LMFDB - Embedded newform 150.2.g.c.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(31,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("150.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.g (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.1064390625.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 3x^{6} - 5x^{5} + 36x^{4} - 35x^{3} + 23x^{2} - 171x + 361 $ x^8 - 2x^7 - 3x^6 - 5x^5 + 36x^4 - 35x^3 + 23x^2 - 171*x + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Root			$-1.86886 + 1.45788i$ of defining polynomial
Character	$\chi$	$=$	150.91
Dual form			150.2.g.c.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.05984 + 0.870094i) q^{5} +(-0.309017 + 0.951057i) q^{6} +2.92807 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.05984 + 0.870094i) q^{5} +(-0.309017 + 0.951057i) q^{6} +2.92807 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-2.17787 - 0.506822i) q^{10} +(-0.154000 - 0.111888i) q^{11} +(-0.809017 + 0.587785i) q^{12} +(-0.250822 + 0.182233i) q^{13} +(2.36886 + 1.72107i) q^{14} +(-1.46403 - 1.69015i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.86886 - 5.75175i) q^{17} -1.00000 q^{18} +(1.00000 - 3.07768i) q^{19} +(-1.46403 - 1.69015i) q^{20} +(0.904822 + 2.78476i) q^{21} +(-0.0588229 - 0.181038i) q^{22} +(-3.61803 - 2.62866i) q^{23} -1.00000 q^{24} +(3.48587 - 3.58451i) q^{25} -0.310033 q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.904822 + 2.78476i) q^{28} +(2.10492 + 6.47829i) q^{29} +(-0.190983 - 2.22790i) q^{30} +(-0.522856 + 1.60919i) q^{31} -1.00000 q^{32} +(0.0588229 - 0.181038i) q^{33} +(4.89273 - 3.55478i) q^{34} +(-6.03135 + 2.54769i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(7.89273 - 5.73440i) q^{37} +(2.61803 - 1.90211i) q^{38} +(-0.250822 - 0.182233i) q^{39} +(-0.190983 - 2.22790i) q^{40} +(-4.10492 + 2.98240i) q^{41} +(-0.904822 + 2.78476i) q^{42} -10.2394 q^{43} +(0.0588229 - 0.181038i) q^{44} +(1.15502 - 1.91466i) q^{45} +(-1.38197 - 4.25325i) q^{46} +(-3.31003 - 10.1872i) q^{47} +(-0.809017 - 0.587785i) q^{48} +1.57358 q^{49} +(4.92705 - 0.850981i) q^{50} +6.04775 q^{51} +(-0.250822 - 0.182233i) q^{52} +(3.08144 + 9.48370i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(0.414569 + 0.0964762i) q^{55} +(-0.904822 + 2.78476i) q^{56} +3.23607 q^{57} +(-2.10492 + 6.47829i) q^{58} +(-6.00810 + 4.36514i) q^{59} +(1.15502 - 1.91466i) q^{60} +(4.48689 + 3.25992i) q^{61} +(-1.36886 + 0.994532i) q^{62} +(-2.36886 + 1.72107i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.358093 - 0.593609i) q^{65} +(0.154000 - 0.111888i) q^{66} +(-4.66375 + 14.3535i) q^{67} +6.04775 q^{68} +(1.38197 - 4.25325i) q^{69} +(-6.37696 - 1.48401i) q^{70} +(2.11842 + 6.51983i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(-9.41496 - 6.84037i) q^{73} +9.75595 q^{74} +(4.48626 + 2.20759i) q^{75} +3.23607 q^{76} +(-0.450924 - 0.327615i) q^{77} +(-0.0958055 - 0.294859i) q^{78} +(0.485246 + 1.49343i) q^{79} +(1.15502 - 1.91466i) q^{80} +(0.309017 - 0.951057i) q^{81} -5.07397 q^{82} +(4.02324 - 12.3823i) q^{83} +(-2.36886 + 1.72107i) q^{84} +(1.15502 + 13.4738i) q^{85} +(-8.28381 - 6.01854i) q^{86} +(-5.51076 + 4.00380i) q^{87} +(0.154000 - 0.111888i) q^{88} +(7.51076 + 5.45689i) q^{89} +(2.05984 - 0.870094i) q^{90} +(-0.734424 + 0.533590i) q^{91} +(1.38197 - 4.25325i) q^{92} -1.69200 q^{93} +(3.31003 - 10.1872i) q^{94} +(0.618034 + 7.20963i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(0.537611 + 1.65460i) q^{97} +(1.27305 + 0.924925i) q^{98} +0.190355 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 4 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 4 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 4 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 4 q^{10} - 5 q^{11} - 2 q^{12} + 6 q^{13} + 2 q^{14} + q^{15} - 2 q^{16} - 2 q^{17} - 8 q^{18} + 8 q^{19} + q^{20} + 3 q^{21} - 20 q^{23} - 8 q^{24} + 14 q^{25} + 14 q^{26} - 2 q^{27} + 3 q^{28} - 18 q^{29} - 6 q^{30} + 9 q^{31} - 8 q^{32} - 3 q^{34} - 4 q^{35} - 2 q^{36} + 21 q^{37} + 12 q^{38} + 6 q^{39} - 6 q^{40} + 2 q^{41} - 3 q^{42} - 32 q^{43} + q^{45} - 20 q^{46} - 10 q^{47} - 2 q^{48} + 22 q^{49} + 26 q^{50} - 2 q^{51} + 6 q^{52} + 7 q^{53} + 2 q^{54} - 40 q^{55} - 3 q^{56} + 8 q^{57} + 18 q^{58} - 25 q^{59} + q^{60} + 10 q^{61} + 6 q^{62} - 2 q^{63} - 2 q^{64} + 37 q^{65} + 5 q^{66} - 2 q^{67} - 2 q^{68} + 20 q^{69} - 11 q^{70} + 2 q^{72} - 24 q^{73} - 26 q^{74} + 14 q^{75} + 8 q^{76} + 35 q^{77} - q^{78} - 6 q^{79} + q^{80} - 2 q^{81} - 42 q^{82} + 11 q^{83} - 2 q^{84} + q^{85} + 2 q^{86} + 7 q^{87} + 5 q^{88} + 9 q^{89} + 4 q^{90} - 4 q^{91} + 20 q^{92} - 6 q^{93} + 10 q^{94} - 4 q^{95} + 2 q^{96} + q^{97} - 7 q^{98} + 10 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 4 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 4 * q^10 - 5 * q^11 - 2 * q^12 + 6 * q^13 + 2 * q^14 + q^15 - 2 * q^16 - 2 * q^17 - 8 * q^18 + 8 * q^19 + q^20 + 3 * q^21 - 20 * q^23 - 8 * q^24 + 14 * q^25 + 14 * q^26 - 2 * q^27 + 3 * q^28 - 18 * q^29 - 6 * q^30 + 9 * q^31 - 8 * q^32 - 3 * q^34 - 4 * q^35 - 2 * q^36 + 21 * q^37 + 12 * q^38 + 6 * q^39 - 6 * q^40 + 2 * q^41 - 3 * q^42 - 32 * q^43 + q^45 - 20 * q^46 - 10 * q^47 - 2 * q^48 + 22 * q^49 + 26 * q^50 - 2 * q^51 + 6 * q^52 + 7 * q^53 + 2 * q^54 - 40 * q^55 - 3 * q^56 + 8 * q^57 + 18 * q^58 - 25 * q^59 + q^60 + 10 * q^61 + 6 * q^62 - 2 * q^63 - 2 * q^64 + 37 * q^65 + 5 * q^66 - 2 * q^67 - 2 * q^68 + 20 * q^69 - 11 * q^70 + 2 * q^72 - 24 * q^73 - 26 * q^74 + 14 * q^75 + 8 * q^76 + 35 * q^77 - q^78 - 6 * q^79 + q^80 - 2 * q^81 - 42 * q^82 + 11 * q^83 - 2 * q^84 + q^85 + 2 * q^86 + 7 * q^87 + 5 * q^88 + 9 * q^89 + 4 * q^90 - 4 * q^91 + 20 * q^92 - 6 * q^93 + 10 * q^94 - 4 * q^95 + 2 * q^96 + q^97 - 7 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−2.05984	+	0.870094i	−0.921188	+	0.389118i
$5$	−2.05984	+	0.870094i	−0.921188	+	0.389118i
$6$	−0.309017	+	0.951057i	−0.126156	+	0.388267i
$7$	2.92807			1.10671			0.553353	−	0.832947i	$-0.313348\pi$
$7$	2.92807			1.10671			0.553353	+	0.832947i	$0.313348\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−2.17787	−	0.506822i	−0.688704	−	0.160271i
$11$	−0.154000	−	0.111888i	−0.0464329	−	0.0337355i	0.564327	−	0.825552i	$-0.309136\pi$
$11$	−0.154000	−	0.111888i	−0.0464329	−	0.0337355i	−0.610760	+	0.791816i	$0.709136\pi$
$12$	−0.809017	+	0.587785i	−0.233543	+	0.169679i
$13$	−0.250822	+	0.182233i	−0.0695655	+	0.0505423i	−0.622025	−	0.782998i	$-0.713690\pi$
$13$	−0.250822	+	0.182233i	−0.0695655	+	0.0505423i	0.552459	+	0.833540i	$0.313690\pi$
$14$	2.36886	+	1.72107i	0.633103	+	0.459977i
$15$	−1.46403	−	1.69015i	−0.378012	−	0.436395i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	1.86886	−	5.75175i	0.453264	−	1.39500i	−0.419897	−	0.907572i	$-0.637934\pi$
$17$	1.86886	−	5.75175i	0.453264	−	1.39500i	0.873161	−	0.487432i	$-0.162066\pi$
$18$	−1.00000			−0.235702
$19$	1.00000	−	3.07768i	0.229416	−	0.706069i	−0.768398	−	0.639973i	$-0.778946\pi$
