LMFDB - Embedded newform 224.2.bd.a.109.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(37,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("224.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	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			109.19
Character	$\chi$	$=$	224.109
Dual form			224.2.bd.a.37.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.674919 + 1.24277i) q^{2} +(-1.68352 - 2.19400i) q^{3} +(-1.08897 + 1.67754i) q^{4} +(-1.03656 - 0.795384i) q^{5} +(1.59041 - 3.57300i) q^{6} +(-2.17678 + 1.50387i) q^{7} +(-2.81977 - 0.221138i) q^{8} +(-1.20296 + 4.48951i) q^{9} +O(q^{10})$	\(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	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{8}\right)$

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	−0.963768	−	0.266742i	$-0.914053\pi$
$3$	−1.68352	−	2.19400i	−0.971979	−	1.26671i	−0.00821140	−	0.999966i	$-0.502614\pi$
$4$	−1.08897	+	1.67754i	−0.544485	+	0.838771i
$5$	−1.03656	−	0.795384i	−0.463566	−	0.355706i	0.350419	−	0.936593i	$-0.386039\pi$
$5$	−1.03656	−	0.795384i	−0.463566	−	0.355706i	−0.813984	+	0.580887i	$0.802706\pi$
$6$	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	−0.542897	−	0.839799i	$-0.682673\pi$
$11$	−4.26070	−	0.560932i	−1.28465	−	0.169127i	−0.741754	+	0.670672i	$0.766006\pi$
$12$	5.51383	−	0.434969i	1.59171	−	0.125565i
$13$	−2.27797	−	0.943568i	−0.631796	−	0.261699i	0.0437199	−	0.999044i	$-0.486079\pi$
$13$	−2.27797	−	0.943568i	−0.631796	−	0.261699i	−0.675516	+	0.737345i	$0.736079\pi$
$14$	−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	0.890385	−	0.455208i	$-0.150435\pi$
$17$	3.88131	+	2.24088i	0.941356	+	0.543492i	0.0509711	+	0.998700i	$0.483768\pi$
$18$	−6.39134	+	1.53505i	−1.50645	+	0.361814i
$19$	−0.511323	−	3.88389i	−0.117306	−	0.891024i	−0.944363	−	0.328906i	$-0.893320\pi$
$19$	−0.511323	−	3.88389i	−0.117306	−	0.891024i	0.827057	−	0.562118i	$-0.190013\pi$
$20$	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	−0.969793	−	0.243929i	$-0.921564\pi$
$23$	−0.0381893	+	0.142524i	−0.00796302	+	0.0297184i	0.961830	+	0.273648i	$0.0882302\pi$
$24$	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	0.704777	+	0.709428i	$0.251047\pi$
$29$	−1.58979	+	3.83810i	−0.295217	+	0.712717i	−0.999995	+	0.00328877i	$0.998953\pi$
$30$	−4.49047	+	2.43866i	−0.819844	+	0.445237i
$31$	0.922443	−	1.59772i	0.165676	−	0.286959i	−0.771219	−	0.636569i	$-0.780353\pi$
$31$	0.922443	−	1.59772i	0.165676	−	0.286959i	0.936895	+	0.349611i	$0.113686\pi$
$32$	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	0.992146	+	0.125084i	$0.0399199\pi$
$37$	8.33189	+	6.39328i	1.36975	+	1.05105i	0.377608	+	0.925966i	$0.376747\pi$
$38$	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	0.341522	−	0.939874i	$-0.389058\pi$
$41$	−3.83132	−	3.83132i	−0.598352	−	0.598352i	−0.939874	+	0.341522i	$0.889058\pi$
$42$	1.91136	+	10.1694i	0.294929	+	1.56918i
$43$	1.05197	+	2.53968i	0.160424	+	0.387297i	0.983569	−	0.180534i	$-0.0577826\pi$
$43$	1.05197	+	2.53968i	0.160424	+	0.387297i	−0.823145	+	0.567831i	$0.807783\pi$
$44$	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	−0.934237	−	0.356654i	$-0.883918\pi$
$47$	−7.48969	+	4.32417i	−1.09248	+	0.630746i	−0.158247	+	0.987400i	$0.550584\pi$
$48$	−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	−0.805706	−	0.592316i	$-0.798214\pi$
$53$	−12.6474	−	1.66507i	−1.73726	−	0.228715i	−0.931555	+	0.363602i	$0.881547\pi$
$54$	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	−0.503608	−	0.863932i	$-0.667995\pi$
$59$	1.58571	−	12.0447i	0.206442	−	1.56808i	0.710050	−	0.704151i	$-0.248672\pi$
$60$	−6.06141	−	3.93474i	−0.782524	−	0.507973i
$61$	1.42005	−	0.186953i	0.181818	−	0.0239368i	−0.0390671	−	0.999237i	$-0.512439\pi$
$61$	1.42005	−	0.186953i	0.181818	−	0.0239368i	0.220886	+	0.975300i	$0.429105\pi$
$62$	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	0.928429	−	0.371511i	$-0.121160\pi$
$67$	2.69528	+	3.51256i	0.329281	+	0.429128i	−0.599147	+	0.800639i	$0.704494\pi$
$68$	−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	−0.999380	−	0.0352007i	$-0.988793\pi$
$71$	−8.12432	+	8.12432i	−0.964180	+	0.964180i	0.0352007	+	0.999380i	$0.488793\pi$
$72$	4.38487	−	12.3934i	0.516762	−	1.46057i
$73$	−14.1106	+	3.78093i	−1.65152	+	0.442524i	−0.960039	−	0.279867i	$-0.909710\pi$
$73$	−14.1106	+	3.78093i	−1.65152	+	0.442524i	−0.691484	+	0.722391i	$0.743043\pi$
$74$	−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	0.186384	−	0.982477i	$-0.440323\pi$
$79$	10.0474	−	5.80089i	1.13043	−	0.652651i	0.944042	+	0.329826i	$0.106990\pi$
$80$	−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	0.227626	−	0.973749i	$-0.426904\pi$
$83$	−2.73278	−	1.13196i	−0.299962	−	0.124248i	−0.527588	+	0.849500i	$0.676904\pi$
$84$	−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	−0.0963834	−	0.995344i	$-0.530727\pi$
$89$	−6.39177	−	1.71267i	−0.677526	−	0.181543i	−0.581143	+	0.813802i	$0.697394\pi$
$90$	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	−0.915558	−	0.402186i	$-0.868251\pi$
