LMFDB - Embedded newform 224.2.bd.a.37.19

Newspace parameters

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.bd (of order $24$, degree $8$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			37.19
Character	$\chi$	$=$	224.37
Dual form			224.2.bd.a.109.19

$q$-expansion

$f(q)$	$=$	$q+(0.674919 - 1.24277i) q^{2} +(-1.68352 + 2.19400i) q^{3} +(-1.08897 - 1.67754i) q^{4} +(-1.03656 + 0.795384i) q^{5} +(1.59041 + 3.57300i) q^{6} +(-2.17678 - 1.50387i) q^{7} +(-2.81977 + 0.221138i) q^{8} +(-1.20296 - 4.48951i) q^{9} +O(q^{10})$	\(q+(0.674919 - 1.24277i) q^{2} +(-1.68352 + 2.19400i) q^{3} +(-1.08897 - 1.67754i) q^{4} +(-1.03656 + 0.795384i) q^{5} +(1.59041 + 3.57300i) q^{6} +(-2.17678 - 1.50387i) q^{7} +(-2.81977 + 0.221138i) q^{8} +(-1.20296 - 4.48951i) q^{9} +(0.288885 + 1.82503i) q^{10} +(-4.26070 + 0.560932i) q^{11} +(5.51383 + 0.434969i) q^{12} +(-2.27797 + 0.943568i) q^{13} +(-3.33812 + 1.69026i) q^{14} -3.61327i q^{15} +(-1.62829 + 3.65358i) q^{16} +(3.88131 - 2.24088i) q^{17} +(-6.39134 - 1.53505i) q^{18} +(-0.511323 + 3.88389i) q^{19} +(2.46308 + 0.872731i) q^{20} +(6.96414 - 2.24407i) q^{21} +(-2.17852 + 5.67367i) q^{22} +(-0.0381893 - 0.142524i) q^{23} +(4.26195 - 6.55887i) q^{24} +(-0.852265 + 3.18070i) q^{25} +(-0.364807 + 3.46784i) q^{26} +(4.21029 + 1.74396i) q^{27} +(-0.152356 + 5.28931i) q^{28} +(-1.58979 - 3.83810i) q^{29} +(-4.49047 - 2.43866i) q^{30} +(0.922443 + 1.59772i) q^{31} +(3.44161 + 4.48947i) q^{32} +(5.94228 - 10.2923i) q^{33} +(-0.165331 - 6.33600i) q^{34} +(3.45253 - 0.172519i) q^{35} +(-6.22135 + 6.90695i) q^{36} +(8.33189 - 6.39328i) q^{37} +(4.48169 + 3.25677i) q^{38} +(1.76482 - 6.58639i) q^{39} +(2.74698 - 2.47202i) q^{40} +(-3.83132 + 3.83132i) q^{41} +(1.91136 - 10.1694i) q^{42} +(1.05197 - 2.53968i) q^{43} +(5.58076 + 6.53667i) q^{44} +(4.81783 + 3.69685i) q^{45} +(-0.202900 - 0.0487317i) q^{46} +(-7.48969 - 4.32417i) q^{47} +(-5.27471 - 9.72335i) q^{48} +(2.47675 + 6.54719i) q^{49} +(3.37767 + 3.20588i) q^{50} +(-1.61777 + 12.2882i) q^{51} +(4.06352 + 2.79388i) q^{52} +(-12.6474 + 1.66507i) q^{53} +(5.00895 - 4.05540i) q^{54} +(3.97034 - 3.97034i) q^{55} +(6.47058 + 3.75920i) q^{56} +(-7.66043 - 7.66043i) q^{57} +(-5.84287 - 0.614654i) q^{58} +(1.58571 + 12.0447i) q^{59} +(-6.06141 + 3.93474i) q^{60} +(1.42005 + 0.186953i) q^{61} +(2.60817 - 0.0680573i) q^{62} +(-4.13305 + 11.5818i) q^{63} +(7.90220 - 1.24711i) q^{64} +(1.61077 - 2.78993i) q^{65} +(-8.78048 - 14.3314i) q^{66} +(2.69528 - 3.51256i) q^{67} +(-7.98579 - 4.07082i) q^{68} +(0.376991 + 0.156155i) q^{69} +(2.11577 - 4.40714i) q^{70} +(-8.12432 - 8.12432i) q^{71} +(4.38487 + 12.3934i) q^{72} +(-14.1106 - 3.78093i) q^{73} +(-2.32205 - 14.6696i) q^{74} +(-5.54365 - 7.22463i) q^{75} +(7.07219 - 3.37167i) q^{76} +(10.1182 + 5.18652i) q^{77} +(-6.99428 - 6.63855i) q^{78} +(10.0474 + 5.80089i) q^{79} +(-1.21817 - 5.08229i) q^{80} +(1.16121 - 0.670423i) q^{81} +(2.17563 + 7.34730i) q^{82} +(-2.73278 + 1.13196i) q^{83} +(-11.3483 - 9.23891i) q^{84} +(-2.24087 + 5.40995i) q^{85} +(-2.44625 - 3.02143i) q^{86} +(11.0972 + 2.97350i) q^{87} +(11.8902 - 2.52390i) q^{88} +(-6.39177 + 1.71267i) q^{89} +(7.84599 - 3.49239i) q^{90} +(6.37765 + 1.37184i) q^{91} +(-0.197504 + 0.219269i) q^{92} +(-5.05835 - 0.665944i) q^{93} +(-10.4289 + 6.38952i) q^{94} +(-2.55916 - 4.43260i) q^{95} +(-15.6439 - 0.00719653i) q^{96} -11.6317 q^{97} +(9.80828 + 1.34078i) q^{98} +(7.64377 + 18.4537i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} + O(q^{10}) $	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{8}\right)$

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 $

$2$	0.674919	−	1.24277i	0.477240	−	0.878773i
$2$	0.674919	−	1.24277i	0.477240	−	0.878773i
$3$	−1.68352	+	2.19400i	−0.971979	+	1.26671i	−0.00821140	+	0.999966i	$0.502614\pi$
$3$	−1.68352	+	2.19400i	−0.971979	+	1.26671i	−0.963768	+	0.266742i	$0.914053\pi$
$4$	−1.08897	−	1.67754i	−0.544485	−	0.838771i
$5$	−1.03656	+	0.795384i	−0.463566	+	0.355706i	−0.813984	−	0.580887i	$-0.802706\pi$
$5$	−1.03656	+	0.795384i	−0.463566	+	0.355706i	0.350419	+	0.936593i	$0.386039\pi$
$6$	1.59041	+	3.57300i	0.649282	+	1.45867i
$7$	−2.17678	−	1.50387i	−0.822746	−	0.568409i
$7$	−2.17678	−	1.50387i	−0.822746	−	0.568409i
$8$	−2.81977	+	0.221138i	−0.996939	+	0.0781839i
$9$	−1.20296	−	4.48951i	−0.400987	−	1.49650i
$10$	0.288885	+	1.82503i	0.0913534	+	0.577126i
$11$	−4.26070	+	0.560932i	−1.28465	+	0.169127i	−0.741754	−	0.670672i	$-0.766006\pi$
$11$	−4.26070	+	0.560932i	−1.28465	+	0.169127i	−0.542897	+	0.839799i	$0.682673\pi$
$12$	5.51383	+	0.434969i	1.59171	+	0.125565i
$13$	−2.27797	+	0.943568i	−0.631796	+	0.261699i	−0.675516	−	0.737345i	$-0.736079\pi$
$13$	−2.27797	+	0.943568i	−0.631796	+	0.261699i	0.0437199	+	0.999044i	$0.486079\pi$
$14$	−3.33812	+	1.69026i	−0.892150	+	0.451740i
$15$		−	3.61327i		−	0.932942i
$16$	−1.62829	+	3.65358i	−0.407073	+	0.913396i
$17$	3.88131	−	2.24088i	0.941356	−	0.543492i	0.0509711	−	0.998700i	$-0.483768\pi$
$17$	3.88131	−	2.24088i	0.941356	−	0.543492i	0.890385	+	0.455208i	$0.150435\pi$
$18$	−6.39134	−	1.53505i	−1.50645	−	0.361814i
$19$	−0.511323	+	3.88389i	−0.117306	+	0.891024i	0.827057	+	0.562118i	$0.190013\pi$
$19$	−0.511323	+	3.88389i	−0.117306	+	0.891024i	−0.944363	+	0.328906i	$0.893320\pi$
$20$	2.46308	+	0.872731i	0.550761	+	0.195149i
$21$	6.96414	−	2.24407i	1.51970	−	0.489697i
$22$	−2.17852	+	5.67367i	−0.464462	+	1.20963i
$23$	−0.0381893	−	0.142524i	−0.00796302	−	0.0297184i	0.961830	−	0.273648i	$-0.0882302\pi$
$23$	−0.0381893	−	0.142524i	−0.00796302	−	0.0297184i	−0.969793	+	0.243929i	$0.921564\pi$
$24$	4.26195	−	6.55887i	0.869968	−	1.33882i
$25$	−0.852265	+	3.18070i	−0.170453	+	0.636139i
$26$	−0.364807	+	3.46784i	−0.0715445	+	0.680098i
$27$	4.21029	+	1.74396i	0.810270	+	0.335625i
$28$	−0.152356	+	5.28931i	−0.0287925	+	0.999585i
$29$	−1.58979	−	3.83810i	−0.295217	−	0.712717i	−0.999995	−	0.00328877i	$-0.998953\pi$
$29$	−1.58979	−	3.83810i	−0.295217	−	0.712717i	0.704777	−	0.709428i	$-0.251047\pi$
$30$	−4.49047	−	2.43866i	−0.819844	−	0.445237i
$31$	0.922443	+	1.59772i	0.165676	+	0.286959i	0.936895	−	0.349611i	$-0.113686\pi$
$31$	0.922443	+	1.59772i	0.165676	+	0.286959i	−0.771219	+	0.636569i	$0.780353\pi$
$32$	3.44161	+	4.48947i	0.608396	+	0.793633i
$33$	5.94228	−	10.2923i	1.03442	−	1.79167i
$34$	−0.165331	−	6.33600i	−0.0283540	−	1.08661i
$35$	3.45253	−	0.172519i	0.583584	−	0.0291610i
$36$	−6.22135	+	6.90695i	−1.03689	+	1.15116i
$37$	8.33189	−	6.39328i	1.36975	−	1.05105i	0.377608	−	0.925966i	$-0.376747\pi$
$37$	8.33189	−	6.39328i	1.36975	−	1.05105i	0.992146	−	0.125084i	$-0.0399199\pi$
$38$	4.48169	+	3.25677i	0.727026	+	0.528317i
$39$	1.76482	−	6.58639i	0.282597	−	1.05467i
$40$	2.74698	−	2.47202i	0.434336	−	0.390861i
$41$	−3.83132	+	3.83132i	−0.598352	+	0.598352i	−0.939874	−	0.341522i	$-0.889058\pi$
$41$	−3.83132	+	3.83132i	−0.598352	+	0.598352i	0.341522	+	0.939874i	$0.389058\pi$
$42$	1.91136	−	10.1694i	0.294929	−	1.56918i
$43$	1.05197	−	2.53968i	0.160424	−	0.387297i	−0.823145	−	0.567831i	$-0.807783\pi$
$43$	1.05197	−	2.53968i	0.160424	−	0.387297i	0.983569	+	0.180534i	$0.0577826\pi$
$44$	5.58076	+	6.53667i	0.841332	+	0.985440i
$45$	4.81783	+	3.69685i	0.718199	+	0.551094i
$46$	−0.202900	−	0.0487317i	−0.0299160	−	0.00718510i
$47$	−7.48969	−	4.32417i	−1.09248	−	0.630746i	−0.158247	−	0.987400i	$-0.550584\pi$
$47$	−7.48969	−	4.32417i	−1.09248	−	0.630746i	−0.934237	+	0.356654i	$0.883918\pi$
