LMFDB - Embedded newform 570.2.u.c.481.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(61,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("570.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.u (of order $9$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			481.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	570.481
Dual form			570.2.u.c.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.173648 + 0.984808i) q^{5} +(0.939693 - 0.342020i) q^{6} +(0.266044 - 0.460802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.173648 + 0.984808i) q^{5} +(0.939693 - 0.342020i) q^{6} +(0.266044 - 0.460802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(-0.766044 - 0.642788i) q^{10} +(-0.326352 - 0.565258i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.439693 - 0.160035i) q^{13} +(0.0923963 + 0.524005i) q^{14} +(0.173648 - 0.984808i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.439693 - 0.368946i) q^{17} -1.00000 q^{18} +(4.07398 - 1.55007i) q^{19} +1.00000 q^{20} +(-0.407604 + 0.342020i) q^{21} +(0.613341 + 0.223238i) q^{22} +(-1.09240 + 6.19529i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(-0.233956 + 0.405223i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-0.407604 - 0.342020i) q^{28} +(4.55303 + 3.82045i) q^{29} +(0.500000 + 0.866025i) q^{30} +(4.05303 - 7.02006i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.113341 + 0.642788i) q^{33} +(-0.0996702 + 0.565258i) q^{34} +(0.500000 + 0.181985i) q^{35} +(0.766044 - 0.642788i) q^{36} +4.17024 q^{37} +(-2.12449 + 3.80612i) q^{38} -0.467911 q^{39} +(-0.766044 + 0.642788i) q^{40} +(9.99660 + 3.63846i) q^{41} +(0.0923963 - 0.524005i) q^{42} +(0.578726 + 3.28212i) q^{43} +(-0.613341 + 0.223238i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-3.14543 - 5.44804i) q^{46} +(3.75490 + 3.15074i) q^{47} +(0.766044 + 0.642788i) q^{48} +(3.35844 + 5.81699i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.539363 + 0.196312i) q^{51} +(-0.0812519 - 0.460802i) q^{52} +(-1.86097 + 10.5541i) q^{53} +(0.939693 + 0.342020i) q^{54} +(0.500000 - 0.419550i) q^{55} +0.532089 q^{56} +(-4.35844 + 0.0632028i) q^{57} -5.94356 q^{58} +(7.07398 - 5.93577i) q^{59} +(-0.939693 - 0.342020i) q^{60} +(-0.503404 + 2.85494i) q^{61} +(1.40760 + 7.98292i) q^{62} +(0.500000 - 0.181985i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.233956 + 0.405223i) q^{65} +(-0.500000 - 0.419550i) q^{66} +(-7.88326 - 6.61484i) q^{67} +(-0.286989 - 0.497079i) q^{68} +(3.14543 - 5.44804i) q^{69} +(-0.500000 + 0.181985i) q^{70} +(-1.17752 - 6.67804i) q^{71} +(-0.173648 + 0.984808i) q^{72} +(-0.247626 - 0.0901285i) q^{73} +(-3.19459 + 2.68058i) q^{74} +1.00000 q^{75} +(-0.819078 - 4.28125i) q^{76} -0.347296 q^{77} +(0.358441 - 0.300767i) q^{78} +(2.49273 + 0.907278i) q^{79} +(0.173648 - 0.984808i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-9.99660 + 3.63846i) q^{82} +(-1.78699 + 3.09516i) q^{83} +(0.266044 + 0.460802i) q^{84} +(0.439693 + 0.368946i) q^{85} +(-2.55303 - 2.14225i) q^{86} +(-2.97178 - 5.14728i) q^{87} +(0.326352 - 0.565258i) q^{88} +(-3.72668 + 1.35640i) q^{89} +(-0.173648 - 0.984808i) q^{90} +(0.0432332 - 0.245188i) q^{91} +(5.91147 + 2.15160i) q^{92} +(-6.20961 + 5.21048i) q^{93} -4.90167 q^{94} +(2.23396 + 3.74292i) q^{95} -1.00000 q^{96} +(2.89440 - 2.42869i) q^{97} +(-6.31180 - 2.29731i) q^{98} +(0.113341 - 0.642788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q - 3 * q^7 + 3 * q^8	$ 6 q - 3 q^{7} + 3 q^{8} - 3 q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} - 3 q^{17} - 6 q^{18} + 9 q^{19} + 6 q^{20} - 6 q^{21} - 3 q^{22} - 3 q^{23} - 6 q^{26} - 3 q^{27} - 6 q^{28} + 15 q^{29} + 3 q^{30} + 12 q^{31} - 6 q^{33} - 15 q^{34} + 3 q^{35} - 18 q^{37} - 12 q^{39} + 18 q^{41} - 3 q^{42} + 21 q^{43} + 3 q^{44} - 3 q^{45} - 3 q^{46} + 24 q^{47} + 12 q^{49} + 3 q^{50} - 12 q^{51} - 3 q^{52} + 12 q^{53} + 3 q^{55} - 6 q^{56} - 18 q^{57} - 6 q^{58} + 27 q^{59} - 45 q^{61} + 12 q^{62} + 3 q^{63} - 3 q^{64} + 6 q^{65} - 3 q^{66} - 12 q^{67} + 6 q^{68} + 3 q^{69} - 3 q^{70} + 18 q^{71} + 15 q^{73} - 15 q^{74} + 6 q^{75} + 12 q^{76} - 6 q^{78} - 3 q^{79} - 18 q^{82} - 3 q^{83} - 3 q^{84} - 3 q^{85} - 3 q^{86} - 3 q^{87} + 3 q^{88} - 9 q^{89} - 15 q^{91} + 15 q^{92} - 3 q^{93} - 6 q^{94} + 18 q^{95} - 6 q^{96} - 24 q^{97} - 3 q^{98} - 6 q^{99}+O(q^{100}) $ 6 * q - 3 * q^7 + 3 * q^8 - 3 * q^11 - 3 * q^12 - 3 * q^13 - 3 * q^14 - 3 * q^17 - 6 * q^18 + 9 * q^19 + 6 * q^20 - 6 * q^21 - 3 * q^22 - 3 * q^23 - 6 * q^26 - 3 * q^27 - 6 * q^28 + 15 * q^29 + 3 * q^30 + 12 * q^31 - 6 * q^33 - 15 * q^34 + 3 * q^35 - 18 * q^37 - 12 * q^39 + 18 * q^41 - 3 * q^42 + 21 * q^43 + 3 * q^44 - 3 * q^45 - 3 * q^46 + 24 * q^47 + 12 * q^49 + 3 * q^50 - 12 * q^51 - 3 * q^52 + 12 * q^53 + 3 * q^55 - 6 * q^56 - 18 * q^57 - 6 * q^58 + 27 * q^59 - 45 * q^61 + 12 * q^62 + 3 * q^63 - 3 * q^64 + 6 * q^65 - 3 * q^66 - 12 * q^67 + 6 * q^68 + 3 * q^69 - 3 * q^70 + 18 * q^71 + 15 * q^73 - 15 * q^74 + 6 * q^75 + 12 * q^76 - 6 * q^78 - 3 * q^79 - 18 * q^82 - 3 * q^83 - 3 * q^84 - 3 * q^85 - 3 * q^86 - 3 * q^87 + 3 * q^88 - 9 * q^89 - 15 * q^91 + 15 * q^92 - 3 * q^93 - 6 * q^94 + 18 * q^95 - 6 * q^96 - 24 * q^97 - 3 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$6$	0.939693	−	0.342020i	0.383628	−	0.139629i
$7$	0.266044	−	0.460802i	0.100555	−	0.174167i	−0.811358	−	0.584549i	$-0.801271\pi$
$7$	0.266044	−	0.460802i	0.100555	−	0.174167i	0.911914	+	0.410382i	$0.134605\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$	−0.766044	−	0.642788i	−0.242245	−	0.203267i
$11$	−0.326352	−	0.565258i	−0.0983988	−	0.170432i	0.812623	−	0.582789i	$-0.198039\pi$
$11$	−0.326352	−	0.565258i	−0.0983988	−	0.170432i	−0.911022	+	0.412358i	$0.864705\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	0.439693	−	0.160035i	0.121949	−	0.0443857i	−0.280325	−	0.959905i	$-0.590442\pi$
$13$	0.439693	−	0.160035i	0.121949	−	0.0443857i	0.402274	+	0.915519i	$0.368220\pi$
$14$	0.0923963	+	0.524005i	0.0246939	+	0.140046i
$15$	0.173648	−	0.984808i	0.0448358	−	0.254276i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.439693	−	0.368946i	0.106641	−	0.0894825i	−0.587908	−	0.808928i	$-0.700048\pi$
$17$	0.439693	−	0.368946i	0.106641	−	0.0894825i	0.694549	+	0.719445i	$0.255604\pi$
$18$	−1.00000			−0.235702
$19$	4.07398	−	1.55007i	0.934635	−	0.355609i
$19$	4.07398	−	1.55007i	0.934635	−	0.355609i
$20$	1.00000			0.223607
$21$	−0.407604	+	0.342020i	−0.0889464	+	0.0746349i
$22$	0.613341	+	0.223238i	0.130765	+	0.0475945i
$23$	−1.09240	+	6.19529i	−0.227780	+	1.29181i	0.629518	+	0.776986i	$0.283253\pi$
$23$	−1.09240	+	6.19529i	−0.227780	+	1.29181i	−0.857298	+	0.514820i	$0.827859\pi$
$24$	−0.173648	−	0.984808i	−0.0354458	−	0.201023i
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	−0.233956	+	0.405223i	−0.0458825	+	0.0794708i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	−0.407604	−	0.342020i	−0.0770299	−	0.0646357i
$29$	4.55303	+	3.82045i	0.845477	+	0.709440i	0.958789	−	0.284120i	$-0.0917014\pi$
$29$	4.55303	+	3.82045i	0.845477	+	0.709440i	−0.113312	+	0.993559i	$0.536146\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$	4.05303	−	7.02006i	0.727946	−	1.26084i	−0.229803	−	0.973237i	$-0.573808\pi$
$31$	4.05303	−	7.02006i	0.727946	−	1.26084i	0.957750	−	0.287603i	$-0.0928583\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	0.113341	+	0.642788i	0.0197301	+	0.111895i
$34$	−0.0996702	+	0.565258i	−0.0170933	+	0.0969409i
$35$	0.500000	+	0.181985i	0.0845154	+	0.0307611i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	4.17024			0.685584			0.342792	−	0.939411i	$-0.388627\pi$
$37$	4.17024			0.685584			0.342792	+	0.939411i	$0.388627\pi$
