LMFDB - Embedded newform 1050.3.p.d.451.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1050,3,Mod(451,1050)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1050.451"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1050, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,12,-8,0,0,0,0,12,0,-4,-24,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.151613669376.6
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 12x^{6} + 95x^{4} - 588x^{2} + 2401 $ x^8 - 12x^6 + 95x^4 - 588*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.1
Root			$-2.56149 + 0.662382i$ of defining polynomial
Character	$\chi$	$=$	1050.451
Dual form			1050.3.p.d.901.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(-0.440173 - 6.98615i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(2.76860 - 4.79536i) q^{11} +(-3.00000 + 1.73205i) q^{12} -3.50434i q^{13} +(-8.24500 + 5.47905i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-7.04933 - 4.06994i) q^{17} +(2.12132 - 3.67423i) q^{18} +(-15.3628 + 8.86974i) q^{19} +(5.38992 - 10.8604i) q^{21} -7.83078 q^{22} +(-5.96495 - 10.3316i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-4.29192 + 2.47794i) q^{26} +5.19615i q^{27} +(12.5405 + 6.22374i) q^{28} -8.52374 q^{29} +(-6.68072 - 3.85711i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(8.30580 - 4.79536i) q^{33} +11.5115i q^{34} -6.00000 q^{36} +(-14.0267 - 24.2950i) q^{37} +(21.7263 + 12.5437i) q^{38} +(3.03484 - 5.25650i) q^{39} -3.14207i q^{41} +(-17.1125 + 1.07820i) q^{42} +43.1943 q^{43} +(5.53720 + 9.59071i) q^{44} +(-8.43572 + 14.6111i) q^{46} +(-16.2037 + 9.35524i) q^{47} -6.92820i q^{48} +(-48.6125 + 6.15023i) q^{49} +(-7.04933 - 12.2098i) q^{51} +(6.06969 + 3.50434i) q^{52} +(1.40895 - 2.44037i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-1.24500 - 19.7598i) q^{56} -30.7257 q^{57} +(6.02720 + 10.4394i) q^{58} +(-26.1612 - 15.1042i) q^{59} +(-41.0095 + 23.6769i) q^{61} +10.9096i q^{62} +(17.4903 - 11.6228i) q^{63} +8.00000 q^{64} +(-11.7462 - 6.78166i) q^{66} +(3.29108 - 5.70032i) q^{67} +(14.0987 - 8.13987i) q^{68} -20.6632i q^{69} -97.7751 q^{71} +(4.24264 + 7.34847i) q^{72} +(52.9672 + 30.5806i) q^{73} +(-19.8368 + 34.3583i) q^{74} -35.4790i q^{76} +(-34.7197 - 17.2311i) q^{77} -8.58383 q^{78} +(-61.5670 - 106.637i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-3.84823 + 2.22178i) q^{82} -89.5815i q^{83} +(13.4209 + 20.1960i) q^{84} +(-30.5430 - 52.9020i) q^{86} +(-12.7856 - 7.38178i) q^{87} +(7.83078 - 13.5633i) q^{88} +(-102.290 + 59.0573i) q^{89} +(-24.4818 + 1.54251i) q^{91} +23.8598 q^{92} +(-6.68072 - 11.5713i) q^{93} +(22.9156 + 13.2303i) q^{94} +(-8.48528 + 4.89898i) q^{96} -65.1965i q^{97} +(41.9067 + 55.1890i) q^{98} +16.6116 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} - 24 q^{12} - 16 q^{14} - 16 q^{16} + 24 q^{17} + 72 q^{19} - 24 q^{22} - 60 q^{23} - 72 q^{26} - 24 q^{29} + 96 q^{31} - 12 q^{33} - 48 q^{36} + 24 q^{37}+ \cdots - 24 q^{99}+O(q^{100}) $ 8 * q + 12 * q^3 - 8 * q^4 + 12 * q^9 - 4 * q^11 - 24 * q^12 - 16 * q^14 - 16 * q^16 + 24 * q^17 + 72 * q^19 - 24 * q^22 - 60 * q^23 - 72 * q^26 - 24 * q^29 + 96 * q^31 - 12 * q^33 - 48 * q^36 + 24 * q^37 + 180 * q^38 - 12 * q^39 - 12 * q^42 + 112 * q^43 - 8 * q^44 + 32 * q^46 - 84 * q^47 - 264 * q^49 + 24 * q^51 - 24 * q^52 - 44 * q^53 + 40 * q^56 + 144 * q^57 - 104 * q^58 + 312 * q^59 - 204 * q^61 + 64 * q^64 - 36 * q^66 - 120 * q^67 - 48 * q^68 - 64 * q^71 - 84 * q^73 - 16 * q^74 - 228 * q^77 - 144 * q^78 - 144 * q^79 - 36 * q^81 + 60 * q^82 + 176 * q^86 - 36 * q^87 + 24 * q^88 - 336 * q^89 - 296 * q^91 + 240 * q^92 + 96 * q^93 + 36 * q^94 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		−	2.44949i		−	0.408248i
$7$	−0.440173	−	6.98615i	−0.0628819	−	0.998021i
$7$	−0.440173	−	6.98615i	−0.0628819	−	0.998021i
$8$	2.82843			0.353553
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	2.76860	−	4.79536i	0.251691	−	0.435942i	−0.712301	−	0.701875i	$-0.752347\pi$
$11$	2.76860	−	4.79536i	0.251691	−	0.435942i	0.963991	+	0.265933i	$0.0856800\pi$
$12$	−3.00000	+	1.73205i	−0.250000	+	0.144338i
$13$		−	3.50434i		−	0.269564i	−0.990875	−	0.134782i	$-0.956967\pi$
$13$		−	3.50434i		−	0.269564i	0.990875	−	0.134782i	$-0.0430335\pi$
$14$	−8.24500	+	5.47905i	−0.588928	+	0.391361i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−7.04933	−	4.06994i	−0.414667	−	0.239408i	0.278126	−	0.960545i	$-0.410287\pi$
$17$	−7.04933	−	4.06994i	−0.414667	−	0.239408i	−0.692793	+	0.721137i	$0.743620\pi$
$18$	2.12132	−	3.67423i	0.117851	−	0.204124i
$19$	−15.3628	+	8.86974i	−0.808571	+	0.466828i	−0.846459	−	0.532454i	$-0.821270\pi$
$19$	−15.3628	+	8.86974i	−0.808571	+	0.466828i	0.0378887	+	0.999282i	$0.487937\pi$
$20$		0			0
$21$	5.38992	−	10.8604i	0.256663	−	0.517163i
$22$	−7.83078			−0.355945
$23$	−5.96495	−	10.3316i	−0.259346	−	0.449200i	0.706721	−	0.707492i	$-0.250174\pi$
$23$	−5.96495	−	10.3316i	−0.259346	−	0.449200i	−0.966067	+	0.258292i	$0.916840\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$		0			0
$26$	−4.29192	+	2.47794i	−0.165074	+	0.0953054i
$27$			5.19615i			0.192450i
$28$	12.5405	+	6.22374i	0.447876	+	0.222277i
$29$	−8.52374			−0.293922			−0.146961	−	0.989142i	$-0.546949\pi$
$29$	−8.52374			−0.293922			−0.146961	+	0.989142i	$0.546949\pi$
$30$		0			0
$31$	−6.68072	−	3.85711i	−0.215507	−	0.124423i	0.388361	−	0.921507i	$-0.373041\pi$
$31$	−6.68072	−	3.85711i	−0.215507	−	0.124423i	−0.603868	+	0.797084i	$0.706375\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$	8.30580	−	4.79536i	0.251691	−	0.145314i
$34$			11.5115i			0.338574i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−14.0267	−	24.2950i	−0.379100	−	0.656621i	0.611831	−	0.790988i	$-0.290433\pi$
$37$	−14.0267	−	24.2950i	−0.379100	−	0.656621i	−0.990932	+	0.134367i	$0.957100\pi$
$38$	21.7263	+	12.5437i	0.571746	+	0.330098i
$39$	3.03484	−	5.25650i	0.0778165	−	0.134782i
$40$		0			0
$41$		−	3.14207i		−	0.0766358i	−0.999266	−	0.0383179i	$-0.987800\pi$
$41$		−	3.14207i		−	0.0766358i	0.999266	−	0.0383179i	$-0.0121999\pi$
$42$	−17.1125	+	1.07820i	−0.407440	+	0.0256714i
$43$	43.1943			1.00452			0.502260	−	0.864717i	$-0.332502\pi$
$43$	43.1943			1.00452			0.502260	+	0.864717i	$0.332502\pi$
$44$	5.53720	+	9.59071i	0.125845	+	0.217971i
$45$		0			0
$46$	−8.43572	+	14.6111i	−0.183385	+	0.317632i
$47$	−16.2037	+	9.35524i	−0.344761	+	0.199048i	−0.662375	−	0.749172i	$-0.730452\pi$
$47$	−16.2037	+	9.35524i	−0.344761	+	0.199048i	0.317615	+	0.948220i	$0.397118\pi$
$48$		−	6.92820i		−	0.144338i
$49$	−48.6125	+	6.15023i	−0.992092	+	0.125515i
$50$		0			0
$51$	−7.04933	−	12.2098i	−0.138222	−	0.239408i
$52$	6.06969	+	3.50434i	0.116725	+	0.0673911i
$53$	1.40895	−	2.44037i	0.0265840	−	0.0460448i	−0.852427	−	0.522846i	$-0.824870\pi$
$53$	1.40895	−	2.44037i	0.0265840	−	0.0460448i	0.879011	+	0.476801i	$0.158204\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$		0			0
$56$	−1.24500	−	19.7598i	−0.0222321	−	0.352854i
$57$	−30.7257			−0.539047
$58$	6.02720	+	10.4394i	0.103917	+	0.179990i
$59$	−26.1612	−	15.1042i	−0.443411	−	0.256003i	0.261633	−	0.965168i	$-0.415739\pi$
$59$	−26.1612	−	15.1042i	−0.443411	−	0.256003i	−0.705043	+	0.709164i	$0.749072\pi$
$60$		0			0
$61$	−41.0095	+	23.6769i	−0.672288	+	0.388145i	−0.796943	−	0.604055i	$-0.793551\pi$
$61$	−41.0095	+	23.6769i	−0.672288	+	0.388145i	0.124655	+	0.992200i	$0.460218\pi$
$62$			10.9096i			0.175961i
$63$	17.4903	−	11.6228i	0.277624	−	0.184489i
$64$	8.00000			0.125000
$65$		0			0
$66$	−11.7462	−	6.78166i	−0.177972	−	0.102752i
$67$	3.29108	−	5.70032i	0.0491206	−	0.0850794i	−0.840420	−	0.541936i	$-0.817691\pi$
$67$	3.29108	−	5.70032i	0.0491206	−	0.0850794i	0.889540	+	0.456857i	$0.151025\pi$
$68$	14.0987	−	8.13987i	0.207333	−	0.119704i
$69$		−	20.6632i		−	0.299467i
$70$		0			0
$71$	−97.7751			−1.37711			−0.688557	−	0.725182i	$-0.741755\pi$