$19$	1.00000	−	3.07768i	0.229416	−	0.706069i	0.997813	−	0.0660962i	$-0.0210544\pi$
$20$	−1.46403	−	1.69015i	−0.327368	−	0.377929i
$21$	0.904822	+	2.78476i	0.197448	+	0.607684i
$22$	−0.0588229	−	0.181038i	−0.0125411	−	0.0385975i
$23$	−3.61803	−	2.62866i	−0.754412	−	0.548113i	0.142779	−	0.989755i	$-0.454396\pi$
$23$	−3.61803	−	2.62866i	−0.754412	−	0.548113i	−0.897191	+	0.441642i	$0.854396\pi$
$24$	−1.00000			−0.204124
$25$	3.48587	−	3.58451i	0.697175	−	0.716901i
$26$	−0.310033			−0.0608025
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	0.904822	+	2.78476i	0.170995	+	0.526270i
$29$	2.10492	+	6.47829i	0.390875	+	1.20299i	0.932128	+	0.362129i	$0.117950\pi$
$29$	2.10492	+	6.47829i	0.390875	+	1.20299i	−0.541253	+	0.840859i	$0.682050\pi$
$30$	−0.190983	−	2.22790i	−0.0348686	−	0.406756i
$31$	−0.522856	+	1.60919i	−0.0939078	+	0.289018i	−0.986968	−	0.160920i	$-0.948554\pi$
$31$	−0.522856	+	1.60919i	−0.0939078	+	0.289018i	0.893060	+	0.449938i	$0.148554\pi$
$32$	−1.00000			−0.176777
$33$	0.0588229	−	0.181038i	0.0102398	−	0.0315147i
$34$	4.89273	−	3.55478i	0.839096	−	0.609639i
$35$	−6.03135	+	2.54769i	−1.01948	+	0.430639i
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	7.89273	−	5.73440i	1.29756	−	0.942730i	0.297628	−	0.954682i	$-0.403804\pi$
$37$	7.89273	−	5.73440i	1.29756	−	0.942730i	0.999929	+	0.0119519i	$0.00380449\pi$
$38$	2.61803	−	1.90211i	0.424701	−	0.308563i
$39$	−0.250822	−	0.182233i	−0.0401637	−	0.0291806i
$40$	−0.190983	−	2.22790i	−0.0301971	−	0.352261i
$41$	−4.10492	+	2.98240i	−0.641081	+	0.465773i	−0.860222	−	0.509920i	$-0.829675\pi$
$41$	−4.10492	+	2.98240i	−0.641081	+	0.465773i	0.219140	+	0.975693i	$0.429675\pi$
$42$	−0.904822	+	2.78476i	−0.139617	+	0.429697i
$43$	−10.2394			−1.56149			−0.780744	−	0.624852i	$-0.785159\pi$
$43$	−10.2394			−1.56149			−0.780744	+	0.624852i	$0.785159\pi$
$44$	0.0588229	−	0.181038i	0.00886789	−	0.0272926i
$45$	1.15502	−	1.91466i	0.172180	−	0.285421i
$46$	−1.38197	−	4.25325i	−0.203760	−	0.627108i
$47$	−3.31003	−	10.1872i	−0.482818	−	1.48596i	−0.835116	−	0.550073i	$-0.814600\pi$
$47$	−3.31003	−	10.1872i	−0.482818	−	1.48596i	0.352299	−	0.935888i	$-0.385400\pi$
$48$	−0.809017	−	0.587785i	−0.116772	−	0.0848395i
$49$	1.57358			0.224797
$50$	4.92705	−	0.850981i	0.696790	−	0.120347i
$51$	6.04775			0.846854
$52$	−0.250822	−	0.182233i	−0.0347828	−	0.0252712i
$53$	3.08144	+	9.48370i	0.423268	+	1.30269i	0.904643	+	0.426171i	$0.140138\pi$
$53$	3.08144	+	9.48370i	0.423268	+	1.30269i	−0.481374	+	0.876515i	$0.659862\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	0.414569	+	0.0964762i	0.0559005	+	0.0130088i
$56$	−0.904822	+	2.78476i	−0.120912	+	0.372129i
$57$	3.23607			0.428628
$58$	−2.10492	+	6.47829i	−0.276390	+	0.850641i
$59$	−6.00810	+	4.36514i	−0.782188	+	0.568293i	−0.905635	−	0.424058i	$-0.860605\pi$
$59$	−6.00810	+	4.36514i	−0.782188	+	0.568293i	0.123447	+	0.992351i	$0.460605\pi$
$60$	1.15502	−	1.91466i	0.149112	−	0.247182i
$61$	4.48689	+	3.25992i	0.574487	+	0.417390i	0.836733	−	0.547612i	$-0.184463\pi$
$61$	4.48689	+	3.25992i	0.574487	+	0.417390i	−0.262245	+	0.965001i	$0.584463\pi$
$62$	−1.36886	+	0.994532i	−0.173845	+	0.126306i
$63$	−2.36886	+	1.72107i	−0.298448	+	0.216835i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.358093	−	0.593609i	0.0444160	−	0.0736282i
$66$	0.154000	−	0.111888i	0.0189561	−	0.0137724i
$67$	−4.66375	+	14.3535i	−0.569767	+	1.75356i	0.0835754	+	0.996501i	$0.473366\pi$
$67$	−4.66375	+	14.3535i	−0.569767	+	1.75356i	−0.653343	+	0.757062i	$0.726634\pi$
$68$	6.04775			0.733397
$69$	1.38197	−	4.25325i	0.166369	−	0.512032i
$70$	−6.37696	−	1.48401i	−0.762192	−	0.177373i
$71$	2.11842	+	6.51983i	0.251410	+	0.773762i	0.994516	+	0.104587i	$0.0333522\pi$
$71$	2.11842	+	6.51983i	0.251410	+	0.773762i	−0.743105	+	0.669175i	$0.766648\pi$
$72$	−0.309017	−	0.951057i	−0.0364180	−	0.112083i
$73$	−9.41496	−	6.84037i	−1.10194	−	0.800604i	−0.120562	−	0.992706i	$-0.538470\pi$
$73$	−9.41496	−	6.84037i	−1.10194	−	0.800604i	−0.981375	+	0.192101i	$0.938470\pi$
$74$	9.75595			1.13411
$75$	4.48626	+	2.20759i	0.518029	+	0.254911i
$76$	3.23607			0.371202
$77$	−0.450924	−	0.327615i	−0.0513875	−	0.0373352i
$78$	−0.0958055	−	0.294859i	−0.0108478	−	0.0333862i
$79$	0.485246	+	1.49343i	0.0545944	+	0.168024i	0.974636	−	0.223797i	$-0.0718452\pi$
$79$	0.485246	+	1.49343i	0.0545944	+	0.168024i	−0.920041	+	0.391821i	$0.871845\pi$
$80$	1.15502	−	1.91466i	0.129135	−	0.214066i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−5.07397			−0.560326
$83$	4.02324	−	12.3823i	0.441608	−	1.35913i	−0.444552	−	0.895753i	$-0.646637\pi$
$83$	4.02324	−	12.3823i	0.441608	−	1.35913i	0.886161	−	0.463378i	$-0.153363\pi$
$84$	−2.36886	+	1.72107i	−0.258463	+	0.187785i
$85$	1.15502	+	13.4738i	0.125279	+	1.46143i
$86$	−8.28381	−	6.01854i	−0.893267	−	0.648996i
$87$	−5.51076	+	4.00380i	−0.590816	+	0.429253i
$88$	0.154000	−	0.111888i	0.0164165	−	0.0119273i
$89$	7.51076	+	5.45689i	0.796139	+	0.578429i	0.909779	−	0.415093i	$-0.136251\pi$
$89$	7.51076	+	5.45689i	0.796139	+	0.578429i	−0.113640	+	0.993522i	$0.536251\pi$
$90$	2.05984	−	0.870094i	0.217126	−	0.0917159i
$91$	−0.734424	+	0.533590i	−0.0769885	+	0.0559354i
$92$	1.38197	−	4.25325i	0.144080	−	0.443432i
$93$	−1.69200			−0.175452
$94$	3.31003	−	10.1872i	0.341404	−	1.05073i
$95$	0.618034	+	7.20963i	0.0634089	+	0.739692i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	0.537611	+	1.65460i	0.0545861	+	0.167999i	0.974633	−	0.223810i	$-0.0718495\pi$
$97$	0.537611	+	1.65460i	0.0545861	+	0.167999i	−0.920047	+	0.391809i	$0.871850\pi$
$98$	1.27305	+	0.924925i	0.128598	+	0.0934316i
$99$	0.190355			0.0191314
$100$	4.48626	+	2.20759i	0.448626	+	0.220759i
$101$	−0.765188			−0.0761391			−0.0380695	−	0.999275i	$-0.512121\pi$
$101$	−0.765188			−0.0761391			−0.0380695	+	0.999275i	$0.512121\pi$
$102$	4.89273	+	3.55478i	0.484452	+	0.351975i
$103$	1.74069	+	5.35728i	0.171515	+	0.527869i	0.999457	−	0.0329445i	$-0.0104885\pi$
$103$	1.74069	+	5.35728i	0.171515	+	0.527869i	−0.827942	+	0.560814i	$0.810488\pi$
$104$	−0.0958055	−	0.294859i	−0.00939450	−	0.0289133i
$105$	−4.28679	−	4.94887i	−0.418348	−	0.482960i
$106$	−3.08144	+	9.48370i	−0.299296	+	0.921138i
$107$	−8.81042			−0.851736			−0.425868	−	0.904785i	$-0.640031\pi$
$107$	−8.81042			−0.851736			−0.425868	+	0.904785i	$0.640031\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	−12.8447	+	9.33220i	−1.23030	+	0.893862i	−0.996912	−	0.0785223i	$-0.974980\pi$
$109$	−12.8447	+	9.33220i	−1.23030	+	0.893862i	−0.233384	+	0.972385i	$0.574980\pi$
$110$	0.278686	+	0.321728i	0.0265717	+	0.0306756i
$111$	7.89273	+	5.73440i	0.749145	+	0.544285i
$112$	−2.36886	+	1.72107i	−0.223836	+	0.162626i
$113$	15.4845	−	11.2502i	1.45666	−	1.05833i	0.472447	−	0.881359i	$-0.343371\pi$
$113$	15.4845	−	11.2502i	1.45666	−	1.05833i	0.984217	−	0.176969i	$-0.0566291\pi$
$114$	2.61803	+	1.90211i	0.245201	+	0.178149i
$115$	9.73974	+	2.26658i	0.908236	+	0.211360i
$116$	−5.51076	+	4.00380i	−0.511661	+	0.371744i