$48$	−5.27471	−	9.72335i	−0.761339	−	1.40344i
$49$	2.47675	+	6.54719i	0.353822	+	0.935313i
$50$	3.37767	+	3.20588i	0.477675	+	0.453380i
$51$	−1.61777	+	12.2882i	−0.226533	+	1.72069i
$52$	4.06352	+	2.79388i	0.563508	+	0.387441i
$53$	−12.6474	+	1.66507i	−1.73726	+	0.228715i	−0.931555	−	0.363602i	$-0.881547\pi$
$53$	−12.6474	+	1.66507i	−1.73726	+	0.228715i	−0.805706	+	0.592316i	$0.798214\pi$
$54$	5.00895	−	4.05540i	0.681631	−	0.551870i
$55$	3.97034	−	3.97034i	0.535360	−	0.535360i
$56$	6.47058	+	3.75920i	0.864668	+	0.502344i
$57$	−7.66043	−	7.66043i	−1.01465	−	1.01465i
$58$	−5.84287	−	0.614654i	−0.767206	−	0.0807080i
$59$	1.58571	+	12.0447i	0.206442	+	1.56808i	0.710050	+	0.704151i	$0.248672\pi$
$59$	1.58571	+	12.0447i	0.206442	+	1.56808i	−0.503608	+	0.863932i	$0.667995\pi$
$60$	−6.06141	+	3.93474i	−0.782524	+	0.507973i
$61$	1.42005	+	0.186953i	0.181818	+	0.0239368i	0.220886	−	0.975300i	$-0.429105\pi$
$61$	1.42005	+	0.186953i	0.181818	+	0.0239368i	−0.0390671	+	0.999237i	$0.512439\pi$
$62$	2.60817	−	0.0680573i	0.331239	−	0.00864329i
$63$	−4.13305	+	11.5818i	−0.520716	+	1.45917i
$64$	7.90220	−	1.24711i	0.987775	−	0.155889i
$65$	1.61077	−	2.78993i	0.199791	−	0.346048i
$66$	−8.78048	−	14.3314i	−1.08080	−	1.76407i
$67$	2.69528	−	3.51256i	0.329281	−	0.429128i	−0.599147	−	0.800639i	$-0.704494\pi$
$67$	2.69528	−	3.51256i	0.329281	−	0.429128i	0.928429	+	0.371511i	$0.121160\pi$
$68$	−7.98579	−	4.07082i	−0.968420	−	0.493659i
$69$	0.376991	+	0.156155i	0.0453844	+	0.0187988i
$70$	2.11577	−	4.40714i	0.252883	−	0.526754i
$71$	−8.12432	−	8.12432i	−0.964180	−	0.964180i	0.0352007	−	0.999380i	$-0.488793\pi$
$71$	−8.12432	−	8.12432i	−0.964180	−	0.964180i	−0.999380	+	0.0352007i	$0.988793\pi$
$72$	4.38487	+	12.3934i	0.516762	+	1.46057i
$73$	−14.1106	−	3.78093i	−1.65152	−	0.442524i	−0.691484	−	0.722391i	$-0.743043\pi$
$73$	−14.1106	−	3.78093i	−1.65152	−	0.442524i	−0.960039	+	0.279867i	$0.909710\pi$
$74$	−2.32205	−	14.6696i	−0.269933	−	1.70531i
$75$	−5.54365	−	7.22463i	−0.640126	−	0.834228i
$76$	7.07219	−	3.37167i	0.811236	−	0.386757i
$77$	10.1182	+	5.18652i	1.15307	+	0.591058i
$78$	−6.99428	−	6.63855i	−0.791947	−	0.751668i
$79$	10.0474	+	5.80089i	1.13043	+	0.652651i	0.944042	−	0.329826i	$-0.106990\pi$
$79$	10.0474	+	5.80089i	1.13043	+	0.652651i	0.186384	+	0.982477i	$0.440323\pi$
$80$	−1.21817	−	5.08229i	−0.136196	−	0.568217i
$81$	1.16121	−	0.670423i	0.129023	−	0.0744914i
$82$	2.17563	+	7.34730i	0.240258	+	0.811373i
$83$	−2.73278	+	1.13196i	−0.299962	+	0.124248i	−0.527588	−	0.849500i	$-0.676904\pi$
$83$	−2.73278	+	1.13196i	−0.299962	+	0.124248i	0.227626	+	0.973749i	$0.426904\pi$
$84$	−11.3483	−	9.23891i	−1.23820	−	1.00805i
$85$	−2.24087	+	5.40995i	−0.243057	+	0.586791i
$86$	−2.44625	−	3.02143i	−0.263786	−	0.325810i
$87$	11.0972	+	2.97350i	1.18975	+	0.318792i
$88$	11.8902	−	2.52390i	1.26750	−	0.269049i
$89$	−6.39177	+	1.71267i	−0.677526	+	0.181543i	−0.581143	−	0.813802i	$-0.697394\pi$
$89$	−6.39177	+	1.71267i	−0.677526	+	0.181543i	−0.0963834	+	0.995344i	$0.530727\pi$
$90$	7.84599	−	3.49239i	0.827040	−	0.368131i
$91$	6.37765	+	1.37184i	0.668560	+	0.143807i
$92$	−0.197504	+	0.219269i	−0.0205912	+	0.0228604i
$93$	−5.05835	−	0.665944i	−0.524526	−	0.0690552i
$94$	−10.4289	+	6.38952i	−1.07566	+	0.659028i
$95$	−2.55916	−	4.43260i	−0.262564	−	0.454775i
$96$	−15.6439	−	0.00719653i	−1.59665	−	0.000734493i
$97$	−11.6317			−1.18102			−0.590512	−	0.807029i	$-0.701074\pi$
$97$	−11.6317			−1.18102			−0.590512	+	0.807029i	$0.701074\pi$
$98$	9.80828	+	1.34078i	0.990786	+	0.135439i
$99$	7.64377	+	18.4537i	0.768228	+	1.85467i
$100$	6.26384	−	2.03397i	0.626384	−	0.203397i
$101$	0.732600	+	5.56465i	0.0728964	+	0.553703i	0.988455	+	0.151518i	$0.0484160\pi$
$101$	0.732600	+	5.56465i	0.0728964	+	0.553703i	−0.915558	+	0.402186i	$0.868251\pi$
$102$	14.1795	+	10.3040i	1.40398	+	1.02025i
$103$	12.7133	−	3.40651i	1.25267	−	0.335653i	0.429305	−	0.903159i	$-0.358758\pi$
$103$	12.7133	−	3.40651i	1.25267	−	0.335653i	0.823369	+	0.567506i	$0.192092\pi$
$104$	6.21470	−	3.16439i	0.609402	−	0.310294i
$105$	−5.43388	+	7.86529i	−0.530293	+	0.767574i
$106$	−6.46670	+	16.8417i	−0.628101	+	1.63581i
$107$	−8.17197	−	10.6499i	−0.790014	−	1.02957i	−0.998669	−	0.0515774i	$-0.983575\pi$
$107$	−8.17197	−	10.6499i	−0.790014	−	1.02957i	0.208655	−	0.977989i	$-0.433092\pi$
$108$	−1.65931	−	8.96205i	−0.159667	−	0.862374i
$109$	1.26328	+	0.969350i	0.121000	+	0.0928469i	0.667489	−	0.744620i	$-0.267369\pi$
$109$	1.26328	+	0.969350i	0.121000	+	0.0928469i	−0.546489	+	0.837467i	$0.684036\pi$
$110$	−2.25457	−	7.61389i	−0.214965	−	0.725955i
$111$			29.0434i			2.75668i
$112$	9.03895	−	5.50431i	0.854100	−	0.520109i
$113$			19.2748i			1.81322i	0.421972	+	0.906609i	$0.361338\pi$
$113$			19.2748i			1.81322i	−0.421972	+	0.906609i	$0.638662\pi$
$114$	−14.6904	+	4.35001i	−1.37588	+	0.407416i
$115$	0.152947	+	0.117361i	0.0142624	+	0.0109439i
$116$	−4.70734	+	6.84652i	−0.437065	+	0.635683i
$117$	6.97647	+	9.09191i	0.644974	+	0.840547i
$118$	16.0390	+	6.15850i	1.47651	+	0.566936i
$119$	−11.8188	−	0.959089i	−1.08342	−	0.0879196i
$120$	0.799029	+	10.1886i	0.0729411	+	0.930086i
$121$	7.21378	−	1.93293i	0.655798	−	0.175720i
$122$	1.19076	−	1.63862i	0.107806	−	0.148354i
$123$	−1.95583	−	14.8560i	−0.176352	−	1.33952i
$124$	1.67573	−	3.28730i	0.150485	−	0.295208i
$125$	−4.14644	−	10.0104i	−0.370869	−	0.895357i
$126$	11.6040	+	12.9532i	1.03377	+	1.15396i
$127$	0.441727			0.0391969			0.0195985	−	0.999808i	$-0.493761\pi$
$127$	0.441727			0.0391969			0.0195985	+	0.999808i	$0.493761\pi$
$128$	3.78346	−	10.6623i	0.334414	−	0.942426i
$129$	3.80105	+	6.58361i	0.334664	+	0.579655i
$130$	−2.38011	−	3.88480i	−0.208750	−	0.340719i
$131$	−17.4744	−	2.30055i	−1.52674	−	0.201000i	−0.680084	−	0.733134i	$-0.738057\pi$
$131$	−17.4744	−	2.30055i	−1.52674	−	0.201000i	−0.846660	+	0.532134i	$0.821390\pi$
$132$	−23.7368	+	1.23961i	−2.06602	+	0.107894i
$133$	6.95390	−	7.68541i	0.602979	−	0.666409i
$134$	−2.54622	−	5.72032i	−0.219960	−	0.494161i
$135$	−5.75135	+	1.54107i	−0.494997	+	0.132634i
$136$	−10.4489	+	7.17706i	−0.895982	+	0.615428i
$137$	16.4922	+	4.41907i	1.40902	+	0.377546i	0.881576	−	0.472042i	$-0.156483\pi$
$137$	16.4922	+	4.41907i	1.40902	+	0.377546i	0.527446	+	0.849589i	$0.323150\pi$
$138$	0.448504	−	0.363123i	0.0381792	−	0.0309111i
$139$	0.644478	−	1.55591i	0.0546639	−	0.131970i	−0.894188	−	0.447691i	$-0.852246\pi$
$139$	0.644478	−	1.55591i	0.0546639	−	0.131970i	0.948852	+	0.315721i	$0.102246\pi$
$140$	−4.04910	−	5.60389i	−0.342212	−	0.473615i
$141$	22.0963	−	9.15258i	1.86084	−	0.770786i
$142$	−15.5799	+	4.61343i	−1.30744	+	0.387150i
$143$	9.17649	−	5.29805i	0.767377	−	0.443045i
$144$	18.3616	+	2.91511i	1.53013	+	0.242926i
$145$	4.70069	+	2.71394i	0.390371	+	0.225381i
$146$	−14.2224	+	14.9845i	−1.17705	+	1.24012i
$147$	−18.5342	−	5.58831i	−1.52868	−	0.460916i
$148$	−19.7982	−	7.01500i	−1.62740	−	0.576629i
$149$	4.28479	+	5.58405i	0.351024	+	0.457463i	0.935177	−	0.354180i	$-0.115240\pi$
$149$	4.28479	+	5.58405i	0.351024	+	0.457463i	−0.584154	+	0.811643i	$0.698573\pi$
$150$	−12.7201	+	2.01346i	−1.03859	+	0.164399i
$151$	−6.84767	−	1.83483i	−0.557255	−	0.149316i	−0.0308102	−	0.999525i	$-0.509809\pi$
$151$	−6.84767	−	1.83483i	−0.557255	−	0.149316i	−0.526445	+	0.850209i	$0.676475\pi$
$152$	0.582941	−	11.0647i	0.0472827	−	0.897468i
$153$	−14.7295	−	14.7295i	−1.19081	−	1.19081i
$154$	13.2746	−	9.07414i	1.06970	−	0.731215i