$71$	−97.7751			−1.37711			−0.688557	+	0.725182i	$0.741755\pi$
$72$	4.24264	+	7.34847i	0.0589256	+	0.102062i
$73$	52.9672	+	30.5806i	0.725578	+	0.418913i	0.816802	−	0.576918i	$-0.195745\pi$
$73$	52.9672	+	30.5806i	0.725578	+	0.418913i	−0.0912244	+	0.995830i	$0.529078\pi$
$74$	−19.8368	+	34.3583i	−0.268064	+	0.464301i
$75$		0			0
$76$		−	35.4790i		−	0.466828i
$77$	−34.7197	−	17.2311i	−0.450906	−	0.223780i
$78$	−8.58383			−0.110049
$79$	−61.5670	−	106.637i	−0.779329	−	1.34984i	−0.932329	−	0.361612i	$-0.882227\pi$
$79$	−61.5670	−	106.637i	−0.779329	−	1.34984i	0.152999	−	0.988226i	$-0.451107\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−3.84823	+	2.22178i	−0.0469296	+	0.0270948i
$83$		−	89.5815i		−	1.07930i	−0.841891	−	0.539648i	$-0.818557\pi$
$83$		−	89.5815i		−	1.07930i	0.841891	−	0.539648i	$-0.181443\pi$
$84$	13.4209	+	20.1960i	0.159772	+	0.240429i
$85$		0			0
$86$	−30.5430	−	52.9020i	−0.355151	−	0.615140i
$87$	−12.7856	−	7.38178i	−0.146961	−	0.0848480i
$88$	7.83078	−	13.5633i	0.0889862	−	0.154129i
$89$	−102.290	+	59.0573i	−1.14933	+	0.663566i	−0.948724	−	0.316107i	$-0.897624\pi$
$89$	−102.290	+	59.0573i	−1.14933	+	0.663566i	−0.200606	+	0.979672i	$0.564291\pi$
$90$		0			0
$91$	−24.4818	+	1.54251i	−0.269031	+	0.0169507i
$92$	23.8598			0.259346
$93$	−6.68072	−	11.5713i	−0.0718357	−	0.124423i
$94$	22.9156	+	13.2303i	0.243783	+	0.140748i
$95$		0			0
$96$	−8.48528	+	4.89898i	−0.0883883	+	0.0510310i
$97$		−	65.1965i		−	0.672128i	−0.941839	−	0.336064i	$-0.890904\pi$
$97$		−	65.1965i		−	0.672128i	0.941839	−	0.336064i	$-0.109096\pi$
$98$	41.9067	+	55.1890i	0.427619	+	0.563153i
$99$	16.6116			0.167794
$100$		0			0
$101$	−120.895	−	69.7987i	−1.19698	−	0.691076i	−0.237099	−	0.971486i	$-0.576196\pi$
$101$	−120.895	−	69.7987i	−1.19698	−	0.691076i	−0.959881	+	0.280409i	$0.909530\pi$
$102$	−9.96926	+	17.2673i	−0.0977379	+	0.169287i
$103$	151.108	−	87.2421i	1.46707	−	0.847011i	0.467746	−	0.883863i	$-0.345066\pi$
$103$	151.108	−	87.2421i	1.46707	−	0.847011i	0.999321	+	0.0368520i	$0.0117330\pi$
$104$		−	9.91176i		−	0.0953054i
$105$		0			0
$106$	−3.98511			−0.0375954
$107$	−30.2382	−	52.3741i	−0.282600	−	0.489477i	0.689424	−	0.724358i	$-0.257864\pi$
$107$	−30.2382	−	52.3741i	−0.282600	−	0.489477i	−0.972024	+	0.234880i	$0.924530\pi$
$108$	−9.00000	−	5.19615i	−0.0833333	−	0.0481125i
$109$	50.4057	−	87.3052i	0.462437	−	0.800965i	−0.536644	−	0.843808i	$-0.680308\pi$
$109$	50.4057	−	87.3052i	0.462437	−	0.800965i	0.999082	+	0.0428435i	$0.0136417\pi$
$110$		0			0
$111$		−	48.5899i		−	0.437747i
$112$	−23.3204	+	15.4971i	−0.208218	+	0.138367i
$113$	−74.1876			−0.656527			−0.328264	−	0.944586i	$-0.606463\pi$
$113$	−74.1876			−0.656527			−0.328264	+	0.944586i	$0.606463\pi$
$114$	21.7263	+	37.6311i	0.190582	+	0.330098i
$115$		0			0
$116$	8.52374	−	14.7636i	0.0734805	−	0.127272i
$117$	9.10453	−	5.25650i	0.0778165	−	0.0449274i
$118$			42.7211i			0.362043i
$119$	−25.3302	+	51.0392i	−0.212859	+	0.428901i
$120$		0			0
$121$	45.1697	+	78.2362i	0.373303	+	0.646580i
$122$	57.9963	+	33.4842i	0.475379	+	0.274460i
$123$	2.72111	−	4.71310i	0.0221228	−	0.0383179i
$124$	13.3614	−	7.71423i	0.107754	−	0.0622115i
$125$		0			0
$126$	−26.6025	−	13.2026i	−0.211131	−	0.104782i
$127$	−151.093			−1.18971			−0.594855	−	0.803833i	$-0.702791\pi$
$127$	−151.093			−1.18971			−0.594855	+	0.803833i	$0.702791\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$	64.7915	+	37.4074i	0.502260	+	0.289980i
$130$		0			0
$131$	−186.820	+	107.861i	−1.42611	+	0.823363i	−0.996811	−	0.0798009i	$-0.974572\pi$
$131$	−186.820	+	107.861i	−1.42611	+	0.823363i	−0.429296	+	0.903164i	$0.641238\pi$
$132$			19.1814i			0.145314i
$133$	68.7276	+	103.423i	0.516749	+	0.777615i
$134$	−9.30859			−0.0694671
$135$		0			0
$136$	−19.9385	−	11.5115i	−0.146607	−	0.0846435i
$137$	66.8203	−	115.736i	0.487739	−	0.844789i	−0.512161	−	0.858889i	$-0.671155\pi$
$137$	66.8203	−	115.736i	0.487739	−	0.844789i	0.999901	+	0.0141000i	$0.00448831\pi$
$138$	−25.3072	+	14.6111i	−0.183385	+	0.105877i
$139$		−	193.762i		−	1.39397i	−0.717085	−	0.696986i	$-0.754524\pi$
$139$		−	193.762i		−	1.39397i	0.717085	−	0.696986i	$-0.245476\pi$
$140$		0			0
$141$	−32.4075			−0.229840
$142$	69.1374	+	119.750i	0.486883	+	0.843306i
$143$	−16.8045	−	9.70210i	−0.117514	−	0.0678469i
$144$	6.00000	−	10.3923i	0.0416667	−	0.0721688i
$145$		0			0
$146$		−	86.4950i		−	0.592432i
$147$	−78.2450	−	32.8743i	−0.532279	−	0.223635i
$148$	56.1068			0.379100
$149$	−33.0032	−	57.1632i	−0.221498	−	0.383646i	0.733765	−	0.679403i	$-0.237761\pi$
$149$	−33.0032	−	57.1632i	−0.221498	−	0.383646i	−0.955263	+	0.295758i	$0.904428\pi$
$150$		0			0
$151$	−17.4410	+	30.2087i	−0.115503	+	0.200057i	−0.917981	−	0.396625i	$-0.870181\pi$
$151$	−17.4410	+	30.2087i	−0.115503	+	0.200057i	0.802478	+	0.596682i	$0.203515\pi$
$152$	−43.4527	+	25.0874i	−0.285873	+	0.165049i
$153$		−	24.4196i		−	0.159605i
$154$	3.44690	+	54.7070i	0.0223825	+	0.355240i
$155$		0			0
$156$	6.06969	+	10.5130i	0.0389082	+	0.0673911i
$157$	46.3329	+	26.7503i	0.295114	+	0.170384i	0.640246	−	0.768170i	$-0.278832\pi$
$157$	46.3329	+	26.7503i	0.295114	+	0.170384i	−0.345132	+	0.938554i	$0.612166\pi$
$158$	−87.0689	+	150.808i	−0.551069	+	0.954480i
$159$	4.22685	−	2.44037i	0.0265840	−	0.0153483i
$160$		0			0
$161$	−69.5525	+	46.2197i	−0.432003	+	0.287079i
$162$	12.7279			0.0785674
$163$	102.992	+	178.387i	0.631852	+	1.09440i	0.987173	+	0.159655i	$0.0510383\pi$
$163$	102.992	+	178.387i	0.631852	+	1.09440i	−0.355321	+	0.934744i	$0.615628\pi$
$164$	5.44222	+	3.14207i	0.0331843	+	0.0191589i
$165$		0			0
$166$	−109.714	+	63.3437i	−0.660931	+	0.381589i
$167$		−	137.945i		−	0.826020i	−0.910727	−	0.413010i	$-0.864477\pi$
$167$		−	137.945i		−	0.826020i	0.910727	−	0.413010i	$-0.135523\pi$
$168$	15.2450	−	30.7179i	0.0907440	−	0.182845i
$169$	156.720			0.927335
$170$		0			0
$171$	−46.0885	−	26.6092i	−0.269524	−	0.155609i
$172$	−43.1943	+	74.8148i	−0.251130	+	0.434970i
$173$	−191.016	+	110.283i	−1.10414	+	0.637475i	−0.937305	−	0.348510i	$-0.886688\pi$
$173$	−191.016	+	110.283i	−1.10414	+	0.637475i	−0.166834	+	0.985985i	$0.553354\pi$
$174$			20.8788i			0.119993i
$175$		0			0
$176$	−22.1488			−0.125845
$177$	−26.1612	−	45.3126i	−0.147804	−	0.256003i
$178$	144.660	+	83.5197i	0.812699	+	0.469212i
$179$	36.6501	−	63.4798i	0.204749	−	0.354636i	−0.745304	−	0.666725i	$-0.767695\pi$
$179$	36.6501	−	63.4798i	0.204749	−	0.354636i	0.950053	+	0.312089i	$0.101029\pi$
$180$		0			0
$181$			61.4619i			0.339568i	0.985481	+	0.169784i	$0.0543071\pi$
$181$			61.4619i			0.339568i	−0.985481	+	0.169784i	$0.945693\pi$
$182$	19.2004	+	28.8932i	0.105497	+	0.158754i
$183$	−82.0191			−0.448192
$184$	−16.8714	−	29.2222i	−0.0916926	−	0.158816i
$185$		0			0
$186$	−9.44796	+	16.3643i	−0.0507955	+	0.0879804i
$187$	−39.0336	+	22.5360i	−0.208736	+	0.120514i
$188$		−	37.4210i		−	0.199048i
$189$	36.3011	−	2.28721i	0.192069	−	0.0121016i
$190$		0			0
$191$	179.931	+	311.650i	0.942048	+	1.63168i	0.761556	+	0.648099i	$0.224436\pi$
$191$	179.931	+	311.650i	0.942048	+	1.63168i	0.180492	+	0.983577i	$0.442231\pi$
$192$	12.0000	+	6.92820i	0.0625000	+	0.0360844i
$193$	−69.8724	+	121.023i	−0.362033	+	0.627060i	−0.988295	−	0.152552i	$-0.951251\pi$
$193$	−69.8724	+	121.023i	−0.362033	+	0.627060i	0.626262	+	0.779613i	$0.284584\pi$
$194$	−79.8490	+	46.1009i	−0.411593	+	0.237633i
$195$		0			0
$196$	37.9600	−	90.3495i	0.193673	−	0.460967i
$197$	−248.343			−1.26062			−0.630311	−	0.776342i	$-0.717073\pi$
$197$	−248.343			−1.26062			−0.630311	+	0.776342i	$0.717073\pi$
$198$	−11.7462	−	20.3450i	−0.0593241	−	0.102752i
$199$	−106.170	−	61.2973i	−0.533518	−	0.308026i	0.208930	−	0.977931i	$-0.433002\pi$
$199$	−106.170	−	61.2973i	−0.533518	−	0.308026i	−0.742448	+	0.669904i	$0.766335\pi$
$200$		0			0
$201$	9.87325	−	5.70032i	0.0491206	−	0.0283598i