$38$	−2.12449	+	3.80612i	−0.344637	+	0.617434i
$39$	−0.467911			−0.0749257
$40$	−0.766044	+	0.642788i	−0.121122	+	0.101634i
$41$	9.99660	+	3.63846i	1.56121	+	0.568233i	0.971012	−	0.239029i	$-0.0768291\pi$
$41$	9.99660	+	3.63846i	1.56121	+	0.568233i	0.590194	+	0.807262i	$0.299051\pi$
$42$	0.0923963	−	0.524005i	0.0142571	−	0.0808558i
$43$	0.578726	+	3.28212i	0.0882548	+	0.500518i	0.996607	+	0.0823112i	$0.0262302\pi$
$43$	0.578726	+	3.28212i	0.0882548	+	0.500518i	−0.908352	+	0.418207i	$0.862659\pi$
$44$	−0.613341	+	0.223238i	−0.0924646	+	0.0336544i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−3.14543	−	5.44804i	−0.463768	−	0.803270i
$47$	3.75490	+	3.15074i	0.547708	+	0.459582i	0.874164	−	0.485631i	$-0.161410\pi$
$47$	3.75490	+	3.15074i	0.547708	+	0.459582i	−0.326456	+	0.945213i	$0.605854\pi$
$48$	0.766044	+	0.642788i	0.110569	+	0.0927784i
$49$	3.35844	+	5.81699i	0.479777	+	0.830999i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−0.539363	+	0.196312i	−0.0755259	+	0.0274892i
$52$	−0.0812519	−	0.460802i	−0.0112676	−	0.0639018i
$53$	−1.86097	+	10.5541i	−0.255623	+	1.44971i	0.538844	+	0.842406i	$0.318861\pi$
$53$	−1.86097	+	10.5541i	−0.255623	+	1.44971i	−0.794467	+	0.607307i	$0.792250\pi$
$54$	0.939693	+	0.342020i	0.127876	+	0.0465430i
$55$	0.500000	−	0.419550i	0.0674200	−	0.0565721i
$56$	0.532089			0.0711034
$57$	−4.35844	+	0.0632028i	−0.577290	+	0.00837141i
$58$	−5.94356			−0.780428
$59$	7.07398	−	5.93577i	0.920953	−	0.772772i	−0.0532176	−	0.998583i	$-0.516948\pi$
$59$	7.07398	−	5.93577i	0.920953	−	0.772772i	0.974171	+	0.225811i	$0.0725032\pi$
$60$	−0.939693	−	0.342020i	−0.121314	−	0.0441546i
$61$	−0.503404	+	2.85494i	−0.0644542	+	0.365538i	0.935472	+	0.353401i	$0.114975\pi$
$61$	−0.503404	+	2.85494i	−0.0644542	+	0.365538i	−0.999926	+	0.0121375i	$0.996136\pi$
$62$	1.40760	+	7.98292i	0.178766	+	1.01383i
$63$	0.500000	−	0.181985i	0.0629941	−	0.0229280i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.233956	+	0.405223i	0.0290186	+	0.0502617i
$66$	−0.500000	−	0.419550i	−0.0615457	−	0.0516430i
$67$	−7.88326	−	6.61484i	−0.963093	−	0.808131i	0.0183605	−	0.999831i	$-0.494155\pi$
$67$	−7.88326	−	6.61484i	−0.963093	−	0.808131i	−0.981453	+	0.191700i	$0.938600\pi$
$68$	−0.286989	−	0.497079i	−0.0348025	−	0.0602797i
$69$	3.14543	−	5.44804i	0.378665	−	0.655867i
$70$	−0.500000	+	0.181985i	−0.0597614	+	0.0217514i
$71$	−1.17752	−	6.67804i	−0.139746	−	0.792537i	−0.971437	−	0.237299i	$-0.923738\pi$
$71$	−1.17752	−	6.67804i	−0.139746	−	0.792537i	0.831691	−	0.555239i	$-0.187373\pi$
$72$	−0.173648	+	0.984808i	−0.0204646	+	0.116061i
$73$	−0.247626	−	0.0901285i	−0.0289824	−	0.0105487i	0.327488	−	0.944855i	$-0.393798\pi$
$73$	−0.247626	−	0.0901285i	−0.0289824	−	0.0105487i	−0.356471	+	0.934307i	$0.616020\pi$
$74$	−3.19459	+	2.68058i	−0.371364	+	0.311611i
$75$	1.00000			0.115470
$76$	−0.819078	−	4.28125i	−0.0939547	−	0.491093i
$77$	−0.347296			−0.0395781
$78$	0.358441	−	0.300767i	0.0405854	−	0.0340552i
$79$	2.49273	+	0.907278i	0.280454	+	0.102077i	0.478417	−	0.878133i	$-0.341211\pi$
$79$	2.49273	+	0.907278i	0.280454	+	0.102077i	−0.197964	+	0.980209i	$0.563433\pi$
$80$	0.173648	−	0.984808i	0.0194145	−	0.110105i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	−9.99660	+	3.63846i	−1.10394	+	0.401801i
$83$	−1.78699	+	3.09516i	−0.196148	+	0.339737i	−0.947276	−	0.320418i	$-0.896176\pi$
$83$	−1.78699	+	3.09516i	−0.196148	+	0.339737i	0.751129	+	0.660156i	$0.229510\pi$
$84$	0.266044	+	0.460802i	0.0290278	+	0.0502777i
$85$	0.439693	+	0.368946i	0.0476914	+	0.0400178i
$86$	−2.55303	−	2.14225i	−0.275301	−	0.231005i
$87$	−2.97178	−	5.14728i	−0.318608	−	0.551846i
$88$	0.326352	−	0.565258i	0.0347892	−	0.0602567i
$89$	−3.72668	+	1.35640i	−0.395027	+	0.143778i	−0.531893	−	0.846811i	$-0.678519\pi$
$89$	−3.72668	+	1.35640i	−0.395027	+	0.143778i	0.136866	+	0.990590i	$0.456297\pi$
$90$	−0.173648	−	0.984808i	−0.0183041	−	0.103808i
$91$	0.0432332	−	0.245188i	0.00453207	−	0.0257027i
$92$	5.91147	+	2.15160i	0.616314	+	0.224320i
$93$	−6.20961	+	5.21048i	−0.643906	+	0.540302i
$94$	−4.90167			−0.505569
$95$	2.23396	+	3.74292i	0.229199	+	0.384015i
$96$	−1.00000			−0.102062
$97$	2.89440	−	2.42869i	0.293882	−	0.246596i	−0.483911	−	0.875117i	$-0.660784\pi$
$97$	2.89440	−	2.42869i	0.293882	−	0.246596i	0.777792	+	0.628521i	$0.216340\pi$
$98$	−6.31180	−	2.29731i	−0.637588	−	0.232063i
$99$	0.113341	−	0.642788i	0.0113912	−	0.0646026i
$100$	0.173648	+	0.984808i	0.0173648	+	0.0984808i
$101$	−6.04323	+	2.19956i	−0.601324	+	0.218864i	−0.624703	−	0.780863i	$-0.714780\pi$
$101$	−6.04323	+	2.19956i	−0.601324	+	0.218864i	0.0233787	+	0.999727i	$0.492558\pi$
$102$	0.286989	−	0.497079i	0.0284161	−	0.0492182i
$103$	−0.198463	−	0.343748i	−0.0195552	−	0.0338705i	0.856082	−	0.516840i	$-0.172892\pi$
$103$	−0.198463	−	0.343748i	−0.0195552	−	0.0338705i	−0.875637	+	0.482969i	$0.839558\pi$
$104$	0.358441	+	0.300767i	0.0351480	+	0.0294927i
$105$	−0.407604	−	0.342020i	−0.0397781	−	0.0333777i
$106$	−5.35844	−	9.28109i	−0.520458	−	0.901459i
$107$	7.78699	−	13.4875i	0.752797	−	1.30388i	−0.193666	−	0.981068i	$-0.562038\pi$
$107$	7.78699	−	13.4875i	0.752797	−	1.30388i	0.946462	−	0.322814i	$-0.104629\pi$
$108$	−0.939693	+	0.342020i	−0.0904220	+	0.0329109i
$109$	−1.17499	−	6.66371i	−0.112544	−	0.638268i	−0.987937	−	0.154856i	$-0.950509\pi$
$109$	−1.17499	−	6.66371i	−0.112544	−	0.638268i	0.875393	−	0.483412i	$-0.160603\pi$
$110$	−0.113341	+	0.642788i	−0.0108066	+	0.0612874i
$111$	−3.91875	−	1.42631i	−0.371951	−	0.135379i
$112$	−0.407604	+	0.342020i	−0.0385149	+	0.0323179i
$113$	−10.7101			−1.00752			−0.503760	−	0.863844i	$-0.668050\pi$
$113$	−10.7101			−1.00752			−0.503760	+	0.863844i	$0.668050\pi$
$114$	3.29813	−	2.84997i	0.308898	−	0.266924i
$115$	−6.29086			−0.586626
$116$	4.55303	−	3.82045i	0.422739	−	0.354720i
$117$	0.439693	+	0.160035i	0.0406496	+	0.0147952i
$118$	−1.60354	+	9.09413i	−0.147618	+	0.837183i
$119$	−0.0530334	−	0.300767i	−0.00486157	−	0.0275713i
$120$	0.939693	−	0.342020i	0.0857818	−	0.0312220i
$121$	5.28699	−	9.15733i	0.480635	−	0.832485i
$122$	−1.44949	−	2.51060i	−0.131231	−	0.227299i
$123$	−8.14930	−	6.83807i	−0.734798	−	0.616568i
$124$	−6.20961	−	5.21048i	−0.557639	−	0.467915i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$	−0.266044	+	0.460802i	−0.0237011	+	0.0410515i
$127$	4.29813	−	1.56439i	0.381398	−	0.138817i	−0.144204	−	0.989548i	$-0.546062\pi$
$127$	4.29813	−	1.56439i	0.381398	−	0.138817i	0.525602	+	0.850731i	$0.323840\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	0.578726	−	3.28212i	0.0509540	−	0.288974i
$130$	−0.439693	−	0.160035i	−0.0385636	−	0.0140360i
$131$	−3.41147	+	2.86257i	−0.298062	+	0.250104i	−0.779537	−	0.626356i	$-0.784546\pi$
$131$	−3.41147	+	2.86257i	−0.298062	+	0.250104i	0.481475	+	0.876460i	$0.340101\pi$
$132$	0.652704			0.0568106
$133$	0.369585	−	2.28969i	0.0320471	−	0.198541i
$134$	10.2909			0.888995
$135$	0.766044	−	0.642788i	0.0659306	−	0.0553223i
$136$	0.539363	+	0.196312i	0.0462500	+	0.0168336i
$137$	0.0136706	−	0.0775297i	0.00116796	−	0.00662381i	−0.984218	−	0.176959i	$-0.943374\pi$
$137$	0.0136706	−	0.0775297i	0.00116796	−	0.00662381i	0.985386	+	0.170335i	$0.0544851\pi$
$138$	1.09240	+	6.19529i	0.0929909	+	0.527378i
$139$	−5.89053	+	2.14398i	−0.499628	+	0.181850i	−0.579527	−	0.814953i	$-0.696763\pi$
$139$	−5.89053	+	2.14398i	−0.499628	+	0.181850i	0.0798986	+	0.996803i	$0.474540\pi$
$140$	0.266044	−	0.460802i	0.0224849	−	0.0389449i
$141$	−2.45084	−	4.24497i	−0.206398	−	0.357491i
$142$	5.19459	+	4.35878i	0.435921	+	0.365781i
$143$	−0.233956	−	0.196312i	−0.0195643	−	0.0164164i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−2.97178	+	5.14728i	−0.246793	+	0.427458i
