LMFDB - Embedded newform 570.2.u.c.301.1

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			301.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	570.301
Dual form			570.2.u.c.481.1

$q$-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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$	$1$

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	0.911914	−	0.410382i	$-0.134605\pi$
$7$	0.266044	+	0.460802i	0.100555	+	0.174167i	−0.811358	+	0.584549i	$0.801271\pi$
$8$	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	−0.911022	−	0.412358i	$-0.864705\pi$
$11$	−0.326352	+	0.565258i	−0.0983988	+	0.170432i	0.812623	+	0.582789i	$0.198039\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	0.439693	+	0.160035i	0.121949	+	0.0443857i	0.402274	−	0.915519i	$-0.368220\pi$
$13$	0.439693	+	0.160035i	0.121949	+	0.0443857i	−0.280325	+	0.959905i	$0.590442\pi$
$14$	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	0.694549	−	0.719445i	$-0.255604\pi$
$17$	0.439693	+	0.368946i	0.106641	+	0.0894825i	−0.587908	+	0.808928i	$0.700048\pi$
$18$	−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	−0.857298	−	0.514820i	$-0.827859\pi$
$23$	−1.09240	−	6.19529i	−0.227780	−	1.29181i	0.629518	−	0.776986i	$-0.283253\pi$
$24$	−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	−0.113312	−	0.993559i	$-0.536146\pi$
$29$	4.55303	−	3.82045i	0.845477	−	0.709440i	0.958789	+	0.284120i	$0.0917014\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	4.05303	+	7.02006i	0.727946	+	1.26084i	0.957750	+	0.287603i	$0.0928583\pi$
$31$	4.05303	+	7.02006i	0.727946	+	1.26084i	−0.229803	+	0.973237i	$0.573808\pi$
$32$	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	0.590194	−	0.807262i	$-0.299051\pi$
$41$	9.99660	−	3.63846i	1.56121	−	0.568233i	0.971012	+	0.239029i	$0.0768291\pi$
$42$	0.0923963	+	0.524005i	0.0142571	+	0.0808558i
$43$	0.578726	−	3.28212i	0.0882548	−	0.500518i	−0.908352	−	0.418207i	$-0.862659\pi$
$43$	0.578726	−	3.28212i	0.0882548	−	0.500518i	0.996607	−	0.0823112i	$-0.0262302\pi$
$44$	−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	−0.326456	−	0.945213i	$-0.605854\pi$
$47$	3.75490	−	3.15074i	0.547708	−	0.459582i	0.874164	+	0.485631i	$0.161410\pi$
$48$	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	−0.794467	−	0.607307i	$-0.792250\pi$
$53$	−1.86097	−	10.5541i	−0.255623	−	1.44971i	0.538844	−	0.842406i	$-0.318861\pi$
$54$	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	0.974171	−	0.225811i	$-0.0725032\pi$
$59$	7.07398	+	5.93577i	0.920953	+	0.772772i	−0.0532176	+	0.998583i	$0.516948\pi$
$60$	−0.939693	+	0.342020i	−0.121314	+	0.0441546i
$61$	−0.503404	−	2.85494i	−0.0644542	−	0.365538i	−0.999926	−	0.0121375i	$-0.996136\pi$
$61$	−0.503404	−	2.85494i	−0.0644542	−	0.365538i	0.935472	−	0.353401i	$-0.114975\pi$
$62$	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	−0.981453	−	0.191700i	$-0.938600\pi$
$67$	−7.88326	+	6.61484i	−0.963093	+	0.808131i	0.0183605	+	0.999831i	$0.494155\pi$
$68$	−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	0.831691	+	0.555239i	$0.187373\pi$
$71$	−1.17752	+	6.67804i	−0.139746	+	0.792537i	−0.971437	+	0.237299i	$0.923738\pi$
$72$	−0.173648	−	0.984808i	−0.0204646	−	0.116061i