$202$			197.421i			0.977329i
$203$	3.75192	+	59.5481i	0.0184824	+	0.293341i
$204$	28.1973			0.138222
$205$		0			0
$206$	−213.699	−	123.379i	−1.03737	−	0.598927i
$207$	17.8949	−	30.9948i	0.0864486	−	0.149733i
$208$	−12.1394	+	7.00867i	−0.0583624	+	0.0336955i
$209$			98.2271i			0.469986i
$210$		0			0
$211$	352.829			1.67218			0.836088	−	0.548596i	$-0.184837\pi$
$211$	352.829			1.67218			0.836088	+	0.548596i	$0.184837\pi$
$212$	2.81790	+	4.88074i	0.0132920	+	0.0230224i
$213$	−146.663	−	84.6757i	−0.688557	−	0.397538i
$214$	−42.7632	+	74.0681i	−0.199828	+	0.346113i
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	−24.0057	+	48.3703i	−0.110625	+	0.222904i
$218$	−142.569			−0.653985
$219$	52.9672	+	91.7418i	0.241859	+	0.418913i
$220$		0			0
$221$	−14.2624	+	24.7032i	−0.0645358	+	0.111779i
$222$	−59.5103	+	34.3583i	−0.268064	+	0.154767i
$223$			61.7420i			0.276870i	0.990372	+	0.138435i	$0.0442072\pi$
$223$			61.7420i			0.276870i	−0.990372	+	0.138435i	$0.955793\pi$
$224$	35.4700	+	17.6034i	0.158348	+	0.0785866i
$225$		0			0
$226$	52.4586	+	90.8609i	0.232118	+	0.402039i
$227$	181.452	+	104.762i	0.799350	+	0.461505i	0.843244	−	0.537531i	$-0.180643\pi$
$227$	181.452	+	104.762i	0.799350	+	0.461505i	−0.0438940	+	0.999036i	$0.513976\pi$
$228$	30.7257	−	53.2184i	0.134762	−	0.233414i
$229$	−93.3568	+	53.8996i	−0.407671	+	0.235369i	−0.689789	−	0.724011i	$-0.742297\pi$
$229$	−93.3568	+	53.8996i	−0.407671	+	0.235369i	0.282117	+	0.959380i	$0.408963\pi$
$230$		0			0
$231$	−37.1571	−	55.9148i	−0.160853	−	0.242055i
$232$	−24.1088			−0.103917
$233$	−163.423	−	283.057i	−0.701387	−	1.21484i	−0.967980	−	0.251029i	$-0.919231\pi$
$233$	−163.423	−	283.057i	−0.701387	−	1.21484i	0.266592	−	0.963809i	$-0.414102\pi$
$234$	−12.8758	−	7.43382i	−0.0550246	−	0.0317685i
$235$		0			0
$236$	52.3224	−	30.2084i	0.221705	−	0.128002i
$237$		−	213.274i		−	0.899892i
$238$	80.4211	−	5.06706i	0.337904	−	0.0212902i
$239$	−9.20117			−0.0384986			−0.0192493	−	0.999815i	$-0.506128\pi$
$239$	−9.20117			−0.0384986			−0.0192493	+	0.999815i	$0.506128\pi$
$240$		0			0
$241$	278.156	+	160.593i	1.15417	+	0.666362i	0.949900	−	0.312553i	$-0.101184\pi$
$241$	278.156	+	160.593i	1.15417	+	0.666362i	0.204272	+	0.978914i	$0.434517\pi$
$242$	63.8796	−	110.643i	0.263965	−	0.457201i
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$		−	94.7075i		−	0.388145i
$245$		0			0
$246$	−7.69646			−0.0312864
$247$	31.0825	+	53.8365i	0.125840	+	0.217962i
$248$	−18.8959	−	10.9096i	−0.0761932	−	0.0439902i
$249$	77.5799	−	134.372i	0.311566	−	0.539648i
$250$		0			0
$251$		−	19.2394i		−	0.0766511i	−0.999265	−	0.0383255i	$-0.987798\pi$
$251$		−	19.2394i		−	0.0766511i	0.999265	−	0.0383255i	$-0.0122024\pi$
$252$	2.64104	+	41.9169i	0.0104803	+	0.166337i
$253$	−66.0583			−0.261100
$254$	106.839	+	185.051i	0.420626	+	0.728546i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−112.083	+	64.7109i	−0.436119	+	0.251793i	−0.701950	−	0.712226i	$-0.747687\pi$
$257$	−112.083	+	64.7109i	−0.436119	+	0.251793i	0.265831	+	0.964020i	$0.414354\pi$
$258$		−	105.804i		−	0.410093i
$259$	−163.554	+	108.687i	−0.631483	+	0.419640i
$260$		0			0
$261$	−12.7856	−	22.1453i	−0.0489870	−	0.0848480i
$262$	264.203	+	152.538i	1.00841	+	0.582206i
$263$	83.4625	−	144.561i	0.317348	−	0.549663i	−0.662586	−	0.748986i	$-0.730541\pi$
$263$	83.4625	−	144.561i	0.317348	−	0.549663i	0.979934	+	0.199323i	$0.0638744\pi$
$264$	23.4924	−	13.5633i	0.0889862	−	0.0513762i
$265$		0			0
$266$	78.0688	−	157.305i	0.293492	−	0.591371i
$267$	−204.581			−0.766220
$268$	6.58217	+	11.4006i	0.0245603	+	0.0425397i
$269$	181.081	+	104.547i	0.673162	+	0.388650i	0.797274	−	0.603618i	$-0.206275\pi$
$269$	181.081	+	104.547i	0.673162	+	0.388650i	−0.124112	+	0.992268i	$0.539608\pi$
$270$		0			0
$271$	123.029	−	71.0308i	0.453981	−	0.262106i	−0.255529	−	0.966801i	$-0.582250\pi$
$271$	123.029	−	71.0308i	0.453981	−	0.262106i	0.709510	+	0.704695i	$0.248916\pi$
$272$			32.5595i			0.119704i
$273$	−38.0586	−	18.8881i	−0.139409	−	0.0691871i
$274$	−188.996			−0.689768
$275$		0			0
$276$	35.7897	+	20.6632i	0.129673	+	0.0748667i
$277$	222.961	−	386.179i	0.804912	−	1.39415i	−0.111438	−	0.993771i	$-0.535546\pi$
$277$	222.961	−	386.179i	0.804912	−	1.39415i	0.916350	−	0.400377i	$-0.131121\pi$
$278$	−237.309	+	137.010i	−0.853630	+	0.492843i
$279$		−	23.1427i		−	0.0829487i
$280$		0			0
$281$	482.012			1.71534			0.857672	−	0.514196i	$-0.171910\pi$
$281$	482.012			1.71534			0.857672	+	0.514196i	$0.171910\pi$
$282$	22.9156	+	39.6909i	0.0812609	+	0.140748i
$283$	187.506	+	108.257i	0.662566	+	0.382533i	0.793254	−	0.608891i	$-0.208385\pi$
$283$	187.506	+	108.257i	0.662566	+	0.382533i	−0.130688	+	0.991424i	$0.541719\pi$
$284$	97.7751	−	169.351i	0.344278	−	0.596308i
$285$		0			0
$286$			27.4417i			0.0959500i
$287$	−21.9509	+	1.38305i	−0.0764841	+	0.00481900i
$288$	−16.9706			−0.0589256
$289$	−111.371	−	192.901i	−0.385368	−	0.667476i
$290$		0			0
$291$	56.4618	−	97.7947i	0.194027	−	0.336064i
$292$	−105.934	+	61.1612i	−0.362789	+	0.209456i
$293$		−	383.704i		−	1.30957i	−0.755815	−	0.654786i	$-0.772759\pi$
$293$		−	383.704i		−	1.30957i	0.755815	−	0.654786i	$-0.227241\pi$
$294$	15.0649	+	119.076i	0.0512412	+	0.405020i
$295$		0			0
$296$	−39.6735	−	68.7166i	−0.134032	−	0.232151i
$297$	24.9174	+	14.3861i	0.0838970	+	0.0484379i
$298$	−46.6736	+	80.8410i	−0.156623	+	0.271278i
$299$	−36.2054	+	20.9032i	−0.121088	+	0.0699104i
$300$		0			0
$301$	−19.0130	−	301.762i	−0.0631661	−	1.00253i
$302$	49.3305			0.163346
$303$	−120.895	−	209.396i	−0.398993	−	0.691076i
$304$	61.4514	+	35.4790i	0.202143	+	0.116707i
$305$		0			0
$306$	−29.9078	+	17.2673i	−0.0977379	+	0.0564290i
$307$		−	21.1264i		−	0.0688155i	−0.999408	−	0.0344078i	$-0.989046\pi$
$307$		−	21.1264i		−	0.0688155i	0.999408	−	0.0344078i	$-0.0109545\pi$
$308$	64.5648	−	42.9053i	0.209626	−	0.139303i
$309$	302.216			0.978044
$310$		0			0
$311$	75.0288	+	43.3179i	0.241250	+	0.139286i	0.615751	−	0.787941i	$-0.288853\pi$
$311$	75.0288	+	43.3179i	0.241250	+	0.139286i	−0.374501	+	0.927226i	$0.622186\pi$
$312$	8.58383	−	14.8676i	0.0275123	−	0.0476527i
$313$	2.45782	−	1.41903i	0.00785247	−	0.00453363i	−0.496069	−	0.868283i	$-0.665224\pi$
$313$	2.45782	−	1.41903i	0.00785247	−	0.00453363i	0.503921	+	0.863750i	$0.331890\pi$
$314$		−	75.6613i		−	0.240960i
$315$		0			0
$316$	246.268			0.779329
$317$	154.925	+	268.338i	0.488723	+	0.846493i	0.999916	−	0.0129730i	$-0.00412956\pi$
$317$	154.925	+	268.338i	0.488723	+	0.846493i	−0.511193	+	0.859466i	$0.670796\pi$
$318$	−5.97767	−	3.45121i	−0.0187977	−	0.0108529i
$319$	−23.5988	+	40.8744i	−0.0739776	+	0.128133i
$320$		0			0
$321$		−	104.748i		−	0.326318i
$322$	105.788	+	52.5018i	0.328535	+	0.163049i
$323$	144.397			0.447050
$324$	−9.00000	−	15.5885i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	145.652	−	252.278i	0.446787	−	0.773857i
$327$	151.217	−	87.3052i	0.462437	−	0.266988i
$328$		−	8.88711i		−	0.0270948i
$329$	72.4895	+	109.084i	0.220333	+	0.331562i
$330$		0			0
$331$	208.295	+	360.777i	0.629289	+	1.08996i	0.987695	+	0.156394i	$0.0499871\pi$
$331$	208.295	+	360.777i	0.629289	+	1.08996i	−0.358406	+	0.933566i	$0.616680\pi$
$332$	155.160	+	89.5815i	0.467349	+	0.269824i
$333$	42.0801	−	72.8849i	0.126367	−	0.218874i
$334$	−168.948	+	97.5421i	−0.505832	+	0.292042i
$335$		0			0
$336$	−48.4014	+	3.04961i	−0.144052	+	0.00907622i
$337$	155.491			0.461399			0.230699	−	0.973025i	$-0.425899\pi$
$337$	155.491			0.461399			0.230699	+	0.973025i	$0.425899\pi$
$338$	−110.818	−	191.942i	−0.327862	−	0.567874i
$339$	−111.281	−	64.2483i	−0.328264	−	0.189523i
$340$		0			0
$341$	−36.9925	+	21.3576i	−0.108482	+	0.0626323i
$342$			75.2622i			0.220065i
$343$	64.3643	+	336.907i	0.187651	+	0.982236i
$344$	122.172			0.355151
$345$		0			0
$346$	270.138	+	155.964i	0.780744	+	0.450763i