$146$	0.247626	−	0.0901285i	0.0204937	−	0.00745909i
$147$	−1.16637	−	6.61484i	−0.0962009	−	0.545583i
$148$	0.724155	−	4.10689i	0.0595252	−	0.337584i
$149$	−13.8293	−	5.03347i	−1.13294	−	0.412358i	−0.293584	−	0.955933i	$-0.594848\pi$
$149$	−13.8293	−	5.03347i	−1.13294	−	0.412358i	−0.839360	+	0.543575i	$0.817070\pi$
$150$	−0.766044	+	0.642788i	−0.0625473	+	0.0524834i
$151$	2.69728			0.219502			0.109751	−	0.993959i	$-0.464995\pi$
$151$	2.69728			0.219502			0.109751	+	0.993959i	$0.464995\pi$
$152$	3.37939	+	2.75314i	0.274104	+	0.223309i
$153$	0.573978			0.0464034
$154$	0.266044	−	0.223238i	0.0214385	−	0.0179890i
$155$	7.61721	+	2.77244i	0.611829	+	0.222688i
$156$	−0.0812519	+	0.460802i	−0.00650536	+	0.0368937i
$157$	−1.06536	−	6.04196i	−0.0850250	−	0.482201i	−0.997351	−	0.0727365i	$-0.976827\pi$
$157$	−1.06536	−	6.04196i	−0.0850250	−	0.482201i	0.912326	−	0.409464i	$-0.134284\pi$
$158$	−2.49273	+	0.907278i	−0.198311	+	0.0721792i
$159$	5.35844	−	9.28109i	0.424952	−	0.736038i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	2.56418	+	2.15160i	0.202086	+	0.169570i
$162$	−0.766044	−	0.642788i	−0.0601861	−	0.0505022i
$163$	−4.53596	−	7.85651i	−0.355284	−	0.615370i	0.631883	−	0.775064i	$-0.282282\pi$
$163$	−4.53596	−	7.85651i	−0.355284	−	0.615370i	−0.987166	+	0.159694i	$0.948949\pi$
$164$	5.31908	−	9.21291i	0.415350	−	0.719408i
$165$	−0.613341	+	0.223238i	−0.0477485	+	0.0173790i
$166$	−0.620615	−	3.51968i	−0.0481690	−	0.273180i
$167$	1.66132	−	9.42182i	0.128557	−	0.729083i	−0.850574	−	0.525855i	$-0.823746\pi$
$167$	1.66132	−	9.42182i	0.128557	−	0.729083i	0.979131	−	0.203228i	$-0.0651433\pi$
$168$	−0.500000	−	0.181985i	−0.0385758	−	0.0140405i
$169$	−9.79086	+	8.21551i	−0.753143	+	0.631962i
$170$	−0.573978			−0.0440221
$171$	4.11721	+	1.43128i	0.314851	+	0.109453i
$172$	3.33275			0.254120
$173$	−17.4722	+	14.6610i	−1.32839	+	1.11465i	−0.343940	+	0.938992i	$0.611762\pi$
$173$	−17.4722	+	14.6610i	−1.32839	+	1.11465i	−0.984451	+	0.175660i	$0.943794\pi$
$174$	5.58512	+	2.03282i	0.423407	+	0.154108i
$175$	−0.0923963	+	0.524005i	−0.00698450	+	0.0396111i
$176$	0.113341	+	0.642788i	0.00854338	+	0.0484519i
$177$	−8.67752	+	3.15836i	−0.652242	+	0.237397i
$178$	1.98293	−	3.43453i	0.148627	−	0.257429i
$179$	−9.51754	−	16.4849i	−0.711374	−	1.23214i	−0.964341	−	0.264662i	$-0.914740\pi$
$179$	−9.51754	−	16.4849i	−0.711374	−	1.23214i	0.252967	−	0.967475i	$-0.418594\pi$
$180$	0.766044	+	0.642788i	0.0570976	+	0.0479106i
$181$	7.55097	+	6.33602i	0.561259	+	0.470953i	0.878732	−	0.477315i	$-0.158390\pi$
$181$	7.55097	+	6.33602i	0.561259	+	0.470953i	−0.317473	+	0.948267i	$0.602834\pi$
$182$	0.124485	+	0.215615i	0.00922745	+	0.0159824i
$183$	1.44949	−	2.51060i	0.107150	−	0.185589i
$184$	−5.91147	+	2.15160i	−0.435800	+	0.158618i
$185$	0.724155	+	4.10689i	0.0532410	+	0.301945i
$186$	1.40760	−	7.98292i	0.103211	−	0.585336i
$187$	−0.352044	−	0.128134i	−0.0257440	−	0.00937005i
$188$	3.75490	−	3.15074i	0.273854	−	0.229791i
$189$	−0.532089			−0.0387038
$190$	−4.11721	−	1.43128i	−0.298694	−	0.103836i
$191$	2.75877			0.199618			0.0998088	−	0.995007i	$-0.468177\pi$
$191$	2.75877			0.199618			0.0998088	+	0.995007i	$0.468177\pi$
$192$	0.766044	−	0.642788i	0.0552845	−	0.0463892i
$193$	22.4329	+	8.16490i	1.61475	+	0.587723i	0.982372	−	0.186934i	$-0.0598551\pi$
$193$	22.4329	+	8.16490i	1.61475	+	0.587723i	0.632382	+	0.774657i	$0.282077\pi$
$194$	−0.656107	+	3.72097i	−0.0471058	+	0.267150i
$195$	−0.0812519	−	0.460802i	−0.00581857	−	0.0329988i
$196$	6.31180	−	2.29731i	0.450843	−	0.164093i
$197$	8.76264	−	15.1773i	0.624312	−	1.08134i	−0.364361	−	0.931258i	$-0.618713\pi$
$197$	8.76264	−	15.1773i	0.624312	−	1.08134i	0.988673	−	0.150083i	$-0.0479541\pi$
$198$	0.326352	+	0.565258i	0.0231928	+	0.0401711i
$199$	7.11721	+	5.97205i	0.504526	+	0.423347i	0.859198	−	0.511643i	$-0.170963\pi$
$199$	7.11721	+	5.97205i	0.504526	+	0.423347i	−0.354672	+	0.934991i	$0.615408\pi$
$200$	−0.766044	−	0.642788i	−0.0541675	−	0.0454519i
$201$	5.14543	+	8.91215i	0.362931	+	0.628614i
$202$	3.21554	−	5.56947i	0.226244	−	0.391867i
$203$	2.97178	−	1.08164i	0.208578	−	0.0759162i
$204$	0.0996702	+	0.565258i	0.00697831	+	0.0395760i
$205$	−1.84730	+	10.4765i	−0.129021	+	0.731713i
$206$	0.372989	+	0.135757i	0.0259873	+	0.00945862i
$207$	−4.81908	+	4.04369i	−0.334949	+	0.281056i
$208$	−0.467911			−0.0324438
$209$	−2.20574	−	1.79698i	−0.152574	−	0.124300i
$210$	0.532089			0.0367176
$211$	−6.16637	+	5.17420i	−0.424511	+	0.356207i	−0.829876	−	0.557948i	$-0.811589\pi$
$211$	−6.16637	+	5.17420i	−0.424511	+	0.356207i	0.405365	+	0.914155i	$0.367144\pi$
$212$	10.0706	+	3.66539i	0.691650	+	0.251740i
$213$	−1.17752	+	6.67804i	−0.0806822	+	0.457572i
$214$	2.70439	+	15.3374i	0.184868	+	1.04844i
$215$	−3.13176	+	1.13987i	−0.213584	+	0.0777383i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	−2.15657	−	3.73530i	−0.146398	−	0.253568i
$218$	5.18345	+	4.34943i	0.351067	+	0.294581i
$219$	0.201867	+	0.169386i	0.0136409	+	0.0114461i
$220$	−0.326352	−	0.565258i	−0.0220026	−	0.0381097i
$221$	0.134285	−	0.232589i	0.00903301	−	0.0156456i
$222$	3.91875	−	1.42631i	0.263009	−	0.0957275i
$223$	0.789210	+	4.47584i	0.0528494	+	0.299724i	0.999763	−	0.0217638i	$-0.00692817\pi$
$223$	0.789210	+	4.47584i	0.0528494	+	0.299724i	−0.946914	+	0.321488i	$0.895817\pi$
$224$	0.0923963	−	0.524005i	0.00617349	−	0.0350116i
$225$	−0.939693	−	0.342020i	−0.0626462	−	0.0228013i
$226$	8.20439	−	6.88430i	0.545748	−	0.457937i
$227$	−24.6486			−1.63598			−0.817992	−	0.575230i	$-0.804913\pi$
$227$	−24.6486			−1.63598			−0.817992	+	0.575230i	$0.804913\pi$
$228$	−0.694593	+	4.30320i	−0.0460005	+	0.284986i
$229$	−13.3473			−0.882014			−0.441007	−	0.897504i	$-0.645379\pi$
$229$	−13.3473			−0.882014			−0.441007	+	0.897504i	$0.645379\pi$
$230$	4.81908	−	4.04369i	0.317761	−	0.266633i
$231$	0.326352	+	0.118782i	0.0214724	+	0.00781530i
$232$	−1.03209	+	5.85327i	−0.0677600	+	0.384286i
$233$	2.39693	+	13.5936i	0.157028	+	0.890549i	0.956908	+	0.290390i	$0.0937850\pi$
$233$	2.39693	+	13.5936i	0.157028	+	0.890549i	−0.799881	+	0.600159i	$0.795104\pi$
$234$	−0.439693	+	0.160035i	−0.0287436	+	0.0104618i
$235$	−2.45084	+	4.24497i	−0.159875	+	0.276912i
$236$	−4.61721	−	7.99724i	−0.300555	−	0.520576i
$237$	−2.03209	−	1.70513i	−0.131998	−	0.110760i
$238$	0.233956	+	0.196312i	0.0151651	+	0.0127250i
$239$	6.28833	+	10.8917i	0.406758	+	0.704526i	0.994524	−	0.104505i	$-0.0333257\pi$
$239$	6.28833	+	10.8917i	0.406758	+	0.704526i	−0.587766	+	0.809031i	$0.699992\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	−1.29901	+	0.472801i	−0.0836766	+	0.0304558i	−0.383519	−	0.923533i	$-0.625288\pi$
$241$	−1.29901	+	0.472801i	−0.0836766	+	0.0304558i	0.299843	+	0.953989i	$0.403066\pi$
$242$	1.83615	+	10.4133i	0.118032	+	0.669395i
$243$	0.173648	−	0.984808i	0.0111395	−	0.0631754i
$244$	2.72416	+	0.991511i	0.174396	+	0.0634750i
$245$	−5.14543	+	4.31753i	−0.328729	+	0.275837i
$246$	10.6382			0.678264
$247$	1.54323	−	1.33353i	0.0981936	−	0.0848506i
$248$	8.10607			0.514736
$249$	2.73783	−	2.29731i	0.173503	−	0.145586i
$250$	0.939693	+	0.342020i	0.0594314	+	0.0216313i
$251$	0.204860	−	1.16182i	0.0129306	−	0.0733333i	−0.977660	−	0.210194i	$-0.932590\pi$
$251$	0.204860	−	1.16182i	0.0129306	−	0.0733333i	0.990590	+	0.136861i	$0.0437014\pi$
$252$	−0.0923963	−	0.524005i	−0.00582042	−	0.0330092i
$253$	3.85844	−	1.40436i	0.242578	−	0.0882912i
$254$	−2.28699	+	3.96118i	−0.143498	+	0.248547i
$255$	−0.286989	−	0.497079i	−0.0179719	−	0.0311283i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	12.1493	+	10.1945i	0.757853	+	0.635914i	0.937567	−	0.347805i	$-0.113073\pi$