$73$	−0.247626	+	0.0901285i	−0.0289824	+	0.0105487i	−0.356471	−	0.934307i	$-0.616020\pi$
$73$	−0.247626	+	0.0901285i	−0.0289824	+	0.0105487i	0.327488	+	0.944855i	$0.393798\pi$
$74$	−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	−0.197964	−	0.980209i	$-0.563433\pi$
$79$	2.49273	−	0.907278i	0.280454	−	0.102077i	0.478417	+	0.878133i	$0.341211\pi$
$80$	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	0.751129	−	0.660156i	$-0.229510\pi$
$83$	−1.78699	−	3.09516i	−0.196148	−	0.339737i	−0.947276	+	0.320418i	$0.896176\pi$
$84$	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	0.136866	−	0.990590i	$-0.456297\pi$
$89$	−3.72668	−	1.35640i	−0.395027	−	0.143778i	−0.531893	+	0.846811i	$0.678519\pi$
$90$	−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	0.777792	−	0.628521i	$-0.216340\pi$
$97$	2.89440	+	2.42869i	0.293882	+	0.246596i	−0.483911	+	0.875117i	$0.660784\pi$
$98$	−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	0.0233787	−	0.999727i	$-0.492558\pi$
$101$	−6.04323	−	2.19956i	−0.601324	−	0.218864i	−0.624703	+	0.780863i	$0.714780\pi$
$102$	0.286989	+	0.497079i	0.0284161	+	0.0492182i
$103$	−0.198463	+	0.343748i	−0.0195552	+	0.0338705i	−0.875637	−	0.482969i	$-0.839558\pi$
$103$	−0.198463	+	0.343748i	−0.0195552	+	0.0338705i	0.856082	+	0.516840i	$0.172892\pi$
$104$	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	0.946462	+	0.322814i	$0.104629\pi$
$107$	7.78699	+	13.4875i	0.752797	+	1.30388i	−0.193666	+	0.981068i	$0.562038\pi$
$108$	−0.939693	−	0.342020i	−0.0904220	−	0.0329109i
$109$	−1.17499	+	6.66371i	−0.112544	+	0.638268i	0.875393	+	0.483412i	$0.160603\pi$
$109$	−1.17499	+	6.66371i	−0.112544	+	0.638268i	−0.987937	+	0.154856i	$0.950509\pi$
$110$	−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	0.525602	−	0.850731i	$-0.323840\pi$
$127$	4.29813	+	1.56439i	0.381398	+	0.138817i	−0.144204	+	0.989548i	$0.546062\pi$
$128$	−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	0.481475	−	0.876460i	$-0.340101\pi$
$131$	−3.41147	−	2.86257i	−0.298062	−	0.250104i	−0.779537	+	0.626356i	$0.784546\pi$
$132$	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	0.985386	−	0.170335i	$-0.0544851\pi$
$137$	0.0136706	+	0.0775297i	0.00116796	+	0.00662381i	−0.984218	+	0.176959i	$0.943374\pi$
$138$	1.09240	−	6.19529i	0.0929909	−	0.527378i
$139$	−5.89053	−	2.14398i	−0.499628	−	0.181850i	0.0798986	−	0.996803i	$-0.474540\pi$
$139$	−5.89053	−	2.14398i	−0.499628	−	0.181850i	−0.579527	+	0.814953i	$0.696763\pi$
$140$	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	−0.839360	−	0.543575i	$-0.817070\pi$
$149$	−13.8293	+	5.03347i	−1.13294	+	0.412358i	−0.293584	+	0.955933i	$0.594848\pi$
$150$	−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	0.912326	+	0.409464i	$0.134284\pi$
$157$	−1.06536	+	6.04196i	−0.0850250	+	0.482201i	−0.997351	+	0.0727365i	$0.976827\pi$
$158$	−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	−0.987166	−	0.159694i	$-0.948949\pi$
$163$	−4.53596	+	7.85651i	−0.355284	+	0.615370i	0.631883	+	0.775064i	$0.282282\pi$
$164$	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	0.979131	+	0.203228i	$0.0651433\pi$
$167$	1.66132	+	9.42182i	0.128557	+	0.729083i	−0.850574	+	0.525855i	$0.823746\pi$