$117$	0.0958055	−	0.294859i	0.00885722	−	0.0272597i
$118$	−7.42642			−0.683658
$119$	5.47214	−	16.8415i	0.501630	−	1.54386i
$120$	2.05984	−	0.870094i	0.188037	−	0.0794283i
$121$	−3.38799	−	10.4272i	−0.307999	−	0.947924i
$122$	1.71384	+	5.27466i	0.155164	+	0.477545i
$123$	−4.10492	−	2.98240i	−0.370129	−	0.268914i
$124$	−1.69200			−0.151946
$125$	−4.06148	+	10.4165i	−0.363270	+	0.931684i
$126$	−2.92807			−0.260853
$127$	6.58371	+	4.78335i	0.584210	+	0.424453i	0.840239	−	0.542216i	$-0.182414\pi$
$127$	6.58371	+	4.78335i	0.584210	+	0.424453i	−0.256029	+	0.966669i	$0.582414\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−3.16414	−	9.73821i	−0.278587	−	0.857401i
$130$	0.638618	−	0.269758i	0.0560105	−	0.0236593i
$131$	5.13588	−	15.8066i	0.448724	−	1.38103i	−0.429623	−	0.903008i	$-0.641354\pi$
$131$	5.13588	−	15.8066i	0.448724	−	1.38103i	0.878347	−	0.478023i	$-0.158646\pi$
$132$	0.190355			0.0165683
$133$	2.92807	−	9.01166i	0.253896	−	0.781410i
$134$	−12.2098	+	8.87097i	−1.05477	+	0.766335i
$135$	2.17787	+	0.506822i	0.187441	+	0.0436203i
$136$	4.89273	+	3.55478i	0.419548	+	0.304819i
$137$	8.60657	−	6.25304i	0.735309	−	0.534233i	−0.155930	−	0.987768i	$-0.549837\pi$
$137$	8.60657	−	6.25304i	0.735309	−	0.534233i	0.891238	+	0.453535i	$0.149837\pi$
$138$	3.61803	−	2.62866i	0.307988	−	0.223766i
$139$	−18.5199	−	13.4555i	−1.57084	−	1.14128i	−0.926351	−	0.376662i	$-0.877072\pi$
$139$	−18.5199	−	13.4555i	−1.57084	−	1.14128i	−0.644485	−	0.764617i	$-0.722928\pi$
$140$	−4.28679	−	4.94887i	−0.362300	−	0.418256i
$141$	8.66578	−	6.29606i	0.729790	−	0.530224i
$142$	−2.11842	+	6.51983i	−0.177774	+	0.547132i
$143$	0.0590164			0.00493520
$144$	0.309017	−	0.951057i	0.0257514	−	0.0792547i
$145$	−9.97252	−	11.5128i	−0.828173	−	0.956082i
$146$	−3.59619	−	11.0679i	−0.297623	−	0.915990i
$147$	0.486262	+	1.49656i	0.0401062	+	0.123434i
$148$	7.89273	+	5.73440i	0.648778	+	0.471365i
$149$	1.40819			0.115363			0.0576815	−	0.998335i	$-0.481629\pi$
$149$	1.40819			0.115363			0.0576815	+	0.998335i	$0.481629\pi$
$150$	2.33187	+	4.42294i	0.190397	+	0.361131i
$151$	−7.87234			−0.640642			−0.320321	−	0.947309i	$-0.603791\pi$
$151$	−7.87234			−0.640642			−0.320321	+	0.947309i	$0.603791\pi$
$152$	2.61803	+	1.90211i	0.212351	+	0.154282i
$153$	1.86886	+	5.75175i	0.151088	+	0.465001i
$154$	−0.172237	−	0.530092i	−0.0138793	−	0.0427161i
$155$	−0.323143	−	3.76960i	−0.0259555	−	0.302782i
$156$	0.0958055	−	0.294859i	0.00767058	−	0.0236076i
$157$	−6.95554			−0.555113			−0.277556	−	0.960709i	$-0.589525\pi$
$157$	−6.95554			−0.555113			−0.277556	+	0.960709i	$0.589525\pi$
$158$	−0.485246	+	1.49343i	−0.0386041	+	0.118811i
$159$	−8.06731	+	5.86125i	−0.639780	+	0.464827i
$160$	2.05984	−	0.870094i	0.162845	−	0.0687869i
$161$	−10.5938	−	7.69688i	−0.834912	−	0.606599i
$162$	0.809017	−	0.587785i	0.0635624	−	0.0461808i
$163$	11.3262	−	8.22899i	0.887139	−	0.644545i	−0.0479912	−	0.998848i	$-0.515282\pi$
$163$	11.3262	−	8.22899i	0.887139	−	0.644545i	0.935131	+	0.354303i	$0.115282\pi$
$164$	−4.10492	−	2.98240i	−0.320541	−	0.232886i
$165$	0.0363546	+	0.424091i	0.00283020	+	0.0330155i
$166$	10.5330	−	7.65267i	0.817519	−	0.593962i
$167$	0.425647	−	1.31001i	0.0329375	−	0.101371i	−0.933236	−	0.359263i	$-0.883028\pi$
$167$	0.425647	−	1.31001i	0.0329375	−	0.101371i	0.966174	+	0.257892i	$0.0830279\pi$
$168$	−2.92807			−0.225905
$169$	−3.98752	+	12.2723i	−0.306732	+	0.944025i
$170$	−6.98525	+	11.5794i	−0.535744	+	0.888099i
$171$	1.00000	+	3.07768i	0.0764719	+	0.235356i
$172$	−3.16414	−	9.73821i	−0.241263	−	0.742531i
$173$	3.33555	+	2.42342i	0.253597	+	0.184249i	0.707320	−	0.706894i	$-0.249904\pi$
$173$	3.33555	+	2.42342i	0.253597	+	0.184249i	−0.453722	+	0.891143i	$0.649904\pi$
$174$	−6.81168			−0.516392
$175$	10.2069	−	10.4957i	0.771567	−	0.793398i
$176$	0.190355			0.0143485
$177$	−6.00810	−	4.36514i	−0.451597	−	0.328104i
$178$	2.86886	+	8.82943i	0.215030	+	0.661794i
$179$	1.33125	+	4.09715i	0.0995020	+	0.306236i	0.988401	−	0.151868i	$-0.0485289\pi$
$179$	1.33125	+	4.09715i	0.0995020	+	0.306236i	−0.888899	+	0.458104i	$0.848529\pi$
$180$	2.17787	+	0.506822i	0.162329	+	0.0377763i
$181$	4.01475	−	12.3561i	0.298414	−	0.918425i	−0.683639	−	0.729820i	$-0.739604\pi$
$181$	4.01475	−	12.3561i	0.298414	−	0.918425i	0.982053	−	0.188604i	$-0.0603964\pi$
$182$	−0.907798			−0.0672904
$183$	−1.71384	+	5.27466i	−0.126691	+	0.389914i
$184$	3.61803	−	2.62866i	0.266725	−	0.193787i
$185$	−11.2683	+	18.6794i	−0.828461	+	1.37333i
$186$	−1.36886	−	0.994532i	−0.100369	−	0.0729226i
$187$	−0.931355	+	0.676669i	−0.0681075	+	0.0494830i
$188$	8.66578	−	6.29606i	0.632017	−	0.459187i
$189$	−2.36886	−	1.72107i	−0.172309	−	0.125190i
$190$	−3.73771	+	6.19598i	−0.271162	+	0.449504i
$191$	1.00000	−	0.726543i	0.0723575	−	0.0525708i	−0.551018	−	0.834493i	$-0.685761\pi$
$191$	1.00000	−	0.726543i	0.0723575	−	0.0525708i	0.623376	+	0.781922i	$0.285761\pi$
$192$	0.309017	−	0.951057i	0.0223014	−	0.0686366i
$193$	17.4250			1.25428			0.627140	−	0.778906i	$-0.284225\pi$
$193$	17.4250			1.25428			0.627140	+	0.778906i	$0.284225\pi$
$194$	−0.537611	+	1.65460i	−0.0385982	+	0.118793i
$195$	0.675213	+	0.157132i	0.0483530	+	0.0112524i
$196$	0.486262	+	1.49656i	0.0347330	+	0.106897i
$197$	4.61741	+	14.2109i	0.328977	+	1.01249i	0.969614	+	0.244642i	$0.0786704\pi$
$197$	4.61741	+	14.2109i	0.328977	+	1.01249i	−0.640637	+	0.767844i	$0.721330\pi$
$198$	0.154000	+	0.111888i	0.0109443	+	0.00795152i
$199$	−4.90436			−0.347661			−0.173830	−	0.984776i	$-0.555614\pi$
$199$	−4.90436			−0.347661			−0.173830	+	0.984776i	$0.555614\pi$
$200$	2.33187	+	4.42294i	0.164888	+	0.312749i
$201$	−15.0922			−1.06452
$202$	−0.619050	−	0.449766i	−0.0435562	−	0.0316454i
$203$	6.16336	+	18.9689i	0.432583	+	1.33135i
$204$	1.86886	+	5.75175i	0.130846	+	0.402703i
$205$	5.86051	−	9.71494i	0.409316	−	0.678521i
$206$	−1.74069	+	5.35728i	−0.121279	+	0.373260i
$207$	4.47214			0.310835
$208$	0.0958055	−	0.294859i	0.00664292	−	0.0204448i
$209$	−0.498356	+	0.362077i	−0.0344720	+	0.0250454i
$210$	−0.559211	−	6.52343i	−0.0385892	−	0.450160i
$211$	0.996712	+	0.724153i	0.0686165	+	0.0498528i	0.621565	−	0.783363i	$-0.286497\pi$
$211$	0.996712	+	0.724153i	0.0686165	+	0.0498528i	−0.552948	+	0.833216i	$0.686497\pi$
$212$	−8.06731	+	5.86125i	−0.554065	+	0.402552i
$213$	−5.54610	+	4.02948i	−0.380013	+	0.276095i
$214$	−7.12778	−	5.17864i	−0.487245	−	0.354004i
$215$	21.0914	−	8.90920i	1.43842	−	0.607602i
$216$	0.809017	−	0.587785i	0.0550466	−	0.0399937i
$217$	−1.53096	+	4.71181i	−0.103928	+	0.319858i
$218$	−15.8769			−1.07532
$219$	3.59619	−	11.0679i	0.243008	−	0.747902i
$220$	0.0363546	+	0.424091i	0.00245102	+	0.0285922i
$221$	0.579407	+	1.78323i	0.0389752	+	0.119953i
$222$	3.01475	+	9.27846i	0.202337	+	0.622729i
$223$	−3.77203	−	2.74054i	−0.252594	−	0.183520i	0.454282	−	0.890858i	$-0.349896\pi$
$223$	−3.77203	−	2.74054i	−0.252594	−	0.183520i	−0.706876	+	0.707338i	$0.749896\pi$
$224$	−2.92807			−0.195640
$225$	−0.713211	+	4.94887i	−0.0475474	+	0.329925i