$155$	−2.22697	−	0.922442i	−0.178875	−	0.0740923i
$156$	−12.9708	+	4.21182i	−1.03849	+	0.337216i
$157$	0.111356	−	0.145122i	0.00888721	−	0.0115820i	−0.788889	−	0.614536i	$-0.789343\pi$
$157$	0.111356	−	0.145122i	0.00888721	−	0.0115820i	0.797776	+	0.602954i	$0.206010\pi$
$158$	13.9904	−	8.57156i	1.11302	−	0.681916i
$159$	17.6390	−	30.5517i	1.39887	−	2.42291i
$160$	−7.13830	−	1.91622i	−0.564332	−	0.151491i
$161$	−0.131208	+	0.367676i	−0.0103407	+	0.0289769i
$162$	−0.0494634	−	1.89560i	−0.00388622	−	0.148932i
$163$	−4.90288	−	0.645476i	−0.384023	−	0.0505576i	−0.0639565	−	0.997953i	$-0.520372\pi$
$163$	−4.90288	−	0.645476i	−0.384023	−	0.0505576i	−0.320066	+	0.947395i	$0.603705\pi$
$164$	10.5994	+	2.25501i	0.827674	+	0.176087i
$165$	2.02680	+	15.3951i	0.157786	+	1.19850i
$166$	−0.437642	+	4.16020i	−0.0339676	+	0.322895i
$167$	−5.95251	−	5.95251i	−0.460619	−	0.460619i	0.438240	−	0.898858i	$-0.355602\pi$
$167$	−5.95251	−	5.95251i	−0.460619	−	0.460619i	−0.898858	+	0.438240i	$0.855602\pi$
$168$	−19.1410	+	7.86780i	−1.47676	+	0.607014i
$169$	−4.89354	+	4.89354i	−0.376426	+	0.376426i
$170$	5.21093	+	6.43617i	0.399660	+	0.493632i
$171$	18.0518	−	2.37657i	1.38046	−	0.181741i
$172$	−5.40598	+	1.00091i	−0.412202	+	0.0763186i
$173$	1.96564	−	14.9305i	0.149445	−	1.13514i	−0.738189	−	0.674594i	$-0.764319\pi$
$173$	1.96564	−	14.9305i	0.149445	−	1.13514i	0.887634	−	0.460550i	$-0.152348\pi$
$174$	11.1851	−	11.7845i	0.847942	−	0.893380i
$175$	6.63855	−	5.64198i	0.501827	−	0.426494i
$176$	4.88826	−	16.4802i	0.368466	−	1.24224i
$177$	−29.0956	−	16.7984i	−2.18696	−	1.26264i
$178$	−2.18546	+	9.09943i	−0.163808	+	0.682031i
$179$	−3.86306	−	2.96423i	−0.288739	−	0.221557i	0.454228	−	0.890886i	$-0.349915\pi$
$179$	−3.86306	−	2.96423i	−0.288739	−	0.221557i	−0.742967	+	0.669329i	$0.766582\pi$
$180$	0.955151	−	12.1079i	0.0711928	−	0.902467i
$181$	−1.85145	+	4.46979i	−0.137617	+	0.332237i	−0.977631	−	0.210328i	$-0.932547\pi$
$181$	−1.85145	+	4.46979i	−0.137617	+	0.332237i	0.840014	+	0.542565i	$0.182547\pi$
$182$	6.00928	−	7.00010i	0.445437	−	0.518882i
$183$	−2.80085	+	2.80085i	−0.207045	+	0.207045i
$184$	0.139202	+	0.393441i	0.0102621	+	0.0290048i
$185$	−3.55143	+	13.2541i	−0.261106	+	0.974461i
$186$	−4.24159	+	5.83692i	−0.311009	+	0.427984i
$187$	−15.2801	+	11.7249i	−1.11739	+	0.857407i
$188$	0.902061	+	17.2732i	0.0657895	+	1.25977i
$189$	−6.54219	−	10.1279i	−0.475874	−	0.736699i
$190$	−7.23594	+	0.188813i	−0.524950	+	0.0136980i
$191$	−2.36651	+	4.09892i	−0.171235	+	0.296587i	−0.938852	−	0.344322i	$-0.888109\pi$
$191$	−2.36651	+	4.09892i	−0.171235	+	0.296587i	0.767617	+	0.640909i	$0.221442\pi$
$192$	−10.5673	+	19.4370i	−0.762630	+	1.40274i
$193$	4.86971	+	8.43459i	0.350530	+	0.607135i	0.986342	−	0.164708i	$-0.0526682\pi$
$193$	4.86971	+	8.43459i	0.350530	+	0.607135i	−0.635813	+	0.771843i	$0.719335\pi$
$194$	−7.85048	+	14.4556i	−0.563631	+	1.03785i
$195$	3.40936	+	8.23093i	0.244150	+	0.589429i
$196$	8.28608	−	11.2845i	0.591863	−	0.806039i
$197$	−1.98138	−	0.820712i	−0.141167	−	0.0584733i	0.310981	−	0.950416i	$-0.399342\pi$
$197$	−1.98138	−	0.820712i	−0.141167	−	0.0584733i	−0.452149	+	0.891943i	$0.649342\pi$
$198$	28.0927	+	2.95527i	1.99646	+	0.210022i
$199$	−0.185187	+	0.691127i	−0.0131276	+	0.0489927i	−0.972179	−	0.234239i	$-0.924740\pi$
$199$	−0.185187	+	0.691127i	−0.0131276	+	0.0489927i	0.959051	+	0.283232i	$0.0914067\pi$
$200$	1.69982	−	9.15730i	0.120195	−	0.647519i
$201$	3.16902	+	11.8269i	0.223525	+	0.834207i
$202$	7.41004	+	2.84523i	0.521369	+	0.200190i
$203$	−2.31137	+	10.7455i	−0.162226	+	0.754189i
$204$	22.3756	−	10.6676i	1.56661	−	0.746879i
$205$	0.924041	−	7.01878i	0.0645378	−	0.490213i
$206$	4.34690	−	18.0988i	0.302863	−	1.26100i
$207$	−0.593924	+	0.342902i	−0.0412806	+	0.0238334i
$208$	0.261802	−	9.85917i	0.0181527	−	0.683610i
$209$		−	16.8349i		−	1.16449i
$210$	6.10735	+	12.0615i	0.421447	+	0.832324i
$211$	21.0923	−	8.73673i	1.45206	−	0.601462i	0.489369	−	0.872077i	$-0.337227\pi$
$211$	21.0923	−	8.73673i	1.45206	−	0.601462i	0.962688	+	0.270615i	$0.0872271\pi$
$212$	16.5659	+	19.4034i	1.13775	+	1.33263i
$213$	31.5022	−	4.14735i	2.15850	−	0.284171i
$214$	−18.7509	+	2.96807i	−1.28178	+	0.202893i
$215$	0.929585	+	3.46926i	0.0633972	+	0.236601i
$216$	−12.2577	−	3.98651i	−0.834030	−	0.271247i
$217$	0.394803	−	4.86512i	0.0268010	−	0.330266i
$218$	2.05729	−	0.915740i	0.139338	−	0.0620217i
$219$	32.0508	−	24.5935i	2.16580	−	1.66187i
$220$	−10.9840	−	2.33683i	−0.740540	−	0.157549i
$221$	−6.72711	+	8.76694i	−0.452514	+	0.589728i
$222$	36.0943	+	19.6019i	2.42249	+	1.31560i
$223$	16.2715			1.08962			0.544810	−	0.838560i	$-0.316602\pi$
$223$	16.2715			1.08962			0.544810	+	0.838560i	$0.316602\pi$
$224$	−0.740057	−	14.9483i	−0.0494472	−	0.998777i
$225$	15.3050			1.02033
$226$	23.9542	+	13.0089i	1.59341	+	0.865339i
$227$	12.6127	−	16.4371i	0.837131	−	1.09097i	−0.157503	−	0.987518i	$-0.550344\pi$
$227$	12.6127	−	16.4371i	0.837131	−	1.09097i	0.994634	−	0.103452i	$-0.0329889\pi$
$228$	−4.50872	+	21.1927i	−0.298597	+	1.40352i
$229$	−18.7477	+	14.3856i	−1.23888	+	0.950628i	−0.999793	−	0.0203699i	$-0.993516\pi$
$229$	−18.7477	+	14.3856i	−1.23888	+	0.950628i	−0.239090	+	0.970998i	$0.576849\pi$
$230$	0.249079	−	0.110870i	0.0164238	−	0.00731054i
$231$	−28.4134	+	13.4677i	−1.86946	+	0.886113i
$232$	5.33160	+	10.4710i	0.350037	+	0.687454i
$233$	1.35310	+	5.04982i	0.0886442	+	0.330825i	0.995979	−	0.0895834i	$-0.0285536\pi$
$233$	1.35310	+	5.04982i	0.0886442	+	0.330825i	−0.907335	+	0.420408i	$0.861887\pi$
$234$	16.0077	−	2.53386i	1.04646	−	0.165644i
$235$	11.2029	−	1.47489i	0.730798	−	0.0962114i
$236$	18.4786	−	15.7764i	1.20286	−	1.02695i
$237$	−29.6422	+	12.2782i	−1.92547	+	0.797555i
$238$	−9.16863	+	14.0407i	−0.594314	+	0.910125i
$239$		−	11.9746i		−	0.774575i	−0.921959	−	0.387287i	$-0.873412\pi$
$239$		−	11.9746i		−	0.774575i	0.921959	−	0.387287i	$-0.126588\pi$
$240$	13.2014	+	5.88345i	0.852145	+	0.379775i
$241$	9.43962	−	5.44997i	0.608060	−	0.351063i	−0.164146	−	0.986436i	$-0.552487\pi$
$241$	9.43962	−	5.44997i	0.608060	−	0.351063i	0.772206	+	0.635373i	$0.219154\pi$
$242$	2.46652	−	10.2697i	0.158554	−	0.660158i
$243$	−2.26850	+	17.2309i	−0.145524	+	1.10537i
$244$	−1.23277	−	2.58577i	−0.0789198	−	0.165537i
$245$	−7.77484	−	4.81662i	−0.496716	−	0.307722i
$246$	−19.7827	−	7.59596i	−1.26130	−	0.484301i
$247$	−2.49993	−	9.32986i	−0.159067	−	0.593645i
$248$	−2.95439	−	4.30121i	−0.187604	−	0.273127i
$249$	2.11717	−	7.90140i	0.134170	−	0.500731i
$250$	−15.2392	−	1.60312i	−0.963809	−	0.101390i
$251$	6.96587	+	2.88536i	0.439682	+	0.182122i	0.591532	−	0.806281i	$-0.298523\pi$
$251$	6.96587	+	2.88536i	0.439682	+	0.182122i	−0.151850	+	0.988403i	$0.548523\pi$
$252$	23.9297	−	5.67883i	1.50743	−	0.357732i
$253$	0.242660	+	0.585833i	0.0152559	+	0.0368310i
$254$	0.298130	−	0.548966i	0.0187063	−	0.0344452i
$255$	−8.09689	−	14.0242i	−0.507047	−	0.878231i
$256$	−10.6973	−	11.8982i	−0.668583	−	0.743637i
$257$	4.74329	−	8.21562i	0.295878	−	0.512476i	−0.679311	−	0.733851i	$-0.737721\pi$
$257$	4.74329	−	8.21562i	0.295878	−	0.512476i	0.975189	+	0.221375i	$0.0710544\pi$
$258$	10.7473	−	0.280439i	0.669100	−	0.0174594i
$259$	−27.7514	+	1.38670i	−1.72439	+	0.0861656i
$260$	−6.43430	+	0.336020i	−0.399039	+	0.0208391i
$261$	−15.3187	+	11.7545i	−0.948205	+	0.727583i
$262$	−14.6528	+	20.1640i	−0.905256	+	1.24574i
$263$	−2.57835	+	9.62254i	−0.158988	+	0.593351i	0.839743	+	0.542984i	$0.182706\pi$