$168$	−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	−0.984451	−	0.175660i	$-0.943794\pi$
$173$	−17.4722	−	14.6610i	−1.32839	−	1.11465i	−0.343940	−	0.938992i	$-0.611762\pi$
$174$	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	0.252967	+	0.967475i	$0.418594\pi$
$179$	−9.51754	+	16.4849i	−0.711374	+	1.23214i	−0.964341	+	0.264662i	$0.914740\pi$
$180$	0.766044	−	0.642788i	0.0570976	−	0.0479106i
$181$	7.55097	−	6.33602i	0.561259	−	0.470953i	−0.317473	−	0.948267i	$-0.602834\pi$
$181$	7.55097	−	6.33602i	0.561259	−	0.470953i	0.878732	+	0.477315i	$0.158390\pi$
$182$	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	0.632382	−	0.774657i	$-0.282077\pi$
$193$	22.4329	−	8.16490i	1.61475	−	0.587723i	0.982372	+	0.186934i	$0.0598551\pi$
$194$	−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	0.988673	+	0.150083i	$0.0479541\pi$
$197$	8.76264	+	15.1773i	0.624312	+	1.08134i	−0.364361	+	0.931258i	$0.618713\pi$
$198$	0.326352	−	0.565258i	0.0231928	−	0.0401711i
$199$	7.11721	−	5.97205i	0.504526	−	0.423347i	−0.354672	−	0.934991i	$-0.615408\pi$
$199$	7.11721	−	5.97205i	0.504526	−	0.423347i	0.859198	+	0.511643i	$0.170963\pi$
$200$	−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	0.405365	−	0.914155i	$-0.367144\pi$
$211$	−6.16637	−	5.17420i	−0.424511	−	0.356207i	−0.829876	+	0.557948i	$0.811589\pi$
$212$	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	−0.946914	−	0.321488i	$-0.895817\pi$
$223$	0.789210	−	4.47584i	0.0528494	−	0.299724i	0.999763	+	0.0217638i	$0.00692817\pi$
$224$	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	−0.799881	−	0.600159i	$-0.795104\pi$
$233$	2.39693	−	13.5936i	0.157028	−	0.890549i	0.956908	−	0.290390i	$-0.0937850\pi$
$234$	−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	−0.587766	−	0.809031i	$-0.699992\pi$
$239$	6.28833	−	10.8917i	0.406758	−	0.704526i	0.994524	+	0.104505i	$0.0333257\pi$
$240$	−0.500000	−	0.866025i	−0.0322749	−	0.0559017i
$241$	−1.29901	−	0.472801i	−0.0836766	−	0.0304558i	0.299843	−	0.953989i	$-0.403066\pi$
$241$	−1.29901	−	0.472801i	−0.0836766	−	0.0304558i	−0.383519	+	0.923533i	$0.625288\pi$
$242$	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	0.990590	−	0.136861i	$-0.0437014\pi$
$251$	0.204860	+	1.16182i	0.0129306	+	0.0733333i	−0.977660	+	0.210194i	$0.932590\pi$
$252$	−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	−0.179714	−	0.983719i	$-0.557517\pi$
$257$	12.1493	−	10.1945i	0.757853	−	0.635914i	0.937567	+	0.347805i	$0.113073\pi$
$258$	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	−0.760842	−	0.648937i	$-0.775214\pi$
$263$	−15.0262	+	5.46907i	−0.926553	+	0.337238i	−0.165710	+	0.986174i	$0.552992\pi$
$264$	−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	−0.698803	−	0.715315i	$-0.746283\pi$
$269$	−12.6998	+	4.62235i	−0.774321	+	0.281830i	−0.0755184	+	0.997144i	$0.524061\pi$
$270$	−0.173648	−	0.984808i	−0.0105679	−	0.0599335i
$271$	4.94444	−	28.0413i	0.300353	−	1.70339i	−0.344255	−	0.938876i	$-0.611869\pi$
$271$	4.94444	−	28.0413i	0.300353	−	1.70339i	0.644609	−	0.764513i	$-0.277020\pi$
$272$	−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	−0.476166	−	0.879356i	$-0.657974\pi$