$347$	256.253	−	443.844i	0.738482	−	1.27909i	−0.214697	−	0.976681i	$-0.568876\pi$
$347$	256.253	−	443.844i	0.738482	−	1.27909i	0.953179	−	0.302408i	$-0.0977904\pi$
$348$	25.5712	−	14.7636i	0.0734805	−	0.0424240i
$349$		−	269.185i		−	0.771305i	−0.922644	−	0.385652i	$-0.873976\pi$
$349$		−	269.185i		−	0.771305i	0.922644	−	0.385652i	$-0.126024\pi$
$350$		0			0
$351$	18.2091			0.0518777
$352$	15.6616	+	27.1266i	0.0444931	+	0.0770643i
$353$	−507.890	−	293.231i	−1.43878	−	0.830682i	−0.441018	−	0.897498i	$-0.645382\pi$
$353$	−507.890	−	293.231i	−1.43878	−	0.830682i	−0.997765	+	0.0668166i	$0.978716\pi$
$354$	−36.9976	+	64.0816i	−0.104513	+	0.181022i
$355$		0			0
$356$		−	236.229i		−	0.663566i
$357$	−82.1966	+	54.6221i	−0.230242	+	0.153003i
$358$	−103.662			−0.289559
$359$	−44.4221	−	76.9413i	−0.123738	−	0.214321i	0.797501	−	0.603318i	$-0.206155\pi$
$359$	−44.4221	−	76.9413i	−0.123738	−	0.214321i	−0.921239	+	0.388997i	$0.872822\pi$
$360$		0			0
$361$	−23.1554	+	40.1064i	−0.0641424	+	0.111098i
$362$	75.2751	−	43.4601i	0.207942	−	0.120056i
$363$			156.472i			0.431054i
$364$	21.8101	−	43.9462i	0.0599178	−	0.120731i
$365$		0			0
$366$	57.9963	+	100.452i	0.158460	+	0.274460i
$367$	611.446	+	353.019i	1.66607	+	0.961904i	0.969727	+	0.244191i	$0.0785222\pi$
$367$	611.446	+	353.019i	1.66607	+	0.961904i	0.696339	+	0.717713i	$0.254811\pi$
$368$	−23.8598	+	41.3264i	−0.0648365	+	0.112300i
$369$	8.16333	−	4.71310i	0.0221228	−	0.0127726i
$370$		0			0
$371$	−17.6690	−	8.76894i	−0.0476253	−	0.0236360i
$372$	26.7229			0.0718357
$373$	25.6211	+	44.3770i	0.0686892	+	0.118973i	0.898325	−	0.439332i	$-0.144785\pi$
$373$	25.6211	+	44.3770i	0.0686892	+	0.118973i	−0.829635	+	0.558306i	$0.811452\pi$
$374$	55.2018	+	31.8708i	0.147598	+	0.0852160i
$375$		0			0
$376$	−45.8311	+	26.4606i	−0.121891	+	0.0703740i
$377$			29.8701i			0.0792309i
$378$	−28.4700	−	42.8423i	−0.0753174	−	0.113339i
$379$	−194.724			−0.513784			−0.256892	−	0.966440i	$-0.582698\pi$
$379$	−194.724			−0.513784			−0.256892	+	0.966440i	$0.582698\pi$
$380$		0			0
$381$	−226.640	−	130.851i	−0.594855	−	0.343440i
$382$	254.461	−	440.740i	0.666129	−	1.15377i
$383$	454.732	−	262.540i	1.18729	−	0.685482i	0.229600	−	0.973285i	$-0.426258\pi$
$383$	454.732	−	262.540i	1.18729	−	0.685482i	0.957690	+	0.287803i	$0.0929249\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	197.629			0.511993
$387$	64.7915	+	112.222i	0.167420	+	0.289980i
$388$	112.924	+	65.1965i	0.291040	+	0.168032i
$389$	201.765	−	349.467i	0.518675	−	0.898372i	−0.481089	−	0.876672i	$-0.659759\pi$
$389$	201.765	−	349.467i	0.518675	−	0.898372i	0.999765	−	0.0217005i	$-0.00690803\pi$
$390$		0			0
$391$			97.1079i			0.248358i
$392$	−137.497	+	17.3955i	−0.350757	+	0.0443762i
$393$	−373.640			−0.950738
$394$	175.605	+	304.156i	0.445697	+	0.771971i
$395$		0			0
$396$	−16.6116	+	28.7721i	−0.0419485	+	0.0726569i
$397$	−139.596	+	80.5960i	−0.351628	+	0.203013i	−0.665402	−	0.746485i	$-0.731740\pi$
$397$	−139.596	+	80.5960i	−0.351628	+	0.203013i	0.313774	+	0.949498i	$0.398407\pi$
$398$			173.375i			0.435615i
$399$	13.5246	+	214.654i	0.0338963	+	0.537980i
$400$		0			0
$401$	212.506	+	368.071i	0.529940	+	0.917883i	0.999390	+	0.0349237i	$0.0111188\pi$
$401$	212.506	+	368.071i	0.529940	+	0.917883i	−0.469450	+	0.882959i	$0.655548\pi$
$402$	−13.9629	−	8.06147i	−0.0347335	−	0.0200534i
$403$	−13.5166	+	23.4115i	−0.0335400	+	0.0580930i
$404$	241.790	−	139.597i	0.598490	−	0.345538i
$405$		0			0
$406$	70.2782	−	46.7020i	0.173099	−	0.115030i
$407$	−155.337			−0.381664
$408$	−19.9385	−	34.5345i	−0.0488689	−	0.0846435i
$409$	373.605	+	215.701i	0.913460	+	0.527386i	0.881543	−	0.472104i	$-0.156505\pi$
$409$	373.605	+	215.701i	0.913460	+	0.527386i	0.0319171	+	0.999491i	$0.489839\pi$
$410$		0			0
$411$	200.461	−	115.736i	0.487739	−	0.281596i
$412$			348.969i			0.847011i
$413$	−94.0046	+	189.415i	−0.227614	+	0.458631i
$414$	−50.6143			−0.122257
$415$		0			0
$416$	17.1677	+	9.91176i	0.0412684	+	0.0238263i
$417$	167.803	−	290.643i	0.402405	−	0.696986i
$418$	120.303	−	69.4570i	0.287806	−	0.166165i
$419$			585.412i			1.39716i	0.715530	+	0.698582i	$0.246185\pi$
$419$			585.412i			1.39716i	−0.715530	+	0.698582i	$0.753815\pi$
$420$		0			0
$421$	400.267			0.950754			0.475377	−	0.879782i	$-0.342312\pi$
$421$	400.267			0.950754			0.475377	+	0.879782i	$0.342312\pi$
$422$	−249.488	−	432.126i	−0.591203	−	1.02399i
$423$	−48.6112	−	28.0657i	−0.114920	−	0.0663492i
$424$	3.98511	−	6.90241i	0.00939885	−	0.0162793i
$425$		0			0
$426$			239.499i			0.562204i
$427$	183.461	+	276.077i	0.429652	+	0.646550i
$428$	120.953			0.282600
$429$	−16.8045	−	29.1063i	−0.0391714	−	0.0678469i
$430$		0			0
$431$	−197.631	+	342.307i	−0.458541	+	0.794216i	−0.998884	−	0.0472289i	$-0.984961\pi$
$431$	−197.631	+	342.307i	−0.458541	+	0.794216i	0.540344	+	0.841445i	$0.318294\pi$
$432$	18.0000	−	10.3923i	0.0416667	−	0.0240563i
$433$		−	2.39222i		−	0.00552477i	−0.999996	−	0.00276238i	$-0.999121\pi$
$433$		−	2.39222i		−	0.00552477i	0.999996	−	0.00276238i	$-0.000879295\pi$
$434$	76.2158	−	4.80210i	0.175613	−	0.0110647i
$435$		0			0
$436$	100.811	+	174.610i	0.231219	+	0.400482i
$437$	183.277	+	105.815i	0.419399	+	0.242140i
$438$	74.9069	−	129.743i	0.171020	−	0.296216i
$439$	−350.264	+	202.225i	−0.797867	+	0.460649i	−0.842725	−	0.538345i	$-0.819050\pi$
$439$	−350.264	+	202.225i	−0.797867	+	0.460649i	0.0448578	+	0.998993i	$0.485717\pi$
$440$		0			0
$441$	−88.8975	−	117.074i	−0.201582	−	0.265473i
$442$	40.3402			0.0912674
$443$	−146.005	−	252.889i	−0.329583	−	0.570855i	0.652846	−	0.757491i	$-0.273575\pi$
$443$	−146.005	−	252.889i	−0.329583	−	0.570855i	−0.982429	+	0.186636i	$0.940242\pi$
$444$	84.1603	+	48.5899i	0.189550	+	0.109437i
$445$		0			0
$446$	75.6182	−	43.6582i	0.169547	−	0.0978883i
$447$		−	114.326i		−	0.255764i
$448$	−3.52139	−	55.8892i	−0.00786024	−	0.124753i
$449$	125.680			0.279911			0.139956	−	0.990158i	$-0.455304\pi$
$449$	125.680			0.279911			0.139956	+	0.990158i	$0.455304\pi$
$450$		0			0
$451$	−15.0673	−	8.69913i	−0.0334087	−	0.0192885i
$452$	74.1876	−	128.497i	0.164132	−	0.284285i
$453$	−52.3229	+	30.2087i	−0.115503	+	0.0666858i
$454$		−	296.310i		−	0.652666i
$455$		0			0
$456$	−86.9054			−0.190582
$457$	−43.0015	−	74.4808i	−0.0940952	−	0.162978i	0.815135	−	0.579270i	$-0.196662\pi$
$457$	−43.0015	−	74.4808i	−0.0940952	−	0.162978i	−0.909231	+	0.416293i	$0.863329\pi$
$458$	132.026	+	76.2255i	0.288267	+	0.166431i
$459$	21.1480	−	36.6294i	0.0460741	−	0.0798027i
$460$		0			0
$461$		−	131.449i		−	0.285138i	−0.989785	−	0.142569i	$-0.954464\pi$
$461$		−	131.449i		−	0.285138i	0.989785	−	0.142569i	$-0.0455362\pi$
$462$	−42.2073	+	85.0456i	−0.0913578	+	0.184081i
$463$	73.9873			0.159800			0.0798999	−	0.996803i	$-0.474540\pi$
$463$	73.9873			0.159800			0.0798999	+	0.996803i	$0.474540\pi$
$464$	17.0475	+	29.5271i	0.0367403	+	0.0636360i
$465$		0			0
$466$	−231.115	+	400.303i	−0.495956	+	0.859020i
$467$	−387.032	+	223.453i	−0.828762	+	0.478486i	−0.853429	−	0.521210i	$-0.825481\pi$
$467$	−387.032	+	223.453i	−0.828762	+	0.478486i	0.0246667	+	0.999696i	$0.492148\pi$
$468$			21.0260i			0.0449274i
$469$	−41.2719	−	20.4829i	−0.0879999	−	0.0436735i
$470$		0			0
$471$	46.3329	+	80.2509i	0.0983713	+	0.170384i
$472$	−73.9951	−	42.7211i	−0.156769	−	0.0905108i
$473$	119.588	−	207.132i	0.252828	−	0.437912i
$474$	−261.207	+	150.808i	−0.551069	+	0.318160i
$475$		0			0
$476$	−63.0722	−	94.9124i	−0.132505	−	0.199396i
$477$	8.45370			0.0177226
$478$	6.50621	+	11.2691i	0.0136113	+	0.0235755i
$479$	513.818	+	296.653i	1.07269	+	0.619318i	0.928915	−	0.370293i	$-0.120743\pi$
$479$	513.818	+	296.653i	1.07269	+	0.619318i	0.143775	+	0.989610i	$0.454076\pi$
$480$		0			0
$481$	−85.1377	+	49.1543i	−0.177002	+	0.102192i
$482$		−	454.226i		−	0.942378i
$483$	−144.356	+	9.09539i	−0.298874	+	0.0188310i
$484$	−180.679			−0.373303
$485$		0			0