$263$	−2.57835	+	9.62254i	−0.158988	+	0.593351i	−0.998731	+	0.0503667i	$0.983961\pi$
$264$	−14.4798	+	30.3361i	−0.891173	+	1.86706i
$265$	11.7855	−	11.7855i	0.723979	−	0.723979i
$266$	−4.85790	−	13.8291i	−0.297857	−	0.847919i
$267$	7.00305	−	16.9069i	0.428580	−	1.03468i
$268$	−8.82755	−	0.696378i	−0.539229	−	0.0425381i
$269$	0.796708	+	0.611336i	0.0485761	+	0.0372738i	0.632764	−	0.774345i	$-0.281920\pi$
$269$	0.796708	+	0.611336i	0.0485761	+	0.0372738i	−0.584188	+	0.811618i	$0.698587\pi$
$270$	−1.96649	+	8.18772i	−0.119677	+	0.498289i
$271$	17.9715	+	10.3759i	1.09169	+	0.630289i	0.934027	−	0.357203i	$-0.116270\pi$
$271$	17.9715	+	10.3759i	1.09169	+	0.630289i	0.157666	+	0.987492i	$0.449603\pi$
$272$	1.86732	+	17.8295i	0.113223	+	1.08107i
$273$	−13.7467	+	11.6831i	−0.831988	+	0.707092i
$274$	16.6228	−	17.5135i	1.00422	−	1.05803i
$275$	1.84709	−	14.0301i	0.111384	−	0.846045i
$276$	−0.148576	−	0.802466i	−0.00894320	−	0.0483028i
$277$	−22.1497	+	2.91607i	−1.33085	+	0.175210i	−0.762184	−	0.647360i	$-0.775873\pi$
$277$	−22.1497	+	2.91607i	−1.33085	+	0.175210i	−0.568664	+	0.822570i	$0.692540\pi$
$278$	−1.49867	−	1.85105i	−0.0898842	−	0.111019i
$279$	6.06331	−	6.06331i	0.363001	−	0.363001i
$280$	−9.69718	+	1.24995i	−0.579517	+	0.0746986i
$281$	−0.637379	−	0.637379i	−0.0380229	−	0.0380229i	0.687840	−	0.725863i	$-0.258559\pi$
$281$	−0.637379	−	0.637379i	−0.0380229	−	0.0380229i	−0.725863	+	0.687840i	$0.758559\pi$
$282$	3.53862	−	33.6379i	0.210721	−	2.00311i
$283$	1.87845	+	14.2682i	0.111662	+	0.848159i	0.952000	+	0.306097i	$0.0990231\pi$
$283$	1.87845	+	14.2682i	0.111662	+	0.848159i	−0.840338	+	0.542063i	$0.817644\pi$
$284$	−4.78175	+	22.4760i	−0.283745	+	1.33371i
$285$	14.0335	+	1.84755i	0.831274	+	0.109439i
$286$	−0.390887	−	14.9801i	−0.0231137	−	0.885789i
$287$	14.1018	−	2.57814i	0.832401	−	0.152183i
$288$	16.0154	−	20.8518i	0.943716	−	1.22870i
$289$	1.54305	−	2.67265i	0.0907678	−	0.157215i
$290$	6.54539	−	4.01019i	0.384359	−	0.235487i
$291$	19.5822	−	25.5201i	1.14793	−	1.49601i
$292$	9.02337	+	27.7885i	0.528053	+	1.62620i
$293$	−8.69072	−	3.59981i	−0.507717	−	0.210303i	0.114095	−	0.993470i	$-0.463603\pi$
$293$	−8.69072	−	3.59981i	−0.507717	−	0.210303i	−0.621812	+	0.783166i	$0.713603\pi$
$294$	−19.4541	+	19.2622i	−1.13459	+	1.12339i
$295$	−11.2238	−	11.2238i	−0.653477	−	0.653477i
$296$	−22.0802	+	19.8701i	−1.28339	+	1.15492i
$297$	−18.9170	−	5.06880i	−1.09768	−	0.294122i
$298$	9.83159	−	1.55624i	0.569529	−	0.0901508i
$299$	0.221476	+	0.288633i	0.0128083	+	0.0166921i
$300$	−6.08275	+	17.1671i	−0.351188	+	0.991143i
$301$	−6.10925	+	3.94630i	−0.352131	+	0.227461i
$302$	−6.90189	+	7.27174i	−0.397159	+	0.418441i
$303$	−13.4422	−	7.76086i	−0.772234	−	0.445850i
$304$	−13.3575	−	8.19226i	−0.766106	−	0.469858i
$305$	−1.62067	+	0.935694i	−0.0927993	+	0.0535777i
$306$	−28.2466	+	8.36421i	−1.61475	+	0.478150i
$307$	−12.2071	+	5.05635i	−0.696696	+	0.288581i	−0.702787	−	0.711401i	$-0.748061\pi$
$307$	−12.2071	+	5.05635i	−0.696696	+	0.288581i	0.00609090	+	0.999981i	$0.498061\pi$
$308$	−2.31780	−	22.6216i	−0.132069	−	1.28899i
$309$	−13.9291	+	33.6278i	−0.792399	+	1.91302i
$310$	−2.64941	+	2.14505i	−0.150476	+	0.121830i
$311$	6.90577	+	1.85039i	0.391590	+	0.104926i	0.449241	−	0.893411i	$-0.351694\pi$
$311$	6.90577	+	1.85039i	0.391590	+	0.104926i	−0.0576511	+	0.998337i	$0.518361\pi$
$312$	−3.51988	+	18.9624i	−0.199274	+	1.07353i
$313$	12.1951	−	3.26768i	0.689310	−	0.184700i	0.102872	−	0.994695i	$-0.467197\pi$
$313$	12.1951	−	3.26768i	0.689310	−	0.184700i	0.586437	+	0.809995i	$0.300530\pi$
$314$	−0.105198	−	0.236337i	−0.00593665	−	0.0133372i
$315$	−4.92778	−	15.2926i	−0.277649	−	0.861641i
$316$	−1.21012	−	23.1720i	−0.0680744	−	1.30353i
$317$	−12.6043	−	1.65939i	−0.707927	−	0.0932004i	−0.232039	−	0.972706i	$-0.574540\pi$
$317$	−12.6043	−	1.65939i	−0.707927	−	0.0932004i	−0.475888	+	0.879506i	$0.657873\pi$
$318$	−26.0639	−	42.5412i	−1.46159	−	2.38559i
$319$	8.92655	+	15.4612i	0.499791	+	0.865663i
$320$	−7.19920	+	7.57799i	−0.402448	+	0.423623i
$321$	37.1236			2.07204
$322$	0.368383	+	0.411214i	0.0205292	+	0.0229160i
$323$	6.71870	+	16.2204i	0.373839	+	0.902526i
$324$	−2.38918	−	1.21790i	−0.132732	−	0.0676612i
$325$	−1.05976	−	8.04971i	−0.0587852	−	0.446518i
$326$	−4.11122	+	5.65752i	−0.227700	+	0.313341i
$327$	−4.25351	+	1.13973i	−0.235220	+	0.0630270i
$328$	9.95620	−	11.6507i	0.549739	−	0.643302i
$329$	9.80042	+	20.6763i	0.540315	+	1.13992i
$330$	20.5005	+	7.87157i	1.12852	+	0.433316i
$331$	17.3087	+	22.5571i	0.951371	+	1.23985i	0.970763	+	0.240038i	$0.0771601\pi$
$331$	17.3087	+	22.5571i	0.951371	+	1.23985i	−0.0193927	+	0.999812i	$0.506173\pi$
$332$	4.87482	+	3.35169i	0.267540	+	0.183948i
$333$	−38.7256	−	29.7152i	−2.12215	−	1.62838i
$334$	−11.4151	+	3.38016i	−0.624605	+	0.184954i
$335$			5.78478i			0.316057i
$336$	−3.14075	+	29.0981i	−0.171342	+	1.58743i
$337$			1.62473i			0.0885049i	0.999020	+	0.0442524i	$0.0140906\pi$
$337$			1.62473i			0.0885049i	−0.999020	+	0.0442524i	$0.985909\pi$
$338$	2.77882	+	9.38431i	0.151148	+	0.510439i
$339$	−42.2889	−	32.4494i	−2.29682	−	1.76241i
$340$	11.5157	−	2.13211i	0.624524	−	0.115630i
$341$	−4.82647	−	6.28998i	−0.261368	−	0.340621i
$342$	9.22999	−	24.0383i	0.499101	−	1.29984i
$343$	4.45477	−	17.9765i	0.240535	−	0.970640i
$344$	−2.40469	+	7.39393i	−0.129652	+	0.398654i
$345$	−0.514979	+	0.137988i	−0.0277255	+	0.00742903i
$346$	−17.2286	−	12.5197i	−0.926213	−	0.673064i
$347$	1.30940	+	9.94589i	0.0702924	+	0.533923i	0.989973	+	0.141256i	$0.0451142\pi$
$347$	1.30940	+	9.94589i	0.0702924	+	0.533923i	−0.919681	+	0.392667i	$0.871552\pi$
$348$	−7.09640	−	21.8541i	−0.380407	−	1.17150i
$349$	0.363706	+	0.878063i	0.0194687	+	0.0470017i	0.933315	−	0.359059i	$-0.116902\pi$
$349$	0.363706	+	0.878063i	0.0194687	+	0.0470017i	−0.913846	+	0.406060i	$0.866902\pi$
$350$	−2.53123	−	12.0581i	−0.135300	−	0.644532i
$351$	−11.2365			−0.599758
$352$	−17.1820	−	17.1978i	−0.915802	−	0.916645i
$353$	2.17787	+	3.77218i	0.115916	+	0.200773i	0.918146	−	0.396243i	$-0.129686\pi$
$353$	2.17787	+	3.77218i	0.115916	+	0.200773i	−0.802229	+	0.597016i	$0.796353\pi$
$354$	−40.5137	+	24.8217i	−2.15328	+	1.31926i
$355$	14.8833	+	1.95943i	0.789925	+	0.103996i
$356$	9.83351	+	8.85741i	0.521175	+	0.469442i
$357$	22.0013	−	24.3157i	1.16443	−	1.28693i
$358$	−6.29112	+	2.80029i	−0.332496	+	0.148000i
$359$	11.9149	−	3.19258i	0.628844	−	0.168498i	0.0696987	−	0.997568i	$-0.477796\pi$
$359$	11.9149	−	3.19258i	0.628844	−	0.168498i	0.559145	+	0.829070i	$0.311130\pi$
$360$	−14.4027	−	9.35886i	−0.759088	−	0.493255i
$361$	3.52948	+	0.945720i	0.185762	+	0.0497747i
$362$	4.30536	+	5.31767i	0.226285	+	0.279491i
$363$	−7.90367	+	19.0812i	−0.414835	+	1.00150i
$364$	−4.64376	−	12.1927i	−0.243399	−	0.639069i
$365$	17.6339	−	7.30418i	0.922998	−	0.382318i
$366$	1.59047	+	5.37116i	0.0831354	+	0.280755i
$367$	−24.2057	+	13.9751i	−1.26353	+	0.729497i	−0.973755	−	0.227599i	$-0.926912\pi$
$367$	−24.2057	+	13.9751i	−1.26353	+	0.729497i	−0.289771	+	0.957096i	$0.593579\pi$
$368$	0.582908	+	0.0925435i	0.0303862	+	0.00482416i
$369$	21.8097	+	12.5918i	1.13537	+	0.655504i
$370$	14.0749	+	13.3591i	0.731720	+	0.694504i
$371$	30.0348	+	15.3956i	1.55933	+	0.799301i
$372$	4.39124	+	9.21078i	0.227675	+	0.477557i
$373$	−0.417193	−	0.543697i	−0.0216015	−	0.0281516i	0.782428	−	0.622741i	$-0.213981\pi$
$373$	−0.417193	−	0.543697i	−0.0216015	−	0.0281516i	−0.804029	+	0.594590i	$0.797314\pi$