$277$	8.71213	−	15.0899i	0.523461	−	0.906662i	0.999627	−	0.0273062i	$-0.00869290\pi$
$278$	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	0.987148	−	0.159808i	$-0.0510874\pi$
$281$	0.0817187	+	0.463450i	0.00487493	+	0.0276471i	−0.982273	+	0.187455i	$0.939976\pi$
$282$	4.60607	−	1.67647i	0.274287	−	0.0998324i
$283$	4.36437	+	3.66214i	0.259435	+	0.217692i	0.763222	−	0.646136i	$-0.223616\pi$
$283$	4.36437	+	3.66214i	0.259435	+	0.217692i	−0.503787	+	0.863828i	$0.668061\pi$
$284$	−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	−0.969492	−	0.245121i	$-0.921172\pi$
$293$	−4.66385	+	8.07802i	−0.272465	+	0.471923i	0.697028	+	0.717044i	$0.254506\pi$
$294$	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	0.358235	−	0.933632i	$-0.383379\pi$
$307$	21.6001	−	7.86181i	1.23278	−	0.448697i	0.874550	+	0.484935i	$0.161157\pi$
$308$	−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	0.987542	−	0.157356i	$-0.0502969\pi$
$311$	6.30453	+	10.9198i	0.357497	+	0.619203i	−0.630045	+	0.776559i	$0.716964\pi$
$312$	−0.233956	+	0.405223i	−0.0132451	+	0.0229412i
$313$	5.82429	−	4.88716i	0.329208	−	0.276239i	−0.463169	−	0.886270i	$-0.653288\pi$
$313$	5.82429	−	4.88716i	0.329208	−	0.276239i	0.792377	+	0.610031i	$0.208843\pi$
$314$	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	0.530778	−	0.847511i	$-0.321900\pi$
$317$	6.99020	+	2.54422i	0.392609	+	0.142898i	−0.138170	+	0.990409i	$0.544122\pi$
$318$	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	−0.849932	−	0.526892i	$-0.823357\pi$
$331$	0.570108	−	0.987455i	0.0313359	−	0.0542754i	0.881268	+	0.472617i	$0.156690\pi$
$332$	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	0.321478	+	0.946917i	$0.395820\pi$
$337$	−5.58946	+	31.6994i	−0.304477	+	1.72678i	−0.625955	+	0.779859i	$0.715291\pi$
$338$	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	0.615932	+	0.787799i	$0.288779\pi$
$347$	−4.32723	+	24.5409i	−0.232298	+	1.31743i	−0.848230	+	0.529628i	$0.822332\pi$
$348$	−5.58512	−	2.03282i	−0.299394	−	0.108970i
$349$	−4.12701	−	7.14819i	−0.220914	−	0.382634i	0.734172	−	0.678964i	$-0.237571\pi$
$349$	−4.12701	−	7.14819i	−0.220914	−	0.382634i	−0.955086	+	0.296330i	$0.904237\pi$
$350$	−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	−0.828962	−	0.559305i	$-0.811068\pi$
$353$	1.31315	−	2.27444i	0.0698918	−	0.121056i	0.898854	+	0.438249i	$0.144401\pi$
$354$	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	0.916837	−	0.399263i	$-0.130734\pi$
$359$	12.9381	+	10.8564i	0.682847	+	0.572977i	−0.233990	+	0.972239i	$0.575178\pi$
$360$	−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	−0.400499	−	0.916297i	$-0.631163\pi$
$367$	−24.8332	−	9.03855i	−1.29628	−	0.471809i	−0.895784	+	0.444489i	$0.853385\pi$
$368$	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	0.808101	+	0.589044i	$0.200495\pi$
$373$	17.6557	+	30.5806i	0.914177	+	1.58340i	0.106076	+	0.994358i	$0.466171\pi$
$374$	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	−0.160553	−	0.987027i	$-0.551328\pi$
$383$	6.86736	−	2.49952i	0.350906	−	0.127719i	0.511458	+	0.859308i	$0.329105\pi$
$384$	−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	−0.840410	−	0.541952i	$-0.817686\pi$