$486$	19.0919	+	11.0227i	0.0392837	+	0.0226805i
$487$	409.771	−	709.744i	0.841418	−	1.45738i	−0.0472773	−	0.998882i	$-0.515054\pi$
$487$	409.771	−	709.744i	0.841418	−	1.45738i	0.888696	−	0.458498i	$-0.151612\pi$
$488$	−115.993	+	66.9683i	−0.237690	+	0.137230i
$489$			356.774i			0.729600i
$490$		0			0
$491$	554.724			1.12978			0.564892	−	0.825165i	$-0.308918\pi$
$491$	554.724			1.12978			0.564892	+	0.825165i	$0.308918\pi$
$492$	5.44222	+	9.42620i	0.0110614	+	0.0191589i
$493$	60.0867	+	34.6911i	0.121880	+	0.0703673i
$494$	43.9574	−	76.1364i	0.0889825	−	0.154122i
$495$		0			0
$496$			30.8569i			0.0622115i
$497$	43.0380	+	683.071i	0.0865955	+	1.37439i
$498$	−219.429			−0.440620
$499$	−317.394	−	549.742i	−0.636060	−	1.10169i	−0.986290	−	0.165024i	$-0.947230\pi$
$499$	−317.394	−	549.742i	−0.636060	−	1.10169i	0.350230	−	0.936664i	$-0.386103\pi$
$500$		0			0
$501$	119.464	−	206.918i	0.238451	−	0.413010i
$502$	−23.5634	+	13.6043i	−0.0469390	+	0.0271003i
$503$			120.116i			0.238800i	0.992846	+	0.119400i	$0.0380970\pi$
$503$			120.116i			0.238800i	−0.992846	+	0.119400i	$0.961903\pi$
$504$	49.4700	−	32.8743i	0.0981547	−	0.0652268i
$505$		0			0
$506$	46.7103	+	80.9046i	0.0923128	+	0.159890i
$507$	235.079	+	135.723i	0.463668	+	0.267699i
$508$	151.093	−	261.701i	0.297428	−	0.515160i
$509$	51.1082	−	29.5073i	0.100409	−	0.0579712i	−0.448955	−	0.893555i	$-0.648204\pi$
$509$	51.1082	−	29.5073i	0.100409	−	0.0579712i	0.549364	+	0.835583i	$0.314870\pi$
$510$		0			0
$511$	190.326	−	383.497i	0.372458	−	0.750484i
$512$	22.6274			0.0441942
$513$	−46.0885	−	79.8277i	−0.0898412	−	0.155609i
$514$	158.509	+	91.5150i	0.308383	+	0.178045i
$515$		0			0
$516$	−129.583	+	74.8148i	−0.251130	+	0.144990i
$517$			103.604i			0.200394i
$518$	248.764	+	123.459i	0.480239	+	0.238338i
$519$	−382.032			−0.736093
$520$		0			0
$521$	−841.241	−	485.691i	−1.61467	−	0.932228i	−0.988269	−	0.152725i	$-0.951195\pi$
$521$	−841.241	−	485.691i	−1.61467	−	0.932228i	−0.626398	−	0.779504i	$-0.715471\pi$
$522$	−18.0816	+	31.3182i	−0.0346391	+	0.0599966i
$523$	598.739	−	345.682i	1.14482	−	0.660960i	0.197197	−	0.980364i	$-0.436816\pi$
$523$	598.739	−	345.682i	1.14482	−	0.660960i	0.947619	+	0.319404i	$0.103483\pi$
$524$		−	431.442i		−	0.823363i
$525$		0			0
$526$	−236.068			−0.448798
$527$	31.3964	+	54.3802i	0.0595757	+	0.103188i
$528$	−33.2232	−	19.1814i	−0.0629227	−	0.0363285i
$529$	193.339	−	334.872i	0.365479	−	0.633029i
$530$		0			0
$531$		−	90.6251i		−	0.170669i
$532$	−247.861	+	15.6169i	−0.465905	+	0.0293551i
$533$	−11.0109			−0.0206583
$534$	144.660	+	250.559i	0.270900	+	0.469212i
$535$		0			0
$536$	9.30859	−	16.1229i	0.0173668	−	0.0300801i
$537$	109.950	−	63.4798i	0.204749	−	0.118212i
$538$		−	295.703i		−	0.549635i
$539$	−105.096	+	250.142i	−0.194983	+	0.464085i
$540$		0			0
$541$	−270.888	−	469.192i	−0.500717	−	0.867267i	−1.00000		0.000828025i	$-0.999736\pi$
$541$	−270.888	−	469.192i	−0.500717	−	0.867267i	0.499283	−	0.866439i	$-0.333597\pi$
$542$	−173.989	−	100.453i	−0.321013	−	0.185337i
$543$	−53.2275	+	92.1928i	−0.0980249	+	0.169784i
$544$	39.8771	−	23.0230i	0.0733034	−	0.0423217i
$545$		0			0
$546$	3.77837	+	59.9679i	0.00692010	+	0.109831i
$547$	−318.491			−0.582251			−0.291126	−	0.956685i	$-0.594030\pi$
$547$	−318.491			−0.582251			−0.291126	+	0.956685i	$0.594030\pi$
$548$	133.641	+	231.472i	0.243870	+	0.422395i
$549$	−123.029	−	71.0306i	−0.224096	−	0.129382i
$550$		0			0
$551$	130.949	−	75.6034i	0.237657	−	0.137211i
$552$		−	58.4444i		−	0.105877i
$553$	−717.883	+	477.055i	−1.29816	+	0.862667i
$554$	−630.628			−1.13832
$555$		0			0
$556$	335.606	+	193.762i	0.603607	+	0.348493i
$557$	−288.479	+	499.660i	−0.517915	+	0.897055i	0.481869	+	0.876244i	$0.339958\pi$
$557$	−288.479	+	499.660i	−0.517915	+	0.897055i	−0.999783	+	0.0208114i	$0.993375\pi$
$558$	−28.3439	+	16.3643i	−0.0507955	+	0.0293268i
$559$		−	151.367i		−	0.270783i
$560$		0			0
$561$	−78.0672			−0.139157
$562$	−340.834	−	590.342i	−0.606466	−	1.05043i
$563$	308.279	+	177.985i	0.547565	+	0.316137i	0.748139	−	0.663542i	$-0.230947\pi$
$563$	308.279	+	177.985i	0.547565	+	0.316137i	−0.200574	+	0.979678i	$0.564281\pi$
$564$	32.4075	−	56.1314i	0.0574601	−	0.0995238i
$565$		0			0
$566$		−	306.196i		−	0.540983i
$567$	56.4324	+	28.0068i	0.0995281	+	0.0493948i
$568$	−276.550			−0.486883
$569$	186.085	+	322.308i	0.327038	+	0.566447i	0.981923	−	0.189282i	$-0.0606161\pi$
$569$	186.085	+	322.308i	0.327038	+	0.566447i	−0.654885	+	0.755729i	$0.727283\pi$
$570$		0			0
$571$	82.9355	−	143.649i	0.145246	−	0.251574i	−0.784219	−	0.620485i	$-0.786936\pi$
$571$	82.9355	−	143.649i	0.145246	−	0.251574i	0.929465	+	0.368911i	$0.120269\pi$
$572$	33.6091	−	19.4042i	0.0587571	−	0.0339234i
$573$			623.300i			1.08778i
$574$	17.2155	+	25.9063i	0.0299922	+	0.0451330i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	13.9714	+	8.06639i	0.0242139	+	0.0139799i	0.512058	−	0.858951i	$-0.328883\pi$
$577$	13.9714	+	8.06639i	0.0242139	+	0.0139799i	−0.487844	+	0.872931i	$0.662217\pi$
$578$	−157.503	+	272.803i	−0.272496	+	0.471977i
$579$	−209.617	+	121.023i	−0.362033	+	0.209020i
$580$		0			0
$581$	−625.830	+	39.4314i	−1.07716	+	0.0678681i
$582$	−159.698			−0.274395
$583$	−7.80164	−	13.5128i	−0.0133819	−	0.0231781i
$584$	149.814	+	86.4950i	0.256530	+	0.148108i
$585$		0			0
$586$	−469.940	+	271.320i	−0.801945	+	0.463003i
$587$			204.516i			0.348409i	0.984709	+	0.174205i	$0.0557354\pi$
$587$			204.516i			0.348409i	−0.984709	+	0.174205i	$0.944265\pi$
$588$	135.185	−	102.650i	0.229906	−	0.174575i
$589$	136.846			0.232337
$590$		0			0
$591$	−372.514	−	215.071i	−0.630311	−	0.363910i
$592$	−56.1068	+	97.1799i	−0.0947751	+	0.164155i
$593$	−597.577	+	345.011i	−1.00772	+	0.581806i	−0.910523	−	0.413459i	$-0.864320\pi$
$593$	−597.577	+	345.011i	−1.00772	+	0.581806i	−0.0971952	+	0.995265i	$0.530987\pi$
$594$		−	40.6899i		−	0.0685016i
$595$		0			0
$596$	132.013			0.221498
$597$	−106.170	−	183.892i	−0.177839	−	0.308026i
$598$	51.2022	+	29.5616i	0.0856224	+	0.0494341i
$599$	477.775	−	827.531i	0.797622	−	1.38152i	−0.123539	−	0.992340i	$-0.539425\pi$
$599$	477.775	−	827.531i	0.797622	−	1.38152i	0.921161	−	0.389182i	$-0.127242\pi$
$600$		0			0
$601$			587.954i			0.978293i	0.872202	+	0.489146i	$0.162692\pi$
$601$			587.954i			0.978293i	−0.872202	+	0.489146i	$0.837308\pi$
$602$	−356.137	+	236.664i	−0.591590	+	0.393130i
$603$	19.7465			0.0327471
$604$	−34.8820	−	60.4173i	−0.0577516	−	0.100029i
$605$		0			0
$606$	−170.971	+	296.131i	−0.282131	+	0.488665i
$607$	−449.438	+	259.483i	−0.740425	+	0.427485i	−0.822224	−	0.569164i	$-0.807267\pi$
$607$	−449.438	+	259.483i	−0.740425	+	0.427485i	0.0817986	+	0.996649i	$0.473934\pi$
$608$		−	100.350i		−	0.165049i
$609$	−45.9423	+	92.5714i	−0.0754389	+	0.152006i
$610$		0			0
$611$	32.7839	+	56.7834i	0.0536561	+	0.0929351i
$612$	42.2960	+	24.4196i	0.0691111	+	0.0399013i
$613$	63.7771	−	110.465i	0.104041	−	0.180204i	−0.809305	−	0.587389i	$-0.800156\pi$
$613$	63.7771	−	110.465i	0.104041	−	0.180204i	0.913346	+	0.407184i	$0.133489\pi$
$614$	−25.8744	+	14.9386i	−0.0421407	+	0.0243300i
$615$		0			0
$616$	−98.2022	−	48.7368i	−0.159419	−	0.0791182i
$617$	−486.581			−0.788624			−0.394312	−	0.918977i	$-0.629017\pi$
$617$	−486.581			−0.788624			−0.394312	+	0.918977i	$0.629017\pi$
$618$	−213.699	−	370.137i	−0.345791	−	0.598927i
$619$	370.662	+	214.002i	0.598808	+	0.345722i	0.768572	−	0.639763i	$-0.220967\pi$
$619$	370.662	+	214.002i	0.598808	+	0.345722i	−0.169765	+	0.985485i	$0.554301\pi$
$620$		0			0
$621$	53.6846	−	30.9948i	0.0864486	−	0.0499111i
$622$		−	122.522i		−	0.196980i
$623$	457.609	+	688.620i	0.734524	+	1.10533i
$624$	−24.2787			−0.0389082
$625$		0			0
$626$	−3.47589	−	2.00680i	−0.00555254	−	0.00320576i
$627$	−85.0671	+	147.341i	−0.135673	+	0.234993i
$628$	−92.6658	+	53.5006i	−0.147557	+	0.0851921i