$101$	0.732600	−	5.56465i	0.0728964	−	0.553703i	0.988455	−	0.151518i	$-0.0484160\pi$
$102$	14.1795	−	10.3040i	1.40398	−	1.02025i
$103$	12.7133	+	3.40651i	1.25267	+	0.335653i	0.823369	−	0.567506i	$-0.192092\pi$
$103$	12.7133	+	3.40651i	1.25267	+	0.335653i	0.429305	+	0.903159i	$0.358758\pi$
$104$	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	0.208655	+	0.977989i	$0.433092\pi$
$107$	−8.17197	+	10.6499i	−0.790014	+	1.02957i	−0.998669	+	0.0515774i	$0.983575\pi$
$108$	−1.65931	+	8.96205i	−0.159667	+	0.862374i
$109$	1.26328	−	0.969350i	0.121000	−	0.0928469i	−0.546489	−	0.837467i	$-0.684036\pi$
$109$	1.26328	−	0.969350i	0.121000	−	0.0928469i	0.667489	+	0.744620i	$0.267369\pi$
$110$	−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	$-0.638662\pi$
$113$		−	19.2748i		−	1.81322i	0.421972	−	0.906609i	$-0.361338\pi$
$114$	−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	−0.846660	−	0.532134i	$-0.821390\pi$
$131$	−17.4744	+	2.30055i	−1.52674	+	0.201000i	−0.680084	+	0.733134i	$0.738057\pi$
$132$	−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	0.527446	−	0.849589i	$-0.323150\pi$
$137$	16.4922	−	4.41907i	1.40902	−	0.377546i	0.881576	+	0.472042i	$0.156483\pi$
$138$	0.448504	+	0.363123i	0.0381792	+	0.0309111i
$139$	0.644478	+	1.55591i	0.0546639	+	0.131970i	0.948852	−	0.315721i	$-0.102246\pi$
$139$	0.644478	+	1.55591i	0.0546639	+	0.131970i	−0.894188	+	0.447691i	$0.852246\pi$
$140$	−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	−0.584154	−	0.811643i	$-0.698573\pi$
$149$	4.28479	−	5.58405i	0.351024	−	0.457463i	0.935177	+	0.354180i	$0.115240\pi$
$150$	−12.7201	−	2.01346i	−1.03859	−	0.164399i
$151$	−6.84767	+	1.83483i	−0.557255	+	0.149316i	−0.526445	−	0.850209i	$-0.676475\pi$
$151$	−6.84767	+	1.83483i	−0.557255	+	0.149316i	−0.0308102	+	0.999525i	$0.509809\pi$
$152$	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	0.797776	−	0.602954i	$-0.206010\pi$
$157$	0.111356	+	0.145122i	0.00888721	+	0.0115820i	−0.788889	+	0.614536i	$0.789343\pi$
$158$	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	−0.320066	−	0.947395i	$-0.603705\pi$
$163$	−4.90288	+	0.645476i	−0.384023	+	0.0505576i	−0.0639565	+	0.997953i	$0.520372\pi$
$164$	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	−0.898858	−	0.438240i	$-0.855602\pi$
$167$	−5.95251	+	5.95251i	−0.460619	+	0.460619i	0.438240	+	0.898858i	$0.355602\pi$
$168$	−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	0.887634	+	0.460550i	$0.152348\pi$
$173$	1.96564	+	14.9305i	0.149445	+	1.13514i	−0.738189	+	0.674594i	$0.764319\pi$
$174$	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	−0.742967	−	0.669329i	$-0.766582\pi$
$179$	−3.86306	+	2.96423i	−0.288739	+	0.221557i	0.454228	+	0.890886i	$0.349915\pi$
$180$	0.955151	+	12.1079i	0.0711928	+	0.902467i
$181$	−1.85145	−	4.46979i	−0.137617	−	0.332237i	0.840014	−	0.542565i	$-0.182547\pi$
$181$	−1.85145	−	4.46979i	−0.137617	−	0.332237i	−0.977631	+	0.210328i	$0.932547\pi$
$182$	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	0.767617	−	0.640909i	$-0.221442\pi$
$191$	−2.36651	−	4.09892i	−0.171235	−	0.296587i	−0.938852	+	0.344322i	$0.888109\pi$
$192$	−10.5673	−	19.4370i	−0.762630	−	1.40274i
$193$	4.86971	−	8.43459i	0.350530	−	0.607135i	−0.635813	−	0.771843i	$-0.719335\pi$
$193$	4.86971	−	8.43459i	0.350530	−	0.607135i	0.986342	+	0.164708i	$0.0526682\pi$
$194$	−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	−0.452149	−	0.891943i	$-0.649342\pi$
$197$	−1.98138	+	0.820712i	−0.141167	+	0.0584733i	0.310981	+	0.950416i	$0.399342\pi$
$198$	28.0927	−	2.95527i	1.99646	−	0.210022i
$199$	−0.185187	−	0.691127i	−0.0131276	−	0.0489927i	0.959051	−	0.283232i	$-0.0914067\pi$
$199$	−0.185187	−	0.691127i	−0.0131276	−	0.0489927i	−0.972179	+	0.234239i	$0.924740\pi$
$200$	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	0.962688	−	0.270615i	$-0.0872271\pi$
$211$	21.0923	+	8.73673i	1.45206	+	0.601462i	0.489369	+	0.872077i	$0.337227\pi$
$212$	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	0.994634	+	0.103452i	$0.0329889\pi$
$227$	12.6127	+	16.4371i	0.837131	+	1.09097i	−0.157503	+	0.987518i	$0.550344\pi$
$228$	−4.50872	−	21.1927i	−0.298597	−	1.40352i
$229$	−18.7477	−	14.3856i	−1.23888	−	0.950628i	−0.239090	−	0.970998i	$-0.576849\pi$
$229$	−18.7477	−	14.3856i	−1.23888	−	0.950628i	−0.999793	+	0.0203699i	$0.993516\pi$
$230$	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	−0.907335	−	0.420408i	$-0.861887\pi$
$233$	1.35310	−	5.04982i	0.0886442	−	0.330825i	0.995979	+	0.0895834i	$0.0285536\pi$
$234$	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	$0.126588\pi$
$239$			11.9746i			0.774575i	−0.921959	+	0.387287i	$0.873412\pi$
$240$	13.2014	−	5.88345i	0.852145	−	0.379775i
$241$	9.43962	+	5.44997i	0.608060	+	0.351063i	0.772206	−	0.635373i	$-0.219154\pi$
$241$	9.43962	+	5.44997i	0.608060	+	0.351063i	−0.164146	+	0.986436i	$0.552487\pi$
$242$	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	−0.151850	−	0.988403i	$-0.548523\pi$
$251$	6.96587	−	2.88536i	0.439682	−	0.182122i	0.591532	+	0.806281i	$0.298523\pi$