$374$	4.25849	+	26.9031i	0.220201	+	1.39113i
$375$	28.9435	+	7.75537i	1.49463	+	0.400486i
$376$	22.0754	+	10.5369i	1.13845	+	0.543400i
$377$	7.24301	+	7.24301i	0.373034	+	0.373034i
$378$	−17.0022	+	1.29492i	−0.874497	+	0.0666035i
$379$	3.29781	+	1.36600i	0.169397	+	0.0701666i	0.465770	−	0.884906i	$-0.345777\pi$
$379$	3.29781	+	1.36600i	0.169397	+	0.0701666i	−0.296373	+	0.955072i	$0.595777\pi$
$380$	−4.64902	+	9.12006i	−0.238490	+	0.467849i
$381$	−0.743655	+	0.969150i	−0.0380986	+	0.0496511i
$382$	3.49682	+	5.70747i	0.178913	+	0.292020i
$383$	−11.8150	+	20.4642i	−0.603720	+	1.04567i	0.388532	+	0.921435i	$0.372982\pi$
$383$	−11.8150	+	20.4642i	−0.603720	+	1.04567i	−0.992252	+	0.124239i	$0.960351\pi$
$384$	17.0237	+	26.2512i	0.868736	+	1.33962i
$385$	−14.6134	+	2.67169i	−0.744769	+	0.136162i
$386$	13.7689	−	0.359285i	0.700821	−	0.0182871i
$387$	−12.6674	−	1.66769i	−0.643919	−	0.0847735i
$388$	12.6666	+	19.5127i	0.643049	+	0.990608i
$389$	1.12506	+	8.54569i	0.0570429	+	0.433284i	0.996007	+	0.0892699i	$0.0284534\pi$
$389$	1.12506	+	8.54569i	0.0570429	+	0.433284i	−0.938965	+	0.344014i	$0.888213\pi$
$390$	12.5302	+	1.31814i	0.634492	+	0.0667469i
$391$	−0.467604	−	0.467604i	−0.0236478	−	0.0236478i
$392$	−8.43170	−	17.9139i	−0.425865	−	0.904787i
$393$	34.4658	−	34.4658i	1.73857	−	1.73857i
$394$	−2.35723	+	1.90849i	−0.118755	+	0.0961481i
$395$	−15.0288	+	1.97857i	−0.756179	+	0.0995528i
$396$	22.6330	−	32.9182i	1.13735	−	1.65420i
$397$	1.45036	−	11.0165i	0.0727912	−	0.552904i	−0.915727	−	0.401801i	$-0.868384\pi$
$397$	1.45036	−	11.0165i	0.0727912	−	0.552904i	0.988518	−	0.151103i	$-0.0482825\pi$
$398$	0.733928	+	0.696600i	0.0367885	+	0.0349174i
$399$	5.15480	+	28.1954i	0.258063	+	1.41153i
$400$	−10.2332	−	8.29292i	−0.511660	−	0.414646i
$401$	−7.74991	−	4.47441i	−0.387012	−	0.223442i	0.293853	−	0.955851i	$-0.405062\pi$
$401$	−7.74991	−	4.47441i	−0.387012	−	0.223442i	−0.680865	+	0.732409i	$0.738396\pi$
$402$	16.8370	+	4.04385i	0.839754	+	0.201689i
$403$	−3.60886	−	2.76917i	−0.179770	−	0.137942i
$404$	8.53715	−	7.28870i	0.424739	−	0.362626i
$405$	−0.670422	+	1.61854i	−0.0333135	+	0.0804260i
$406$	11.7943	+	10.1249i	0.585341	+	0.502489i
$407$	−31.9135	+	31.9135i	−1.58189	+	1.58189i
$408$	1.84436	−	35.0075i	0.0913092	−	1.73313i
$409$	−6.05030	+	22.5800i	−0.299168	+	1.11651i	0.638682	+	0.769470i	$0.279480\pi$
$409$	−6.05030	+	22.5800i	−0.299168	+	1.11651i	−0.937850	+	0.347040i	$0.887187\pi$
$410$	−8.09910	−	5.88548i	−0.399986	−	0.290663i
$411$	−37.4603	+	28.7443i	−1.84778	+	1.41785i
$412$	−19.5589	−	17.6174i	−0.963598	−	0.867949i
$413$	14.6619	−	28.6033i	0.721464	−	1.40748i
$414$	0.0252991	+	0.969544i	0.00124338	+	0.0476505i
$415$	1.93237	−	3.34695i	0.0948561	−	0.164296i
$416$	−12.0760	−	6.97950i	−0.592075	−	0.342198i
$417$	2.32867	+	4.03338i	0.114036	+	0.197516i
$418$	−20.9220	−	11.3622i	−1.02333	−	0.555743i
$419$	0.761838	+	1.83924i	0.0372182	+	0.0898527i	0.941396	−	0.337304i	$-0.109515\pi$
$419$	0.761838	+	1.83924i	0.0372182	+	0.0898527i	−0.904177	+	0.427157i	$0.859515\pi$
$420$	19.1117	+	0.550502i	0.932555	+	0.0268617i
$421$	−30.7141	−	12.7222i	−1.49691	−	0.620041i	−0.524104	−	0.851654i	$-0.675600\pi$
$421$	−30.7141	−	12.7222i	−1.49691	−	0.620041i	−0.972808	+	0.231613i	$0.925600\pi$
$422$	3.37784	−	32.1096i	0.164431	−	1.56307i
$423$	−10.4036	+	38.8268i	−0.505841	+	1.88783i
$424$	35.2947	−	7.49193i	1.71406	−	0.363840i
$425$	3.81964	+	14.2551i	0.185280	+	0.691474i
$426$	16.1072	−	41.9492i	0.780398	−	2.03245i
$427$	−2.80998	−	2.54252i	−0.135984	−	0.123041i
$428$	−8.96666	+	25.3063i	−0.433420	+	1.22322i
$429$	−3.82485	+	29.0526i	−0.184666	+	1.40267i
$430$	4.93889	+	1.18620i	0.238175	+	0.0572038i
$431$	−19.8876	+	11.4821i	−0.957952	+	0.553074i	−0.895542	−	0.444977i	$-0.853212\pi$
$431$	−19.8876	+	11.4821i	−0.957952	+	0.553074i	−0.0624100	+	0.998051i	$0.519879\pi$
$432$	−13.2273	+	12.5430i	−0.636397	+	0.603473i
$433$		−	20.8480i		−	1.00189i	−0.865479	−	0.500945i	$-0.832986\pi$
$433$		−	20.8480i		−	1.00189i	0.865479	−	0.500945i	$-0.167014\pi$
$434$	−5.77978	−	3.77421i	−0.277438	−	0.181168i
$435$	−13.8681	+	5.74435i	−0.664924	+	0.275420i
$436$	0.250450	−	3.17480i	0.0119944	−	0.152045i
$437$	0.573075	−	0.0754468i	0.0274139	−	0.00360911i
$438$	−8.93240	−	56.4305i	−0.426806	−	2.69635i
$439$	−1.91791	−	7.15772i	−0.0915366	−	0.341619i	0.904935	−	0.425550i	$-0.139919\pi$
$439$	−1.91791	−	7.15772i	−0.0915366	−	0.341619i	−0.996472	+	0.0839305i	$0.973253\pi$
$440$	−10.3174	+	12.0734i	−0.491865	+	0.575578i
$441$	26.4142	−	18.9954i	1.25782	−	0.904543i
$442$	6.35506	+	14.2772i	0.302279	+	0.679099i
$443$	12.6839	−	9.73270i	0.602630	−	0.462415i	−0.261831	−	0.965114i	$-0.584326\pi$
$443$	12.6839	−	9.73270i	0.602630	−	0.462415i	0.864461	+	0.502699i	$0.167660\pi$
$444$	48.7215	−	31.6274i	2.31222	−	1.50097i
$445$	5.26325	−	6.85920i	0.249502	−	0.325157i
$446$	10.9819	−	20.2218i	0.520009	−	0.957528i
$447$	−19.4649			−0.920660
$448$	−19.0768	−	9.16918i	−0.901296	−	0.433203i
$449$	−11.1501			−0.526206			−0.263103	−	0.964768i	$-0.584746\pi$
$449$	−11.1501			−0.526206			−0.263103	+	0.964768i	$0.584746\pi$
$450$	10.3296	−	19.0206i	0.486944	−	0.896642i
$451$	14.1750	−	18.4732i	0.667476	−	0.869871i
$452$	32.3342	−	20.9896i	1.52087	−	0.987269i
$453$	15.5538	−	11.9348i	0.730780	−	0.560748i
$454$	−11.9151	−	26.7684i	−0.559204	−	1.25630i
$455$	−7.70198	+	3.65069i	−0.361075	+	0.171147i
$456$	23.2947	+	19.9066i	1.09087	+	0.932214i
$457$	2.92960	+	10.9334i	0.137041	+	0.511444i	0.999981	+	0.00613797i	$0.00195379\pi$
$457$	2.92960	+	10.9334i	0.137041	+	0.511444i	−0.862940	+	0.505306i	$0.831380\pi$
$458$	5.22488	+	33.0082i	0.244143	+	1.54237i
$459$	20.2494	−	2.66589i	0.945162	−	0.124433i
$460$	0.0303223	−	0.384377i	0.00141379	−	0.0179217i
$461$	19.1556	−	7.93451i	0.892165	−	0.369547i	0.110963	−	0.993825i	$-0.464607\pi$
$461$	19.1556	−	7.93451i	0.892165	−	0.369547i	0.781203	+	0.624278i	$0.214607\pi$
$462$	−2.43937	+	44.4010i	−0.113490	+	2.06572i
$463$		−	23.0901i		−	1.07309i	−0.843873	−	0.536543i	$-0.819730\pi$
$463$		−	23.0901i		−	1.07309i	0.843873	−	0.536543i	$-0.180270\pi$
$464$	16.6115	+	0.441104i	0.771168	+	0.0204777i
$465$	5.77298	−	3.33303i	0.267716	−	0.154566i
$466$	7.18901	+	1.72663i	0.333024	+	0.0799845i
$467$	−1.98835	+	15.1030i	−0.0920098	+	0.698884i	0.881817	+	0.471592i	$0.156320\pi$
$467$	−1.98835	+	15.1030i	−0.0920098	+	0.698884i	−0.973827	+	0.227292i	$0.927013\pi$
$468$	7.65489	−	21.6041i	0.353848	−	0.998651i
$469$	−11.1495	+	3.59273i	−0.514835	+	0.165897i
$470$	5.72811	−	14.9181i	0.264218	−	0.688122i
$471$	0.130929	+	0.488632i	0.00603287	+	0.0225150i
$472$	−7.13487	−	33.6125i	−0.328409	−	1.54714i
$473$	−3.05754	+	11.4109i	−0.140586	+	0.524674i
$474$	−4.74706	+	45.1253i	−0.218040	+	2.07268i
$475$	−11.9177	−	4.93646i	−0.546820	−	0.226500i
$476$	11.2613	+	20.8709i	0.516163	+	0.956615i
$477$	22.6897	+	54.7778i	1.03889	+	2.50810i
$478$	−14.8818	−	8.08191i	−0.680676	−	0.369658i
$479$	−7.99275	−	13.8439i	−0.365198	−	0.632542i	0.623610	−	0.781736i	$-0.285665\pi$
$479$	−7.99275	−	13.8439i	−0.365198	−	0.632542i	−0.988808	+	0.149194i	$0.952332\pi$
$480$	16.2217	−	12.4355i	0.740414	−	0.567598i
$481$	−12.9473	+	22.4254i	−0.590347	+	1.02251i
$482$	−0.402096	−	15.4096i	−0.0183150	−	0.701888i
$483$	−0.585791	−	0.906861i	−0.0266544	−	0.0412636i
$484$	−11.0981	−	9.99651i	−0.504461	−	0.454387i
$485$	12.0570	−	9.25170i	0.547482	−	0.420098i
