +20.1592 q^{82} -1.26264 q^{83} +12.3800 q^{84} -8.36724 q^{85} +18.8607 q^{86} -8.16808 q^{87} +1.21826 q^{88} -1.86082 q^{89} -5.45661 q^{90} -21.2021 q^{92} -3.71249 q^{93} -6.63289 q^{94} +14.0358 q^{95} -7.85665 q^{96} -8.44116 q^{97} -34.6459 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} - 12 q^{3} + 5 q^{4} + 6 q^{5} + q^{6} + q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q - q^2 - 12 * q^3 + 5 * q^4 + 6 * q^5 + q^6 + q^7 + 12 * q^9	\( 12 q - q^{2} - 12 q^{3} + 5 q^{4} + 6 q^{5} + q^{6} + q^{7} + 12 q^{9} - 11 q^{10} - 12 q^{11} - 5 q^{12} + 9 q^{14} - 6 q^{15} - 9 q^{16} + 3 q^{17} - q^{18} - 6 q^{19} + 20 q^{20} - q^{21} + q^{22} - 22 q^{23} - 2 q^{25} - 12 q^{27} + 11 q^{28} + 13 q^{29} + 11 q^{30} - 2 q^{31} - 11 q^{32} + 12 q^{33} - 10 q^{34} - 14 q^{35} + 5 q^{36} - 3 q^{37} - 18 q^{38} - 18 q^{40} - 4 q^{41} - 9 q^{42} - 26 q^{43} - 5 q^{44} + 6 q^{45} + 18 q^{46} + 9 q^{47} + 9 q^{48} - 3 q^{49} - 29 q^{50} - 3 q^{51} - 5 q^{53} + q^{54} - 6 q^{55} + 5 q^{56} + 6 q^{57} - 37 q^{58} + 22 q^{59} - 20 q^{60} - 11 q^{61} - 18 q^{62} + q^{63} - 10 q^{64} - q^{66} + 28 q^{67} + 12 q^{68} + 22 q^{69} + 29 q^{70} - 10 q^{71} + 7 q^{73} - 6 q^{74} + 2 q^{75} - 32 q^{76} - q^{77} - 40 q^{79} - 30 q^{80} + 12 q^{81} + 26 q^{82} - q^{83} - 11 q^{84} + 32 q^{85} + 9 q^{86} - 13 q^{87} - 11 q^{89} - 11 q^{90} - 38 q^{92} + 2 q^{93} - 25 q^{94} - 10 q^{95} + 11 q^{96} - 7 q^{97} - 28 q^{98} - 12 q^{99}+O(q^{100}) \) 12 * q - q^2 - 12 * q^3 + 5 * q^4 + 6 * q^5 + q^6 + q^7 + 12 * q^9 - 11 * q^10 - 12 * q^11 - 5 * q^12 + 9 * q^14 - 6 * q^15 - 9 * q^16 + 3 * q^17 - q^18 - 6 * q^19 + 20 * q^20 - q^21 + q^22 - 22 * q^23 - 2 * q^25 - 12 * q^27 + 11 * q^28 + 13 * q^29 + 11 * q^30 - 2 * q^31 - 11 * q^32 + 12 * q^33 - 10 * q^34 - 14 * q^35 + 5 * q^36 - 3 * q^37 - 18 * q^38 - 18 * q^40 - 4 * q^41 - 9 * q^42 - 26 * q^43 - 5 * q^44 + 6 * q^45 + 18 * q^46 + 9 * q^47 + 9 * q^48 - 3 * q^49 - 29 * q^50 - 3 * q^51 - 5 * q^53 + q^54 - 6 * q^55 + 5 * q^56 + 6 * q^57 - 37 * q^58 + 22 * q^59 - 20 * q^60 - 11 * q^61 - 18 * q^62 + q^63 - 10 * q^64 - q^66 + 28 * q^67 + 12 * q^68 + 22 * q^69 + 29 * q^70 - 10 * q^71 + 7 * q^73 - 6 * q^74 + 2 * q^75 - 32 * q^76 - q^77 - 40 * q^79 - 30 * q^80 + 12 * q^81 + 26 * q^82 - q^83 - 11 * q^84 + 32 * q^85 + 9 * q^86 - 13 * q^87 - 11 * q^89 - 11 * q^90 - 38 * q^92 + 2 * q^93 - 25 * q^94 - 10 * q^95 + 11 * q^96 - 7 * q^97 - 28 * q^98 - 12 * q^99

Introduction

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