$252$	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	0.975189	−	0.221375i	$-0.0710544\pi$
$257$	4.74329	+	8.21562i	0.295878	+	0.512476i	−0.679311	+	0.733851i	$0.737721\pi$
$258$	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	−0.998731	−	0.0503667i	$-0.983961\pi$
$263$	−2.57835	−	9.62254i	−0.158988	−	0.593351i	0.839743	−	0.542984i	$-0.182706\pi$
$264$	−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	−0.584188	−	0.811618i	$-0.698587\pi$
$269$	0.796708	−	0.611336i	0.0485761	−	0.0372738i	0.632764	+	0.774345i	$0.281920\pi$
$270$	−1.96649	−	8.18772i	−0.119677	−	0.498289i
$271$	17.9715	−	10.3759i	1.09169	−	0.630289i	0.157666	−	0.987492i	$-0.449603\pi$
$271$	17.9715	−	10.3759i	1.09169	−	0.630289i	0.934027	+	0.357203i	$0.116270\pi$
$272$	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	−0.568664	−	0.822570i	$-0.692540\pi$
$277$	−22.1497	−	2.91607i	−1.33085	−	0.175210i	−0.762184	+	0.647360i	$0.775873\pi$
$278$	−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	−0.725863	−	0.687840i	$-0.758559\pi$
$281$	−0.637379	+	0.637379i	−0.0380229	+	0.0380229i	0.687840	+	0.725863i	$0.258559\pi$
$282$	3.53862	+	33.6379i	0.210721	+	2.00311i
$283$	1.87845	−	14.2682i	0.111662	−	0.848159i	−0.840338	−	0.542063i	$-0.817644\pi$
$283$	1.87845	−	14.2682i	0.111662	−	0.848159i	0.952000	−	0.306097i	$-0.0990231\pi$
$284$	−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	−0.621812	−	0.783166i	$-0.713603\pi$
$293$	−8.69072	+	3.59981i	−0.507717	+	0.210303i	0.114095	+	0.993470i	$0.463603\pi$
$294$	−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	0.00609090	−	0.999981i	$-0.498061\pi$
$307$	−12.2071	−	5.05635i	−0.696696	−	0.288581i	−0.702787	+	0.711401i	$0.748061\pi$
$308$	−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	−0.0576511	−	0.998337i	$-0.518361\pi$
$311$	6.90577	−	1.85039i	0.391590	−	0.104926i	0.449241	+	0.893411i	$0.351694\pi$
$312$	−3.51988	−	18.9624i	−0.199274	−	1.07353i
$313$	12.1951	+	3.26768i	0.689310	+	0.184700i	0.586437	−	0.809995i	$-0.300530\pi$
$313$	12.1951	+	3.26768i	0.689310	+	0.184700i	0.102872	+	0.994695i	$0.467197\pi$
$314$	−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	−0.475888	−	0.879506i	$-0.657873\pi$
$317$	−12.6043	+	1.65939i	−0.707927	+	0.0932004i	−0.232039	+	0.972706i	$0.574540\pi$
$318$	−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	−0.0193927	−	0.999812i	$-0.506173\pi$
$331$	17.3087	−	22.5571i	0.951371	−	1.23985i	0.970763	−	0.240038i	$-0.0771601\pi$
$332$	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	$-0.985909\pi$
$337$		−	1.62473i		−	0.0885049i	0.999020	−	0.0442524i	$-0.0140906\pi$
$338$	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	−0.919681	−	0.392667i	$-0.871552\pi$
$347$	1.30940	−	9.94589i	0.0702924	−	0.533923i	0.989973	−	0.141256i	$-0.0451142\pi$
$348$	−7.09640	+	21.8541i	−0.380407	+	1.17150i
$349$	0.363706	−	0.878063i	0.0194687	−	0.0470017i	−0.913846	−	0.406060i	$-0.866902\pi$
$349$	0.363706	−	0.878063i	0.0194687	−	0.0470017i	0.933315	+	0.359059i	$0.116902\pi$
$350$	−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	−0.802229	−	0.597016i	$-0.796353\pi$
$353$	2.17787	−	3.77218i	0.115916	−	0.200773i	0.918146	+	0.396243i	$0.129686\pi$
$354$	−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	0.559145	−	0.829070i	$-0.311130\pi$
$359$	11.9149	+	3.19258i	0.628844	+	0.168498i	0.0696987	+	0.997568i	$0.477796\pi$
$360$	−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	−0.289771	−	0.957096i	$-0.593579\pi$
$367$	−24.2057	−	13.9751i	−1.26353	−	0.729497i	−0.973755	+	0.227599i	$0.926912\pi$
$368$	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	−0.804029	−	0.594590i	$-0.797314\pi$
$373$	−0.417193	+	0.543697i	−0.0216015	+	0.0281516i	0.782428	+	0.622741i	$0.213981\pi$
$374$	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	−0.296373	−	0.955072i	$-0.595777\pi$
$379$	3.29781	−	1.36600i	0.169397	−	0.0701666i	0.465770	+	0.884906i	$0.345777\pi$
$380$	−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	−0.992252	−	0.124239i	$-0.960351\pi$
$383$	−11.8150	−	20.4642i	−0.603720	−	1.04567i	0.388532	−	0.921435i	$-0.372982\pi$
$384$	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	−0.938965	−	0.344014i	$-0.888213\pi$
$389$	1.12506	−	8.54569i	0.0570429	−	0.433284i	0.996007	−	0.0892699i	$-0.0284534\pi$
$390$	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	0.988518	+	0.151103i	$0.0482825\pi$
$397$	1.45036	+	11.0165i	0.0727912	+	0.552904i	−0.915727	+	0.401801i	$0.868384\pi$
$398$	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	−0.680865	−	0.732409i	$-0.738396\pi$
$401$	−7.74991	+	4.47441i	−0.387012	+	0.223442i	0.293853	+	0.955851i	$0.405062\pi$
$402$	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	−0.937850	−	0.347040i	$-0.887187\pi$
$409$	−6.05030	−	22.5800i	−0.299168	−	1.11651i	0.638682	−	0.769470i	$-0.279480\pi$
$410$	−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	−0.904177	−	0.427157i	$-0.859515\pi$
$419$	0.761838	−	1.83924i	0.0372182	−	0.0898527i	0.941396	+	0.337304i	$0.109515\pi$