$257$	12.1493	+	10.1945i	0.757853	+	0.635914i	−0.179714	+	0.983719i	$0.557517\pi$
$258$	1.66637	+	2.88624i	0.103744	+	0.179690i
$259$	1.10947	−	1.92166i	0.0689391	−	0.119406i
$260$	0.439693	−	0.160035i	0.0272686	−	0.00992495i
$261$	1.03209	+	5.85327i	0.0638847	+	0.362308i
$262$	0.773318	−	4.38571i	0.0477758	−	0.270950i
$263$	−15.0262	−	5.46907i	−0.926553	−	0.337238i	−0.165710	−	0.986174i	$-0.552992\pi$
$263$	−15.0262	−	5.46907i	−0.926553	−	0.337238i	−0.760842	+	0.648937i	$0.775214\pi$
$264$	−0.500000	+	0.419550i	−0.0307729	+	0.0258215i
$265$	−10.7169			−0.658333
$266$	1.18866	+	1.99157i	0.0728816	+	0.122111i
$267$	3.96585			0.242706
$268$	−7.88326	+	6.61484i	−0.481546	+	0.404065i
$269$	−12.6998	−	4.62235i	−0.774321	−	0.281830i	−0.0755184	−	0.997144i	$-0.524061\pi$
$269$	−12.6998	−	4.62235i	−0.774321	−	0.281830i	−0.698803	+	0.715315i	$0.746283\pi$
$270$	−0.173648	+	0.984808i	−0.0105679	+	0.0599335i
$271$	4.94444	+	28.0413i	0.300353	+	1.70339i	0.644609	+	0.764513i	$0.277020\pi$
$271$	4.94444	+	28.0413i	0.300353	+	1.70339i	−0.344255	+	0.938876i	$0.611869\pi$
$272$	−0.539363	+	0.196312i	−0.0327037	+	0.0119032i
$273$	−0.124485	+	0.215615i	−0.00753418	+	0.0130496i
$274$	0.0393628	+	0.0681784i	0.00237800	+	0.00411881i
$275$	0.500000	+	0.419550i	0.0301511	+	0.0252998i
$276$	−4.81908	−	4.04369i	−0.290074	−	0.243401i
$277$	8.71213	+	15.0899i	0.523461	+	0.906662i	0.999627	+	0.0273062i	$0.00869290\pi$
$277$	8.71213	+	15.0899i	0.523461	+	0.906662i	−0.476166	+	0.879356i	$0.657974\pi$
$278$	3.13429	−	5.42874i	0.187982	−	0.325594i
$279$	7.61721	−	2.77244i	0.456031	−	0.165982i
$280$	0.0923963	+	0.524005i	0.00552173	+	0.0313153i
$281$	0.0817187	−	0.463450i	0.00487493	−	0.0276471i	−0.982273	−	0.187455i	$-0.939976\pi$
$281$	0.0817187	−	0.463450i	0.00487493	−	0.0276471i	0.987148	+	0.159808i	$0.0510874\pi$
$282$	4.60607	+	1.67647i	0.274287	+	0.0998324i
$283$	4.36437	−	3.66214i	0.259435	−	0.217692i	−0.503787	−	0.863828i	$-0.668061\pi$
$283$	4.36437	−	3.66214i	0.259435	−	0.217692i	0.763222	+	0.646136i	$0.223616\pi$
$284$	−6.78106			−0.402382
$285$	−0.819078	−	4.28125i	−0.0485180	−	0.253599i
$286$	0.305407			0.0180591
$287$	4.33615	−	3.63846i	0.255955	−	0.214772i
$288$	0.939693	+	0.342020i	0.0553719	+	0.0201537i
$289$	−2.89481	+	16.4173i	−0.170283	+	0.965723i
$290$	−1.03209	−	5.85327i	−0.0606063	−	0.343716i
$291$	−3.55051	+	1.29228i	−0.208134	+	0.0757547i
$292$	−0.131759	+	0.228213i	−0.00771062	+	0.0133552i
$293$	−4.66385	−	8.07802i	−0.272465	−	0.471923i	0.697028	−	0.717044i	$-0.254506\pi$
$293$	−4.66385	−	8.07802i	−0.272465	−	0.471923i	−0.969492	+	0.245121i	$0.921172\pi$
$294$	5.14543	+	4.31753i	0.300088	+	0.251803i
$295$	7.07398	+	5.93577i	0.411863	+	0.345594i
$296$	2.08512	+	3.61154i	0.121195	+	0.209916i
$297$	−0.326352	+	0.565258i	−0.0189369	+	0.0327996i
$298$	13.8293	−	5.03347i	0.801112	−	0.291581i
$299$	0.511144	+	2.89884i	0.0295602	+	0.167644i
$300$	0.173648	−	0.984808i	0.0100256	−	0.0568579i
$301$	1.66637	+	0.606511i	0.0960482	+	0.0349587i
$302$	−2.06624	+	1.73378i	−0.118899	+	0.0997678i
$303$	6.43107			0.369456
$304$	−4.35844	+	0.0632028i	−0.249974	+	0.00362493i
$305$	−2.89899			−0.165995
$306$	−0.439693	+	0.368946i	−0.0251356	+	0.0210912i
$307$	21.6001	+	7.86181i	1.23278	+	0.448697i	0.874550	−	0.484935i	$-0.161157\pi$
$307$	21.6001	+	7.86181i	1.23278	+	0.448697i	0.358235	+	0.933632i	$0.383379\pi$
$308$	−0.0603074	+	0.342020i	−0.00343633	+	0.0194884i
$309$	0.0689255	+	0.390896i	0.00392104	+	0.0222373i
$310$	−7.61721	+	2.77244i	−0.432629	+	0.157464i
$311$	6.30453	−	10.9198i	0.357497	−	0.619203i	−0.630045	−	0.776559i	$-0.716964\pi$
$311$	6.30453	−	10.9198i	0.357497	−	0.619203i	0.987542	+	0.157356i	$0.0502969\pi$
$312$	−0.233956	−	0.405223i	−0.0132451	−	0.0229412i
$313$	5.82429	+	4.88716i	0.329208	+	0.276239i	0.792377	−	0.610031i	$-0.208843\pi$
$313$	5.82429	+	4.88716i	0.329208	+	0.276239i	−0.463169	+	0.886270i	$0.653288\pi$
$314$	4.69981	+	3.94361i	0.265225	+	0.222551i
$315$	0.266044	+	0.460802i	0.0149899	+	0.0259633i
$316$	1.32635	−	2.29731i	0.0746131	−	0.129234i
$317$	6.99020	−	2.54422i	0.392609	−	0.142898i	−0.138170	−	0.990409i	$-0.544122\pi$
$317$	6.99020	−	2.54422i	0.392609	−	0.142898i	0.530778	+	0.847511i	$0.321900\pi$
$318$	1.86097	+	10.5541i	0.104358	+	0.591843i
$319$	0.673648	−	3.82045i	0.0377171	−	0.213904i
$320$	−0.939693	−	0.342020i	−0.0525304	−	0.0191195i
$321$	−11.9304	+	10.0108i	−0.665888	+	0.558746i
$322$	−3.34730			−0.186538
$323$	1.21941	−	2.18463i	0.0678497	−	0.121556i
$324$	1.00000			0.0555556
$325$	−0.358441	+	0.300767i	−0.0198827	+	0.0166836i
$326$	8.52481	+	3.10278i	0.472146	+	0.171847i
$327$	−1.17499	+	6.66371i	−0.0649772	+	0.368504i
$328$	1.84730	+	10.4765i	0.102000	+	0.578470i
$329$	2.45084	−	0.892032i	0.135119	−	0.0491793i
$330$	0.326352	−	0.565258i	0.0179651	−	0.0311164i
$331$	0.570108	+	0.987455i	0.0313359	+	0.0542754i	0.881268	−	0.472617i	$-0.156690\pi$
$331$	0.570108	+	0.987455i	0.0313359	+	0.0542754i	−0.849932	+	0.526892i	$0.823357\pi$
$332$	2.73783	+	2.29731i	0.150258	+	0.126081i
$333$	3.19459	+	2.68058i	0.175063	+	0.146895i
$334$	4.78359	+	8.28541i	0.261746	+	0.453358i
$335$	5.14543	−	8.91215i	0.281125	−	0.486923i
$336$	0.500000	−	0.181985i	0.0272772	−	0.00992810i
$337$	−5.58946	−	31.6994i	−0.304477	−	1.72678i	−0.625955	−	0.779859i	$-0.715291\pi$
$337$	−5.58946	−	31.6994i	−0.304477	−	1.72678i	0.321478	−	0.946917i	$-0.395820\pi$
$338$	2.21941	−	12.5869i	0.120720	−	0.684636i
$339$	10.0642	+	3.66306i	0.546611	+	0.198950i
$340$	0.439693	−	0.368946i	0.0238457	−	0.0200089i
$341$	−5.29086			−0.286516
$342$	−4.07398	+	1.55007i	−0.220295	+	0.0838180i
$343$	7.29860			0.394087
$344$	−2.55303	+	2.14225i	−0.137650	+	0.115502i
$345$	5.91147	+	2.15160i	0.318263	+	0.115838i
$346$	3.96064	−	22.4619i	0.212925	−	1.20756i
$347$	−4.32723	−	24.5409i	−0.232298	−	1.31743i	−0.848230	−	0.529628i	$-0.822332\pi$
$347$	−4.32723	−	24.5409i	−0.232298	−	1.31743i	0.615932	−	0.787799i	$-0.288779\pi$
$348$	−5.58512	+	2.03282i	−0.299394	+	0.108970i
$349$	−4.12701	+	7.14819i	−0.220914	+	0.382634i	−0.955086	−	0.296330i	$-0.904237\pi$
$349$	−4.12701	+	7.14819i	−0.220914	+	0.382634i	0.734172	+	0.678964i	$0.237571\pi$
$350$	−0.266044	−	0.460802i	−0.0142207	−	0.0246309i
$351$	−0.358441	−	0.300767i	−0.0191321	−	0.0160538i
$352$	−0.500000	−	0.419550i	−0.0266501	−	0.0223621i
$353$	1.31315	+	2.27444i	0.0698918	+	0.121056i	0.898854	−	0.438249i	$-0.144401\pi$
$353$	1.31315	+	2.27444i	0.0698918	+	0.121056i	−0.828962	+	0.559305i	$0.811068\pi$
$354$	4.61721	−	7.99724i	0.245402	−	0.425049i
$355$	6.37211	−	2.31926i	0.338197	−	0.123093i
$356$	0.688663	+	3.90560i	0.0364991	+	0.206996i
$357$	−0.0530334	+	0.300767i	−0.00280683	+	0.0159183i
$358$	17.8871	+	6.51038i	0.945364	+	0.344084i
$359$	12.9381	−	10.8564i	0.682847	−	0.572977i	−0.233990	−	0.972239i	$-0.575178\pi$
$359$	12.9381	−	10.8564i	0.682847	−	0.572977i	0.916837	+	0.399263i	$0.130734\pi$
$360$	−1.00000			−0.0527046
$361$	14.1946	−	12.6299i	0.747084	−	0.664730i
$362$	−9.85710			−0.518077
$363$	−8.10014	+	6.79682i	−0.425147	+	0.356741i
$364$	−0.233956	−	0.0851529i	−0.0122626	−	0.00446322i
$365$	0.0457595	−	0.259515i	0.00239516	−	0.0135836i
$366$	0.503404	+	2.85494i	0.0263133	+	0.149230i
$367$	−24.8332	+	9.03855i	−1.29628	+	0.471809i	−0.895784	−	0.444489i	$-0.853385\pi$
$367$	−24.8332	+	9.03855i	−1.29628	+	0.471809i	−0.400499	+	0.916297i	$0.631163\pi$
$368$	3.14543	−	5.44804i	0.163967	−	0.283999i
$369$	5.31908	+	9.21291i	0.276900	+	0.479605i
$370$	−3.19459	−	2.68058i	−0.166079	−	0.139357i
$371$	4.36824	+	3.66539i	0.226788	+	0.190298i
$372$	4.05303	+	7.02006i	0.210140	+	0.363973i
$373$	17.6557	−	30.5806i	0.914177	−	1.58340i	0.106076	−	0.994358i	$-0.466171\pi$