$629$			228.351i			0.363038i
$630$		0			0
$631$	−64.4987			−0.102217			−0.0511083	−	0.998693i	$-0.516275\pi$
$631$	−64.4987			−0.102217			−0.0511083	+	0.998693i	$0.516275\pi$
$632$	−174.138	−	301.616i	−0.275535	−	0.477240i
$633$	529.244	+	305.559i	0.836088	+	0.482716i
$634$	219.097	−	379.488i	0.345579	−	0.598561i
$635$		0			0
$636$			9.76149i			0.0153483i
$637$	21.5525	+	170.354i	0.0338343	+	0.267432i
$638$	66.7476			0.104620
$639$	−146.663	−	254.027i	−0.229519	−	0.397538i
$640$		0			0
$641$	−352.662	+	610.829i	−0.550175	+	0.952932i	0.448086	+	0.893990i	$0.352106\pi$
$641$	−352.662	+	610.829i	−0.550175	+	0.952932i	−0.998261	+	0.0589413i	$0.981228\pi$
$642$	−128.290	+	74.0681i	−0.199828	+	0.115371i
$643$			1092.83i			1.69958i	0.527124	+	0.849788i	$0.323270\pi$
$643$			1092.83i			1.69958i	−0.527124	+	0.849788i	$0.676730\pi$
$644$	−10.5025	−	166.688i	−0.0163082	−	0.258833i
$645$		0			0
$646$	−102.104	−	176.850i	−0.158056	−	0.273761i
$647$	446.083	+	257.546i	0.689463	+	0.398062i	0.803411	−	0.595425i	$-0.203016\pi$
$647$	446.083	+	257.546i	0.689463	+	0.398062i	−0.113948	+	0.993487i	$0.536350\pi$
$648$	−12.7279	+	22.0454i	−0.0196419	+	0.0340207i
$649$	−144.860	+	83.6349i	−0.223205	+	0.128867i
$650$		0			0
$651$	−77.8984	+	51.7659i	−0.119660	+	0.0795175i
$652$	−411.967			−0.631852
$653$	−393.317	−	681.245i	−0.602323	−	1.04325i	−0.992468	−	0.122501i	$-0.960909\pi$
$653$	−393.317	−	681.245i	−0.602323	−	1.04325i	0.390145	−	0.920753i	$-0.372425\pi$
$654$	−213.853	−	123.468i	−0.326993	−	0.188789i
$655$		0			0
$656$	−10.8844	+	6.28413i	−0.0165921	+	0.00957947i
$657$			183.484i			0.279275i
$658$	82.3420	−	165.915i	0.125140	−	0.252151i
$659$	−819.425			−1.24344			−0.621719	−	0.783241i	$-0.713565\pi$
$659$	−819.425			−1.24344			−0.621719	+	0.783241i	$0.713565\pi$
$660$		0			0
$661$	−889.453	−	513.526i	−1.34562	−	0.776892i	−0.357991	−	0.933725i	$-0.616538\pi$
$661$	−889.453	−	513.526i	−1.34562	−	0.776892i	−0.987625	+	0.156833i	$0.949872\pi$
$662$	294.573	−	510.216i	0.444974	−	0.770718i
$663$	−42.7873	+	24.7032i	−0.0645358	+	0.0372598i
$664$		−	253.375i		−	0.381589i
$665$		0			0
$666$	−119.021			−0.178710
$667$	50.8437	+	88.0639i	0.0762275	+	0.132030i
$668$	238.928	+	137.945i	0.357677	+	0.206505i
$669$	−53.4701	+	92.6130i	−0.0799254	+	0.138435i
$670$		0			0
$671$			262.207i			0.390771i
$672$	37.9600	+	57.1230i	0.0564881	+	0.0850045i
$673$	−669.779			−0.995213			−0.497607	−	0.867403i	$-0.665788\pi$
$673$	−669.779			−0.995213			−0.497607	+	0.867403i	$0.665788\pi$
$674$	−109.949	−	190.437i	−0.163129	−	0.282548i
$675$		0			0
$676$	−156.720	+	271.446i	−0.231834	+	0.401548i
$677$	−786.522	+	454.099i	−1.16178	+	0.670751i	−0.951729	−	0.306940i	$-0.900695\pi$
$677$	−786.522	+	454.099i	−1.16178	+	0.670751i	−0.210047	+	0.977691i	$0.567362\pi$
$678$			181.722i			0.268026i
$679$	−455.472	+	28.6977i	−0.670798	+	0.0422647i
$680$		0			0
$681$	181.452	+	314.285i	0.266450	+	0.461505i
$682$	52.3153	+	30.2042i	0.0767086	+	0.0442877i
$683$	330.668	−	572.733i	0.484140	−	0.838555i	−0.515694	−	0.856773i	$-0.672466\pi$
$683$	330.668	−	572.733i	0.484140	−	0.838555i	0.999834	+	0.0182177i	$0.00579920\pi$
$684$	92.1770	−	53.2184i	0.134762	−	0.0778047i
$685$		0			0
$686$	367.112	−	317.059i	0.535149	−	0.462185i
$687$	−186.714			−0.271781
$688$	−86.3887	−	149.630i	−0.125565	−	0.217485i
$689$	−8.55188	−	4.93743i	−0.0124120	−	0.00716608i
$690$		0			0
$691$	−239.610	+	138.339i	−0.346759	+	0.200201i	−0.663257	−	0.748392i	$-0.730826\pi$
$691$	−239.610	+	138.339i	−0.346759	+	0.200201i	0.316498	+	0.948593i	$0.397493\pi$
$692$		−	441.133i		−	0.637475i
$693$	−7.31198	−	116.051i	−0.0105512	−	0.167462i
$694$	−724.794			−1.04437
$695$		0			0
$696$	−36.1632	−	20.8788i	−0.0519586	−	0.0299983i
$697$	−12.7880	+	22.1495i	−0.0183472	+	0.0317783i
$698$	−329.683	+	190.343i	−0.472326	+	0.272697i
$699$		−	566.115i		−	0.809892i
$700$		0			0
$701$	−415.967			−0.593391			−0.296696	−	0.954972i	$-0.595885\pi$
$701$	−415.967			−0.593391			−0.296696	+	0.954972i	$0.595885\pi$
$702$	−12.8758	−	22.3015i	−0.0183415	−	0.0317685i
$703$	430.980	+	248.827i	0.613059	+	0.353950i
$704$	22.1488	−	38.3629i	0.0314614	−	0.0544927i
$705$		0			0
$706$			829.382i			1.17476i
$707$	−434.409	+	875.313i	−0.614440	+	1.23807i
$708$	104.645			0.147804
$709$	−136.620	−	236.632i	−0.192693	−	0.333755i	0.753449	−	0.657507i	$-0.228389\pi$
$709$	−136.620	−	236.632i	−0.192693	−	0.333755i	−0.946142	+	0.323752i	$0.895056\pi$
$710$		0			0
$711$	184.701	−	319.912i	0.259776	−	0.449946i
$712$	−289.321	+	167.039i	−0.406349	+	0.234606i
$713$			92.0300i			0.129074i
$714$	125.020	+	62.0462i	0.175098	+	0.0868994i
$715$		0			0
$716$	73.3002	+	126.960i	0.102375	+	0.177318i
$717$	−13.8018	−	7.96845i	−0.0192493	−	0.0111136i
$718$	−62.8223	+	108.811i	−0.0874962	+	0.151548i
$719$	361.463	−	208.691i	0.502731	−	0.290252i	−0.227110	−	0.973869i	$-0.572928\pi$
$719$	361.463	−	208.691i	0.502731	−	0.290252i	0.729840	+	0.683617i	$0.239594\pi$
$720$		0			0
$721$	−676.000	−	1017.26i	−0.937587	−	1.41090i
$722$	65.4934			0.0907111
$723$	278.156	+	481.779i	0.384724	+	0.666362i
$724$	−106.455	−	61.4619i	−0.147037	−	0.0848921i
$725$		0			0
$726$	191.639	−	110.643i	0.263965	−	0.152400i
$727$		−	357.267i		−	0.491426i	−0.969343	−	0.245713i	$-0.920978\pi$
$727$		−	357.267i		−	0.491426i	0.969343	−	0.245713i	$-0.0790221\pi$
$728$	−69.2450	+	4.36289i	−0.0951167	+	0.00599298i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−304.491	−	175.798i	−0.416541	−	0.240490i
$732$	82.0191	−	142.061i	0.112048	−	0.194073i
$733$	373.293	−	215.521i	0.509267	−	0.294026i	−0.223265	−	0.974758i	$-0.571672\pi$
$733$	373.293	−	215.521i	0.509267	−	0.294026i	0.732532	+	0.680732i	$0.238338\pi$
$734$		−	998.488i		−	1.36034i
$735$		0			0
$736$	67.4858			0.0916926
$737$	−18.2234	−	31.5638i	−0.0247264	−	0.0428274i
$738$	−11.5447	−	6.66533i	−0.0156432	−	0.00903161i
$739$	−159.512	+	276.282i	−0.215848	+	0.373860i	−0.953535	−	0.301284i	$-0.902585\pi$
$739$	−159.512	+	276.282i	−0.215848	+	0.373860i	0.737687	+	0.675143i	$0.235918\pi$
$740$		0			0
$741$			107.673i			0.145308i
$742$	1.75414	+	27.8406i	0.00236407	+	0.0375210i
$743$	1303.33			1.75414			0.877072	−	0.480360i	$-0.159494\pi$
$743$	1303.33			1.75414			0.877072	+	0.480360i	$0.159494\pi$
$744$	−18.8959	−	32.7287i	−0.0253977	−	0.0439902i
$745$		0			0
$746$	36.2337	−	62.7585i	0.0485706	−	0.0841267i
$747$	232.740	−	134.372i	0.311566	−	0.179883i
$748$		−	90.1442i		−	0.120514i
$749$	−352.583	+	234.302i	−0.470738	+	0.312820i
$750$		0			0
$751$	−614.473	−	1064.30i	−0.818206	−	1.41717i	−0.907003	−	0.421124i	$-0.861636\pi$
$751$	−614.473	−	1064.30i	−0.818206	−	1.41717i	0.0887971	−	0.996050i	$-0.471698\pi$
$752$	64.8150	+	37.4210i	0.0861901	+	0.0497619i
$753$	16.6618	−	28.8591i	0.0221273	−	0.0383255i
$754$	36.5832	−	21.1213i	0.0485188	−	0.0280124i
$755$		0			0
$756$	−32.3395	+	65.1625i	−0.0427771	+	0.0861938i
$757$	−1206.22			−1.59342			−0.796712	−	0.604359i	$-0.793429\pi$
$757$	−1206.22			−1.59342			−0.796712	+	0.604359i	$0.793429\pi$
$758$	137.691	+	238.487i	0.181650	+	0.314627i
$759$	−99.0874	−	57.2082i	−0.130550	−	0.0753731i
$760$		0			0
$761$	−204.456	+	118.043i	−0.268667	+	0.155115i	−0.628282	−	0.777986i	$-0.716242\pi$
$761$	−204.456	+	118.043i	−0.268667	+	0.155115i	0.359614	+	0.933101i	$0.382908\pi$
$762$			370.101i			0.485697i
$763$	−632.114	−	313.712i	−0.828459	−	0.411156i
$764$	−719.725			−0.942048
$765$		0			0
$766$	−643.088	−	371.287i	−0.839540	−	0.484709i
$767$	−52.9301	+	91.6777i	−0.0690093	+	0.119528i
$768$	−24.0000	+	13.8564i	−0.0312500	+	0.0180422i
$769$			1341.44i			1.74440i	0.489149	+	0.872200i	$0.337307\pi$
$769$			1341.44i			1.74440i	−0.489149	+	0.872200i	$0.662693\pi$
$770$		0			0
$771$	−224.165			−0.290746
$772$	−139.745	−	242.045i	−0.181017	−	0.313530i
$773$	155.933	+	90.0279i	0.201724	+	0.116466i	0.597460	−	0.801899i	$-0.296177\pi$