$226$	19.1399			1.27317
$227$	−0.464034	−	0.337140i	−0.0307990	−	0.0223768i	0.572279	−	0.820059i	$-0.306059\pi$
$227$	−0.464034	−	0.337140i	−0.0307990	−	0.0223768i	−0.603078	+	0.797682i	$0.706059\pi$
$228$	1.00000	+	3.07768i	0.0662266	+	0.203825i
$229$	9.18801	+	28.2778i	0.607161	+	1.86865i	0.481195	+	0.876614i	$0.340203\pi$
$229$	9.18801	+	28.2778i	0.607161	+	1.86865i	0.125966	+	0.992035i	$0.459797\pi$
$230$	6.54736	+	7.55858i	0.431720	+	0.498398i
$231$	0.172237	−	0.530092i	0.0113324	−	0.0348775i
$232$	−6.81168			−0.447209
$233$	−4.28819	+	13.1977i	−0.280929	+	0.864610i	0.706661	+	0.707553i	$0.250201\pi$
$233$	−4.28819	+	13.1977i	−0.280929	+	0.864610i	−0.987589	+	0.157057i	$0.949799\pi$
$234$	0.250822	−	0.182233i	0.0163968	−	0.0119129i
$235$	15.6820	+	18.1040i	1.02298	+	1.18098i
$236$	−6.00810	−	4.36514i	−0.391094	−	0.284147i
$237$	−1.27039	+	0.922993i	−0.0825207	+	0.0599548i
$238$	14.3262	−	10.4086i	0.928632	−	0.674691i
$239$	1.73442	+	1.26013i	0.112191	+	0.0815112i	0.642466	−	0.766314i	$-0.277911\pi$
$239$	1.73442	+	1.26013i	0.112191	+	0.0815112i	−0.530275	+	0.847825i	$0.677911\pi$
$240$	2.17787	+	0.506822i	0.140581	+	0.0327152i
$241$	−1.40748	+	1.02260i	−0.0906639	+	0.0658712i	−0.632194	−	0.774810i	$-0.717845\pi$
$241$	−1.40748	+	1.02260i	−0.0906639	+	0.0658712i	0.541530	+	0.840682i	$0.317845\pi$
$242$	3.38799	−	10.4272i	0.217788	−	0.670283i
$243$	1.00000			0.0641500
$244$	−1.71384	+	5.27466i	−0.109717	+	0.337675i
$245$	−3.24132	+	1.36916i	−0.207080	+	0.0874724i
$246$	−1.56794	−	4.82563i	−0.0999683	−	0.307671i
$247$	0.310033	+	0.954184i	0.0197269	+	0.0607133i
$248$	−1.36886	−	0.994532i	−0.0869224	−	0.0631529i
$249$	13.0195			0.825077
$250$	−9.40850	+	6.03988i	−0.595046	+	0.381996i
$251$	−6.39691			−0.403770			−0.201885	−	0.979409i	$-0.564707\pi$
$251$	−6.39691			−0.403770			−0.201885	+	0.979409i	$0.564707\pi$
$252$	−2.36886	−	1.72107i	−0.149224	−	0.108418i
$253$	0.263064	+	0.809628i	0.0165387	+	0.0509009i
$254$	2.51475	+	7.73962i	0.157790	+	0.485627i
$255$	−12.4574	+	5.26211i	−0.780112	+	0.329526i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−6.31003			−0.393609			−0.196805	−	0.980443i	$-0.563056\pi$
$257$	−6.31003			−0.393609			−0.196805	+	0.980443i	$0.563056\pi$
$258$	3.16414	−	9.73821i	0.196990	−	0.606274i
$259$	23.1104	−	16.7907i	1.43601	−	1.04332i
$260$	0.675213	+	0.157132i	0.0418749	+	0.00974490i
$261$	−5.51076	−	4.00380i	−0.341108	−	0.247829i
$262$	13.4459	−	9.76903i	0.830691	−	0.603533i
$263$	−2.31332	+	1.68073i	−0.142646	+	0.103638i	−0.656819	−	0.754048i	$-0.728099\pi$
$263$	−2.31332	+	1.68073i	−0.142646	+	0.103638i	0.514174	+	0.857686i	$0.328099\pi$
$264$	0.154000	+	0.111888i	0.00947807	+	0.00688622i
$265$	−14.5990	−	16.8537i	−0.896808	−	1.03532i
$266$	7.66578	−	5.56951i	0.470019	−	0.341489i
$267$	−2.86886	+	8.82943i	−0.175571	+	0.540352i
$268$	−15.0922			−0.921903
$269$	−2.99937	+	9.23112i	−0.182875	+	0.562831i	−0.999905	−	0.0137635i	$-0.995619\pi$
$269$	−2.99937	+	9.23112i	−0.182875	+	0.562831i	0.817030	+	0.576595i	$0.195619\pi$
$270$	1.46403	+	1.69015i	0.0890982	+	0.102859i
$271$	5.30503	+	16.3272i	0.322257	+	0.991806i	0.972663	+	0.232219i	$0.0745988\pi$
$271$	5.30503	+	16.3272i	0.322257	+	0.991806i	−0.650406	+	0.759587i	$0.725401\pi$
$272$	1.86886	+	5.75175i	0.113316	+	0.348751i
$273$	−0.734424	−	0.533590i	−0.0444494	−	0.0322943i
$274$	10.6383			0.642683
$275$	−0.937889	+	0.161988i	−0.0565568	+	0.00976827i
$276$	4.47214			0.269191
$277$	1.65337	+	1.20125i	0.0993415	+	0.0721758i	0.636347	−	0.771403i	$-0.280445\pi$
$277$	1.65337	+	1.20125i	0.0993415	+	0.0721758i	−0.537006	+	0.843579i	$0.680445\pi$
$278$	−7.07397	−	21.7714i	−0.424268	−	1.30576i
$279$	−0.522856	−	1.60919i	−0.0313026	−	0.0963395i
$280$	−0.559211	−	6.52343i	−0.0334193	−	0.389850i
$281$	1.59416	−	4.90632i	0.0950997	−	0.292687i	−0.892180	−	0.451680i	$-0.850825\pi$
$281$	1.59416	−	4.90632i	0.0950997	−	0.292687i	0.987280	+	0.158993i	$0.0508248\pi$
$282$	10.7115			0.637860
$283$	−2.90059	+	8.92710i	−0.172422	+	0.530661i	−0.999506	−	0.0314171i	$-0.989998\pi$
$283$	−2.90059	+	8.92710i	−0.172422	+	0.530661i	0.827084	+	0.562078i	$0.189998\pi$
$284$	−5.54610	+	4.02948i	−0.329101	+	0.239106i
$285$	−6.66578	+	2.81568i	−0.394847	+	0.166787i
$286$	0.0477452	+	0.0346889i	0.00282323	+	0.00205120i
$287$	−12.0195	+	8.73267i	−0.709488	+	0.515473i
$288$	0.809017	−	0.587785i	0.0476718	−	0.0346356i
$289$	−15.8367	−	11.5060i	−0.931570	−	0.676825i
$290$	−1.30091	−	15.1757i	−0.0763923	−	0.891149i
$291$	−1.40748	+	1.02260i	−0.0825081	+	0.0599456i
$292$	3.59619	−	11.0679i	0.210451	−	0.647703i
$293$	−8.18160			−0.477974			−0.238987	−	0.971023i	$-0.576815\pi$
$293$	−8.18160			−0.477974			−0.238987	+	0.971023i	$0.576815\pi$
$294$	−0.486262	+	1.49656i	−0.0283594	+	0.0872812i
$295$	8.57764	−	14.2191i	0.499410	−	0.827868i
$296$	3.01475	+	9.27846i	0.175229	+	0.539299i
$297$	0.0588229	+	0.181038i	0.00341325	+	0.0105049i
$298$	1.13925	+	0.827711i	0.0659948	+	0.0479480i
$299$	1.38651			0.0801840
$300$	−0.713211	+	4.94887i	−0.0411773	+	0.285723i
$301$	−29.9815			−1.72811
$302$	−6.36886	−	4.62724i	−0.366486	−	0.266268i
$303$	−0.236456	−	0.727737i	−0.0135840	−	0.0418074i
$304$	1.00000	+	3.07768i	0.0573539	+	0.176517i
$305$	−12.0787	−	2.81089i	−0.691625	−	0.160951i
$306$	−1.86886	+	5.75175i	−0.106835	+	0.328806i
$307$	5.85865			0.334371			0.167185	−	0.985925i	$-0.446532\pi$
$307$	5.85865			0.334371			0.167185	+	0.985925i	$0.446532\pi$
$308$	0.172237	−	0.530092i	0.00981414	−	0.0302048i
$309$	−4.55718	+	3.31098i	−0.259249	+	0.188355i
$310$	1.95429	−	3.23961i	0.110996	−	0.183997i
$311$	15.4035	+	11.1913i	0.873452	+	0.634600i	0.931511	−	0.363713i	$-0.118491\pi$
$311$	15.4035	+	11.1913i	0.873452	+	0.634600i	−0.0580591	+	0.998313i	$0.518491\pi$
$312$	0.250822	−	0.182233i	0.0142000	−	0.0103169i
$313$	9.70542	−	7.05140i	0.548583	−	0.398569i	−0.278680	−	0.960384i	$-0.589897\pi$
$313$	9.70542	−	7.05140i	0.548583	−	0.398569i	0.827263	+	0.561815i	$0.189897\pi$
$314$	−5.62715	−	4.08837i	−0.317559	−	0.230720i
$315$	3.38197	−	5.60626i	0.190552	−	0.315877i
$316$	−1.27039	+	0.922993i	−0.0714650	+	0.0519224i
$317$	10.0778	−	31.0164i	0.566028	−	1.74205i	−0.0988506	−	0.995102i	$-0.531517\pi$
$317$	10.0778	−	31.0164i	0.566028	−	1.74205i	0.664878	−	0.746952i	$-0.268483\pi$
$318$	−9.97175			−0.559188
$319$	0.400683	−	1.23317i	0.0224339	−	0.0690445i
$320$	2.17787	+	0.506822i	0.121747	+	0.0283322i
$321$	−2.72257	−	8.37921i	−0.151959	−	0.467682i
$322$	−4.04649	−	12.4538i	−0.225502	−	0.694024i
$323$	−15.8332	−	11.5035i	−0.880983	−	0.640072i
$324$	1.00000			0.0555556
$325$	−0.221119	+	1.53431i	−0.0122655	+	0.0851084i
$326$	14.0000			0.775388
$327$	−12.8447	−	9.33220i	−0.710312	−	0.516072i
$328$	−1.56794	−	4.82563i	−0.0865751	−	0.266451i
$329$	−9.69200	−	29.8289i	−0.534337	−	1.64452i
$330$	−0.219863	+	0.364466i	−0.0121031	+	0.0200632i
$331$	0.998744	−	3.07382i	0.0548959	−	0.168952i	−0.919849	−	0.392272i	$-0.871689\pi$