$420$	19.1117	−	0.550502i	0.932555	−	0.0268617i
$421$	−30.7141	+	12.7222i	−1.49691	+	0.620041i	−0.972808	−	0.231613i	$-0.925600\pi$
$421$	−30.7141	+	12.7222i	−1.49691	+	0.620041i	−0.524104	+	0.851654i	$0.675600\pi$
$422$	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	−0.0624100	−	0.998051i	$-0.519879\pi$
$431$	−19.8876	−	11.4821i	−0.957952	−	0.553074i	−0.895542	+	0.444977i	$0.853212\pi$
$432$	−13.2273	−	12.5430i	−0.636397	−	0.603473i
$433$			20.8480i			1.00189i	0.865479	+	0.500945i	$0.167014\pi$
$433$			20.8480i			1.00189i	−0.865479	+	0.500945i	$0.832986\pi$
$434$	−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	−0.996472	−	0.0839305i	$-0.973253\pi$
$439$	−1.91791	+	7.15772i	−0.0915366	+	0.341619i	0.904935	+	0.425550i	$0.139919\pi$
$440$	−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	0.864461	−	0.502699i	$-0.167660\pi$
$443$	12.6839	+	9.73270i	0.602630	+	0.462415i	−0.261831	+	0.965114i	$0.584326\pi$
$444$	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	−0.862940	−	0.505306i	$-0.831380\pi$
$457$	2.92960	−	10.9334i	0.137041	−	0.511444i	0.999981	−	0.00613797i	$-0.00195379\pi$
$458$	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	0.781203	−	0.624278i	$-0.214607\pi$
$461$	19.1556	+	7.93451i	0.892165	+	0.369547i	0.110963	+	0.993825i	$0.464607\pi$
$462$	−2.43937	−	44.4010i	−0.113490	−	2.06572i
$463$			23.0901i			1.07309i	0.843873	+	0.536543i	$0.180270\pi$
$463$			23.0901i			1.07309i	−0.843873	+	0.536543i	$0.819730\pi$
$464$	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	−0.973827	−	0.227292i	$-0.927013\pi$
$467$	−1.98835	−	15.1030i	−0.0920098	−	0.698884i	0.881817	−	0.471592i	$-0.156320\pi$
$468$	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	−0.988808	−	0.149194i	$-0.952332\pi$
$479$	−7.99275	+	13.8439i	−0.365198	+	0.632542i	0.623610	+	0.781736i	$0.285665\pi$
$480$	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	0.999552	+	0.0299282i	$0.00952788\pi$
$487$	3.28547	+	12.2615i	0.148879	+	0.555623i	−0.850673	+	0.525695i	$0.823805\pi$
$488$	−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	0.999970	−	0.00770731i	$-0.00245334\pi$
$491$	6.36913	+	15.3764i	0.287435	+	0.693929i	−0.712536	+	0.701636i	$0.752453\pi$
$492$	−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	−0.715840	−	0.698264i	$-0.753956\pi$
$499$	−4.58194	−	34.8033i	−0.205116	−	1.55801i	0.510724	−	0.859745i	$-0.329377\pi$
$500$	−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	0.485990	−	0.873964i	$-0.338459\pi$
$503$	−8.70134	−	8.70134i	−0.387974	−	0.387974i	−0.873964	+	0.485990i	$0.838459\pi$
$504$	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	−0.876906	−	0.480662i	$-0.840396\pi$
$509$	−36.0870	+	4.75094i	−1.59953	+	0.210582i	−0.722622	+	0.691244i	$0.757063\pi$
$510$	−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	−0.685709	−	0.727876i	$-0.740508\pi$
$521$	−20.8992	+	5.59993i	−0.915611	+	0.245337i	−0.229903	+	0.973214i	$0.573841\pi$
$522$	4.26924	−	26.9710i	0.186860	−	1.18049i
$523$	−7.85228	+	10.2333i	−0.343356	+	0.447471i	−0.932830	−	0.360317i	$-0.882669\pi$
$523$	−7.85228	+	10.2333i	−0.343356	+	0.447471i	0.589474	+	0.807788i	$0.299335\pi$
$524$	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	0.700053	−	0.714091i	$-0.253160\pi$
$541$	36.3096	−	4.78025i	1.56107	−	0.205519i	0.861020	+	0.508571i	$0.169826\pi$
$542$	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	0.692234	+	0.721673i	$0.256627\pi$
$547$	−7.19297	+	17.3654i	−0.307549	+	0.742490i	−0.999783	+	0.0208166i	$0.993373\pi$
$548$	−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	−0.534790	−	0.844985i	$-0.679609\pi$
$557$	3.37464	−	2.58945i	0.142988	−	0.109719i	0.677779	+	0.735266i	$0.262943\pi$
$558$	−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	−0.681724	−	0.731610i	$-0.738769\pi$
$563$	−3.59441	+	2.75809i	−0.151486	+	0.116240i	0.530238	+	0.847849i	$0.322103\pi$
$564$	−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	0.430751	−	0.902471i	$-0.358249\pi$
$569$	8.40979	+	2.25340i	0.352557	+	0.0944673i	−0.0781942	+	0.996938i	$0.524915\pi$
$570$	11.7676	+	16.1935i	0.492889	+	0.678273i
$571$	1.73055	−	13.1449i	0.0724215	−	0.550096i	−0.916318	−	0.400451i	$-0.868854\pi$
$571$	1.73055	−	13.1449i	0.0724215	−	0.550096i	0.988740	−	0.149645i	$-0.0478131\pi$
$572$	−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	−0.0321725	+	0.999482i	$0.510243\pi$
$577$	−21.1783	+	36.6819i	−0.881663	+	1.52709i	−0.849491	+	0.527603i	$0.823091\pi$
$578$	−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	0.856812	−	0.515629i	$-0.172442\pi$
$587$	−2.75353	−	6.64762i	−0.113650	−	0.274377i	−0.970462	+	0.241253i	$0.922442\pi$
$588$	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	0.0627188	−	0.998031i	$-0.480023\pi$
$593$	23.3385	−	13.4745i	0.958399	−	0.553332i	0.895680	+	0.444700i	$0.146690\pi$
$594$	−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	−0.601293	−	0.799029i	$-0.705347\pi$
$599$	−17.6831	+	4.73818i	−0.722513	+	0.193597i	−0.121220	+	0.992626i	$0.538681\pi$