$486$	19.8831	+	14.4487i	0.901916	+	0.655407i
$487$	3.28547	−	12.2615i	0.148879	−	0.555623i	−0.850673	−	0.525695i	$-0.823805\pi$
$487$	3.28547	−	12.2615i	0.148879	−	0.555623i	0.999552	−	0.0299282i	$-0.00952788\pi$
$488$	−4.04555	−	0.213138i	−0.183133	−	0.00964830i
$489$	9.67025	−	9.67025i	0.437304	−	0.437304i
$490$	−11.2333	+	6.41154i	−0.507471	+	0.289644i
$491$	6.36913	−	15.3764i	0.287435	−	0.693929i	−0.712536	−	0.701636i	$-0.752453\pi$
$491$	6.36913	−	15.3764i	0.287435	−	0.693929i	0.999970	+	0.00770731i	$0.00245334\pi$
$492$	−22.7918	+	19.4588i	−1.02753	+	0.877268i
$493$	−14.7712	−	11.3343i	−0.665261	−	0.510473i
$494$	−13.2821	−	3.19005i	−0.597592	−	0.143527i
$495$	−22.6010	−	13.0487i	−1.01584	−	0.586496i
$496$	−7.33940	+	0.768671i	−0.329549	+	0.0345144i
$497$	5.46695	+	29.9028i	0.245226	+	1.34132i
$498$	−8.39072	−	7.96397i	−0.375997	−	0.356874i
$499$	−4.58194	+	34.8033i	−0.205116	+	1.55801i	0.510724	+	0.859745i	$0.329377\pi$
$499$	−4.58194	+	34.8033i	−0.205116	+	1.55801i	−0.715840	+	0.698264i	$0.753956\pi$
$500$	−12.2775	+	17.8568i	−0.549067	+	0.798582i
$501$	23.0810	−	3.03867i	1.03118	−	0.135758i
$502$	8.28724	−	6.70962i	0.369878	−	0.299465i
$503$	−8.70134	+	8.70134i	−0.387974	+	0.387974i	−0.873964	−	0.485990i	$-0.838459\pi$
$503$	−8.70134	+	8.70134i	−0.387974	+	0.387974i	0.485990	+	0.873964i	$0.338459\pi$
$504$	9.09309	−	33.5719i	0.405039	−	1.49541i
$505$	−5.18542	−	5.18542i	−0.230748	−	0.230748i
$506$	0.891833	+	0.0938183i	0.0396468	+	0.00417073i
$507$	−2.49808	−	18.9748i	−0.110944	−	0.842701i
$508$	−0.481027	−	0.741015i	−0.0213421	−	0.0328772i
$509$	−36.0870	−	4.75094i	−1.59953	−	0.210582i	−0.722622	−	0.691244i	$-0.757063\pi$
$509$	−36.0870	−	4.75094i	−1.59953	−	0.210582i	−0.876906	+	0.480662i	$0.840396\pi$
$510$	−22.8937	+	0.597384i	−1.01375	+	0.0264526i
$511$	25.0297	+	29.4508i	1.10725	+	1.30283i
$512$	−22.0066	+	5.26405i	−0.972563	+	0.232640i
$513$	−8.92615	+	15.4605i	−0.394099	+	0.682600i
$514$	−7.00881	−	11.4397i	−0.309146	−	0.504584i
$515$	−10.4686	+	13.6430i	−0.461303	+	0.601182i
$516$	6.90506	−	13.5458i	0.303978	−	0.596319i
$517$	34.3369	+	14.2228i	1.51014	+	0.625519i
$518$	−17.0066	+	35.4246i	−0.747225	+	1.55647i
$519$	29.4484	+	29.4484i	1.29264	+	1.29264i
$520$	−3.92504	+	8.22317i	−0.172124	+	0.360610i
$521$	−20.8992	−	5.59993i	−0.915611	−	0.245337i	−0.229903	−	0.973214i	$-0.573841\pi$
$521$	−20.8992	−	5.59993i	−0.915611	−	0.245337i	−0.685709	+	0.727876i	$0.740508\pi$
$522$	4.26924	+	26.9710i	0.186860	+	1.18049i
$523$	−7.85228	−	10.2333i	−0.343356	−	0.447471i	0.589474	−	0.807788i	$-0.299335\pi$
$523$	−7.85228	−	10.2333i	−0.343356	−	0.447471i	−0.932830	+	0.360317i	$0.882669\pi$
$524$	15.1698	+	31.8192i	0.662696	+	1.39003i
$525$	1.20242	+	24.0634i	0.0524779	+	1.05021i
$526$	10.2185	+	9.69873i	0.445546	+	0.422885i
$527$	7.16058	+	4.13416i	0.311920	+	0.180087i
$528$	27.9281	+	38.4696i	1.21542	+	1.67417i
$529$	19.8997	−	11.4891i	0.865206	−	0.499527i
$530$	−6.69246	−	22.6010i	−0.290702	−	0.981725i
$531$	52.1671	−	21.6083i	2.26386	−	0.937721i
$532$	−20.4652	−	3.29628i	−0.887278	−	0.142912i
$533$	5.11254	−	12.3428i	0.221449	−	0.534624i
$534$	−16.2849	−	20.1140i	−0.704717	−	0.870416i
$535$	16.9416	+	4.53948i	0.732447	+	0.196259i
$536$	−6.82332	+	10.5006i	−0.294723	+	0.453559i
$537$	13.0071	−	3.48523i	0.561296	−	0.150399i
$538$	1.29746	−	0.577525i	0.0559377	−	0.0248989i
$539$	−14.2252	−	26.5064i	−0.612725	−	1.14171i
$540$	8.84825	+	7.96995i	0.380768	+	0.342972i
$541$	36.3096	+	4.78025i	1.56107	+	0.205519i	0.861020	−	0.508571i	$-0.169826\pi$
$541$	36.3096	+	4.78025i	1.56107	+	0.205519i	0.700053	+	0.714091i	$0.253160\pi$
$542$	25.0242	−	15.3317i	1.07488	−	0.658551i
$543$	−6.68979	−	11.5871i	−0.287086	−	0.497248i
$544$	23.4183	+	9.71280i	1.00405	+	0.416433i
$545$	−2.08048			−0.0891179
$546$	5.24151	+	24.9692i	0.224316	+	1.06858i
$547$	−7.19297	−	17.3654i	−0.307549	−	0.742490i	−0.999783	−	0.0208166i	$-0.993373\pi$
$547$	−7.19297	−	17.3654i	−0.307549	−	0.742490i	0.692234	−	0.721673i	$-0.256627\pi$
$548$	−10.5463	−	32.4785i	−0.450516	−	1.38741i
$549$	−0.868934	−	6.60021i	−0.0370852	−	0.281690i
$550$	−16.1896	−	11.7647i	−0.690325	−	0.501647i
$551$	15.7196	−	4.21206i	0.669679	−	0.179440i
$552$	−1.09756	−	0.356954i	−0.0467153	−	0.0151930i
$553$	−13.1473	−	27.7373i	−0.559080	−	1.17951i
$554$	−11.3253	+	29.4952i	−0.481164	+	1.25313i
$555$	−23.1006	−	30.1053i	−0.980568	−	1.27790i
$556$	−3.31191	+	0.613197i	−0.140456	+	0.0260053i
$557$	3.37464	+	2.58945i	0.142988	+	0.109719i	0.677779	−	0.735266i	$-0.262943\pi$
$557$	3.37464	+	2.58945i	0.142988	+	0.109719i	−0.534790	+	0.844985i	$0.679609\pi$
$558$	−3.44307	−	11.6276i	−0.145757	−	0.492234i
$559$			6.77792i			0.286675i
$560$	−4.99141	+	12.8950i	−0.210926	+	0.544913i
$561$		−	53.2637i		−	2.24880i
$562$	−1.22230	+	0.361939i	−0.0515595	+	0.0152675i
$563$	−3.59441	−	2.75809i	−0.151486	−	0.116240i	0.530238	−	0.847849i	$-0.322103\pi$
$563$	−3.59441	−	2.75809i	−0.151486	−	0.116240i	−0.681724	+	0.731610i	$0.738769\pi$
$564$	−39.4160	−	27.1005i	−1.65971	−	1.14114i
$565$	−15.3308	−	19.9795i	−0.644973	−	0.840546i
$566$	19.0000	+	7.29542i	0.798629	+	0.306649i
$567$	−3.53592	−	0.286939i	−0.148495	−	0.0120503i
$568$	24.7053	+	21.1121i	1.03661	+	0.885845i
$569$	8.40979	−	2.25340i	0.352557	−	0.0944673i	−0.0781942	−	0.996938i	$-0.524915\pi$
$569$	8.40979	−	2.25340i	0.352557	−	0.0944673i	0.430751	+	0.902471i	$0.358249\pi$
$570$	11.7676	−	16.1935i	0.492889	−	0.678273i
$571$	1.73055	+	13.1449i	0.0724215	+	0.550096i	0.988740	+	0.149645i	$0.0478131\pi$
$571$	1.73055	+	13.1449i	0.0724215	+	0.550096i	−0.916318	+	0.400451i	$0.868854\pi$
$572$	−18.8806	−	9.62454i	−0.789439	−	0.402422i
$573$	−5.00897	−	12.0927i	−0.209253	−	0.505181i
$574$	6.31350	−	19.2653i	0.263520	−	0.804119i
$575$	0.485874			0.0202623
$576$	−15.1050	−	33.9767i	−0.629373	−	1.41570i
$577$	−21.1783	−	36.6819i	−0.881663	−	1.52709i	−0.849491	−	0.527603i	$-0.823091\pi$
$577$	−21.1783	−	36.6819i	−0.881663	−	1.52709i	−0.0321725	−	0.999482i	$-0.510243\pi$
$578$	−2.28006	−	3.72148i	−0.0948379	−	0.154793i
$579$	−26.7038	−	3.51562i	−1.10977	−	0.146104i
$580$	−0.566152	−	10.8410i	−0.0235082	−	0.450148i
$581$	7.65098	+	1.64573i	0.317416	+	0.0682763i
$582$	−18.4992	−	41.5602i	−0.766818	−	1.72273i
$583$	52.9530	−	14.1887i	2.19309	−	0.587637i
$584$	40.6248	+	7.54096i	1.68107	+	0.312047i
$585$	−14.4631	−	3.87538i	−0.597976	−	0.160227i
$586$	−10.3393	+	8.37101i	−0.427112	+	0.345803i
$587$	−2.75353	+	6.64762i	−0.113650	+	0.274377i	−0.970462	−	0.241253i	$-0.922442\pi$
$587$	−2.75353	+	6.64762i	−0.113650	+	0.274377i	0.856812	+	0.515629i	$0.172442\pi$
$588$	10.8086	+	37.1774i	0.445738	+	1.53317i
$589$	−6.67702	+	2.76571i	−0.275122	+	0.113959i
$590$	−21.5238	+	6.37350i	−0.886123	+	0.262393i
$591$	5.13633	−	2.96546i	0.211280	−	0.121983i
$592$	9.79165	+	40.8514i	0.402434	+	1.67898i
$593$	23.3385	+	13.4745i	0.958399	+	0.553332i	0.895680	−	0.444700i	$-0.146690\pi$
$593$	23.3385	+	13.4745i	0.958399	+	0.553332i	0.0627188	+	0.998031i	$0.480023\pi$
$594$	−19.0668	+	20.0885i	−0.782322	+	0.824243i
$595$	13.0137	−	8.40629i	0.533511	−	0.344624i
$596$	4.70147	−	13.2688i	0.192580	−	0.543510i
$597$	−1.20457	−	1.56983i	−0.0492998	−	0.0642487i
$598$	0.508183	−	0.0804403i	0.0207811	−	0.00328945i
$599$	−17.6831	−	4.73818i	−0.722513	−	0.193597i	−0.121220	−	0.992626i	$-0.538681\pi$
$599$	−17.6831	−	4.73818i	−0.722513	−	0.193597i	−0.601293	+	0.799029i	$0.705347\pi$
$600$	17.2295	+	19.1459i	0.703390	+	0.781627i