$331$	0.998744	−	3.07382i	0.0548959	−	0.168952i	0.974745	+	0.223319i	$0.0716893\pi$
$332$	13.0195			0.714538
$333$	−3.01475	+	9.27846i	−0.165208	+	0.508456i
$334$	1.11436	−	0.809628i	0.0609749	−	0.0443009i
$335$	−2.88235	−	33.6239i	−0.157480	−	1.83707i
$336$	−2.36886	−	1.72107i	−0.129232	−	0.0938923i
$337$	−17.2445	+	12.5289i	−0.939367	+	0.682490i	−0.948268	−	0.317470i	$-0.897167\pi$
$337$	−17.2445	+	12.5289i	−0.939367	+	0.682490i	0.00890132	+	0.999960i	$0.497167\pi$
$338$	−10.4395	+	7.58471i	−0.567832	+	0.412554i
$339$	15.4845	+	11.2502i	0.841005	+	0.611026i
$340$	−12.4574	+	5.26211i	−0.675596	+	0.285378i
$341$	0.260569	−	0.189314i	0.0141106	−	0.0102519i
$342$	−1.00000	+	3.07768i	−0.0540738	+	0.166422i
$343$	−15.8889			−0.857922
$344$	3.16414	−	9.73821i	0.170599	−	0.525049i
$345$	0.854102	+	9.96346i	0.0459833	+	0.536415i
$346$	1.27407	+	3.92117i	0.0684942	+	0.210804i
$347$	5.91496	+	18.2044i	0.317532	+	0.977262i	0.974700	+	0.223518i	$0.0717541\pi$
$347$	5.91496	+	18.2044i	0.317532	+	0.977262i	−0.657168	+	0.753744i	$0.728246\pi$
$348$	−5.51076	−	4.00380i	−0.295408	−	0.214626i
$349$	14.3745			0.769447			0.384724	−	0.923032i	$-0.374297\pi$
$349$	14.3745			0.769447			0.384724	+	0.923032i	$0.374297\pi$
$350$	14.4267	−	2.49173i	0.771141	−	0.133189i
$351$	0.310033			0.0165483
$352$	0.154000	+	0.111888i	0.00820825	+	0.00596364i
$353$	7.53609	+	23.1937i	0.401105	+	1.23448i	0.924104	+	0.382142i	$0.124813\pi$
$353$	7.53609	+	23.1937i	0.401105	+	1.23448i	−0.522998	+	0.852334i	$0.675187\pi$
$354$	−2.29489	−	7.06295i	−0.121972	−	0.375391i
$355$	−10.0365	−	11.5866i	−0.532681	−	0.614952i
$356$	−2.86886	+	8.82943i	−0.152049	+	0.467959i
$357$	17.7082			0.937218
$358$	−1.33125	+	4.09715i	−0.0703585	+	0.216541i
$359$	17.2576	−	12.5384i	0.910821	−	0.661750i	−0.0304014	−	0.999538i	$-0.509679\pi$
$359$	17.2576	−	12.5384i	0.910821	−	0.661750i	0.941222	+	0.337788i	$0.109679\pi$
$360$	1.46403	+	1.69015i	0.0771613	+	0.0890787i
$361$	6.89919	+	5.01255i	0.363115	+	0.263819i
$362$	10.5108	−	7.63652i	0.552433	−	0.401366i
$363$	8.86987	−	6.44434i	0.465548	−	0.338240i
$364$	−0.734424	−	0.533590i	−0.0384943	−	0.0279677i
$365$	25.3451	+	5.89816i	1.32662	+	0.308724i
$366$	−4.48689	+	3.25992i	−0.234533	+	0.170399i
$367$	−3.28553	+	10.1118i	−0.171503	+	0.527833i	−0.999457	−	0.0329641i	$-0.989505\pi$
$367$	−3.28553	+	10.1118i	−0.171503	+	0.527833i	0.827953	+	0.560797i	$0.189505\pi$
$368$	4.47214			0.233126
$369$	1.56794	−	4.82563i	0.0816238	−	0.251212i
$370$	−20.0957	+	8.48859i	−1.04472	+	0.441301i
$371$	9.02266	+	27.7689i	0.468433	+	1.44169i
$372$	−0.522856	−	1.60919i	−0.0271088	−	0.0834324i
$373$	−0.997968	−	0.725066i	−0.0516728	−	0.0375425i	0.561649	−	0.827376i	$-0.310167\pi$
$373$	−0.997968	−	0.725066i	−0.0516728	−	0.0375425i	−0.613322	+	0.789833i	$0.710167\pi$
$374$	−1.15122			−0.0595281
$375$	−11.1618	−	0.643811i	−0.576392	−	0.0332463i
$376$	10.7115			0.552403
$377$	−1.70852	−	1.24131i	−0.0879932	−	0.0639308i
$378$	−0.904822	−	2.78476i	−0.0465390	−	0.143232i
$379$	7.82585	+	24.0855i	0.401987	+	1.23719i	0.923385	+	0.383875i	$0.125411\pi$
$379$	7.82585	+	24.0855i	0.401987	+	1.23719i	−0.521398	+	0.853314i	$0.674589\pi$
$380$	−6.66578	+	2.81568i	−0.341947	+	0.144441i
$381$	−2.51475	+	7.73962i	−0.128835	+	0.396513i
$382$	1.23607			0.0632427
$383$	5.92681	−	18.2408i	0.302846	−	0.932064i	−0.677626	−	0.735406i	$-0.736991\pi$
$383$	5.92681	−	18.2408i	0.302846	−	0.932064i	0.980472	−	0.196657i	$-0.0630087\pi$
$384$	0.809017	−	0.587785i	0.0412850	−	0.0299953i
$385$	1.21389	+	0.282489i	0.0618654	+	0.0143970i
$386$	14.0971	+	10.2422i	0.717525	+	0.521313i
$387$	8.28381	−	6.01854i	0.421090	−	0.305940i
$388$	−1.40748	+	1.02260i	−0.0714541	+	0.0519145i
$389$	6.71282	+	4.87715i	0.340354	+	0.247281i	0.744811	−	0.667275i	$-0.232540\pi$
$389$	6.71282	+	4.87715i	0.340354	+	0.247281i	−0.404457	+	0.914557i	$0.632540\pi$
$390$	0.453899	+	0.524002i	0.0229841	+	0.0265339i
$391$	−21.8809	+	15.8974i	−1.10657	+	0.803968i
$392$	−0.486262	+	1.49656i	−0.0245599	+	0.0755877i
$393$	16.6201			0.838371
$394$	−4.61741	+	14.2109i	−0.232622	+	0.715936i
$395$	−2.29896	−	2.65402i	−0.115673	−	0.133538i
$396$	0.0588229	+	0.181038i	0.00295596	+	0.00909752i
$397$	−9.73897	−	29.9735i	−0.488785	−	1.50432i	−0.826423	−	0.563049i	$-0.809628\pi$
$397$	−9.73897	−	29.9735i	−0.488785	−	1.50432i	0.337639	−	0.941276i	$-0.390372\pi$
$398$	−3.96771	−	2.88271i	−0.198883	−	0.144497i
$399$	9.47542			0.474365
$400$	−0.713211	+	4.94887i	−0.0356606	+	0.247444i
$401$	−13.6940			−0.683847			−0.341924	−	0.939728i	$-0.611078\pi$
$401$	−13.6940			−0.683847			−0.341924	+	0.939728i	$0.611078\pi$
$402$	−12.2098	−	8.87097i	−0.608972	−	0.442444i
$403$	−0.162103	−	0.498901i	−0.00807492	−	0.0248520i
$404$	−0.236456	−	0.727737i	−0.0117641	−	0.0362063i
$405$	0.190983	+	2.22790i	0.00949002	+	0.110705i
$406$	−6.16336	+	18.9689i	−0.305882	+	0.941409i
$407$	−1.85709			−0.0920527
$408$	−1.86886	+	5.75175i	−0.0925222	+	0.284754i
$409$	24.3488	−	17.6904i	1.20397	−	0.874735i	0.209300	−	0.977851i	$-0.432881\pi$
$409$	24.3488	−	17.6904i	1.20397	−	0.874735i	0.994669	+	0.103116i	$0.0328814\pi$
$410$	10.4516	−	4.41483i	0.516165	−	0.218033i
$411$	8.60657	+	6.25304i	0.424531	+	0.308440i
$412$	−4.55718	+	3.31098i	−0.224516	+	0.163120i
$413$	−17.5921	+	12.7814i	−0.865652	+	0.628933i
$414$	3.61803	+	2.62866i	0.177817	+	0.129191i
$415$	2.48650	+	29.0061i	0.122058	+	1.42385i
$416$	0.250822	−	0.182233i	0.0122976	−	0.00893470i
$417$	7.07397	−	21.7714i	0.346414	−	1.06615i
$418$	−0.616002			−0.0301296
$419$	3.28756	−	10.1181i	0.160608	−	0.494301i	−0.838078	−	0.545551i	$-0.816321\pi$
$419$	3.28756	−	10.1181i	0.160608	−	0.494301i	0.998686	+	0.0512500i	$0.0163205\pi$
$420$	3.38197	−	5.60626i	0.165023	−	0.273558i
$421$	3.73916	+	11.5080i	0.182236	+	0.560864i	0.999890	−	0.0148461i	$-0.00472583\pi$
$421$	3.73916	+	11.5080i	0.182236	+	0.560864i	−0.817654	+	0.575710i	$0.804726\pi$
$422$	0.380710	+	1.17170i	0.0185327	+	0.0570377i
$423$	8.66578	+	6.29606i	0.421345	+	0.306125i
$424$	−9.97175			−0.484271
$425$	−14.1026	−	26.7488i	−0.684075	−	1.29751i
$426$	−6.85536			−0.332143
$427$	13.1379	+	9.54525i	0.635788	+	0.461927i
$428$	−2.72257	−	8.37921i	−0.131600	−	0.405024i
$429$	0.0182371	+	0.0561279i	0.000880493	+	0.00270988i
$430$	22.3000	+	5.18954i	1.07540	+	0.250262i
$431$	−0.337509	+	1.03875i	−0.0162572	+	0.0500346i	−0.958856	−	0.283893i	$-0.908374\pi$
$431$	−0.337509	+	1.03875i	−0.0162572	+	0.0500346i	0.942599	+	0.333927i	$0.108374\pi$
$432$	1.00000			0.0481125
$433$	3.74722	−	11.5328i	0.180080	−	0.554229i	−0.819749	−	0.572723i	$-0.805887\pi$
$433$	3.74722	−	11.5328i	0.180080	−	0.554229i	0.999829	+	0.0184940i	$0.00588716\pi$
$434$	−4.00810	+	2.91206i	−0.192395	+	0.139783i
$435$	7.86760	−	13.0421i	0.377223	−	0.625319i
$436$	−12.8447	−	9.33220i	−0.615148	−	0.446931i
$437$	−11.7082	+	8.50651i	−0.560079	+	0.406921i
$438$	9.41496	−	6.84037i	0.449864	−	0.326845i
$439$	−11.2409	−	8.16698i	−0.536498	−	0.389789i	0.286285	−	0.958145i	$-0.407580\pi$