$373$	17.6557	−	30.5806i	0.914177	−	1.58340i	0.808101	−	0.589044i	$-0.200495\pi$
$374$	0.352044	−	0.128134i	0.0182038	−	0.00662563i
$375$	0.173648	+	0.984808i	0.00896715	+	0.0508553i
$376$	−0.851167	+	4.82721i	−0.0438956	+	0.248944i
$377$	2.61334	+	0.951178i	0.134594	+	0.0489882i
$378$	0.407604	−	0.342020i	0.0209649	−	0.0175916i
$379$	−26.0729			−1.33927			−0.669636	−	0.742689i	$-0.733550\pi$
$379$	−26.0729			−1.33927			−0.669636	+	0.742689i	$0.733550\pi$
$380$	4.07398	−	1.55007i	0.208991	−	0.0795167i
$381$	−4.57398			−0.234332
$382$	−2.11334	+	1.77330i	−0.108128	+	0.0907301i
$383$	6.86736	+	2.49952i	0.350906	+	0.127719i	0.511458	−	0.859308i	$-0.329105\pi$
$383$	6.86736	+	2.49952i	0.350906	+	0.127719i	−0.160553	+	0.987027i	$0.551328\pi$
$384$	−0.173648	+	0.984808i	−0.00886145	+	0.0502558i
$385$	−0.0603074	−	0.342020i	−0.00307355	−	0.0174310i
$386$	−22.4329	+	8.16490i	−1.14180	+	0.415583i
$387$	−1.66637	+	2.88624i	−0.0847066	+	0.146716i
$388$	−1.88919	−	3.27217i	−0.0959089	−	0.166119i
$389$	−8.92720	−	7.49081i	−0.452627	−	0.379799i	0.387782	−	0.921751i	$-0.373241\pi$
$389$	−8.92720	−	7.49081i	−0.452627	−	0.379799i	−0.840410	+	0.541952i	$0.817686\pi$
$390$	0.358441	+	0.300767i	0.0181504	+	0.0152300i
$391$	1.80541	+	3.12706i	0.0913034	+	0.158142i
$392$	−3.35844	+	5.81699i	−0.169627	+	0.293802i
$393$	4.18479	−	1.52314i	0.211095	−	0.0768322i
$394$	3.04323	+	17.2590i	0.153316	+	0.869498i
$395$	−0.460637	+	2.61240i	−0.0231772	+	0.131444i
$396$	−0.613341	−	0.223238i	−0.0308215	−	0.0112181i
$397$	−13.3229	+	11.1793i	−0.668660	+	0.561072i	−0.912668	−	0.408701i	$-0.865982\pi$
$397$	−13.3229	+	11.1793i	−0.668660	+	0.561072i	0.244009	+	0.969773i	$0.421537\pi$
$398$	−9.29086			−0.465709
$399$	−1.13041	+	2.02520i	−0.0565915	+	0.101387i
$400$	1.00000			0.0500000
$401$	1.72281	−	1.44561i	0.0860331	−	0.0721903i	−0.598757	−	0.800931i	$-0.704338\pi$
$401$	1.72281	−	1.44561i	0.0860331	−	0.0721903i	0.684790	+	0.728741i	$0.259894\pi$
$402$	−9.67024	−	3.51968i	−0.482308	−	0.175546i
$403$	0.658633	−	3.73530i	0.0328089	−	0.186068i
$404$	1.11674	+	6.33337i	0.0555601	+	0.315097i
$405$	−0.939693	+	0.342020i	−0.0466937	+	0.0169951i
$406$	−1.58125	+	2.73881i	−0.0784762	+	0.135925i
$407$	−1.36097	−	2.35726i	−0.0674606	−	0.116845i
$408$	−0.439693	−	0.368946i	−0.0217680	−	0.0182655i
$409$	1.85323	+	1.55504i	0.0916361	+	0.0768918i	0.687455	−	0.726227i	$-0.258728\pi$
$409$	1.85323	+	1.55504i	0.0916361	+	0.0768918i	−0.595819	+	0.803119i	$0.703172\pi$
$410$	−5.31908	−	9.21291i	−0.262691	−	0.454993i
$411$	−0.0393628	+	0.0681784i	−0.00194163	+	0.00336299i
$412$	−0.372989	+	0.135757i	−0.0183758	+	0.00668826i
$413$	−0.853226	−	4.83889i	−0.0419845	−	0.238106i
$414$	1.09240	−	6.19529i	0.0536883	−	0.304482i
$415$	−3.35844	−	1.22237i	−0.164859	−	0.0600039i
$416$	0.358441	−	0.300767i	0.0175740	−	0.0147463i
$417$	6.26857			0.306973
$418$	2.84477	−	0.0412527i	0.139142	−	0.00201773i
$419$	7.72462			0.377372			0.188686	−	0.982037i	$-0.439577\pi$
$419$	7.72462			0.377372			0.188686	+	0.982037i	$0.439577\pi$
$420$	−0.407604	+	0.342020i	−0.0198890	+	0.0166889i
$421$	34.0244	+	12.3839i	1.65825	+	0.603553i	0.990086	−	0.140463i	$-0.0448591\pi$
$421$	34.0244	+	12.3839i	1.65825	+	0.603553i	0.668162	+	0.744016i	$0.267081\pi$
$422$	1.39780	−	7.92734i	0.0680440	−	0.385897i
$423$	0.851167	+	4.82721i	0.0413851	+	0.234707i
$424$	−10.0706	+	3.66539i	−0.489070	+	0.178007i
$425$	−0.286989	+	0.497079i	−0.0139210	+	0.0241119i
$426$	−3.39053	−	5.87257i	−0.164272	−	0.284527i
$427$	1.18164	+	0.991511i	0.0571834	+	0.0479826i
$428$	−11.9304	−	10.0108i	−0.576676	−	0.483888i
$429$	0.152704	+	0.264490i	0.00737260	+	0.0127697i
$430$	1.66637	−	2.88624i	0.0803597	−	0.139187i
$431$	−19.0205	+	6.92291i	−0.916187	+	0.333465i	−0.756720	−	0.653739i	$-0.773200\pi$
$431$	−19.0205	+	6.92291i	−0.916187	+	0.333465i	−0.159466	+	0.987203i	$0.550977\pi$
$432$	0.173648	+	0.984808i	0.00835465	+	0.0473816i
$433$	5.96467	−	33.8273i	0.286644	−	1.62564i	−0.412711	−	0.910862i	$-0.635418\pi$
$433$	5.96467	−	33.8273i	0.286644	−	1.62564i	0.699354	−	0.714775i	$-0.253471\pi$
$434$	4.05303	+	1.47518i	0.194552	+	0.0708111i
$435$	4.55303	−	3.82045i	0.218301	−	0.183176i
$436$	−6.76651			−0.324057
$437$	5.15270	+	26.9327i	0.246487	+	1.28837i
$438$	−0.263518			−0.0125914
$439$	−28.4145	+	23.8426i	−1.35615	+	1.13794i	−0.378997	+	0.925398i	$0.623731\pi$
$439$	−28.4145	+	23.8426i	−1.35615	+	1.13794i	−0.977151	+	0.212546i	$0.931824\pi$
$440$	0.613341	+	0.223238i	0.0292399	+	0.0106424i
$441$	−1.16637	+	6.61484i	−0.0555416	+	0.314992i
$442$	0.0466368	+	0.264490i	0.00221829	+	0.0125805i
$443$	−11.9201	+	4.33856i	−0.566341	+	0.206131i	−0.609292	−	0.792946i	$-0.708546\pi$
$443$	−11.9201	+	4.33856i	−0.566341	+	0.206131i	0.0429512	+	0.999077i	$0.486324\pi$
$444$	−2.08512	+	3.61154i	−0.0989555	+	0.171396i
$445$	−1.98293	−	3.43453i	−0.0939997	−	0.162812i
$446$	−3.48158	−	2.92139i	−0.164858	−	0.138332i
$447$	11.2738	+	9.45983i	0.533232	+	0.447435i
$448$	0.266044	+	0.460802i	0.0125694	+	0.0217709i
$449$	16.4265	−	28.4515i	0.775214	−	1.34271i	−0.159460	−	0.987204i	$-0.550975\pi$
$449$	16.4265	−	28.4515i	0.775214	−	1.34271i	0.934674	−	0.355506i	$-0.115691\pi$
$450$	0.939693	−	0.342020i	0.0442975	−	0.0161230i
$451$	−1.20574	−	6.83807i	−0.0567759	−	0.321992i
$452$	−1.85978	+	10.5474i	−0.0874769	+	0.496106i
$453$	−2.53462	−	0.922524i	−0.119087	−	0.0433440i
$454$	18.8819	−	15.8438i	0.886172	−	0.743587i
$455$	0.248970			0.0116719
$456$	−2.23396	−	3.74292i	−0.104615	−	0.175278i
$457$	−12.5594			−0.587505			−0.293753	−	0.955881i	$-0.594904\pi$
$457$	−12.5594			−0.587505			−0.293753	+	0.955881i	$0.594904\pi$
$458$	10.2246	−	8.57948i	0.477765	−	0.400893i
$459$	−0.539363	−	0.196312i	−0.0251753	−	0.00916306i
$460$	−1.09240	+	6.19529i	−0.0509332	+	0.288857i
$461$	0.861377	+	4.88511i	0.0401183	+	0.227522i	0.998274	−	0.0587245i	$-0.0187033\pi$
$461$	0.861377	+	4.88511i	0.0401183	+	0.227522i	−0.958156	+	0.286247i	$0.907592\pi$
$462$	−0.326352	+	0.118782i	−0.0151833	+	0.00552626i
$463$	18.4684	−	31.9882i	0.858298	−	1.48662i	−0.0152527	−	0.999884i	$-0.504855\pi$
$463$	18.4684	−	31.9882i	0.858298	−	1.48662i	0.873551	−	0.486733i	$-0.161811\pi$
$464$	−2.97178	−	5.14728i	−0.137961	−	0.238956i
$465$	−6.20961	−	5.21048i	−0.287964	−	0.241630i
$466$	−10.5740	−	8.87262i	−0.489830	−	0.411016i
$467$	−4.61334	−	7.99054i	−0.213480	−	0.369758i	0.739321	−	0.673353i	$-0.235146\pi$
$467$	−4.61334	−	7.99054i	−0.213480	−	0.369758i	−0.952801	+	0.303595i	$0.901813\pi$
$468$	0.233956	−	0.405223i	0.0108146	−	0.0187314i
$469$	−5.14543	+	1.87278i	−0.237594	+	0.0864771i
$470$	−0.851167	−	4.82721i	−0.0392614	−	0.222662i
$471$	−1.06536	+	6.04196i	−0.0490892	+	0.278399i
$472$	8.67752	+	3.15836i	0.399415	+	0.145375i
$473$	1.66637	−	1.39825i	0.0766200	−	0.0642918i
$474$	2.65270			0.121843
$475$	−3.29813	+	2.84997i	−0.151329	+	0.130765i
$476$	−0.305407			−0.0139983
$477$	−8.20961	+	6.88868i	−0.375892	+	0.315411i
$478$	−11.8182	−	4.30147i	−0.540552	−	0.196745i
$479$	5.43763	−	30.8384i	0.248452	−	1.40904i	−0.563886	−	0.825853i	$-0.690694\pi$
$479$	5.43763	−	30.8384i	0.248452	−	1.40904i	0.812338	−	0.583187i	$-0.198195\pi$
$480$	−0.173648	−	0.984808i	−0.00792592	−	0.0449501i
$481$	1.83363	−	0.667385i	0.0836061	−	0.0304301i
$482$	0.691189	−	1.19717i	0.0314828	−	0.0545298i
$483$	−1.67365	−	2.89884i	−0.0761536	−	0.131902i
$484$	−8.10014	−	6.79682i	−0.368188	−	0.308946i
$485$	2.89440	+	2.42869i	0.131428	+	0.110281i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−10.6322	+	18.4156i	−0.481792	+	0.834488i	−0.999782	−	0.0208985i	$-0.993347\pi$
$487$	−10.6322	+	18.4156i	−0.481792	+	0.834488i	0.517989	+	0.855387i	$0.326681\pi$