$600$	17.2295	−	19.1459i	0.703390	−	0.781627i
$601$	−20.0216	+	20.0216i	−0.816699	+	0.816699i	−0.985628	−	0.168929i	$-0.945969\pi$
$601$	−20.0216	+	20.0216i	−0.816699	+	0.816699i	0.168929	+	0.985628i	$0.445969\pi$
$602$	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	0.612638	−	0.790363i	$-0.290108\pi$
$607$	−9.31676	−	16.1371i	−0.378155	−	0.654985i	−0.990794	+	0.135379i	$0.956775\pi$
$608$	−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	0.918684	+	0.394993i	$0.129253\pi$
$613$	−1.75610	+	13.3389i	−0.0709283	+	0.538754i	−0.989612	+	0.143761i	$0.954080\pi$
$614$	−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	0.317191	−	0.948362i	$-0.397260\pi$
$617$	−15.6780	−	15.6780i	−0.631171	−	0.631171i	−0.948362	+	0.317191i	$0.897260\pi$
$618$	32.3908	−	40.0068i	1.30295	−	1.60931i
$619$	3.36698	+	0.443271i	0.135330	+	0.0178166i	0.197887	−	0.980225i	$-0.436592\pi$
$619$	3.36698	+	0.443271i	0.135330	+	0.0178166i	−0.0625567	+	0.998041i	$0.519925\pi$
$620$	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	0.458694	−	0.888594i	$-0.348317\pi$
$631$	−10.7990	−	10.7990i	−0.429900	−	0.429900i	−0.888594	+	0.458694i	$0.848317\pi$
$632$	−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	0.444987	+	0.895537i	$0.353208\pi$
$641$	−14.0025	+	24.2530i	−0.553065	+	0.957936i	−0.998051	+	0.0623990i	$0.980125\pi$
$642$	25.0554	+	46.1362i	0.988859	+	1.82085i
$643$	−9.24532	+	22.3202i	−0.364600	+	0.880221i	0.630015	+	0.776583i	$0.283049\pi$
$643$	−9.24532	+	22.3202i	−0.364600	+	0.880221i	−0.994615	+	0.103639i	$0.966951\pi$
$644$	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	0.955014	−	0.296561i	$-0.0958399\pi$
$647$	−0.517194	−	1.93019i	−0.0203330	−	0.0758838i	−0.975347	+	0.220677i	$0.929173\pi$
$648$	−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	0.999251	−	0.0386895i	$-0.0123183\pi$
$653$	0.614189	+	4.66523i	0.0240351	+	0.182565i	−0.975216	+	0.221254i	$0.928985\pi$
$654$	−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	0.744721	−	0.667376i	$-0.232582\pi$
$659$	20.5217	+	8.50038i	0.799413	+	0.331128i	0.0546917	+	0.998503i	$0.482582\pi$
$660$	23.6187	+	20.1648i	0.919358	+	0.784914i
$661$	−46.7909	−	6.16014i	−1.81996	−	0.239602i	−0.858163	−	0.513378i	$-0.828394\pi$
$661$	−46.7909	−	6.16014i	−1.81996	−	0.239602i	−0.961793	+	0.273776i	$0.911727\pi$
$662$	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	0.978431	−	0.206573i	$-0.0662311\pi$
$677$	26.8553	+	20.6068i	1.03213	+	0.791984i	0.0537024	+	0.998557i	$0.482898\pi$
$678$	−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	−0.713428	−	0.700729i	$-0.752858\pi$
$683$	−41.3943	−	5.44966i	−1.58391	−	0.208525i	−0.870480	+	0.492203i	$0.836192\pi$
$684$	−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	0.905578	+	0.424180i	$0.139438\pi$
$691$	3.69706	+	28.0819i	0.140643	+	1.06829i	−0.764935	+	0.644107i	$0.777229\pi$
$692$	−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	−0.714579	−	0.699555i	$-0.753382\pi$
$701$	7.55543	−	18.2404i	0.285365	−	0.688931i	0.999944	+	0.0106238i	$0.00338173\pi$
$702$	−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	−0.973482	−	0.228766i	$-0.926531\pi$
$709$	−38.5136	−	29.5525i	−1.44641	−	1.10987i	−0.472926	−	0.881102i	$-0.656802\pi$
$710$	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	−0.599653	−	0.800260i	$-0.704695\pi$
$719$	−5.53533	+	3.19583i	−0.206433	+	0.119184i	0.393220	+	0.919445i	$0.371361\pi$
$720$	−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	0.524596	−	0.851351i	$-0.324216\pi$
$727$	−8.81027	−	8.81027i	−0.326755	−	0.326755i	−0.851351	+	0.524596i	$0.824216\pi$
$728$	−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	0.251488	−	0.967860i	$-0.419080\pi$
$733$	20.1676	−	2.65512i	0.744907	−	0.0980689i	0.493419	+	0.869792i	$0.335747\pi$
$734$	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	0.634398	−	0.773007i	$-0.281248\pi$
$739$	−7.51554	−	9.79444i	−0.276464	−	0.360294i	−0.910861	+	0.412712i	$0.864581\pi$
$740$	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	−0.961667	−	0.274218i	$-0.911581\pi$
$743$	−18.7385	+	18.7385i	−0.687449	+	0.687449i	0.274218	+	0.961667i	$0.411581\pi$
$744$	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	−0.754242	+	0.656596i	$0.771996\pi$
$751$	−46.5872	+	26.8972i	−1.69999	+	0.981491i	−0.945750	+	0.324895i	$0.894671\pi$
$752$	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	−0.996093	−	0.0883072i	$-0.971854\pi$
$757$	−9.74510	−	23.5267i	−0.354192	−	0.855094i	0.641902	−	0.766787i	$-0.278146\pi$
$758$	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	0.420133	−	0.907463i	$-0.361984\pi$
$761$	9.11027	+	2.44109i	0.330247	+	0.0884894i	−0.0898858	+	0.995952i	$0.528650\pi$
$762$	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
$773$	−3.45654	+	26.2550i	−0.124323	+	0.944328i	0.809632	+	0.586938i	$0.199667\pi$
$773$	−3.45654	+	26.2550i	−0.124323	+	0.944328i	−0.933955	+	0.357390i	$0.883667\pi$
$774$	−10.6220	−	14.6171i	−0.381800	−	0.525401i
$775$	−5.86802	−	1.57233i	−0.210786	−	0.0564798i