$439$	−11.2409	−	8.16698i	−0.536498	−	0.389789i	−0.822783	+	0.568356i	$0.807580\pi$
$440$	−0.219863	+	0.364466i	−0.0104816	+	0.0173752i
$441$	−1.27305	+	0.924925i	−0.0606215	+	0.0440441i
$442$	−0.579407	+	1.78323i	−0.0275596	+	0.0848197i
$443$	−38.2047			−1.81516			−0.907579	−	0.419880i	$-0.862072\pi$
$443$	−38.2047			−1.81516			−0.907579	+	0.419880i	$0.862072\pi$
$444$	−3.01475	+	9.27846i	−0.143074	+	0.440336i
$445$	−20.2190	−	4.70524i	−0.958471	−	0.223050i
$446$	−1.44079	−	4.43429i	−0.0682233	−	0.209970i
$447$	0.435153	+	1.33926i	0.0205820	+	0.0633450i
$448$	−2.36886	−	1.72107i	−0.111918	−	0.0813131i
$449$	14.8092			0.698888			0.349444	−	0.936957i	$-0.386371\pi$
$449$	14.8092			0.698888			0.349444	+	0.936957i	$0.386371\pi$
$450$	−3.48587	+	3.58451i	−0.164326	+	0.168975i
$451$	0.965855			0.0454803
$452$	15.4845	+	11.2502i	0.728332	+	0.529164i
$453$	−2.43269	−	7.48704i	−0.114298	−	0.351772i
$454$	−0.177245	−	0.545504i	−0.00831852	−	0.0256018i
$455$	1.04852	−	1.73813i	0.0491554	−	0.0814847i
$456$	−1.00000	+	3.07768i	−0.0468293	+	0.144126i
$457$	4.86286			0.227475			0.113738	−	0.993511i	$-0.463718\pi$
$457$	4.86286			0.227475			0.113738	+	0.993511i	$0.463718\pi$
$458$	−9.18801	+	28.2778i	−0.429327	+	1.32133i
$459$	−4.89273	+	3.55478i	−0.228373	+	0.165923i
$460$	0.854102	+	9.96346i	0.0398227	+	0.464549i
$461$	16.4278	+	11.9355i	0.765117	+	0.555890i	0.900475	−	0.434907i	$-0.143219\pi$
$461$	16.4278	+	11.9355i	0.765117	+	0.555890i	−0.135359	+	0.990797i	$0.543219\pi$
$462$	0.450924	−	0.327615i	0.0209789	−	0.0152420i
$463$	−32.3465	+	23.5011i	−1.50327	+	1.09219i	−0.534213	+	0.845350i	$0.679392\pi$
$463$	−32.3465	+	23.5011i	−1.50327	+	1.09219i	−0.969056	+	0.246840i	$0.920608\pi$
$464$	−5.51076	−	4.00380i	−0.255831	−	0.185872i
$465$	3.48525	−	1.47220i	0.161624	−	0.0682715i
$466$	−11.2266	+	8.15663i	−0.520064	+	0.377848i
$467$	−4.92623	+	15.1614i	−0.227959	+	0.701585i	0.770019	+	0.638021i	$0.220247\pi$
$467$	−4.92623	+	15.1614i	−0.227959	+	0.701585i	−0.997978	+	0.0635638i	$0.979753\pi$
$468$	0.310033			0.0143313
$469$	−13.6558	+	42.0281i	−0.630565	+	1.94068i
$470$	2.04571	+	23.8641i	0.0943617	+	1.10077i
$471$	−2.14938	−	6.61511i	−0.0990382	−	0.304808i
$472$	−2.29489	−	7.06295i	−0.105631	−	0.325099i
$473$	1.57687	+	1.14566i	0.0725043	+	0.0526775i
$474$	−1.57029			−0.0721258
$475$	−7.54610	−	14.3129i	−0.346239	−	0.656722i
$476$	17.7082			0.811654
$477$	−8.06731	−	5.86125i	−0.369377	−	0.268368i
$478$	0.662491	+	2.03894i	0.0303016	+	0.0932588i
$479$	−2.42768	−	7.47163i	−0.110923	−	0.341387i	0.880152	−	0.474693i	$-0.157441\pi$
$479$	−2.42768	−	7.47163i	−0.110923	−	0.341387i	−0.991075	+	0.133305i	$0.957441\pi$
$480$	1.46403	+	1.69015i	0.0668237	+	0.0771444i
$481$	−0.934674	+	2.87663i	−0.0426174	+	0.131163i
$482$	−1.73974			−0.0792432
$483$	4.04649	−	12.4538i	0.184122	−	0.566668i
$484$	8.86987	−	6.44434i	0.403176	−	0.292925i
$485$	−2.54704	−	2.94043i	−0.115655	−	0.133518i
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	33.1264	−	24.0677i	1.50110	−	1.09061i	0.531158	−	0.847273i	$-0.321757\pi$
$487$	33.1264	−	24.0677i	1.50110	−	1.09061i	0.969941	−	0.243340i	$-0.0782430\pi$
$488$	−4.48689	+	3.25992i	−0.203112	+	0.147569i
$489$	11.3262	+	8.22899i	0.512190	+	0.372128i
$490$	−3.42705	−	0.797524i	−0.154818	−	0.0360285i
$491$	6.08238	−	4.41911i	0.274494	−	0.199432i	−0.442018	−	0.897006i	$-0.645737\pi$
$491$	6.08238	−	4.41911i	0.274494	−	0.199432i	0.716512	+	0.697574i	$0.245737\pi$
$492$	1.56794	−	4.82563i	0.0706883	−	0.217556i
$493$	41.1953			1.85534
$494$	−0.310033	+	0.954184i	−0.0139490	+	0.0429308i
$495$	−0.392101	+	0.165627i	−0.0176236	+	0.00744437i
$496$	−0.522856	−	1.60919i	−0.0234769	−	0.0722546i
$497$	6.20288	+	19.0905i	0.278237	+	0.856326i
$498$	10.5330	+	7.65267i	0.471995	+	0.342924i
$499$	15.7513			0.705123			0.352561	−	0.935789i	$-0.385311\pi$
$499$	15.7513			0.705123			0.352561	+	0.935789i	$0.385311\pi$
$500$	−11.1618	−	0.643811i	−0.499170	−	0.0287921i
$501$	1.37742			0.0615387
$502$	−5.17521	−	3.76001i	−0.230981	−	0.167818i
$503$	0.253049	+	0.778805i	0.0112829	+	0.0347252i	0.956539	−	0.291603i	$-0.0941886\pi$
$503$	0.253049	+	0.778805i	0.0112829	+	0.0347252i	−0.945257	+	0.326328i	$0.894189\pi$
$504$	−0.904822	−	2.78476i	−0.0403040	−	0.124043i
$505$	1.57616	−	0.665785i	0.0701384	−	0.0296271i
$506$	−0.263064	+	0.809628i	−0.0116946	+	0.0359924i
$507$	−12.9039			−0.573081
$508$	−2.51475	+	7.73962i	−0.111574	+	0.343390i
$509$	−21.8047	+	15.8420i	−0.966477	+	0.702186i	−0.954646	−	0.297744i	$-0.903766\pi$
$509$	−21.8047	+	15.8420i	−0.966477	+	0.702186i	−0.0118309	+	0.999930i	$0.503766\pi$
$510$	−13.1712	−	3.06513i	−0.583231	−	0.135726i
$511$	−27.5676	−	20.0291i	−1.21952	−	0.886033i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−2.61803	+	1.90211i	−0.115589	+	0.0839803i
$514$	−5.10492	−	3.70894i	−0.225169	−	0.163595i
$515$	−8.24688	−	9.52058i	−0.363401	−	0.419527i
$516$	8.28381	−	6.01854i	0.364675	−	0.264952i
$517$	−0.630081	+	1.93919i	−0.0277109	+	0.0852855i
$518$	28.5661			1.25512
$519$	−1.27407	+	3.92117i	−0.0559253	+	0.172120i
$520$	0.453899	+	0.524002i	0.0199048	+	0.0229790i
$521$	−4.77653	−	14.7007i	−0.209264	−	0.644048i	−0.999511	−	0.0312598i	$-0.990048\pi$
$521$	−4.77653	−	14.7007i	−0.209264	−	0.644048i	0.790248	−	0.612788i	$-0.209952\pi$
$522$	−2.10492	−	6.47829i	−0.0921300	−	0.283547i
$523$	−8.35778	−	6.07228i	−0.365460	−	0.265522i	0.389866	−	0.920872i	$-0.372521\pi$
$523$	−8.35778	−	6.07228i	−0.365460	−	0.265522i	−0.755326	+	0.655349i	$0.772521\pi$
$524$	16.6201			0.726051
$525$	13.1361	+	6.46397i	0.573305	+	0.282111i
$526$	−2.85942			−0.124677
$527$	8.27849	+	6.01468i	0.360617	+	0.262003i
$528$	0.0588229	+	0.181038i	0.00255994	+	0.00787868i
$529$	−0.927051	−	2.85317i	−0.0403066	−	0.124051i
$530$	−1.90443	−	22.2160i	−0.0827233	−	0.965003i
$531$	2.29489	−	7.06295i	0.0995898	−	0.306506i
$532$	9.47542			0.410812
$533$	0.486114	−	1.49610i	0.0210559	−	0.0648035i
$534$	−7.51076	+	5.45689i	−0.325022	+	0.236143i
$535$	18.1480	−	7.66589i	0.784609	−	0.331425i
$536$	−12.2098	−	8.87097i	−0.527385	−	0.383168i
$537$	−3.48525	+	2.53218i	−0.150399	+	0.109272i
$538$	−7.85246	+	5.70514i	−0.338543	+	0.245966i
$539$	−0.242332	−	0.176064i	−0.0104380	−	0.00758362i
$540$	0.190983	+	2.22790i	0.00821860	+	0.0958734i
$541$	29.9620	−	21.7687i	1.28817	−	0.935908i	0.288400	−	0.957510i	$-0.406877\pi$
$541$	29.9620	−	21.7687i	1.28817	−	0.935908i	0.999767	+	0.0216018i	$0.00687662\pi$
$542$	−5.30503	+	16.3272i	−0.227870	+	0.701313i
$543$	12.9920			0.557541
$544$	−1.86886	+	5.75175i	−0.0801265	+	0.246604i
$545$	18.3381	−	30.3989i	0.785516	−	1.30215i
$546$	−0.280525	−	0.863367i	−0.0120054	−	0.0369487i
$547$	−7.48341	−	23.0316i	−0.319967	−	0.984758i	−0.973661	−	0.227999i	$-0.926782\pi$
$547$	−7.48341	−	23.0316i	−0.319967	−	0.984758i	0.653694	−	0.756759i	$-0.273218\pi$
$548$	8.60657	+	6.25304i	0.367654	+	0.267117i
$549$	−5.54610			−0.236702
$550$	−0.853982	−	0.420226i	−0.0364139	−	0.0179185i