$488$	−2.72416	+	0.991511i	−0.123317	+	0.0448836i
$489$	1.57532	+	8.93410i	0.0712385	+	0.404014i
$490$	1.16637	−	6.61484i	0.0526914	−	0.298828i
$491$	−39.1207	−	14.2388i	−1.76549	−	0.642586i	−0.765492	−	0.643446i	$-0.777504\pi$
$491$	−39.1207	−	14.2388i	−1.76549	−	0.642586i	−1.00000		0.000859724i	$0.999726\pi$
$492$	−8.14930	+	6.83807i	−0.367399	+	0.308284i
$493$	3.41147			0.153645
$494$	−0.325008	+	2.01352i	−0.0146228	+	0.0905924i
$495$	0.652704			0.0293368
$496$	−6.20961	+	5.21048i	−0.278820	+	0.233957i
$497$	−3.39053	−	1.23405i	−0.152086	−	0.0553548i
$498$	−0.620615	+	3.51968i	−0.0278104	+	0.157721i
$499$	−0.175459	−	0.995078i	−0.00785463	−	0.0445458i	0.980629	−	0.195877i	$-0.0627552\pi$
$499$	−0.175459	−	0.995078i	−0.00785463	−	0.0445458i	−0.988483	+	0.151331i	$0.951644\pi$
$500$	−0.939693	+	0.342020i	−0.0420243	+	0.0152956i
$501$	−4.78359	+	8.28541i	−0.213715	+	0.370165i
$502$	0.589870	+	1.02168i	0.0263272	+	0.0456000i
$503$	12.4847	+	10.4759i	0.556667	+	0.467099i	0.877191	−	0.480141i	$-0.159415\pi$
$503$	12.4847	+	10.4759i	0.556667	+	0.467099i	−0.320524	+	0.947240i	$0.603859\pi$
$504$	0.407604	+	0.342020i	0.0181561	+	0.0152348i
$505$	−3.21554	−	5.56947i	−0.143090	−	0.247838i
$506$	−2.05303	+	3.55596i	−0.0912685	+	0.158082i
$507$	12.0103	−	4.37138i	0.533395	−	0.194140i
$508$	−0.794263	−	4.50449i	−0.0352397	−	0.199854i
$509$	−3.36184	+	19.0660i	−0.149011	+	0.845084i	0.815047	+	0.579394i	$0.196711\pi$
$509$	−3.36184	+	19.0660i	−0.149011	+	0.845084i	−0.964059	+	0.265690i	$0.914400\pi$
$510$	0.539363	+	0.196312i	0.0238834	+	0.00869284i
$511$	−0.107411	+	0.0901285i	−0.00475158	+	0.00398705i
$512$	−1.00000			−0.0441942
$513$	−3.37939	−	2.75314i	−0.149204	−	0.121554i
$514$	−15.8598			−0.699545
$515$	0.304063	−	0.255139i	0.0133986	−	0.0112428i
$516$	−3.13176	−	1.13987i	−0.137868	−	0.0501799i
$517$	0.555560	−	3.15074i	0.0244335	−	0.138569i
$518$	0.385315	+	2.18523i	0.0169298	+	0.0960135i
$519$	21.4329	−	7.80093i	0.940799	−	0.342423i
$520$	−0.233956	+	0.405223i	−0.0102596	+	0.0177702i
$521$	−17.6634	−	30.5940i	−0.773849	−	1.34035i	−0.935439	−	0.353488i	$-0.884995\pi$
$521$	−17.6634	−	30.5940i	−0.773849	−	1.34035i	0.161590	−	0.986858i	$-0.448338\pi$
$522$	−4.55303	−	3.82045i	−0.199281	−	0.167216i
$523$	−6.66637	−	5.59375i	−0.291500	−	0.244598i	0.485296	−	0.874350i	$-0.338712\pi$
$523$	−6.66637	−	5.59375i	−0.291500	−	0.244598i	−0.776796	+	0.629752i	$0.783156\pi$
$524$	2.22668	+	3.85673i	0.0972730	+	0.168482i
$525$	0.266044	−	0.460802i	0.0116111	−	0.0201111i
$526$	15.0262	−	5.46907i	0.655172	−	0.238463i
$527$	−0.807934	−	4.58202i	−0.0351941	−	0.199596i
$528$	0.113341	−	0.642788i	0.00493253	−	0.0279737i
$529$	−15.5753	−	5.66895i	−0.677188	−	0.246476i
$530$	8.20961	−	6.88868i	0.356603	−	0.299225i
$531$	9.23442			0.400740
$532$	−2.19072	−	0.761570i	−0.0949799	−	0.0330182i
$533$	4.97771			0.215609
$534$	−3.03802	+	2.54920i	−0.131468	+	0.110315i
$535$	14.6348	+	5.32661i	0.632716	+	0.230290i
$536$	1.78699	−	10.1345i	0.0771862	−	0.437745i
$537$	3.30541	+	18.7459i	0.142639	+	0.808945i
$538$	12.6998	−	4.62235i	0.547528	−	0.199284i
$539$	2.19207	−	3.79677i	0.0944190	−	0.163538i
$540$	−0.500000	−	0.866025i	−0.0215166	−	0.0372678i
$541$	10.4677	+	8.78341i	0.450040	+	0.377628i	0.839451	−	0.543436i	$-0.182877\pi$
$541$	10.4677	+	8.78341i	0.450040	+	0.377628i	−0.389411	+	0.921064i	$0.627321\pi$
$542$	−21.8123	−	18.3027i	−0.936917	−	0.786167i
$543$	−4.92855	−	8.53650i	−0.211504	−	0.366336i
$544$	0.286989	−	0.497079i	0.0123046	−	0.0213121i
$545$	6.35844	−	2.31428i	0.272366	−	0.0991330i
$546$	−0.0432332	−	0.245188i	−0.00185021	−	0.0104931i
$547$	3.21317	−	18.2228i	0.137385	−	0.779151i	−0.835784	−	0.549059i	$-0.814986\pi$
$547$	3.21317	−	18.2228i	0.137385	−	0.779151i	0.973169	−	0.230092i	$-0.0739027\pi$
$548$	−0.0739780	−	0.0269258i	−0.00316018	−	0.00115021i
$549$	−2.22075	+	1.86343i	−0.0947794	+	0.0795293i
$550$	−0.652704			−0.0278314
$551$	24.4709	+	8.50692i	1.04250	+	0.362407i
$552$	6.29086			0.267757
$553$	1.08125	−	0.907278i	0.0459795	−	0.0385814i
$554$	−16.3735	−	5.95945i	−0.695641	−	0.253193i
$555$	0.724155	−	4.10689i	0.0307387	−	0.174328i
$556$	1.08853	+	6.17334i	0.0461638	+	0.261808i
$557$	−20.1459	+	7.33251i	−0.853609	+	0.310688i	−0.731511	−	0.681830i	$-0.761184\pi$
$557$	−20.1459	+	7.33251i	−0.853609	+	0.310688i	−0.122098	+	0.992518i	$0.538962\pi$
$558$	−4.05303	+	7.02006i	−0.171579	+	0.297183i
$559$	0.779715	+	1.35051i	0.0329784	+	0.0571203i
$560$	−0.407604	−	0.342020i	−0.0172244	−	0.0144530i
$561$	0.286989	+	0.240812i	0.0121167	+	0.0101671i
$562$	0.235300	+	0.407551i	0.00992552	+	0.0171915i
$563$	6.14883	−	10.6501i	0.259142	−	0.448848i	−0.706870	−	0.707343i	$-0.749893\pi$
$563$	6.14883	−	10.6501i	0.259142	−	0.448848i	0.966012	+	0.258496i	$0.0832268\pi$
$564$	−4.60607	+	1.67647i	−0.193950	+	0.0705922i
$565$	−1.85978	−	10.5474i	−0.0782417	−	0.443731i
$566$	−0.989322	+	5.61073i	−0.0415843	+	0.235836i
$567$	0.500000	+	0.181985i	0.0209980	+	0.00764266i
$568$	5.19459	−	4.35878i	0.217960	−	0.182890i
$569$	−40.9299			−1.71587			−0.857936	−	0.513756i	$-0.828254\pi$
$569$	−40.9299			−1.71587			−0.857936	+	0.513756i	$0.828254\pi$
$570$	3.37939	+	2.75314i	0.141547	+	0.115316i
$571$	−43.9796			−1.84049			−0.920244	−	0.391345i	$-0.872010\pi$
$571$	−43.9796			−1.84049			−0.920244	+	0.391345i	$0.872010\pi$
$572$	−0.233956	+	0.196312i	−0.00978217	+	0.00820822i
$573$	−2.59240	−	0.943555i	−0.108299	−	0.0394176i
$574$	−0.982926	+	5.57445i	−0.0410265	+	0.232673i
$575$	−1.09240	−	6.19529i	−0.0455561	−	0.258361i
$576$	−0.939693	+	0.342020i	−0.0391539	+	0.0142508i
$577$	17.6250	−	30.5273i	0.733736	−	1.27087i	−0.221539	−	0.975151i	$-0.571108\pi$
$577$	17.6250	−	30.5273i	0.733736	−	1.27087i	0.955276	−	0.295717i	$-0.0955586\pi$
$578$	−8.33527	−	14.4371i	−0.346702	−	0.600505i
$579$	−18.2875	−	15.3450i	−0.760001	−	0.637716i
$580$	4.55303	+	3.82045i	0.189054	+	0.158635i
$581$	0.950837	+	1.64690i	0.0394474	+	0.0683248i
$582$	1.88919	−	3.27217i	0.0783093	−	0.135636i
$583$	6.57310	−	2.39241i	0.272230	−	0.0990836i
$584$	−0.0457595	−	0.259515i	−0.00189354	−	0.0107388i
$585$	−0.0812519	+	0.460802i	−0.00335935	+	0.0190518i
$586$	8.76517	+	3.19026i	0.362086	+	0.131788i
$587$	−30.1864	+	25.3294i	−1.24593	+	1.04546i	−0.248891	+	0.968532i	$0.580066\pi$
$587$	−30.1864	+	25.3294i	−1.24593	+	1.04546i	−0.997037	+	0.0769260i	$0.975489\pi$
$588$	−6.71688			−0.277000
$589$	5.63041	−	34.8820i	0.231997	−	1.43729i
$590$	−9.23442			−0.380175
$591$	−13.4251	+	11.2650i	−0.552237	+	0.463382i
$592$	−3.91875	−	1.42631i	−0.161060	−	0.0586209i
$593$	0.709197	−	4.02206i	0.0291232	−	0.165166i	−0.966777	−	0.255620i	$-0.917721\pi$
$593$	0.709197	−	4.02206i	0.0291232	−	0.165166i	0.995901	+	0.0904535i	$0.0288317\pi$
$594$	−0.113341	−	0.642788i	−0.00465043	−	0.0263739i
$595$	0.286989	−	0.104455i	0.0117654	−	0.00428226i
$596$	−7.35844	+	12.7452i	−0.301413	+	0.522063i
$597$	−4.64543	−	8.04612i	−0.190125	−	0.329306i
$598$	−2.25490	−	1.89209i	−0.0922097	−	0.0773731i
$599$	31.4545	+	26.3935i	1.28520	+	1.07841i	0.992505	+	0.122203i	$0.0389957\pi$
$599$	31.4545	+	26.3935i	1.28520	+	1.07841i	0.292693	+	0.956207i	$0.405449\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	−18.0355	+	31.2385i	−0.735685	+	1.27424i	0.218737	+	0.975784i	$0.429806\pi$
$601$	−18.0355	+	31.2385i	−0.735685	+	1.27424i	−0.954422	+	0.298461i	$0.903527\pi$
$602$	−1.66637	+	0.606511i	−0.0679163	+	0.0247195i
$603$	−1.78699	−	10.1345i	−0.0727718	−	0.412709i
$604$	0.468378	−	2.65630i	0.0190580	−	0.108083i
$605$	9.93629	+	3.61651i	0.403968	+	0.147032i
$606$	−4.92649	+	4.13381i	−0.200125	+	0.167925i
$607$	11.4365			0.464191			0.232096	−	0.972693i	$-0.425442\pi$