$776$	32.7988	+	2.57221i	1.17741	+	0.0923371i
$777$	43.6775	+	63.2211i	1.56692	+	2.26804i
$778$	11.3797	−	4.36945i	0.407981	−	0.156652i
$779$	−12.9214	+	16.8395i	−0.462956	+	0.603336i
$780$	10.0950	+	14.6826i	0.361460	+	0.525721i
$781$	39.1725	−	30.0581i	1.40170	−	1.07556i
$782$	−0.896720	−	0.265531i	−0.0320667	−	0.00949537i
$783$			18.9320i			0.676576i
$784$	−27.9536	+	1.61171i	−0.998342	+	0.0575611i
$785$		−	0.239000i		−	0.00853027i
$786$	−19.5716	+	66.0949i	−0.698095	+	2.35753i
$787$	−34.5545	+	26.5146i	−1.23173	+	0.945143i	−0.999621	−	0.0275461i	$-0.991231\pi$
$787$	−34.5545	+	26.5146i	−1.23173	+	0.945143i	−0.232113	+	0.972689i	$0.574564\pi$
$788$	0.780878	−	4.21757i	0.0278176	−	0.150245i
$789$	−16.7712	+	21.8566i	−0.597070	+	0.778116i
$790$	−7.68427	−	20.0127i	−0.273394	−	0.712020i
$791$	28.9867	+	41.9570i	1.03065	+	1.49182i
$792$	−25.6345	+	50.3448i	−0.910881	+	1.78893i
$793$	−3.41123	−	0.914037i	−0.121136	−	0.0324584i
$794$	−12.7122	+	9.23773i	−0.451139	+	0.327835i
$795$	6.01634	−	45.6986i	0.213377	−	1.62076i
$796$	1.36106	+	0.441958i	0.0482414	+	0.0156648i
$797$	−7.23808	+	17.4743i	−0.256386	+	0.618971i	−0.998694	−	0.0510879i	$-0.983731\pi$
$797$	−7.23808	+	17.4743i	−0.256386	+	0.618971i	0.742308	+	0.670059i	$0.233731\pi$
$798$	38.5195	−	12.6234i	1.36358	−	0.446862i
$799$	−38.7598			−1.37122
$800$	−17.2128	−	7.12050i	−0.608564	−	0.251748i
$801$	15.3781	−	26.6356i	0.543358	−	0.941123i
$802$	−10.7912	−	6.61151i	−0.381052	−	0.233461i
$803$	62.2420	−	8.19432i	2.19647	−	0.289171i
$804$	16.3892	+	18.1953i	0.578002	+	0.641699i
$805$	−0.156438	+	0.485481i	−0.00551371	+	0.0171110i
$806$	−5.87714	−	2.61602i	−0.207013	−	0.0921454i
$807$	−2.68254	−	0.718786i	−0.0944300	−	0.0253024i
$808$	−3.29631	+	15.5290i	−0.115964	+	0.546309i
$809$	3.30100	−	0.884500i	0.116057	−	0.0310974i	−0.200323	−	0.979730i	$-0.564199\pi$
$809$	3.30100	−	0.884500i	0.116057	−	0.0310974i	0.316380	+	0.948633i	$0.397533\pi$
$810$	1.55900	−	1.92557i	0.0547777	−	0.0676575i
$811$	−14.2681	−	34.4464i	−0.501022	−	1.20958i	−0.948928	−	0.315494i	$-0.897830\pi$
$811$	−14.2681	−	34.4464i	−0.501022	−	1.20958i	0.447905	−	0.894081i	$-0.352170\pi$
$812$	20.5431	+	7.82415i	0.720922	+	0.274574i
$813$	−53.0201	−	21.9616i	−1.85949	−	0.770228i
$814$	18.1222	−	61.2003i	0.635184	−	2.14507i
$815$	5.59555	+	3.23059i	0.196003	+	0.113163i
$816$	−42.2616	+	25.9194i	−1.47945	+	0.907359i
$817$	9.32592	−	5.38432i	0.326273	−	0.188374i
$818$	23.9784	−	22.7588i	0.838384	−	0.795744i
$819$	−1.51320	+	30.2828i	−0.0528754	+	1.05817i
$820$	−12.7806	−	6.09313i	−0.446316	−	0.212781i
$821$	−9.33723	+	12.1685i	−0.325872	+	0.424684i	−0.927344	−	0.374209i	$-0.877914\pi$
$821$	−9.33723	+	12.1685i	−0.325872	+	0.424684i	0.601473	+	0.798893i	$0.294581\pi$
$822$	10.4400	−	65.9547i	0.364136	−	2.30044i
$823$	−7.52433	+	2.01614i	−0.262282	+	0.0702781i	−0.387563	−	0.921843i	$-0.626683\pi$
$823$	−7.52433	+	2.01614i	−0.262282	+	0.0702781i	0.125282	+	0.992121i	$0.460016\pi$
$824$	−35.0951	−	12.4169i	−1.22260	−	0.432565i
$825$	27.6724	−	27.6724i	0.963429	−	0.963429i
$826$	−25.6519	+	37.5263i	−0.892542	+	1.30571i
$827$	51.3339	−	21.2632i	1.78505	−	0.739393i	0.793678	−	0.608338i	$-0.208164\pi$
$827$	51.3339	−	21.2632i	1.78505	−	0.739393i	0.991375	−	0.131055i	$-0.0418365\pi$
$828$	1.22200	−	0.622922i	0.0424674	−	0.0216480i
$829$	18.8133	+	24.5180i	0.653414	+	0.851545i	0.996130	−	0.0878937i	$-0.0280136\pi$
$829$	18.8133	+	24.5180i	0.653414	+	0.851545i	−0.342716	+	0.939439i	$0.611347\pi$
$830$	−2.85532	+	4.66041i	−0.0991095	+	0.161765i
$831$	30.8916	+	53.5058i	1.07162	+	1.85610i
$832$	−16.8243	−	10.2971i	−0.583276	−	0.356989i
$833$	24.2845	−	19.8616i	0.841408	−	0.688163i
$834$	6.58424	+	0.171808i	0.227994	+	0.00594924i
$835$	10.9047	−	1.43563i	0.377372	−	0.0496820i
$836$	−28.2413	−	18.3327i	−0.976744	−	0.634050i
$837$	1.09740	−	8.33555i	0.0379316	−	0.288119i
$838$	2.79994	−	0.294546i	0.0967222	−	0.0101749i
$839$	−15.1080	+	15.1080i	−0.521587	+	0.521587i	−0.918050	−	0.396463i	$-0.870237\pi$
$839$	−15.1080	+	15.1080i	−0.521587	+	0.521587i	0.396463	+	0.918050i	$0.370237\pi$
$840$	13.5830	+	23.3800i	0.468658	+	0.806685i
$841$	8.30253	+	8.30253i	0.286294	+	0.286294i
$842$	−36.5403	−	29.5842i	−1.25926	−	1.01954i
$843$	2.47145	+	0.325373i	0.0851213	+	0.0112064i
$844$	−37.6251	+	25.8692i	−1.29511	+	0.890456i
$845$	1.18023	+	8.96472i	0.0406011	+	0.308396i
$846$	41.2313	−	39.1343i	1.41756	−	1.34546i
$847$	−18.6097	+	6.64102i	−0.639436	+	0.228188i
$848$	14.5103	+	48.9197i	0.498284	+	1.67991i
$849$	−34.4670	+	19.8995i	−1.18290	+	0.682950i
$850$	20.2938	−	4.87408i	0.696071	−	0.167180i
$851$	−1.22939	+	0.943342i	−0.0421429	+	0.0323374i
$852$	−41.2623	+	48.3300i	−1.41362	+	1.65576i
$853$	4.41815	+	10.6664i	0.151275	+	0.365209i	0.981291	−	0.192529i	$-0.0616691\pi$
$853$	4.41815	+	10.6664i	0.151275	+	0.365209i	−0.830016	+	0.557739i	$0.811669\pi$
$854$	−5.05628	−	1.77617i	−0.173022	−	0.0607793i
$855$	−16.8216	−	16.8216i	−0.575287	−	0.575287i
$856$	25.3982	−	28.2232i	0.868092	−	0.964649i