$551$	22.0431			0.939066
$552$	3.61803	+	2.62866i	0.153994	+	0.111883i
$553$	1.42083	+	4.37287i	0.0604199	+	0.185953i
$554$	0.631532	+	1.94366i	0.0268312	+	0.0825780i
$555$	−21.2472	−	4.94453i	−0.901894	−	0.209884i
$556$	7.07397	−	21.7714i	0.300003	−	0.923314i
$557$	26.3623			1.11701			0.558504	−	0.829502i	$-0.311376\pi$
$557$	26.3623			1.11701			0.558504	+	0.829502i	$0.311376\pi$
$558$	0.522856	−	1.60919i	0.0221343	−	0.0681223i
$559$	2.56826	−	1.86595i	0.108626	−	0.0789212i
$560$	3.38197	−	5.60626i	0.142914	−	0.236908i
$561$	−0.931355	−	0.676669i	−0.0393219	−	0.0285690i
$562$	4.17357	−	3.03228i	0.176051	−	0.127909i
$563$	−12.2197	+	8.87811i	−0.514998	+	0.374168i	−0.814716	−	0.579860i	$-0.803107\pi$
$563$	−12.2197	+	8.87811i	−0.514998	+	0.374168i	0.299718	+	0.954028i	$0.403107\pi$
$564$	8.66578	+	6.29606i	0.364895	+	0.265112i
$565$	−22.1070	+	36.6466i	−0.930047	+	1.54173i
$566$	−7.59385	+	5.51725i	−0.319193	+	0.231907i
$567$	0.904822	−	2.78476i	0.0379990	−	0.116949i
$568$	−6.85536			−0.287644
$569$	−3.55757	+	10.9491i	−0.149141	+	0.459009i	−0.997520	−	0.0703802i	$-0.977579\pi$
$569$	−3.55757	+	10.9491i	−0.149141	+	0.459009i	0.848379	+	0.529389i	$0.177579\pi$
$570$	−7.04775	−	1.64011i	−0.295198	−	0.0686967i
$571$	−9.73974	−	29.9759i	−0.407596	−	1.25445i	−0.918708	−	0.394937i	$-0.870767\pi$
$571$	−9.73974	−	29.9759i	−0.407596	−	1.25445i	0.511113	−	0.859514i	$-0.329233\pi$
$572$	0.0182371	+	0.0561279i	0.000762530	+	0.00234682i
$573$	1.00000	+	0.726543i	0.0417756	+	0.0303517i
$574$	−14.8569			−0.620115
$575$	−22.0344	+	3.80570i	−0.918900	+	0.158709i
$576$	1.00000			0.0416667
$577$	10.6769	+	7.75719i	0.444483	+	0.322936i	0.787414	−	0.616425i	$-0.211420\pi$
$577$	10.6769	+	7.75719i	0.444483	+	0.322936i	−0.342930	+	0.939361i	$0.611420\pi$
$578$	−6.04908	−	18.6171i	−0.251608	−	0.774371i
$579$	5.38463	+	16.5722i	0.223777	+	0.688716i
$580$	7.86760	−	13.0421i	0.326684	−	0.541543i
$581$	11.7803	−	36.2561i	0.488730	−	1.50416i
$582$	−1.73974			−0.0721147
$583$	0.586567	−	1.80527i	0.0242931	−	0.0747666i
$584$	9.41496	−	6.84037i	0.389594	−	0.283056i
$585$	0.0592111	+	0.690722i	0.00244808	+	0.0285578i
$586$	−6.61905	−	4.80902i	−0.273430	−	0.198659i
$587$	−24.9839	+	18.1519i	−1.03120	+	0.749208i	−0.968548	−	0.248828i	$-0.919955\pi$
$587$	−24.9839	+	18.1519i	−1.03120	+	0.749208i	−0.0626487	+	0.998036i	$0.519955\pi$
$588$	−1.27305	+	0.924925i	−0.0524997	+	0.0381433i
$589$	4.42971	+	3.21837i	0.182523	+	0.132611i
$590$	15.2972	−	6.46168i	0.629777	−	0.266023i
$591$	−12.0885	+	8.78283i	−0.497256	+	0.361277i
$592$	−3.01475	+	9.27846i	−0.123906	+	0.381342i
$593$	5.13588			0.210905			0.105453	−	0.994424i	$-0.466371\pi$
$593$	5.13588			0.210905			0.105453	+	0.994424i	$0.466371\pi$
$594$	−0.0588229	+	0.181038i	−0.00241353	+	0.00742809i
$595$	3.38197	+	39.4521i	0.138647	+	1.61738i
$596$	0.435153	+	1.33926i	0.0178246	+	0.0548584i
$597$	−1.51553	−	4.66432i	−0.0620265	−	0.190898i
$598$	1.12171	+	0.814970i	0.0458701	+	0.0333266i
$599$	−42.2558			−1.72653			−0.863263	−	0.504755i	$-0.831583\pi$
$599$	−42.2558			−1.72653			−0.863263	+	0.504755i	$0.831583\pi$
$600$	−3.48587	+	3.58451i	−0.142310	+	0.146337i
$601$	4.38893			0.179028			0.0895141	−	0.995986i	$-0.471469\pi$
$601$	4.38893			0.179028			0.0895141	+	0.995986i	$0.471469\pi$
$602$	−24.2556	−	17.6227i	−0.988583	−	0.718247i
$603$	−4.66375	−	14.3535i	−0.189922	−	0.584521i
$604$	−2.43269	−	7.48704i	−0.0989846	−	0.304643i
$605$	16.0513	+	18.5304i	0.652579	+	0.753368i
$606$	0.236456	−	0.727737i	0.00960537	−	0.0295623i
$607$	−30.0265			−1.21874			−0.609368	−	0.792887i	$-0.708577\pi$
$607$	−30.0265			−1.21874			−0.609368	+	0.792887i	$0.708577\pi$
$608$	−1.00000	+	3.07768i	−0.0405554	+	0.124817i
$609$	−16.1359	+	11.7234i	−0.653859	+	0.475056i
$610$	−8.11968	−	9.37374i	−0.328756	−	0.379532i
$611$	2.68668	+	1.95199i	0.108691	+	0.0789689i
$612$	−4.89273	+	3.55478i	−0.197777	+	0.143693i
$613$	−3.62512	+	2.63380i	−0.146417	+	0.106378i	−0.658582	−	0.752509i	$-0.728844\pi$
$613$	−3.62512	+	2.63380i	−0.146417	+	0.106378i	0.512165	+	0.858887i	$0.328844\pi$
$614$	4.73974	+	3.44363i	0.191281	+	0.138973i
$615$	11.0505	+	2.57160i	0.445597	+	0.103697i
$616$	0.450924	−	0.327615i	0.0181682	−	0.0132000i
$617$	−4.31692	+	13.2861i	−0.173793	+	0.534879i	−0.999576	−	0.0291080i	$-0.990733\pi$
$617$	−4.31692	+	13.2861i	−0.173793	+	0.534879i	0.825783	+	0.563987i	$0.190733\pi$
$618$	−5.63298			−0.226592
$619$	7.54813	−	23.2308i	0.303385	−	0.933723i	−0.676890	−	0.736084i	$-0.736673\pi$
$619$	7.54813	−	23.2308i	0.303385	−	0.933723i	0.980275	−	0.197639i	$-0.0633274\pi$
$620$	3.48525	−	1.47220i	0.139971	−	0.0591249i
$621$	1.38197	+	4.25325i	0.0554564	+	0.170677i
$622$	5.88361	+	18.1079i	0.235911	+	0.726060i
$623$	21.9920	+	15.9781i	0.881092	+	0.640150i
$624$	0.310033			0.0124113
$625$	−0.697366	−	24.9903i	−0.0278946	−	0.999611i
$626$	11.9966			0.479479
$627$	−0.498356	−	0.362077i	−0.0199024	−	0.0144600i
$628$	−2.14938	−	6.61511i	−0.0857696	−	0.263972i
$629$	−18.2325	−	56.1138i	−0.726976	−	2.23740i
$630$	6.03135	−	2.54769i	0.240295	−	0.101503i
$631$	3.06269	−	9.42600i	0.121924	−	0.375243i	−0.871404	−	0.490566i	$-0.836790\pi$
$631$	3.06269	−	9.42600i	0.121924	−	0.375243i	0.993328	+	0.115322i	$0.0367901\pi$
$632$	−1.57029			−0.0624627
$633$	−0.380710	+	1.17170i	−0.0151319	+	0.0465711i
$634$	26.3841	−	19.1692i	1.04785	−	0.761306i
$635$	−17.7233	−	4.12448i	−0.703330	−	0.163675i
$636$	−8.06731	−	5.86125i	−0.319890	−	0.232414i
$637$	−0.394688	+	0.286758i	−0.0156381	+	0.0113617i
$638$	1.04900	−	0.762144i	0.0415304	−	0.0301736i
$639$	−5.54610	−	4.02948i	−0.219400	−	0.159404i
$640$	1.46403	+	1.69015i	0.0578710	+	0.0668090i
$641$	−31.9691	+	23.2269i	−1.26270	+	0.917407i	−0.998887	−	0.0471657i	$-0.984981\pi$
$641$	−31.9691	+	23.2269i	−1.26270	+	0.917407i	−0.263816	+	0.964573i	$0.584981\pi$
$642$	2.72257	−	8.37921i	0.107451	−	0.330701i
$643$	22.9508			0.905093			0.452547	−	0.891741i	$-0.350516\pi$
$643$	22.9508			0.905093			0.452547	+	0.891741i	$0.350516\pi$
$644$	4.04649	−	12.4538i	0.159454	−	0.490749i
$645$	14.9908	+	17.3060i	0.590261	+	0.681425i
$646$	−6.04775	−	18.6130i	−0.237945	−	0.732320i
$647$	−0.761900	−	2.34489i	−0.0299534	−	0.0921870i	0.934962	−	0.354747i	$-0.115433\pi$
$647$	−0.761900	−	2.34489i	−0.0299534	−	0.0921870i	−0.964916	+	0.262560i	$0.915433\pi$
$648$	0.809017	+	0.587785i	0.0317812	+	0.0230904i
$649$	1.41366			0.0554909
$650$	−1.08074	+	1.11132i	−0.0423900	+	0.0435894i
$651$	−4.95429			−0.194174
$652$	11.3262	+	8.22899i	0.443570	+	0.322272i
$653$	−8.27484	−	25.4673i	−0.323820	−	0.996614i	−0.971971	−	0.235102i	$-0.924457\pi$
$653$	−8.27484	−	25.4673i	−0.323820	−	0.996614i	0.648151	−	0.761512i	$-0.275543\pi$
$654$	−4.90623	−	15.0998i	−0.191849	−	0.590449i
$655$	3.17415	+	37.0278i	0.124024	+	1.44680i
$656$	1.56794	−	4.82563i	0.0612178	−	0.188409i
$657$	11.6375			0.454023
$658$	9.69200	−	29.8289i	0.377833	−	1.16285i
$659$	−23.1334	+	16.8074i	−0.901150	+	0.654724i	−0.938761	−	0.344569i	$-0.888025\pi$