$601$	−20.0216	−	20.0216i	−0.816699	−	0.816699i	0.168929	−	0.985628i	$-0.445969\pi$
$601$	−20.0216	−	20.0216i	−0.816699	−	0.816699i	−0.985628	+	0.168929i	$0.945969\pi$
$602$	0.781106	+	10.2558i	0.0318355	+	0.417997i
$603$	−19.0120	−	7.87503i	−0.774229	−	0.320696i
$604$	4.37890	+	13.4853i	0.178175	+	0.548710i
$605$	−5.94013	+	7.74132i	−0.241500	+	0.314729i
$606$	−18.7174	+	11.4677i	−0.760341	+	0.465842i
$607$	−9.31676	+	16.1371i	−0.378155	+	0.654985i	−0.990794	−	0.135379i	$-0.956775\pi$
$607$	−9.31676	+	16.1371i	−0.378155	+	0.654985i	0.612638	+	0.790363i	$0.290108\pi$
$608$	−19.1964	+	11.0712i	−0.778515	+	0.448998i
$609$	−19.6845	−	23.1615i	−0.797657	−	0.938550i
$610$	0.0690350	+	2.64564i	0.00279514	+	0.107119i
$611$	21.1415	+	2.78333i	0.855292	+	0.112601i
$612$	−8.66937	+	40.7493i	−0.350439	+	1.64719i
$613$	−1.75610	−	13.3389i	−0.0709283	−	0.538754i	−0.989612	−	0.143761i	$-0.954080\pi$
$613$	−1.75610	−	13.3389i	−0.0709283	−	0.538754i	0.918684	−	0.394993i	$-0.129253\pi$
$614$	−1.95491	+	18.5833i	−0.0788937	+	0.749960i
$615$	13.8436	+	13.8436i	0.558228	+	0.558228i
$616$	−29.6779	−	12.3873i	−1.19576	−	0.499097i
$617$	−15.6780	+	15.6780i	−0.631171	+	0.631171i	−0.948362	−	0.317191i	$-0.897260\pi$
$617$	−15.6780	+	15.6780i	−0.631171	+	0.631171i	0.317191	+	0.948362i	$0.397260\pi$
$618$	32.3908	+	40.0068i	1.30295	+	1.60931i
$619$	3.36698	−	0.443271i	0.135330	−	0.0178166i	−0.0625567	−	0.998041i	$-0.519925\pi$
$619$	3.36698	−	0.443271i	0.135330	−	0.0178166i	0.197887	+	0.980225i	$0.436592\pi$
$620$	0.877669	+	4.74035i	0.0352480	+	0.190377i
$621$	0.0877686	−	0.666669i	0.00352203	−	0.0267525i
$622$	6.96045	−	7.33343i	0.279089	−	0.294044i
$623$	16.4891	+	5.88428i	0.660622	+	0.235749i
$624$	21.1903	+	17.1725i	0.848291	+	0.687449i
$625$	−1.99850	−	1.15384i	−0.0799402	−	0.0461535i
$626$	4.16975	−	17.3612i	0.166657	−	0.693893i
$627$	36.9358	+	28.3419i	1.47508	+	1.13187i
$628$	−0.364713	−	0.0287710i	−0.0145536	−	0.00114809i
$629$	18.0121	−	43.4851i	0.718189	−	1.73386i
$630$	−22.3311	−	4.19716i	−0.889692	−	0.167219i
$631$	−10.7990	+	10.7990i	−0.429900	+	0.429900i	−0.888594	−	0.458694i	$-0.848317\pi$
$631$	−10.7990	+	10.7990i	−0.429900	+	0.429900i	0.458694	+	0.888594i	$0.348317\pi$
$632$	−29.6143	−	14.1353i	−1.17799	−	0.562273i
$633$	−16.3409	+	60.9851i	−0.649493	+	2.42394i
$634$	−10.5691	+	14.5443i	−0.419753	+	0.577628i
$635$	−0.457878	+	0.351342i	−0.0181703	+	0.0139426i
$636$	−70.4601	+	3.67966i	−2.79393	+	0.145908i
$637$	−11.8197	−	12.5773i	−0.468313	−	0.498332i
$638$	25.2395	−	0.658596i	0.999242	−	0.0260741i
$639$	−26.7010	+	46.2474i	−1.05627	+	1.82952i
$640$	4.55885	+	14.0615i	0.180204	+	0.555830i
$641$	−14.0025	−	24.2530i	−0.553065	−	0.957936i	−0.998051	−	0.0623990i	$-0.980125\pi$
$641$	−14.0025	−	24.2530i	−0.553065	−	0.957936i	0.444987	−	0.895537i	$-0.353208\pi$
$642$	25.0554	−	46.1362i	0.988859	−	1.82085i
$643$	−9.24532	−	22.3202i	−0.364600	−	0.880221i	−0.994615	−	0.103639i	$-0.966951\pi$
$643$	−9.24532	−	22.3202i	−0.364600	−	0.880221i	0.630015	−	0.776583i	$-0.283049\pi$
$644$	0.759674	−	0.180281i	0.0299353	−	0.00710405i
$645$	−9.17653	−	3.80104i	−0.361326	−	0.149666i
$646$	24.6928	+	2.59762i	0.971526	+	0.102202i
$647$	−0.517194	+	1.93019i	−0.0203330	+	0.0758838i	−0.975347	−	0.220677i	$-0.929173\pi$
$647$	−0.517194	+	1.93019i	−0.0203330	+	0.0758838i	0.955014	+	0.296561i	$0.0958399\pi$
$648$	−3.12608	+	2.14722i	−0.122804	+	0.0843510i
$649$	−13.5125	−	50.4293i	−0.530412	−	1.97952i
$650$	−10.7192	−	4.11585i	−0.420442	−	0.161437i
$651$	10.0094	+	9.05671i	0.392300	+	0.354960i
$652$	4.25627	+	8.92768i	0.166688	+	0.349635i
$653$	0.614189	−	4.66523i	0.0240351	−	0.182565i	−0.975216	−	0.221254i	$-0.928985\pi$
$653$	0.614189	−	4.66523i	0.0240351	−	0.182565i	0.999251	+	0.0386895i	$0.0123183\pi$
$654$	−1.45436	+	6.05538i	−0.0568698	+	0.236784i
$655$	19.9431	−	11.5142i	0.779243	−	0.449896i
$656$	−7.75954	−	20.2366i	−0.302959	−	0.790105i
$657$			67.8980i			2.64896i
$658$	32.3104	+	1.77512i	1.25959	+	0.0692015i
$659$	20.5217	−	8.50038i	0.799413	−	0.331128i	0.0546917	−	0.998503i	$-0.482582\pi$
$659$	20.5217	−	8.50038i	0.799413	−	0.331128i	0.744721	+	0.667376i	$0.232582\pi$
$660$	23.6187	−	20.1648i	0.919358	−	0.784914i
$661$	−46.7909	+	6.16014i	−1.81996	+	0.239602i	−0.961793	−	0.273776i	$-0.911727\pi$
$661$	−46.7909	+	6.16014i	−1.81996	+	0.239602i	−0.858163	+	0.513378i	$0.828394\pi$
$662$	39.7153	−	6.28654i	1.54358	−	0.244333i
$663$	−7.90948	−	29.5186i	−0.307179	−	1.14641i
$664$	7.45550	−	3.79617i	0.289329	−	0.147320i
$665$	−1.09531	+	13.4974i	−0.0424744	+	0.523408i
$666$	−63.0659	+	28.0718i	−2.44375	+	1.08776i
$667$	−0.486310	+	0.373159i	−0.0188300	+	0.0144488i
$668$	−3.50348	+	16.4677i	−0.135554	+	0.637153i
$669$	−27.3933	+	35.6997i	−1.05909	+	1.38023i
$670$	7.18917	+	3.90426i	0.277742	+	0.150835i
$671$	−6.15527			−0.237622
$672$	34.0426	+	23.5421i	1.31322	+	0.908155i
$673$	25.0361			0.965071			0.482536	−	0.875876i	$-0.339716\pi$
$673$	25.0361			0.965071			0.482536	+	0.875876i	$0.339716\pi$
$674$	2.01918	+	1.09656i	0.0777757	+	0.0422380i
$675$	−9.13528	+	11.9053i	−0.351617	+	0.458236i
$676$	13.5380	+	2.88020i	0.520694	+	0.110777i
$677$	26.8553	−	20.6068i	1.03213	−	0.791984i	0.0537024	−	0.998557i	$-0.482898\pi$
$677$	26.8553	−	20.6068i	1.03213	−	0.791984i	0.978431	+	0.206573i	$0.0662311\pi$
$678$	−68.8688	+	30.6548i	−2.64489	+	1.17729i
$679$	25.3197	+	17.4926i	0.971683	+	0.671305i
$680$	5.12240	−	15.7503i	0.196435	−	0.603998i
$681$	14.8295	+	55.3444i	0.568267	+	2.12080i
$682$	−11.0745	+	1.75298i	−0.424064	+	0.0671252i
$683$	−41.3943	+	5.44966i	−1.58391	+	0.208525i	−0.870480	−	0.492203i	$-0.836192\pi$
$683$	−41.3943	+	5.44966i	−1.58391	+	0.208525i	−0.713428	+	0.700729i	$0.752858\pi$
$684$	−23.6447	−	27.6947i	−0.904077	−	1.05893i
$685$	−20.6101	+	8.53697i	−0.787470	+	0.326181i
$686$	−19.3341	−	17.6690i	−0.738180	−	0.674604i
$687$		−	65.3509i		−	2.49329i
$688$	7.56601	+	7.97879i	0.288451	+	0.304188i
$689$	27.2394	−	15.7267i	1.03774	−	0.599139i
$690$	−0.176081	+	0.733133i	−0.00670328	+	0.0279099i
$691$	3.69706	−	28.0819i	0.140643	−	1.06829i	−0.764935	−	0.644107i	$-0.777229\pi$
$691$	3.69706	−	28.0819i	0.140643	−	1.06829i	0.905578	−	0.424180i	$-0.139438\pi$
$692$	−27.1870	+	12.9614i	−1.03350	+	0.492719i
$693$	11.1131	−	51.6649i	0.422153	−	1.96259i
$694$	13.2442	+	5.08538i	0.502744	+	0.193038i
$695$	0.569501	+	2.12540i	0.0216024	+	0.0806212i
$696$	−31.9492	−	5.93056i	−1.21103	−	0.224797i
$697$	−6.28504	+	23.4561i	−0.238063	+	0.888462i
$698$	1.33671	+	0.140618i	0.0505950	+	0.00532246i
$699$	−13.3573	−	5.53277i	−0.505219	−	0.209268i
$700$	−16.6938	−	4.99249i	−0.630968	−	0.188698i
$701$	7.55543	+	18.2404i	0.285365	+	0.688931i	0.999944	−	0.0106238i	$-0.00338173\pi$
$701$	7.55543	+	18.2404i	0.285365	+	0.688931i	−0.714579	+	0.699555i	$0.753382\pi$
$702$	−7.58370	+	13.9644i	−0.286228	+	0.527051i
$703$	20.5705	+	35.6291i	0.775831	+	1.34378i
$704$	−32.9694	+	9.74618i	−1.24258	+	0.367323i
$705$	−15.6244	+	27.0623i	−0.588449	+	1.01922i
$706$	6.15785	−	0.160682i	0.231754	−	0.00604735i
$707$	6.77379	−	13.2148i	0.254755	−	0.496992i
$708$	3.50429	+	67.1020i	0.131699	+	2.52185i
$709$	−38.5136	+	29.5525i	−1.44641	+	1.10987i	−0.472926	+	0.881102i	$0.656802\pi$
$709$	−38.5136	+	29.5525i	−1.44641	+	1.10987i	−0.973482	+	0.228766i	$0.926531\pi$
$710$	12.4802	−	17.1742i	0.468372	−	0.644535i
$711$	13.9565	−	52.0863i	0.523409	−	1.95339i