$857$	11.0683	+	41.3075i	0.378087	+	1.41104i	0.848782	+	0.528743i	$0.177336\pi$
$857$	11.0683	+	41.3075i	0.378087	+	1.41104i	−0.470695	+	0.882296i	$0.655997\pi$
$858$	33.5243	−	24.3616i	1.14450	−	0.831691i
$859$	29.4746	+	22.6167i	1.00566	+	0.771671i	0.973704	−	0.227818i	$-0.0731592\pi$
$859$	29.4746	+	22.6167i	1.00566	+	0.771671i	0.0319577	+	0.999489i	$0.489826\pi$
$860$	4.80753	+	5.33733i	0.163936	+	0.182002i
$861$	−18.0841	−	35.2796i	−0.616305	−	1.20233i
$862$	0.847144	−	32.4653i	0.0288538	−	1.10577i
$863$	−4.02820	−	6.97705i	−0.137122	−	0.237502i	0.789284	−	0.614028i	$-0.210452\pi$
$863$	−4.02820	−	6.97705i	−0.137122	−	0.237502i	−0.926406	+	0.376526i	$0.877118\pi$
$864$	6.66072	−	24.9040i	0.226602	−	0.847250i
$865$	9.83796	−	17.0399i	0.334501	−	0.579372i
$866$	−25.9093	+	14.0707i	−0.880435	+	0.478142i
$867$	3.26604	−	7.88491i	0.110920	−	0.267786i
$868$	−8.59136	−	4.63566i	−0.291610	−	0.157345i
$869$	−46.0631	+	19.0800i	−1.56258	+	0.647243i
$870$	−2.22091	−	21.1118i	−0.0752959	−	0.715759i
$871$	−2.82545	−	10.5447i	−0.0957366	−	0.357294i
$872$	−3.77652	+	2.45398i	−0.127889	+	0.0831024i
$873$	13.9925	−	52.2208i	0.473575	−	1.76741i
$874$	0.293016	+	0.763123i	0.00991142	+	0.0258130i
$875$	−6.02843	−	28.0262i	−0.203798	−	0.947457i
$876$	−76.1590	+	26.9851i	−2.57317	+	0.911741i
$877$	−1.39516	−	10.5973i	−0.0471113	−	0.357846i	−0.998722	−	0.0505398i	$-0.983906\pi$
$877$	−1.39516	−	10.5973i	−0.0471113	−	0.357846i	0.951611	−	0.307306i	$-0.0994275\pi$
$878$	−10.1898	+	2.44736i	−0.343891	+	0.0825943i
$879$	22.5290	+	13.0071i	0.759884	+	0.438719i
$880$	8.04109	−	20.9708i	0.271065	−	0.706926i
$881$			1.92026i			0.0646951i	0.999477	+	0.0323476i	$0.0102983\pi$
$881$			1.92026i			0.0646951i	−0.999477	+	0.0323476i	$0.989702\pi$
$882$	−5.77952	+	45.6472i	−0.194607	+	1.53702i
$883$	−14.4315	−	5.97774i	−0.485660	−	0.201167i	0.126398	−	0.991980i	$-0.459658\pi$
$883$	−14.4315	−	5.97774i	−0.485660	−	0.201167i	−0.612058	+	0.790813i	$0.709658\pi$
$884$	22.0325	−	1.73808i	0.741034	−	0.0584578i
$885$	43.5206	+	5.72960i	1.46293	+	0.192598i
$886$	−3.53493	+	22.3320i	−0.118758	+	0.750258i
$887$	12.3508	−	46.0936i	0.414698	−	1.54767i	−0.370743	−	0.928736i	$-0.620897\pi$
$887$	12.3508	−	46.0936i	0.414698	−	1.54767i	0.785441	−	0.618937i	$-0.212436\pi$
$888$	−6.42258	+	81.8957i	−0.215528	+	2.74824i
$889$	−0.961543	+	0.664300i	−0.0322491	+	0.0222799i
$890$	−4.97216	+	11.1704i	−0.166667	+	0.374434i
$891$	−4.57150	−	3.50783i	−0.153151	−	0.117517i
$892$	−17.7191	+	27.2961i	−0.593281	+	0.913941i
$893$	20.6243	+	26.8780i	0.690164	+	0.899440i
$894$	−13.1372	−	24.1905i	−0.439375	−	0.809051i
$895$	6.36201			0.212659
$896$	−24.2705	−	17.5197i	−0.810822	−	0.585293i
$897$	−1.00612			−0.0335933
$898$	−7.52542	−	13.8571i	−0.251127	−	0.462416i
$899$	4.66571	+	6.08047i	0.155610	+	0.202795i
$900$	−16.6667	+	25.6748i	−0.555556	+	0.855826i
$901$	−45.3575	−	34.8040i	−1.51108	−	1.15949i
$902$	−13.3911	+	30.0843i	−0.445874	+	1.00170i
$903$	1.62684	+	20.0474i	0.0541378	+	0.667135i
$904$	−4.26238	+	54.3504i	−0.141765	+	1.80767i
$905$	−1.63605	+	6.10584i	−0.0543843	+	0.202965i
$906$	−4.33475	+	27.3849i	−0.144013	+	0.909801i
$907$	−12.5113	−	1.64714i	−0.415430	−	0.0546924i	−0.0800855	−	0.996788i	$-0.525519\pi$
$907$	−12.5113	−	1.64714i	−0.415430	−	0.0546924i	−0.335344	+	0.942096i	$0.608853\pi$
$908$	−41.3088	+	3.25872i	−1.37088	+	0.108144i
$909$	24.1012	+	9.98306i	0.799388	+	0.331117i
$910$	−0.661238	−	12.0357i	−0.0219198	−	0.398981i
$911$		−	32.1472i		−	1.06508i	−0.846404	−	0.532542i	$-0.821237\pi$
$911$		−	32.1472i		−	1.06508i	0.846404	−	0.532542i	$-0.178763\pi$
$912$	40.4615	+	15.5146i	1.33981	+	0.513740i
$913$	11.0086	+	6.35583i	0.364332	+	0.210347i
$914$	15.5650	−	3.73834i	0.514845	−	0.123653i
$915$	0.675510	+	5.13101i	0.0223317	+	0.169626i
$916$	44.5481	−	15.7845i	1.47191	−	0.521536i
$917$	34.5782	−	31.2870i	1.14187	−	1.03319i
$918$	10.3536	+	26.9647i	0.341721	+	0.889968i
$919$	8.34841	−	31.1567i	0.275389	−	1.02776i	−0.680192	−	0.733034i	$-0.738103\pi$
$919$	8.34841	−	31.1567i	0.275389	−	1.02776i	0.955580	−	0.294730i	$-0.0952299\pi$
$920$	−0.457229	+	0.297107i	−0.0150744	+	0.00979534i
$921$	9.45723	+	35.2949i	0.311626	+	1.16301i
$922$	3.06768	+	29.1612i	0.101029	+	0.960374i
$923$	26.1728	−	10.8411i	0.861489	−	0.356841i
$924$	53.5340	−	32.9987i	1.76114	−	1.08558i
$925$	13.2341	−	31.9500i	0.435135	−	1.05051i
$926$	−28.6957	+	15.5839i	−0.943000	+	0.512119i
$927$	−30.5871	+	52.9784i	−1.00461	+	1.74004i
$928$	11.7596	+	20.3466i	0.386027	+	0.667909i
$929$	14.5403	+	25.1845i	0.477052	+	0.826278i	0.999654	−	0.0262987i	$-0.00837211\pi$
$929$	14.5403	+	25.1845i	0.477052	+	0.826278i	−0.522602	+	0.852577i	$0.675039\pi$
$930$	−0.245909	+	9.42404i	−0.00806369	+	0.309026i
$931$	−26.6950	−	6.27169i	−0.874892	−	0.205546i
$932$	6.99780	+	7.76897i	0.229221	+	0.254481i
$933$	−15.6857	−	12.0361i	−0.513528	−	0.394044i
$934$	17.4276	−	12.6644i	0.570250	−	0.414391i
$935$	6.51308	+	24.3072i	0.213001	+	0.794929i
$936$	−21.6826	+	24.0943i	−0.708717	+	0.787547i