$773$	155.933	+	90.0279i	0.201724	+	0.116466i	−0.395735	+	0.918365i	$0.629510\pi$
$774$	91.6290	−	158.706i	0.118384	−	0.205047i
$775$		0			0
$776$		−	184.403i		−	0.237633i
$777$	−339.456	+	21.3880i	−0.436881	+	0.0275264i
$778$	−570.677			−0.733518
$779$	27.8693	+	48.2711i	0.0357758	+	0.0619654i
$780$		0			0
$781$	−270.700	+	468.866i	−0.346607	+	0.600341i
$782$	118.932	−	68.6657i	0.152087	−	0.0878078i
$783$		−	44.2907i		−	0.0565654i
$784$	118.530	+	156.098i	0.151186	+	0.199105i
$785$		0			0
$786$	264.203	+	457.614i	0.336137	+	0.582206i
$787$	1012.19	+	584.386i	1.28613	+	0.742549i	0.977962	−	0.208783i	$-0.0669501\pi$
$787$	1012.19	+	584.386i	1.28613	+	0.742549i	0.308170	+	0.951331i	$0.400283\pi$
$788$	248.343	−	430.142i	0.315156	−	0.545866i
$789$	250.387	−	144.561i	0.317348	−	0.183221i
$790$		0			0
$791$	32.6554	+	518.285i	0.0412837	+	0.655228i
$792$	46.9847			0.0593241
$793$	82.9717	+	143.711i	0.104630	+	0.181225i
$794$	197.419	+	113.980i	0.248639	+	0.143552i
$795$		0			0
$796$	212.340	−	122.595i	0.266759	−	0.154013i
$797$		−	1242.38i		−	1.55883i	−0.626510	−	0.779413i	$-0.715517\pi$
$797$		−	1242.38i		−	1.55883i	0.626510	−	0.779413i	$-0.284483\pi$
$798$	253.333	−	168.348i	0.317460	−	0.210962i
$799$	152.301			0.190614
$800$		0			0
$801$	−306.871	−	177.172i	−0.383110	−	0.221189i
$802$	300.529	−	520.531i	0.374724	−	0.649041i
$803$	293.290	−	169.331i	0.365243	−	0.210873i
$804$			22.8013i			0.0283598i
$805$		0			0
$806$	38.2308			0.0474327
$807$	181.081	+	313.641i	0.224387	+	0.388650i
$808$	−341.942	−	197.421i	−0.423196	−	0.244332i
$809$	44.8275	−	77.6435i	0.0554110	−	0.0959747i	−0.836989	−	0.547219i	$-0.815686\pi$
$809$	44.8275	−	77.6435i	0.0554110	−	0.0959747i	0.892400	+	0.451244i	$0.149020\pi$
$810$		0			0
$811$		−	234.127i		−	0.288689i	−0.989527	−	0.144345i	$-0.953893\pi$
$811$		−	234.127i		−	0.288689i	0.989527	−	0.144345i	$-0.0461074\pi$
$812$	−106.892	−	53.0496i	−0.131641	−	0.0653320i
$813$	246.058			0.302654
$814$	109.840	+	190.249i	0.134939	+	0.233721i
$815$		0			0
$816$	−28.1973	+	48.8392i	−0.0345556	+	0.0598520i
$817$	−663.588	+	383.123i	−0.812225	+	0.468938i
$818$		−	610.095i		−	0.745837i
$819$	−40.7303	−	61.2918i	−0.0497317	−	0.0748374i
$820$		0			0
$821$	−331.873	−	574.821i	−0.404231	−	0.700148i	0.590001	−	0.807403i	$-0.299127\pi$
$821$	−331.873	−	574.821i	−0.404231	−	0.700148i	−0.994232	+	0.107255i	$0.965794\pi$
$822$	−283.494	−	163.676i	−0.344884	−	0.199119i
$823$	430.147	−	745.037i	0.522657	−	0.905269i	−0.476995	−	0.878906i	$-0.658274\pi$
$823$	430.147	−	745.037i	0.522657	−	0.905269i	0.999652	−	0.0263632i	$-0.00839264\pi$
$824$	427.398	−	246.758i	0.518686	−	0.299464i
$825$		0			0
$826$	298.456	−	18.8047i	0.361327	−	0.0227660i
$827$	−703.661			−0.850860			−0.425430	−	0.904991i	$-0.639877\pi$
$827$	−703.661			−0.850860			−0.425430	+	0.904991i	$0.639877\pi$
$828$	35.7897	+	61.9896i	0.0432243	+	0.0748667i
$829$	1282.06	+	740.196i	1.54651	+	0.892878i	0.998404	+	0.0564693i	$0.0179843\pi$
$829$	1282.06	+	740.196i	1.54651	+	0.892878i	0.548106	+	0.836409i	$0.315349\pi$
$830$		0			0
$831$	668.882	−	386.179i	0.804912	−	0.464716i
$832$		−	28.0347i		−	0.0336955i
$833$	367.717	+	154.495i	0.441437	+	0.185468i
$834$	−474.618			−0.569086
$835$		0			0
$836$	−170.134	−	98.2271i	−0.203510	−	0.117496i
$837$	20.0422	−	34.7140i	0.0239452	−	0.0414743i
$838$	716.980	−	413.949i	0.855585	−	0.493972i
$839$			1377.82i			1.64222i	0.570769	+	0.821111i	$0.306645\pi$
$839$			1377.82i			1.64222i	−0.570769	+	0.821111i	$0.693355\pi$
$840$		0			0
$841$	−768.346			−0.913610
$842$	−283.032	−	490.225i	−0.336142	−	0.582215i
$843$	723.018	+	417.435i	0.857672	+	0.495177i
$844$	−352.829	+	611.118i	−0.418044	+	0.724073i
$845$		0			0
$846$			79.3818i			0.0938319i
$847$	526.687	−	350.000i	0.621827	−	0.413223i
$848$	−11.2716			−0.0132920
$849$	187.506	+	324.770i	0.220855	+	0.382533i
$850$		0			0
$851$	−167.337	+	289.837i	−0.196636	+	0.340584i
$852$	293.325	−	169.351i	0.344278	−	0.198769i
$853$		−	383.511i		−	0.449602i	−0.974405	−	0.224801i	$-0.927827\pi$
$853$		−	383.511i		−	0.449602i	0.974405	−	0.224801i	$-0.0721733\pi$
$854$	208.397	−	419.909i	0.244024	−	0.491697i
$855$		0			0
$856$	−85.5265	−	148.136i	−0.0999141	−	0.173056i
$857$	284.273	+	164.125i	0.331708	+	0.191512i	0.656599	−	0.754240i	$-0.271994\pi$
$857$	284.273	+	164.125i	0.331708	+	0.191512i	−0.324891	+	0.945751i	$0.605328\pi$
$858$	−23.7652	+	41.1625i	−0.0276984	+	0.0479750i
$859$	−168.842	+	97.4811i	−0.196557	+	0.113482i	−0.595048	−	0.803690i	$-0.702867\pi$
$859$	−168.842	+	97.4811i	−0.196557	+	0.113482i	0.398492	+	0.917172i	$0.369534\pi$
$860$		0			0
$861$	−34.1242	−	16.9355i	−0.0396332	−	0.0196696i
$862$	558.985			0.648474
$863$	267.881	+	463.984i	0.310407	+	0.537641i	0.978451	−	0.206481i	$-0.0662013\pi$
$863$	267.881	+	463.984i	0.310407	+	0.537641i	−0.668043	+	0.744122i	$0.732868\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$		0			0
$866$	−2.92986	+	1.69156i	−0.00338321	+	0.00195330i
$867$		−	385.801i		−	0.444984i
$868$	−59.7741	−	89.9493i	−0.0688641	−	0.103628i
$869$	−681.818			−0.784601
$870$		0			0
$871$	−19.9758	−	11.5331i	−0.0229344	−	0.0132412i
$872$	142.569	−	246.936i	0.163496	−	0.283184i
$873$	169.385	−	97.7947i	0.194027	−	0.112021i
$874$		−	299.291i		−	0.342438i
$875$		0			0
$876$	−211.869			−0.241859
$877$	−603.606	−	1045.48i	−0.688262	−	1.19210i	−0.972400	−	0.233321i	$-0.925041\pi$
$877$	−603.606	−	1045.48i	−0.688262	−	1.19210i	0.284138	−	0.958784i	$-0.408293\pi$
$878$	495.348	+	285.989i	0.564177	+	0.325728i
$879$	332.298	−	575.557i	0.378041	−	0.654786i
$880$		0			0
$881$			629.491i			0.714519i	0.934005	+	0.357259i	$0.116289\pi$
$881$			629.491i			0.714519i	−0.934005	+	0.357259i	$0.883711\pi$
$882$	−80.5253	+	191.660i	−0.0912985	+	0.217302i
$883$	177.196			0.200675			0.100337	−	0.994953i	$-0.468008\pi$
$883$	177.196			0.200675			0.100337	+	0.994953i	$0.468008\pi$
$884$	−28.5248	−	49.4065i	−0.0322679	−	0.0558897i
$885$		0			0
$886$	−206.483	+	357.639i	−0.233051	+	0.403655i
$887$	1101.94	−	636.205i	1.24232	−	0.717255i	0.272755	−	0.962083i	$-0.412065\pi$
$887$	1101.94	−	636.205i	1.24232	−	0.717255i	0.969566	+	0.244829i	$0.0787317\pi$
$888$		−	137.433i		−	0.154767i
$889$	66.5072	+	1055.56i	0.0748112	+	1.18736i
$890$		0			0
$891$	24.9174	+	43.1582i	0.0279657	+	0.0484379i
$892$	−106.940	−	61.7420i	−0.119888	−	0.0692175i
$893$	165.957	−	287.446i	0.185842	−	0.321888i
$894$	−140.021	+	80.8410i	−0.156623	+	0.0904261i
$895$		0			0
$896$	−65.9600	+	43.8324i	−0.0736161	+	0.0489201i
$897$	−72.4108			−0.0807255
$898$	−88.8693	−	153.926i	−0.0989636	−	0.171410i
$899$	56.9447	+	32.8770i	0.0633423	+	0.0365707i
$900$		0			0
$901$	−19.8643	+	11.4687i	−0.0220470	+	0.0127288i
$902$			24.6048i			0.0272781i
$903$	232.814	−	469.109i	0.257823	−	0.519500i
$904$	−209.834			−0.232118
$905$		0			0
$906$	73.9958	+	42.7215i	0.0816731	+	0.0471540i
$907$	−89.6364	+	155.255i	−0.0988273	+	0.171174i	−0.911200	−	0.411965i	$-0.864842\pi$
$907$	−89.6364	+	155.255i	−0.0988273	+	0.171174i	0.812372	+	0.583139i	$0.198176\pi$
$908$	−362.905	+	209.523i	−0.399675	+	0.230752i
$909$		−	418.792i		−	0.460718i
$910$		0			0
$911$	684.893			0.751803			0.375902	−	0.926660i	$-0.377333\pi$
$911$	684.893			0.751803			0.375902	+	0.926660i	$0.377333\pi$
$912$	61.4514	+	106.437i	0.0673809	+	0.116707i
$913$	−429.575	−	248.015i	−0.470510	−	0.271649i
$914$	−60.8133	+	105.332i	−0.0665353	+	0.115243i
$915$		0			0
$916$		−	215.598i		−	0.235369i
$917$	835.763	+	1257.67i	0.911410	+	1.37151i
$918$	−59.8156			−0.0651586
$919$	−470.376	−	814.715i	−0.511835	−	0.886523i	−0.999906	−	0.0137197i	$-0.995633\pi$
$919$	−470.376	−	814.715i	−0.511835	−	0.886523i	0.488071	−	0.872804i	$-0.337701\pi$
$920$		0			0
$921$	18.2960	−	31.6896i	0.0198653	−	0.0344078i
$922$	−160.991	+	92.9481i	−0.174611	+	0.100811i