$607$	11.4365			0.464191			0.232096	+	0.972693i	$0.425442\pi$
$608$	3.29813	−	2.84997i	0.133757	−	0.115581i
$609$	−3.16250			−0.128151
$610$	2.22075	−	1.86343i	0.0899156	−	0.0754482i
$611$	2.15523	+	0.784440i	0.0871913	+	0.0317350i
$612$	0.0996702	−	0.565258i	0.00402893	−	0.0228492i
$613$	−0.495414	−	2.80963i	−0.0200096	−	0.113480i	0.973167	−	0.230100i	$-0.0739053\pi$
$613$	−0.495414	−	2.80963i	−0.0200096	−	0.113480i	−0.993177	+	0.116620i	$0.962794\pi$
$614$	−21.6001	+	7.86181i	−0.871711	+	0.317277i
$615$	5.31908	−	9.21291i	0.214486	−	0.371501i
$616$	−0.173648	−	0.300767i	−0.00699648	−	0.0121183i
$617$	6.33094	+	5.31229i	0.254874	+	0.213865i	0.761268	−	0.648438i	$-0.224577\pi$
$617$	6.33094	+	5.31229i	0.254874	+	0.213865i	−0.506394	+	0.862302i	$0.669022\pi$
$618$	−0.304063	−	0.255139i	−0.0122312	−	0.0102632i
$619$	24.0868	+	41.7195i	0.968129	+	1.67685i	0.700962	+	0.713198i	$0.252754\pi$
$619$	24.0868	+	41.7195i	0.968129	+	1.67685i	0.267167	+	0.963650i	$0.413912\pi$
$620$	4.05303	−	7.02006i	0.162774	−	0.281932i
$621$	5.91147	−	2.15160i	0.237219	−	0.0863408i
$622$	2.18954	+	12.4175i	0.0877926	+	0.497896i
$623$	−0.366430	+	2.07813i	−0.0146807	+	0.0832584i
$624$	0.439693	+	0.160035i	0.0176018	+	0.00640653i
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	−7.60307			−0.303880
$627$	1.45811	+	2.44302i	0.0582313	+	0.0975647i
$628$	−6.13516			−0.244820
$629$	1.83363	−	1.53859i	0.0731114	−	0.0613478i
$630$	−0.500000	−	0.181985i	−0.0199205	−	0.00725046i
$631$	1.03121	−	5.84829i	0.0410519	−	0.232817i	−0.957378	−	0.288839i	$-0.906731\pi$
$631$	1.03121	−	5.84829i	0.0410519	−	0.232817i	0.998430	+	0.0560224i	$0.0178418\pi$
$632$	0.460637	+	2.61240i	0.0183232	+	0.103916i
$633$	7.56418	−	2.75314i	0.300649	−	0.109427i
$634$	−3.71941	+	6.44220i	−0.147717	+	0.255853i
$635$	2.28699	+	3.96118i	0.0907564	+	0.157195i
$636$	−8.20961	−	6.88868i	−0.325532	−	0.273154i
$637$	2.40760	+	2.02022i	0.0953927	+	0.0800440i
$638$	1.93969	+	3.35965i	0.0767932	+	0.133010i
$639$	3.39053	−	5.87257i	0.134127	−	0.232315i
$640$	0.939693	−	0.342020i	0.0371446	−	0.0135195i
$641$	6.02553	+	34.1725i	0.237994	+	1.34973i	0.836216	+	0.548401i	$0.184763\pi$
$641$	6.02553	+	34.1725i	0.237994	+	1.34973i	−0.598221	+	0.801331i	$0.704126\pi$
$642$	2.70439	−	15.3374i	0.106734	−	0.605318i
$643$	−28.8282	−	10.4926i	−1.13687	−	0.413787i	−0.296089	−	0.955160i	$-0.595683\pi$
$643$	−28.8282	−	10.4926i	−1.13687	−	0.413787i	−0.840783	+	0.541373i	$0.817905\pi$
$644$	2.56418	−	2.15160i	0.101043	−	0.0847849i
$645$	3.33275			0.131227
$646$	0.470133	+	2.45734i	0.0184971	+	0.0966829i
$647$	36.6144			1.43946			0.719731	−	0.694253i	$-0.244265\pi$
$647$	36.6144			1.43946			0.719731	+	0.694253i	$0.244265\pi$
$648$	−0.766044	+	0.642788i	−0.0300931	+	0.0252511i
$649$	−5.66385	−	2.06147i	−0.222325	−	0.0809199i
$650$	0.0812519	−	0.460802i	0.00318696	−	0.0180742i
$651$	0.748970	+	4.24762i	0.0293545	+	0.166477i
$652$	−8.52481	+	3.10278i	−0.333858	+	0.121514i
$653$	−4.09152	+	7.08672i	−0.160114	+	0.277325i	−0.934909	−	0.354887i	$-0.884519\pi$
$653$	−4.09152	+	7.08672i	−0.160114	+	0.277325i	0.774796	+	0.632212i	$0.217853\pi$
$654$	−3.38326	−	5.85997i	−0.132296	−	0.229143i
$655$	−3.41147	−	2.86257i	−0.133297	−	0.111850i
$656$	−8.14930	−	6.83807i	−0.318177	−	0.266982i
$657$	−0.131759	−	0.228213i	−0.00514041	−	0.00890346i
$658$	−1.30406	+	2.25870i	−0.0508377	+	0.0880534i
$659$	19.3871	−	7.05634i	0.755215	−	0.274876i	0.0644166	−	0.997923i	$-0.479481\pi$
$659$	19.3871	−	7.05634i	0.755215	−	0.274876i	0.690799	+	0.723047i	$0.257259\pi$
$660$	0.113341	+	0.642788i	0.00441178	+	0.0250205i
$661$	4.49226	−	25.4769i	0.174729	−	0.990935i	−0.763728	−	0.645538i	$-0.776633\pi$
$661$	4.49226	−	25.4769i	0.174729	−	0.990935i	0.938457	−	0.345397i	$-0.112256\pi$
$662$	−1.07145	−	0.389977i	−0.0416432	−	0.0151569i
$663$	−0.205737	+	0.172634i	−0.00799017	+	0.00670454i
$664$	−3.57398			−0.138697
$665$	2.31908	−	0.0336295i	0.0899300	−	0.00130410i
$666$	−4.17024			−0.161594
$667$	−28.6425	+	24.0339i	−1.10904	+	0.930597i
$668$	−8.99020	−	3.27217i	−0.347841	−	0.126604i
$669$	0.789210	−	4.47584i	0.0305126	−	0.173046i
$670$	1.78699	+	10.1345i	0.0690374	+	0.391531i
$671$	1.77807	−	0.647163i	0.0686415	−	0.0249835i
$672$	−0.266044	+	0.460802i	−0.0102629	+	0.0177758i
$673$	−5.96404	−	10.3300i	−0.229897	−	0.398193i	0.727880	−	0.685704i	$-0.240506\pi$
$673$	−5.96404	−	10.3300i	−0.229897	−	0.398193i	−0.957777	+	0.287511i	$0.907172\pi$
$674$	24.6578	+	20.6903i	0.949781	+	0.796961i
$675$	0.766044	+	0.642788i	0.0294851	+	0.0247409i
$676$	6.39053	+	11.0687i	0.245790	+	0.425720i
$677$	−0.997474	+	1.72768i	−0.0383360	+	0.0664000i	−0.884557	−	0.466432i	$-0.845539\pi$
$677$	−0.997474	+	1.72768i	−0.0383360	+	0.0664000i	0.846221	+	0.532832i	$0.178872\pi$
$678$	−10.0642	+	3.66306i	−0.386512	+	0.140679i
$679$	−0.349107	−	1.97989i	−0.0133975	−	0.0759811i
$680$	−0.0996702	+	0.565258i	−0.00382218	+	0.0216767i
$681$	23.1621	+	8.43031i	0.887573	+	0.323050i
$682$	4.05303	−	3.40090i	0.155199	−	0.130227i
$683$	−17.1334			−0.655592			−0.327796	−	0.944749i	$-0.606306\pi$
$683$	−17.1334			−0.655592			−0.327796	+	0.944749i	$0.606306\pi$
$684$	2.12449	−	3.80612i	0.0812317	−	0.145531i
$685$	0.0787257			0.00300795
$686$	−5.59105	+	4.69145i	−0.213467	+	0.179120i
$687$	12.5424	+	4.56504i	0.478521	+	0.174167i
$688$	0.578726	−	3.28212i	0.0220637	−	0.125130i
$689$	0.870767	+	4.93837i	0.0331736	+	0.188137i
$690$	−5.91147	+	2.15160i	−0.225046	+	0.0819100i
$691$	−18.2108	+	31.5420i	−0.692771	+	1.19991i	0.278155	+	0.960536i	$0.410277\pi$
$691$	−18.2108	+	31.5420i	−0.692771	+	1.19991i	−0.970926	+	0.239379i	$0.923056\pi$
$692$	11.4042	+	19.7527i	0.433523	+	0.750883i
$693$	−0.266044	−	0.223238i	−0.0101062	−	0.00848010i
$694$	19.0895	+	16.0180i	0.724626	+	0.608033i
$695$	−3.13429	−	5.42874i	−0.118890	−	0.205924i
$696$	2.97178	−	5.14728i	0.112645	−	0.195107i
$697$	5.73783	−	2.08840i	0.217336	−	0.0791037i
$698$	−1.43330	−	8.12863i	−0.0542511	−	0.307673i
$699$	2.39693	−	13.5936i	0.0906601	−	0.514159i
$700$	0.500000	+	0.181985i	0.0188982	+	0.00687839i
$701$	18.7083	−	15.6981i	0.706601	−	0.592909i	−0.217042	−	0.976162i	$-0.569641\pi$
$701$	18.7083	−	15.6981i	0.706601	−	0.592909i	0.923643	+	0.383253i	$0.125196\pi$
$702$	0.467911			0.0176602
$703$	16.9895	−	6.46415i	0.640771	−	0.243800i
$704$	0.652704			0.0245997
$705$	3.75490	−	3.15074i	0.141418	−	0.118664i
$706$	−2.46791	−	0.898246i	−0.0928811	−	0.0338059i
$707$	−0.594207	+	3.36992i	−0.0223475	+	0.126739i
$708$	1.60354	+	9.09413i	0.0602647	+	0.341778i
$709$	−1.08853	+	0.396191i	−0.0408804	+	0.0148793i	−0.362379	−	0.932031i	$-0.618036\pi$
$709$	−1.08853	+	0.396191i	−0.0408804	+	0.0148793i	0.321499	+	0.946910i	$0.395813\pi$
$710$	−3.39053	+	5.87257i	−0.127244	+	0.220394i
$711$	1.32635	+	2.29731i	0.0497421	+	0.0861558i
$712$	−3.03802	−	2.54920i	−0.113855	−	0.0955353i
$713$	39.0638	+	32.7784i	1.46295	+	1.22756i
$714$	−0.152704	−	0.264490i	−0.00571479	−	0.00989831i
$715$	0.152704	−	0.264490i	0.00571079	−	0.00989138i
$716$	−17.8871	+	6.51038i	−0.668473	+	0.243304i
$717$	−2.18392	−	12.3856i	−0.0815598	−	0.462549i
$718$	−2.93283	+	16.6329i	−0.109452	+	0.620734i
$719$	10.6395	+	3.87246i	0.396786	+	0.144418i	0.532704	−	0.846302i	$-0.321176\pi$
$719$	10.6395	+	3.87246i	0.396786	+	0.144418i	−0.135917	+	0.990720i	$0.543398\pi$
$720$	0.766044	−	0.642788i	0.0285488	−	0.0239553i
$721$	−0.211200			−0.00786550
$722$	−2.75537	+	18.7991i	−0.102544	+	0.699632i
$723$	1.38238			0.0514112
$724$	7.55097	−	6.33602i	0.280630	−	0.235476i
$725$	−5.58512	−	2.03282i	−0.207426	−	0.0754970i
$726$	1.83615	−	10.4133i	0.0681460	−	0.386475i