$389$	−8.92720	+	7.49081i	−0.452627	+	0.379799i	0.387782	+	0.921751i	$0.373241\pi$
$390$	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	0.244009	−	0.969773i	$-0.421537\pi$
$397$	−13.3229	−	11.1793i	−0.668660	−	0.561072i	−0.912668	+	0.408701i	$0.865982\pi$
$398$	−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	0.684790	−	0.728741i	$-0.259894\pi$
$401$	1.72281	+	1.44561i	0.0860331	+	0.0721903i	−0.598757	+	0.800931i	$0.704338\pi$
$402$	−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	−0.595819	−	0.803119i	$-0.703172\pi$
$409$	1.85323	−	1.55504i	0.0916361	−	0.0768918i	0.687455	+	0.726227i	$0.258728\pi$
$410$	−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	0.668162	−	0.744016i	$-0.267081\pi$
$421$	34.0244	−	12.3839i	1.65825	−	0.603553i	0.990086	+	0.140463i	$0.0448591\pi$
$422$	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	−0.159466	−	0.987203i	$-0.550977\pi$
$431$	−19.0205	−	6.92291i	−0.916187	−	0.333465i	−0.756720	+	0.653739i	$0.773200\pi$
$432$	0.173648	−	0.984808i	0.00835465	−	0.0473816i
$433$	5.96467	+	33.8273i	0.286644	+	1.62564i	0.699354	+	0.714775i	$0.253471\pi$
$433$	5.96467	+	33.8273i	0.286644	+	1.62564i	−0.412711	+	0.910862i	$0.635418\pi$
$434$	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	−0.977151	−	0.212546i	$-0.931824\pi$
$439$	−28.4145	−	23.8426i	−1.35615	−	1.13794i	−0.378997	−	0.925398i	$-0.623731\pi$
$440$	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	0.0429512	−	0.999077i	$-0.486324\pi$
$443$	−11.9201	−	4.33856i	−0.566341	−	0.206131i	−0.609292	+	0.792946i	$0.708546\pi$
$444$	−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	0.934674	+	0.355506i	$0.115691\pi$
$449$	16.4265	+	28.4515i	0.775214	+	1.34271i	−0.159460	+	0.987204i	$0.550975\pi$
$450$	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	−0.958156	−	0.286247i	$-0.907592\pi$
$461$	0.861377	−	4.88511i	0.0401183	−	0.227522i	0.998274	+	0.0587245i	$0.0187033\pi$
$462$	−0.326352	−	0.118782i	−0.0151833	−	0.00552626i
$463$	18.4684	+	31.9882i	0.858298	+	1.48662i	0.873551	+	0.486733i	$0.161811\pi$
$463$	18.4684	+	31.9882i	0.858298	+	1.48662i	−0.0152527	+	0.999884i	$0.504855\pi$
$464$	−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	−0.952801	−	0.303595i	$-0.901813\pi$
$467$	−4.61334	+	7.99054i	−0.213480	+	0.369758i	0.739321	+	0.673353i	$0.235146\pi$
$468$	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	0.812338	+	0.583187i	$0.198195\pi$
$479$	5.43763	+	30.8384i	0.248452	+	1.40904i	−0.563886	+	0.825853i	$0.690694\pi$
$480$	−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	0.517989	−	0.855387i	$-0.326681\pi$
$487$	−10.6322	−	18.4156i	−0.481792	−	0.834488i	−0.999782	+	0.0208985i	$0.993347\pi$
$488$	−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	−1.00000		0.000859724i	$-0.999726\pi$
$491$	−39.1207	+	14.2388i	−1.76549	+	0.642586i	−0.765492	+	0.643446i	$0.777504\pi$
$492$	−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	−0.988483	−	0.151331i	$-0.951644\pi$
$499$	−0.175459	+	0.995078i	−0.00785463	+	0.0445458i	0.980629	+	0.195877i	$0.0627552\pi$
$500$	−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	−0.320524	−	0.947240i	$-0.603859\pi$
$503$	12.4847	−	10.4759i	0.556667	−	0.467099i	0.877191	+	0.480141i	$0.159415\pi$