$937$	2.90284	+	2.90284i	0.0948317	+	0.0948317i	0.752931	−	0.658099i	$-0.228639\pi$
$937$	2.90284	+	2.90284i	0.0948317	+	0.0948317i	−0.658099	+	0.752931i	$0.728639\pi$
$938$	−3.06005	−	16.2811i	−0.0999143	−	0.531596i
$939$	−13.3614	−	32.2574i	−0.436034	−	1.05268i
$940$	−14.6738	+	17.1873i	−0.478608	+	0.560587i
$941$	18.2425	−	13.9980i	0.594688	−	0.456320i	−0.267044	−	0.963684i	$-0.586047\pi$
$941$	18.2425	−	13.9980i	0.594688	−	0.456320i	0.861732	+	0.507364i	$0.169380\pi$
$942$	0.695625	−	0.167073i	0.0226647	−	0.00544352i
$943$	0.692372	−	0.399741i	0.0225467	−	0.0130174i
$944$	−46.5882	+	13.8187i	−1.51632	+	0.449761i
$945$	14.8370	−	5.29471i	0.482648	−	0.172237i
$946$	12.1176	−	11.5013i	0.393976	−	0.373938i
$947$	3.35463	+	25.4809i	0.109011	+	0.828019i	0.955371	+	0.295409i	$0.0954558\pi$
$947$	3.35463	+	25.4809i	0.109011	+	0.828019i	−0.846360	+	0.532611i	$0.821211\pi$
$948$	52.8767	−	36.3555i	1.71735	−	1.18077i
$949$	35.7112	+	4.70147i	1.15923	+	0.152616i
$950$	−14.1784	−	11.4793i	−0.460007	−	0.372436i
$951$	24.8602	+	24.8602i	0.806148	+	0.806148i
$952$	33.5382	−	0.0908400i	1.08698	−	0.00294414i
$953$	31.6185	−	31.6185i	1.02422	−	1.02422i	0.0245248	−	0.999699i	$-0.492193\pi$
$953$	31.6185	−	31.6185i	1.02422	−	1.02422i	0.999699	−	0.0245248i	$-0.00780728\pi$
$954$	83.3901	−	8.77241i	2.69985	−	0.284017i
$955$	−0.807171	+	6.13108i	−0.0261195	+	0.198397i
$956$	−20.0879	−	13.0400i	−0.649691	−	0.421744i
$957$	−48.9500	+	6.44439i	−1.58233	+	0.208318i
$958$	−22.5992	−	0.589701i	−0.730148	−	0.0190524i
$959$	−29.2542	+	34.4214i	−0.944666	+	1.11153i
$960$	−4.50616	+	28.5528i	−0.145436	+	0.921536i
$961$	13.7982	+	23.8992i	0.445103	+	0.770941i
$962$	19.1313	−	31.2259i	0.616819	−	1.00676i
$963$	−37.9824	−	49.4996i	−1.22396	−	1.59510i
$964$	−19.4220	+	9.90051i	−0.625541	+	0.318874i
$965$	−11.7565	+	4.86971i	−0.378455	+	0.156761i
$966$	−1.52238	−	0.115948i	−0.0489819	−	0.00373056i
$967$	39.7411	−	39.7411i	1.27799	−	1.27799i	0.336196	−	0.941792i	$-0.390860\pi$
$967$	39.7411	−	39.7411i	1.27799	−	1.27799i	0.941792	−	0.336196i	$-0.109140\pi$
$968$	−19.9137	−	7.04564i	−0.640052	−	0.226455i
$969$	−46.8986	+	12.5664i	−1.50660	+	0.403692i
$970$	−3.36023	+	21.2283i	−0.107891	+	0.681600i
$971$	21.6895	−	28.2663i	0.696049	−	0.907109i	−0.302896	−	0.953024i	$-0.597954\pi$
$971$	21.6895	−	28.2663i	0.696049	−	0.907109i	0.998945	+	0.0459147i	$0.0146202\pi$
$972$	31.3759	+	14.9585i	1.00638	+	0.479793i
$973$	−3.74277	−	2.41766i	−0.119988	−	0.0775066i
$974$	−13.0209	+	12.3586i	−0.417216	+	0.395996i
$975$	19.4452	−	11.2267i	0.622745	−	0.359542i
$976$	−2.99530	−	4.88385i	−0.0958771	−	0.156328i
$977$	−26.7554	−	15.4473i	−0.855982	−	0.494202i	0.00668263	−	0.999978i	$-0.497873\pi$
$977$	−26.7554	−	15.4473i	−0.855982	−	0.494202i	−0.862665	+	0.505776i	$0.831206\pi$
$978$	−5.49129	+	18.5446i	−0.175592	+	0.592990i
$979$	26.2727	+	10.8825i	0.839680	+	0.347807i
$980$	0.386494	−	18.2878i	0.0123461	−	0.584181i
$981$	2.83223	+	6.83760i	0.0904261	+	0.218308i
$982$	−14.8108	+	18.2932i	−0.472631	+	0.583760i
$983$	7.47041	−	2.00169i	0.238269	−	0.0638440i	−0.137708	−	0.990473i	$-0.543974\pi$
$983$	7.47041	−	2.00169i	0.238269	−	0.0638440i	0.375977	+	0.926629i	$0.377307\pi$
$984$	8.80023	−	41.4581i	0.280541	−	1.32164i
$985$	2.70660	+	0.725232i	0.0862396	+	0.0231078i
$986$	−24.0554	−	10.7075i	−0.766079	−	0.340996i
$987$	−61.8630	+	13.3068i	−1.96912	+	0.423559i
$988$	−12.9289	−	14.3537i	−0.411322	−	0.456651i
$989$	−0.402140	+	0.0529427i	−0.0127873	+	0.00168348i
$990$	−31.4704	−	19.2811i	−1.00020	−	0.612794i
$991$	−5.26325	+	9.11622i	−0.167193	+	0.289586i	−0.937432	−	0.348169i	$-0.886804\pi$
$991$	−5.26325	+	9.11622i	−0.167193	+	0.289586i	0.770239	+	0.637755i	$0.220137\pi$
$992$	−3.99822	−	9.64000i	−0.126943	−	0.306070i
$993$	−78.6298			−2.49524
$994$	40.8521	−	13.3878i	1.29575	−	0.424634i
$995$	−0.357753	+	0.863693i	−0.0113415	+	0.0273809i
$996$	−15.5605	−	5.05273i	−0.493052	−	0.160102i
$997$	4.12598	−	31.3399i	0.130671	−	0.992545i	−0.792963	−	0.609269i	$-0.791463\pi$
$997$	4.12598	−	31.3399i	0.130671	−	0.992545i	0.923634	−	0.383275i	$-0.125204\pi$
$998$	40.1601	−	29.1837i	1.27125	−	0.923794i
$999$	46.2293	+	12.3871i	1.46263	+	0.391910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.109.19	yes	240
4.3	odd	2		896.2.bh.a.529.28		240
7.2	even	3	inner	224.2.bd.a.205.22	yes	240
28.23	odd	6		896.2.bh.a.401.3		240
32.5	even	8	inner	224.2.bd.a.165.22	yes	240
32.27	odd	8		896.2.bh.a.753.3		240
224.37	even	24	inner	224.2.bd.a.37.19	✓	240
224.219	odd	24		896.2.bh.a.625.28		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.19	✓	240	224.37	even	24	inner
224.2.bd.a.109.19	yes	240	1.1	even	1	trivial
224.2.bd.a.165.22	yes	240	32.5	even	8	inner
224.2.bd.a.205.22	yes	240	7.2	even	3	inner
896.2.bh.a.401.3		240	28.23	odd	6
896.2.bh.a.529.28		240	4.3	odd	2
896.2.bh.a.625.28		240	224.219	odd	24
896.2.bh.a.753.3		240	32.27	odd	8

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	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

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