$712$	17.6446	−	6.24279i	0.661258	−	0.233958i
$713$	0.192486	−	0.192486i	0.00720867	−	0.00720867i
$714$	−15.3698	−	43.7538i	−0.575202	−	1.63744i
$715$	−5.29804	+	12.7906i	−0.198136	+	0.478342i
$716$	−0.765865	+	9.70840i	−0.0286217	+	0.362820i
$717$	26.2724	+	20.1595i	0.981160	+	0.752871i
$718$	4.07392	−	16.9622i	0.152037	−	0.633025i
$719$	−5.53533	−	3.19583i	−0.206433	−	0.119184i	0.393220	−	0.919445i	$-0.371361\pi$
$719$	−5.53533	−	3.19583i	−0.206433	−	0.119184i	−0.599653	+	0.800260i	$0.704695\pi$
$720$	−21.3516	+	11.5828i	−0.795726	+	0.431665i
$721$	−32.7969	−	11.7039i	−1.22142	−	0.435875i
$722$	3.55742	−	3.74805i	0.132394	−	0.139488i
$723$	−3.93452	+	29.8857i	−0.146327	+	1.11146i
$724$	9.51443	−	1.76158i	0.353601	−	0.0654688i
$725$	13.5628	−	1.78557i	0.503708	−	0.0663144i
$726$	18.3792	+	22.7007i	0.682116	+	0.842502i
$727$	−8.81027	+	8.81027i	−0.326755	+	0.326755i	−0.851351	−	0.524596i	$-0.824216\pi$
$727$	−8.81027	+	8.81027i	−0.326755	+	0.326755i	0.524596	+	0.851351i	$0.324216\pi$
$728$	−18.2869	−	2.45792i	−0.677757	−	0.0910966i
$729$	−31.1413	−	31.1413i	−1.15338	−	1.15338i
$730$	2.82398	−	26.8446i	0.104520	−	0.993564i
$731$	−1.60808	−	12.2146i	−0.0594771	−	0.451774i
$732$	7.74858	+	1.64850i	0.286396	+	0.0609304i
$733$	20.1676	+	2.65512i	0.744907	+	0.0980689i	0.493419	−	0.869792i	$-0.335747\pi$
$733$	20.1676	+	2.65512i	0.744907	+	0.0980689i	0.251488	+	0.967860i	$0.419080\pi$
$734$	1.03108	+	39.5142i	0.0380578	+	1.45850i
$735$	23.6568	−	8.94917i	0.872593	−	0.330095i
$736$	0.508426	−	0.661963i	0.0187408	−	0.0244003i
$737$	−9.51350	+	16.4779i	−0.350434	+	0.606970i
$738$	30.3685	−	18.6060i	1.11788	−	0.684897i
$739$	−7.51554	+	9.79444i	−0.276464	+	0.360294i	−0.910861	−	0.412712i	$-0.864581\pi$
$739$	−7.51554	+	9.79444i	−0.276464	+	0.360294i	0.634398	+	0.773007i	$0.281248\pi$
$740$	26.1017	−	8.47565i	0.959517	−	0.311571i
$741$	24.6784	+	10.2221i	0.906584	+	0.375519i
$742$	39.4043	−	26.9356i	1.44658	−	0.988837i
$743$	−18.7385	−	18.7385i	−0.687449	−	0.687449i	0.274218	−	0.961667i	$-0.411581\pi$
$743$	−18.7385	−	18.7385i	−0.687449	−	0.687449i	−0.961667	+	0.274218i	$0.911581\pi$
$744$	14.4106	+	0.759218i	0.528320	+	0.0278343i
$745$	−8.88292	−	2.38017i	−0.325445	−	0.0872027i
$746$	−0.957264	+	0.151525i	−0.0350479	+	0.00554774i
$747$	8.36935	+	10.9071i	0.306218	+	0.399072i
$748$	36.3086	+	12.8651i	1.32757	+	0.470393i
$749$	1.77250	+	35.4721i	0.0647658	+	1.29612i
$750$	29.1726	−	30.7359i	1.06523	−	1.12232i
$751$	−46.5872	−	26.8972i	−1.69999	−	0.981491i	−0.945750	−	0.324895i	$-0.894671\pi$
$751$	−46.5872	−	26.8972i	−1.69999	−	0.981491i	−0.754242	−	0.656596i	$-0.771996\pi$
$752$	27.9941	−	20.3232i	1.02084	−	0.741110i
$753$	−18.0577	+	10.4256i	−0.658058	+	0.379930i
$754$	13.8899	−	4.11298i	0.505839	−	0.149786i
$755$	8.55744	−	3.54461i	0.311437	−	0.129001i
$756$	−9.86579	+	22.0038i	−0.358815	+	0.800271i
$757$	−9.74510	+	23.5267i	−0.354192	+	0.855094i	0.641902	+	0.766787i	$0.278146\pi$
$757$	−9.74510	+	23.5267i	−0.354192	+	0.855094i	−0.996093	+	0.0883072i	$0.971854\pi$
$758$	3.92338	−	3.17649i	0.142503	−	0.115375i
$759$	−1.69384	−	0.453863i	−0.0614825	−	0.0164742i
$760$	8.19646	+	11.9330i	0.297317	+	0.432854i
$761$	9.11027	−	2.44109i	0.330247	−	0.0884894i	−0.0898858	−	0.995952i	$-0.528650\pi$
$761$	9.11027	−	2.44109i	0.330247	−	0.0884894i	0.420133	+	0.907463i	$0.361984\pi$
$762$	0.702527	+	1.57829i	0.0254499	+	0.0571755i
$763$	−1.29211	−	4.00987i	−0.0467776	−	0.145167i
$764$	9.45316	−	0.493675i	0.342003	−	0.0178605i
$765$	26.9837	+	3.55247i	0.975597	+	0.128440i
$766$	17.4582	+	28.4951i	0.630791	+	1.02957i
$767$	−14.9772	−	25.9412i	−0.540794	−	0.936683i
$768$	44.1138	−	3.43916i	1.59182	−	0.124100i
$769$	−40.4467			−1.45855			−0.729273	−	0.684223i	$-0.760142\pi$
$769$	−40.4467			−1.45855			−0.729273	+	0.684223i	$0.760142\pi$
$770$	−6.54258	+	19.9643i	−0.235778	+	0.719465i
$771$	10.0397	+	24.2379i	0.361570	+	0.872908i
$772$	8.84641	−	17.3542i	0.318389	−	0.624590i
$773$

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.bd (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.674919 - 1.24277i) q^{2} +(-1.68352 + 2.19400i) q^{3} +(-1.08897 - 1.67754i) q^{4} +(-1.03656 + 0.795384i) q^{5} +(1.59041 + 3.57300i) q^{6} +(-2.17678 - 1.50387i) q^{7} +(-2.81977 + 0.221138i) q^{8} +(-1.20296 - 4.48951i) q^{9} +O(q^{10})\)	\(q+(0.674919 - 1.24277i) q^{2} +(-1.68352 + 2.19400i) q^{3} +(-1.08897 - 1.67754i) q^{4} +(-1.03656 + 0.795384i) q^{5} +(1.59041 + 3.57300i) q^{6} +(-2.17678 - 1.50387i) q^{7} +(-2.81977 + 0.221138i) q^{8} +(-1.20296 - 4.48951i) q^{9} +(0.288885 + 1.82503i) q^{10} +(-4.26070 + 0.560932i) q^{11} +(5.51383 + 0.434969i) q^{12} +(-2.27797 + 0.943568i) q^{13} +(-3.33812 + 1.69026i) q^{14} -3.61327i q^{15} +(-1.62829 + 3.65358i) q^{16} +(3.88131 - 2.24088i) q^{17} +(-6.39134 - 1.53505i) q^{18} +(-0.511323 + 3.88389i) q^{19} +(2.46308 + 0.872731i) q^{20} +(6.96414 - 2.24407i) q^{21} +(-2.17852 + 5.67367i) q^{22} +(-0.0381893 - 0.142524i) q^{23} +(4.26195 - 6.55887i) q^{24} +(-0.852265 + 3.18070i) q^{25} +(-0.364807 + 3.46784i) q^{26} +(4.21029 + 1.74396i) q^{27} +(-0.152356 + 5.28931i) q^{28} +(-1.58979 - 3.83810i) q^{29} +(-4.49047 - 2.43866i) q^{30} +(0.922443 + 1.59772i) q^{31} +(3.44161 + 4.48947i) q^{32} +(5.94228 - 10.2923i) q^{33} +(-0.165331 - 6.33600i) q^{34} +(3.45253 - 0.172519i) q^{35} +(-6.22135 + 6.90695i) q^{36} +(8.33189 - 6.39328i) q^{37} +(4.48169 + 3.25677i) q^{38} +(1.76482 - 6.58639i) q^{39} +(2.74698 - 2.47202i) q^{40} +(-3.83132 + 3.83132i) q^{41} +(1.91136 - 10.1694i) q^{42} +(1.05197 - 2.53968i) q^{43} +(5.58076 + 6.53667i) q^{44} +(4.81783 + 3.69685i) q^{45} +(-0.202900 - 0.0487317i) q^{46} +(-7.48969 - 4.32417i) q^{47} +(-5.27471 - 9.72335i) q^{48} +(2.47675 + 6.54719i) q^{49} +(3.37767 + 3.20588i) q^{50} +(-1.61777 + 12.2882i) q^{51} +(4.06352 + 2.79388i) q^{52} +(-12.6474 + 1.66507i) q^{53} +(5.00895 - 4.05540i) q^{54} +(3.97034 - 3.97034i) q^{55} +(6.47058 + 3.75920i) q^{56} +(-7.66043 - 7.66043i) q^{57} +(-5.84287 - 0.614654i) q^{58} +(1.58571 + 12.0447i) q^{59} +(-6.06141 + 3.93474i) q^{60} +(1.42005 + 0.186953i) q^{61} +(2.60817 - 0.0680573i) q^{62} +(-4.13305 + 11.5818i) q^{63} +(7.90220 - 1.24711i) q^{64} +(1.61077 - 2.78993i) q^{65} +(-8.78048 - 14.3314i) q^{66} +(2.69528 - 3.51256i) q^{67} +(-7.98579 - 4.07082i) q^{68} +(0.376991 + 0.156155i) q^{69} +(2.11577 - 4.40714i) q^{70} +(-8.12432 - 8.12432i) q^{71} +(4.38487 + 12.3934i) q^{72} +(-14.1106 - 3.78093i) q^{73} +(-2.32205 - 14.6696i) q^{74} +(-5.54365 - 7.22463i) q^{75} +(7.07219 - 3.37167i) q^{76} +(10.1182 + 5.18652i) q^{77} +(-6.99428 - 6.63855i) q^{78} +(10.0474 + 5.80089i) q^{79} +(-1.21817 - 5.08229i) q^{80} +(1.16121 - 0.670423i) q^{81} +(2.17563 + 7.34730i) q^{82} +(-2.73278 + 1.13196i) q^{83} +(-11.3483 - 9.23891i) q^{84} +(-2.24087 + 5.40995i) q^{85} +(-2.44625 - 3.02143i) q^{86} +(11.0972 + 2.97350i) q^{87} +(11.8902 - 2.52390i) q^{88} +(-6.39177 + 1.71267i) q^{89} +(7.84599 - 3.49239i) q^{90} +(6.37765 + 1.37184i) q^{91} +(-0.197504 + 0.219269i) q^{92} +(-5.05835 - 0.665944i) q^{93} +(-10.4289 + 6.38952i) q^{94} +(-2.55916 - 4.43260i) q^{95} +(-15.6439 - 0.00719653i) q^{96} -11.6317 q^{97} +(9.80828 + 1.34078i) q^{98} +(7.64377 + 18.4537i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} + O(q^{10}) \)	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99} + O(q^{100}) \)

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