$504$	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	−0.964059	−	0.265690i	$-0.914400\pi$
$509$	−3.36184	−	19.0660i	−0.149011	−	0.845084i	0.815047	−	0.579394i	$-0.196711\pi$
$510$	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	0.161590	+	0.986858i	$0.448338\pi$
$521$	−17.6634	+	30.5940i	−0.773849	+	1.34035i	−0.935439	+	0.353488i	$0.884995\pi$
$522$	−4.55303	+	3.82045i	−0.199281	+	0.167216i
$523$	−6.66637	+	5.59375i	−0.291500	+	0.244598i	−0.776796	−	0.629752i	$-0.783156\pi$
$523$	−6.66637	+	5.59375i	−0.291500	+	0.244598i	0.485296	+	0.874350i	$0.338712\pi$
$524$	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	−0.389411	−	0.921064i	$-0.627321\pi$
$541$	10.4677	−	8.78341i	0.450040	−	0.377628i	0.839451	+	0.543436i	$0.182877\pi$
$542$	−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	0.973169	+	0.230092i	$0.0739027\pi$
$547$	3.21317	+	18.2228i	0.137385	+	0.779151i	−0.835784	+	0.549059i	$0.814986\pi$
$548$	−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	−0.122098	−	0.992518i	$-0.538962\pi$
$557$	−20.1459	−	7.33251i	−0.853609	−	0.310688i	−0.731511	+	0.681830i	$0.761184\pi$
$558$	−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	0.966012	−	0.258496i	$-0.0832268\pi$
$563$	6.14883	+	10.6501i	0.259142	+	0.448848i	−0.706870	+	0.707343i	$0.749893\pi$
$564$	−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	0.955276	+	0.295717i	$0.0955586\pi$
$577$	17.6250	+	30.5273i	0.733736	+	1.27087i	−0.221539	+	0.975151i	$0.571108\pi$
$578$	−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	−0.997037	−	0.0769260i	$-0.975489\pi$
$587$	−30.1864	−	25.3294i	−1.24593	−	1.04546i	−0.248891	−	0.968532i	$-0.580066\pi$
$588$	−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	0.995901	−	0.0904535i	$-0.0288317\pi$
$593$	0.709197	+	4.02206i	0.0291232	+	0.165166i	−0.966777	+	0.255620i	$0.917721\pi$
$594$	−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	0.292693	−	0.956207i	$-0.405449\pi$
$599$	31.4545	−	26.3935i	1.28520	−	1.07841i	0.992505	−	0.122203i	$-0.0389957\pi$
$600$	0.500000	−	0.866025i	0.0204124	−	0.0353553i
$601$	−18.0355	−	31.2385i	−0.735685	−	1.27424i	−0.954422	−	0.298461i	$-0.903527\pi$
$601$	−18.0355	−	31.2385i	−0.735685	−	1.27424i	0.218737	−	0.975784i	$-0.429806\pi$
$602$	−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	−0.993177	−	0.116620i	$-0.962794\pi$
$613$	−0.495414	+	2.80963i	−0.0200096	+	0.113480i	0.973167	+	0.230100i	$0.0739053\pi$
$614$	−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	−0.506394	−	0.862302i	$-0.669022\pi$
$617$	6.33094	−	5.31229i	0.254874	−	0.213865i	0.761268	+	0.648438i	$0.224577\pi$
$618$	−0.304063	+	0.255139i	−0.0122312	+	0.0102632i
$619$	24.0868	−	41.7195i	0.968129	−	1.67685i	0.267167	−	0.963650i	$-0.413912\pi$
$619$	24.0868	−	41.7195i	0.968129	−	1.67685i	0.700962	−	0.713198i	$-0.252754\pi$
$620$	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	0.998430	−	0.0560224i	$-0.0178418\pi$
$631$	1.03121	+	5.84829i	0.0410519	+	0.232817i	−0.957378	+	0.288839i	$0.906731\pi$
$632$	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	−0.598221	−	0.801331i	$-0.704126\pi$
$641$	6.02553	−	34.1725i	0.237994	−	1.34973i	0.836216	−	0.548401i	$-0.184763\pi$