$727$	2.71394	+	15.3915i	0.100655	+	0.570841i	0.992867	+	0.119225i	$0.0380410\pi$
$727$	2.71394	+	15.3915i	0.100655	+	0.570841i	−0.892213	+	0.451616i	$0.850848\pi$
$728$	0.233956	−	0.0851529i	0.00867097	−	0.00315597i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	0.131759	+	0.228213i	0.00487662	+	0.00844656i
$731$	1.46538	+	1.22960i	0.0541992	+	0.0454785i
$732$	−2.22075	−	1.86343i	−0.0820813	−	0.0688744i
$733$	3.44222	+	5.96210i	0.127141	+	0.220215i	0.922568	−	0.385835i	$-0.126087\pi$
$733$	3.44222	+	5.96210i	0.127141	+	0.220215i	−0.795427	+	0.606050i	$0.792753\pi$
$734$	13.2135	−	22.8864i	0.487718	−	0.844753i
$735$	6.31180	−	2.29731i	0.232814	−	0.0847375i
$736$	1.09240	+	6.19529i	0.0402663	+	0.228361i
$737$	−1.16637	+	6.61484i	−0.0429639	+	0.243661i
$738$	−9.99660	−	3.63846i	−0.367980	−	0.133934i
$739$	−1.21617	+	1.02048i	−0.0447374	+	0.0375391i	−0.664882	−	0.746948i	$-0.731518\pi$
$739$	−1.21617	+	1.02048i	−0.0447374	+	0.0375391i	0.620145	+	0.784487i	$0.287074\pi$
$740$	4.17024			0.153301
$741$	−1.90626	+	0.725293i	−0.0700282	+	0.0266443i
$742$	−5.70233			−0.209339
$743$	−35.8410	+	30.0741i	−1.31488	+	1.10331i	−0.327513	+	0.944847i	$0.606210\pi$
$743$	−35.8410	+	30.0741i	−1.31488	+	1.10331i	−0.987364	+	0.158466i	$0.949345\pi$
$744$	−7.61721	−	2.77244i	−0.279261	−	0.101643i
$745$	2.55556	−	14.4933i	0.0936285	−	0.530993i
$746$	6.13176	+	34.7749i	0.224500	+	1.27320i
$747$	−3.35844	+	1.22237i	−0.122879	+	0.0447243i
$748$	−0.187319	+	0.324446i	−0.00684905	+	0.0118629i
$749$	−4.14337	−	7.17653i	−0.151395	−	0.262225i
$750$	−0.766044	−	0.642788i	−0.0279720	−	0.0234713i
$751$	−9.52481	−	7.99227i	−0.347565	−	0.291642i	0.452246	−	0.891893i	$-0.350623\pi$
$751$	−9.52481	−	7.99227i	−0.347565	−	0.291642i	−0.799812	+	0.600251i	$0.795067\pi$
$752$	−2.45084	−	4.24497i	−0.0893728	−	0.154798i
$753$	−0.589870	+	1.02168i	−0.0214961	+	0.0372323i
$754$	−2.61334	+	0.951178i	−0.0951723	+	0.0346399i
$755$	0.468378	+	2.65630i	0.0170460	+	0.0966728i
$756$	−0.0923963	+	0.524005i	−0.00336042	+	0.0190579i
$757$	26.9200	+	9.79807i	0.978424	+	0.356117i	0.781227	−	0.624247i	$-0.214594\pi$
$757$	26.9200	+	9.79807i	0.978424	+	0.356117i	0.197196	+	0.980364i	$0.436816\pi$
$758$	19.9730	−	16.7593i	0.725451	−	0.608725i
$759$	−4.10607			−0.149041
$760$	−2.12449	+	3.80612i	−0.0770632	+	0.138063i
$761$	6.84699			0.248203			0.124102	−	0.992270i	$-0.460395\pi$
$761$	6.84699			0.248203			0.124102	+	0.992270i	$0.460395\pi$
$762$	3.50387	−	2.94010i	0.126932	−	0.106508i
$763$	−3.38326	−	1.23140i	−0.122482	−	0.0445798i
$764$	0.479055	−	2.71686i	0.0173316	−	0.0982925i
$765$	0.0996702	+	0.565258i	0.00360358	+	0.0204369i
$766$	−6.86736	+	2.49952i	−0.248128	+	0.0903112i
$767$	2.16044	−	3.74200i	0.078009

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.173648 + 0.984808i) q^{5} +(0.939693 - 0.342020i) q^{6} +(0.266044 - 0.460802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.173648 + 0.984808i) q^{5} +(0.939693 - 0.342020i) q^{6} +(0.266044 - 0.460802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(-0.766044 - 0.642788i) q^{10} +(-0.326352 - 0.565258i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.439693 - 0.160035i) q^{13} +(0.0923963 + 0.524005i) q^{14} +(0.173648 - 0.984808i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.439693 - 0.368946i) q^{17} -1.00000 q^{18} +(4.07398 - 1.55007i) q^{19} +1.00000 q^{20} +(-0.407604 + 0.342020i) q^{21} +(0.613341 + 0.223238i) q^{22} +(-1.09240 + 6.19529i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(-0.233956 + 0.405223i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-0.407604 - 0.342020i) q^{28} +(4.55303 + 3.82045i) q^{29} +(0.500000 + 0.866025i) q^{30} +(4.05303 - 7.02006i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.113341 + 0.642788i) q^{33} +(-0.0996702 + 0.565258i) q^{34} +(0.500000 + 0.181985i) q^{35} +(0.766044 - 0.642788i) q^{36} +4.17024 q^{37} +(-2.12449 + 3.80612i) q^{38} -0.467911 q^{39} +(-0.766044 + 0.642788i) q^{40} +(9.99660 + 3.63846i) q^{41} +(0.0923963 - 0.524005i) q^{42} +(0.578726 + 3.28212i) q^{43} +(-0.613341 + 0.223238i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-3.14543 - 5.44804i) q^{46} +(3.75490 + 3.15074i) q^{47} +(0.766044 + 0.642788i) q^{48} +(3.35844 + 5.81699i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.539363 + 0.196312i) q^{51} +(-0.0812519 - 0.460802i) q^{52} +(-1.86097 + 10.5541i) q^{53} +(0.939693 + 0.342020i) q^{54} +(0.500000 - 0.419550i) q^{55} +0.532089 q^{56} +(-4.35844 + 0.0632028i) q^{57} -5.94356 q^{58} +(7.07398 - 5.93577i) q^{59} +(-0.939693 - 0.342020i) q^{60} +(-0.503404 + 2.85494i) q^{61} +(1.40760 + 7.98292i) q^{62} +(0.500000 - 0.181985i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.233956 + 0.405223i) q^{65} +(-0.500000 - 0.419550i) q^{66} +(-7.88326 - 6.61484i) q^{67} +(-0.286989 - 0.497079i) q^{68} +(3.14543 - 5.44804i) q^{69} +(-0.500000 + 0.181985i) q^{70} +(-1.17752 - 6.67804i) q^{71} +(-0.173648 + 0.984808i) q^{72} +(-0.247626 - 0.0901285i) q^{73} +(-3.19459 + 2.68058i) q^{74} +1.00000 q^{75} +(-0.819078 - 4.28125i) q^{76} -0.347296 q^{77} +(0.358441 - 0.300767i) q^{78} +(2.49273 + 0.907278i) q^{79} +(0.173648 - 0.984808i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-9.99660 + 3.63846i) q^{82} +(-1.78699 + 3.09516i) q^{83} +(0.266044 + 0.460802i) q^{84} +(0.439693 + 0.368946i) q^{85} +(-2.55303 - 2.14225i) q^{86} +(-2.97178 - 5.14728i) q^{87} +(0.326352 - 0.565258i) q^{88} +(-3.72668 + 1.35640i) q^{89} +(-0.173648 - 0.984808i) q^{90} +(0.0432332 - 0.245188i) q^{91} +(5.91147 + 2.15160i) q^{92} +(-6.20961 + 5.21048i) q^{93} -4.90167 q^{94} +(2.23396 + 3.74292i) q^{95} -1.00000 q^{96} +(2.89440 - 2.42869i) q^{97} +(-6.31180 - 2.29731i) q^{98} +(0.113341 - 0.642788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q - 3 * q^7 + 3 * q^8	\( 6 q - 3 q^{7} + 3 q^{8} - 3 q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} - 3 q^{17} - 6 q^{18} + 9 q^{19} + 6 q^{20} - 6 q^{21} - 3 q^{22} - 3 q^{23} - 6 q^{26} - 3 q^{27} - 6 q^{28} + 15 q^{29} + 3 q^{30} + 12 q^{31} - 6 q^{33} - 15 q^{34} + 3 q^{35} - 18 q^{37} - 12 q^{39} + 18 q^{41} - 3 q^{42} + 21 q^{43} + 3 q^{44} - 3 q^{45} - 3 q^{46} + 24 q^{47} + 12 q^{49} + 3 q^{50} - 12 q^{51} - 3 q^{52} + 12 q^{53} + 3 q^{55} - 6 q^{56} - 18 q^{57} - 6 q^{58} + 27 q^{59} - 45 q^{61} + 12 q^{62} + 3 q^{63} - 3 q^{64} + 6 q^{65} - 3 q^{66} - 12 q^{67} + 6 q^{68} + 3 q^{69} - 3 q^{70} + 18 q^{71} + 15 q^{73} - 15 q^{74} + 6 q^{75} + 12 q^{76} - 6 q^{78} - 3 q^{79} - 18 q^{82} - 3 q^{83} - 3 q^{84} - 3 q^{85} - 3 q^{86} - 3 q^{87} + 3 q^{88} - 9 q^{89} - 15 q^{91} + 15 q^{92} - 3 q^{93} - 6 q^{94} + 18 q^{95} - 6 q^{96} - 24 q^{97} - 3 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q - 3 * q^7 + 3 * q^8 - 3 * q^11 - 3 * q^12 - 3 * q^13 - 3 * q^14 - 3 * q^17 - 6 * q^18 + 9 * q^19 + 6 * q^20 - 6 * q^21 - 3 * q^22 - 3 * q^23 - 6 * q^26 - 3 * q^27 - 6 * q^28 + 15 * q^29 + 3 * q^30 + 12 * q^31 - 6 * q^33 - 15 * q^34 + 3 * q^35 - 18 * q^37 - 12 * q^39 + 18 * q^41 - 3 * q^42 + 21 * q^43 + 3 * q^44 - 3 * q^45 - 3 * q^46 + 24 * q^47 + 12 * q^49 + 3 * q^50 - 12 * q^51 - 3 * q^52 + 12 * q^53 + 3 * q^55 - 6 * q^56 - 18 * q^57 - 6 * q^58 + 27 * q^59 - 45 * q^61 + 12 * q^62 + 3 * q^63 - 3 * q^64 + 6 * q^65 - 3 * q^66 - 12 * q^67 + 6 * q^68 + 3 * q^69 - 3 * q^70 + 18 * q^71 + 15 * q^73 - 15 * q^74 + 6 * q^75 + 12 * q^76 - 6 * q^78 - 3 * q^79 - 18 * q^82 - 3 * q^83 - 3 * q^84 - 3 * q^85 - 3 * q^86 - 3 * q^87 + 3 * q^88 - 9 * q^89 - 15 * q^91 + 15 * q^92 - 3 * q^93 - 6 * q^94 + 18 * q^95 - 6 * q^96 - 24 * q^97 - 3 * q^98 - 6 * q^99

Introduction

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