$923$			342.637i			0.371221i
$924$	134.004	−	8.44315i	0.145026	−	0.00913761i
$925$		0			0
$926$	−52.3169	−	90.6156i	−0.0564978	−	0.0978570i
$927$	453.324	+	261.726i	0.489022	+	0.282337i
$928$	24.1088	−	41.7576i	0.0259793	−	0.0449975i
$929$	5.55322	−	3.20616i	0.00597764	−	0.00345119i	−0.497008	−	0.867746i	$-0.665568\pi$
$929$	5.55322	−	3.20616i	0.00597764	−	0.00345119i	0.502986	+	0.864295i	$0.332235\pi$
$930$		0			0
$931$	692.275	−	525.665i	0.743582	−	0.564624i
$932$	653.693			0.701387
$933$	75.0288	+	129.954i	0.0804167	+	0.139286i
$934$	547.346	+	316.010i	0.586023	+	0.338341i
$935$		0			0
$936$	25.7515	−	14.8676i	0.0275123	−	0.0158842i
$937$		−	867.253i		−	0.925564i	−0.886472	−	0.462782i	$-0.846851\pi$
$937$		−	867.253i		−	0.925564i	0.886472	−	0.462782i	$-0.153149\pi$
$938$	4.09739	+	65.0312i	0.00436822	+	0.0693296i
$939$	4.91565			0.00523498
$940$		0			0
$941$	−500.609	−	289.026i	−0.531996	−	0.307148i	0.209833	−	0.977737i	$-0.432708\pi$
$941$	−500.609	−	289.026i	−0.531996	−	0.307148i	−0.741829	+	0.670589i	$0.766041\pi$
$942$	65.5246	−	113.492i	0.0695590	−	0.120480i
$943$	−32.4626	+	18.7423i	−0.0344248	+	0.0198752i
$944$			120.833i			0.128002i
$945$		0			0
$946$	−338.246			−0.357553
$947$	374.280	+	648.272i	0.395227	+	0.684553i	0.993130	−	0.117015i	$-0.0373326\pi$
$947$	374.280	+	648.272i	0.395227	+	0.684553i	−0.597903	+	0.801568i	$0.703999\pi$
$948$	369.402	+	213.274i	0.389665	+	0.224973i
$949$	107.165	−	185.615i	0.112924	−	0.195590i
$950$		0			0
$951$			536.677i			0.564329i
$952$	−71.6447	+	144.361i	−0.0752571	+	0.151639i
$953$	−21.6304			−0.0226972			−0.0113486	−	0.999936i	$-0.503612\pi$
$953$	−21.6304			−0.0226972			−0.0113486	+	0.999936i	$0.503612\pi$
$954$	−5.97767	−	10.3536i	−0.00626590	−	0.0108529i
$955$		0			0
$956$	9.20117	−	15.9369i	0.00962466	−	0.0166704i
$957$	−70.7965	+	40.8744i	−0.0739776	+	0.0427110i
$958$		−	839.062i		−	0.875847i
$959$	−837.962	−	415.872i	−0.873787	−	0.433652i
$960$		0			0
$961$	−450.745	−	780.714i	−0.469038	−	0.812397i
$962$	120.403	+	69.5147i	0.125159	+	0.0722606i
$963$	90.7146	−	157.122i	0.0941999	−	0.163159i
$964$	−556.311	+	321.186i	−0.577086	+	0.333181i
$965$		0			0
$966$	113.215	+	170.368i	0.117200	+	0.176365i
$967$	−452.988			−0.468447			−0.234224	−	0.972183i	$-0.575255\pi$
$967$	−452.988			−0.468447			−0.234224	+	0.972183i	$0.575255\pi$
$968$	127.759	+	221.285i	0.131983	+	0.228601i
$969$	216.596	+	125.052i	0.223525	+	0.129052i
$970$		0			0
$971$	1137.95	−	656.994i	1.17193	−	0.676616i	0.217798	−	0.975994i	$-0.430112\pi$
$971$	1137.95	−	656.994i	1.17193	−	0.676616i	0.954135	+	0.299378i	$0.0967791\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	−1353.65	+	85.2889i	−1.39121	+	0.0876556i
$974$	−1159.01			−1.18995
$975$		0			0
$976$	164.038	+	94.7075i	0.168072	+	0.0970364i
$977$	588.653	−	1019.58i	0.602511	−	1.04358i	−0.389929	−	0.920845i	$-0.627500\pi$
$977$	588.653	−	1019.58i	0.602511	−	1.04358i	0.992440	−	0.122734i	$-0.0391663\pi$
$978$	436.957	−	252.278i	0.446787	−	0.257952i
$979$			654.025i			0.668054i
$980$		0			0
$981$	302.434			0.308292
$982$	−392.249	−	679.395i	−0.399439	−	0.691848i
$983$	695.029	+	401.275i	0.707049	+	0.408215i	0.809967	−	0.586475i	$-0.199485\pi$
$983$	695.029	+	401.275i	0.707049	+	0.408215i	−0.102918	+	0.994690i	$0.532818\pi$
$984$	7.69646	−	13.3307i	0.00782161	−	0.0135474i
$985$		0			0
$986$		−	98.1212i		−	0.0995144i
$987$	14.2649	+	226.404i	0.0144528	+	0.229386i
$988$	−124.330			−0.125840
$989$	−257.652	−	446.267i	−0.260518	−	0.451230i
$990$		0			0
$991$	91.7946	−	158.993i	0.0926283	−	0.160437i	−0.815988	−	0.578069i	$-0.803807\pi$
$991$	91.7946	−	158.993i	0.0926283	−	0.160437i	0.908616	+	0.417632i	$0.137140\pi$
$992$	37.7918	−	21.8191i	0.0380966	−	0.0219951i
$993$			721.554i			0.726640i
$994$	806.155	−	535.715i	0.811021	−	0.538948i
$995$		0			0
$996$	155.160	+	268.745i	0.155783	+	0.269824i
$997$	808.088	+	466.550i	0.810519	+	0.467953i	0.847136	−	0.531376i	$-0.178325\pi$
$997$	808.088	+	466.550i	0.810519	+	0.467953i	−0.0366170	+	0.999329i	$0.511658\pi$
$998$	−448.862	+	777.453i	−0.449762	+	0.779011i
$999$	126.240	−	72.8849i	0.126367	−	0.0729579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.p.d.451.1	yes	8
5.2	odd	4		1050.3.q.b.199.8		16
5.3	odd	4		1050.3.q.b.199.1		16
5.4	even	2		1050.3.p.c.451.4	✓	8
7.5	odd	6	inner	1050.3.p.d.901.1	yes	8
35.12	even	12		1050.3.q.b.649.1		16
35.19	odd	6		1050.3.p.c.901.4	yes	8
35.33	even	12		1050.3.q.b.649.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.c.451.4	✓	8	5.4	even	2
1050.3.p.c.901.4	yes	8	35.19	odd	6
1050.3.p.d.451.1	yes	8	1.1	even	1	trivial
1050.3.p.d.901.1	yes	8	7.5	odd	6	inner
1050.3.q.b.199.1		16	5.3	odd	4
1050.3.q.b.199.8		16	5.2	odd	4
1050.3.q.b.649.1		16	35.12	even	12
1050.3.q.b.649.8		16	35.33	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(-0.440173 - 6.98615i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(2.76860 - 4.79536i) q^{11} +(-3.00000 + 1.73205i) q^{12} -3.50434i q^{13} +(-8.24500 + 5.47905i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-7.04933 - 4.06994i) q^{17} +(2.12132 - 3.67423i) q^{18} +(-15.3628 + 8.86974i) q^{19} +(5.38992 - 10.8604i) q^{21} -7.83078 q^{22} +(-5.96495 - 10.3316i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-4.29192 + 2.47794i) q^{26} +5.19615i q^{27} +(12.5405 + 6.22374i) q^{28} -8.52374 q^{29} +(-6.68072 - 3.85711i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(8.30580 - 4.79536i) q^{33} +11.5115i q^{34} -6.00000 q^{36} +(-14.0267 - 24.2950i) q^{37} +(21.7263 + 12.5437i) q^{38} +(3.03484 - 5.25650i) q^{39} -3.14207i q^{41} +(-17.1125 + 1.07820i) q^{42} +43.1943 q^{43} +(5.53720 + 9.59071i) q^{44} +(-8.43572 + 14.6111i) q^{46} +(-16.2037 + 9.35524i) q^{47} -6.92820i q^{48} +(-48.6125 + 6.15023i) q^{49} +(-7.04933 - 12.2098i) q^{51} +(6.06969 + 3.50434i) q^{52} +(1.40895 - 2.44037i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-1.24500 - 19.7598i) q^{56} -30.7257 q^{57} +(6.02720 + 10.4394i) q^{58} +(-26.1612 - 15.1042i) q^{59} +(-41.0095 + 23.6769i) q^{61} +10.9096i q^{62} +(17.4903 - 11.6228i) q^{63} +8.00000 q^{64} +(-11.7462 - 6.78166i) q^{66} +(3.29108 - 5.70032i) q^{67} +(14.0987 - 8.13987i) q^{68} -20.6632i q^{69} -97.7751 q^{71} +(4.24264 + 7.34847i) q^{72} +(52.9672 + 30.5806i) q^{73} +(-19.8368 + 34.3583i) q^{74} -35.4790i q^{76} +(-34.7197 - 17.2311i) q^{77} -8.58383 q^{78} +(-61.5670 - 106.637i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-3.84823 + 2.22178i) q^{82} -89.5815i q^{83} +(13.4209 + 20.1960i) q^{84} +(-30.5430 - 52.9020i) q^{86} +(-12.7856 - 7.38178i) q^{87} +(7.83078 - 13.5633i) q^{88} +(-102.290 + 59.0573i) q^{89} +(-24.4818 + 1.54251i) q^{91} +23.8598 q^{92} +(-6.68072 - 11.5713i) q^{93} +(22.9156 + 13.2303i) q^{94} +(-8.48528 + 4.89898i) q^{96} -65.1965i q^{97} +(41.9067 + 55.1890i) q^{98} +16.6116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} - 24 q^{12} - 16 q^{14} - 16 q^{16} + 24 q^{17} + 72 q^{19} - 24 q^{22} - 60 q^{23} - 72 q^{26} - 24 q^{29} + 96 q^{31} - 12 q^{33} - 48 q^{36} + 24 q^{37}+ \cdots - 24 q^{99}+O(q^{100}) \) 8 * q + 12 * q^3 - 8 * q^4 + 12 * q^9 - 4 * q^11 - 24 * q^12 - 16 * q^14 - 16 * q^16 + 24 * q^17 + 72 * q^19 - 24 * q^22 - 60 * q^23 - 72 * q^26 - 24 * q^29 + 96 * q^31 - 12 * q^33 - 48 * q^36 + 24 * q^37 + 180 * q^38 - 12 * q^39 - 12 * q^42 + 112 * q^43 - 8 * q^44 + 32 * q^46 - 84 * q^47 - 264 * q^49 + 24 * q^51 - 24 * q^52 - 44 * q^53 + 40 * q^56 + 144 * q^57 - 104 * q^58 + 312 * q^59 - 204 * q^61 + 64 * q^64 - 36 * q^66 - 120 * q^67 - 48 * q^68 - 64 * q^71 - 84 * q^73 - 16 * q^74 - 228 * q^77 - 144 * q^78 - 144 * q^79 - 36 * q^81 + 60 * q^82 + 176 * q^86 - 36 * q^87 + 24 * q^88 - 336 * q^89 - 296 * q^91 + 240 * q^92 + 96 * q^93 + 36 * q^94 - 24 * q^99

Introduction

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