$642$	2.70439	+	15.3374i	0.106734	+	0.605318i
$643$	−28.8282	+	10.4926i	−1.13687	+	0.413787i	−0.840783	−	0.541373i	$-0.817905\pi$
$643$	−28.8282	+	10.4926i	−1.13687	+	0.413787i	−0.296089	+	0.955160i	$0.595683\pi$
$644$	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	0.774796	−	0.632212i	$-0.217853\pi$
$653$	−4.09152	−	7.08672i	−0.160114	−	0.277325i	−0.934909	+	0.354887i	$0.884519\pi$
$654$	−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	0.690799	−	0.723047i	$-0.257259\pi$
$659$	19.3871	+	7.05634i	0.755215	+	0.274876i	0.0644166	+	0.997923i	$0.479481\pi$
$660$	0.113341	−	0.642788i	0.00441178	−	0.0250205i
$661$	4.49226	+	25.4769i	0.174729	+	0.990935i	0.938457	+	0.345397i	$0.112256\pi$
$661$	4.49226	+	25.4769i	0.174729	+	0.990935i	−0.763728	+	0.645538i	$0.776633\pi$
$662$	−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	−0.957777	−	0.287511i	$-0.907172\pi$
$673$	−5.96404	+	10.3300i	−0.229897	+	0.398193i	0.727880	+	0.685704i	$0.240506\pi$
$674$	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	0.846221	−	0.532832i	$-0.178872\pi$
$677$	−0.997474	−	1.72768i	−0.0383360	−	0.0664000i	−0.884557	+	0.466432i	$0.845539\pi$
$678$	−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	−0.970926	−	0.239379i	$-0.923056\pi$
$691$	−18.2108	−	31.5420i	−0.692771	−	1.19991i	0.278155	−	0.960536i	$-0.410277\pi$
$692$	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	0.923643	−	0.383253i	$-0.125196\pi$
$701$	18.7083	+	15.6981i	0.706601	+	0.592909i	−0.217042	+	0.976162i	$0.569641\pi$
$702$	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	0.321499	−	0.946910i	$-0.395813\pi$
$709$	−1.08853	−	0.396191i	−0.0408804	−	0.0148793i	−0.362379	+	0.932031i	$0.618036\pi$
$710$	−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	−0.135917	−	0.990720i	$-0.543398\pi$
$719$	10.6395	−	3.87246i	0.396786	−	0.144418i	0.532704	+	0.846302i	$0.321176\pi$
$720$	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	−0.892213	−	0.451616i	$-0.850848\pi$
$727$	2.71394	−	15.3915i	0.100655	−	0.570841i	0.992867	−	0.119225i	$-0.0380410\pi$
$728$	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	−0.795427	−	0.606050i	$-0.792753\pi$
$733$	3.44222	−	5.96210i	0.127141	−	0.220215i	0.922568	+	0.385835i	$0.126087\pi$
$734$	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	0.620145	−	0.784487i	$-0.287074\pi$
$739$	−1.21617	−	1.02048i	−0.0447374	−	0.0375391i	−0.664882	+	0.746948i	$0.731518\pi$
$740$	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	−0.987364	−	0.158466i	$-0.949345\pi$
$743$	−35.8410	−	30.0741i	−1.31488	−	1.10331i	−0.327513	−	0.944847i	$-0.606210\pi$
$744$	−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	−0.799812	−	0.600251i	$-0.795067\pi$
$751$	−9.52481	+	7.99227i	−0.347565	+	0.291642i	0.452246	+	0.891893i	$0.350623\pi$
$752$	−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	0.197196	−	0.980364i	$-0.436816\pi$
$757$	26.9200	−	9.79807i	0.978424	−	0.356117i	0.781227	+	0.624247i	$0.214594\pi$
$758$	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	0.0780091

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

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