$659$	−23.1334	+	16.8074i	−0.901150	+	0.654724i	0.0376112	+	0.999292i	$0.488025\pi$
$660$	−0.392101	+	0.165627i	−0.0152625	+	0.00644701i
$661$	1.89981	+	1.38030i	0.0738942	+	0.0536873i	0.624119	−	0.781329i	$-0.285458\pi$
$661$	1.89981	+	1.38030i	0.0738942	+	0.0536873i	−0.550225	+	0.835017i	$0.685458\pi$
$662$	2.61475	−	1.89972i	0.101625	−	0.0738349i
$663$	−1.51691	+	1.10210i	−0.0589118	+	0.0428019i
$664$	10.5330	+	7.65267i	0.408759	+	0.296981i
$665$	1.80964	+	21.1103i	0.0701750	+	0.818621i
$666$	−7.89273	+	5.73440i	−0.305837	+	0.222204i
$667$	9.41351	−	28.9718i	0.364492	−	1.12179i
$668$	1.37742			0.0532940
$669$	1.44079	−	4.43429i	0.0557041	−	0.171440i
$670$	17.4317	−	28.8965i	0.673447	−	1.11637i
$671$	−0.326238	−	1.00406i	−0.0125943	−	0.0387612i
$672$	−0.904822	−	2.78476i	−0.0349043	−	0.107424i
$673$	28.3700	+	20.6120i	1.09358	+	0.794534i	0.980001	−	0.198994i	$-0.0637675\pi$
$673$	28.3700	+	20.6120i	1.09358	+	0.794534i	0.113582	+	0.993529i	$0.463767\pi$
$674$	−21.3154			−0.821037
$675$	−4.92705	+	0.850981i	−0.189642	+	0.0327543i
$676$	−12.9039			−0.496303
$677$	−26.0549	−	18.9300i	−1.00137	−	0.727539i	−0.0389895	−	0.999240i	$-0.512414\pi$
$677$	−26.0549	−	18.9300i	−1.00137	−	0.727539i	−0.962382	+	0.271701i	$0.912414\pi$
$678$	5.91457	+	18.2032i	0.227148	+	0.699089i
$679$	1.57416	+	4.84477i	0.0604107	+	0.185925i
$680$	−13.1712	−	3.06513i	−0.505093	−	0.117542i
$681$	0.177245	−	0.545504i	0.00679204	−	0.0209038i
$682$	0.322080			0.0123331
$683$	4.26867	−	13.1376i	0.163336	−	0.502697i	−0.835574	−	0.549378i	$-0.814865\pi$
$683$	4.26867	−	13.1376i	0.163336	−	0.502697i	0.998910	+	0.0466814i	$0.0148646\pi$
$684$	−2.61803	+	1.90211i	−0.100103	+	0.0727291i
$685$	−12.2874	+	20.3688i	−0.469478	+	0.778251i
$686$	−12.8544	−	9.33928i	−0.490784	−	0.356575i
$687$	−24.0545	+	17.4766i	−0.917737	+	0.666775i
$688$	8.28381	−	6.01854i	0.315817	−	0.229455i
$689$	−2.50113	−	1.81718i	−0.0952856	−	0.0692291i
$690$	−5.16539	+	8.56264i	−0.196643	+	0.325974i
$691$	20.9940	−	15.2531i	0.798651	−	0.580254i	−0.111867	−	0.993723i	$-0.535683\pi$
$691$	20.9940	−	15.2531i	0.798651	−	0.580254i	0.910518	+	0.413469i	$0.135683\pi$
$692$	−1.27407	+	3.92117i	−0.0484327	+	0.149061i
$693$	0.557372			0.0211728
$694$	−5.91496	+	18.2044i	−0.224529	+	0.691028i
$695$	49.8555	+	11.6021i	1.89113	+	0.440093i
$696$	−2.10492	−	6.47829i	−0.0797869	−	0.245559i
$697$	9.48251	+	29.1842i	0.359176	+	1.10543i
$698$	11.6292	+	8.44910i	0.440171	+	0.319803i
$699$	−13.8769			−0.524872
$700$	13.1361	+	6.46397i	0.496497	+	0.244315i
$701$	37.4437			1.41423			0.707115	−	0.707098i	$-0.249996\pi$
$701$	37.4437			1.41423			0.707115	+	0.707098i	$0.249996\pi$
$702$	0.250822	+	0.182233i	0.00946667	+	0.00687794i
$703$	−9.75595	−	30.0257i	−0.367953	−	1.13244i
$704$	0.0588229	+	0.181038i	0.00221697	+	0.00682314i
$705$	−12.3720	+	20.5089i	−0.465955	+	0.772410i
$706$	−7.53609	+	23.1937i	−0.283624	+	0.872906i
$707$	−2.24052			−0.0842635
$708$	2.29489	−	7.06295i	0.0862473	−	0.265442i
$709$	14.0996	−	10.2440i	0.529522	−	0.384720i	−0.290657	−	0.956827i	$-0.593874\pi$
$709$	14.0996	−	10.2440i	0.529522	−	0.384720i	0.820179	+	0.572107i	$0.193874\pi$
$710$	−1.30926	−	15.2730i	−0.0491355	−	0.573187i
$711$	−1.27039	−	0.922993i	−0.0476434	−	0.0346149i
$712$	−7.51076	+	5.45689i	−0.281478	+	0.204506i
$713$	6.12171	−	4.44768i	0.229260	−	0.166567i
$714$	14.3262	+	10.4086i	0.536146	+	0.389533i
$715$	−0.121564	+	0.0513498i	−0.00454624	+	0.00192037i
$716$	−3.48525	+	2.53218i	−0.130250	+	0.0946320i
$717$	−0.662491	+	2.03894i	−0.0247412	+	0.0761455i
$718$	21.3316			0.796087
$719$	−10.9650	+	33.7469i	−0.408926	+	1.25855i	0.508646	+	0.860976i	$0.330146\pi$
$719$	−10.9650	+	33.7469i	−0.408926	+	1.25855i	−0.917572	+	0.397570i	$0.869854\pi$
$720$	0.190983	+	2.22790i	0.00711752	+	0.0830288i
$721$	5.09685	+	15.6865i	0.189817	+	0.584195i
$722$	2.63525	+	8.11048i	0.0980740	+	0.301841i
$723$	−1.40748	−	1.02260i	−0.0523448	−	0.0380308i
$724$	12.9920			0.482845
$725$	30.5590	+	15.0374i	1.13493	+	0.558475i
$726$	10.9638			0.406903
$727$	15.4459	+	11.2221i	0.572857	+	0.416205i	0.836142	−	0.548513i	$-0.184806\pi$
$727$	15.4459	+	11.2221i	0.572857	+	0.416205i	−0.263285	+	0.964718i	$0.584806\pi$
$728$	−0.280525	−	0.863367i	−0.0103969	−	0.0319985i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	17.0377	+	19.6692i	0.630595	+	0.727988i
$731$	−19.1359	+	58.8942i	−0.707766	+	2.17828i
$732$	−5.54610			−0.204990
$733$	3.38352	−	10.4134i	0.124973	−	0.384628i	−0.868923	−	0.494947i	$-0.835187\pi$
$733$	3.38352	−	10.4134i	0.124973	−	0.384628i	0.993896	+	0.110319i	$0.0351874\pi$
$734$	−8.60164	+	6.24945i	−0.317492	+	0.230672i
$735$	−2.30377	−	2.65958i	−0.0849758	−	0.0981001i
$736$	3.61803	+	2.62866i	0.133363	+	0.0968935i
$737$	2.32421	−	1.68863i	0.0856132	−	0.0622016i
$738$	4.10492	−	2.98240i	0.151104	−	0.109784i
$739$	−38.7566	−	28.1583i	−1.42568	−	1.03582i	−0.990800	−	0.135333i	$-0.956790\pi$
$739$	−38.7566	−	28.1583i	−1.42568	−	1.03582i	−0.434884	−	0.900487i	$-0.643210\pi$
$740$	−21.2472	−	4.94453i	−0.781063	−	0.181765i
$741$	−0.811677	+	0.589718i	−0.0298177	+	0.0216638i
$742$	−9.02266	+	27.7689i	−0.331232	+	1.01943i
$743$	38.6016			1.41615			0.708077	−	0.706135i	$-0.249563\pi$
$743$	38.6016			1.41615			0.708077	+	0.706135i	$0.249563\pi$
$744$	0.522856	−	1.60919i	0.0191688	−	0.0589957i
$745$	−2.90064	+	1.22525i	−0.106271	+	0.0448898i
$746$	−0.381190	−	1.17318i	−0.0139563	−	0.0429532i
$747$	4.02324	+	12.3823i	0.147203	+	0.453044i
$748$	−0.931355	−	0.676669i	−0.0340537	−	0.0247415i
$749$	−25.7975			−0.942620
$750$	−8.65165	−	7.08159i	−0.315914	−	0.258583i
$751$	−29.2670			−1.06797			−0.533984	−	0.845495i	$-0.679306\pi$
$751$	−29.2670			−1.06797			−0.533984	+	0.845495i	$0.679306\pi$
$752$	8.66578	+	6.29606i	0.316008	+	0.229594i
$753$	−1.97676	−	6.08383i	−0.0720370	−	0.221707i
$754$	−0.652596	−	2.00848i	−0.0237662	−	0.0731447i
$755$	16.2158	−	6.84967i	0.590152	−	0.249285i
$756$	0.904822	−	2.78476i	0.0329081	−	0.101281i
$757$	−12.0788			−0.439012			−0.219506	−	0.975611i	$-0.570444\pi$
$757$	−12.0788			−0.439012			−0.219506	+	0.975611i	$0.570444\pi$
$758$	−7.82585	+	24.0855i	−0.284248	+	0.874824i
$759$	−0.688711	+	0.500378i	−0.0249986	+	0.0181626i
$760$	−7.04775	−	1.64011i	−0.255649	−	0.0594931i
$761$	1.72093	+	1.25033i	0.0623835	+	0.0453243i	0.618540	−	0.785753i	$-0.287724\pi$
$761$	1.72093	+	1.25033i	0.0623835	+	0.0453243i	−0.556156	+	0.831078i	$0.687724\pi$
$762$	−6.58371	+	4.78335i	−0.238503	+	0.173282i
$763$	−37.6101	+	27.3253i	−1.36158	+	0.989242i
$764$	1.00000	+	0.726543i	0.0361787	+	0.0262854i
$765$	−8.85410	−	10.2216i	−0.320121	−	0.369563i
$766$	15.5166	−	11.2735i	0.560637	−	0.407327i
$767$	0.711492	−	2.18975i	0.0256905	−	0.0790672i
$768$	1.00000			0.0360844
$769$	−2.77310	+	8.53471i	−0.100000	+	0.307770i	−0.988525	−	0.151060i	$-0.951731\pi$
$769$	−2.77310	+	8.53471i	−0.100000	+	0.307770i	0.888524	+	0.458830i	$0.151731\pi$
$770$	0.816012	+	0.942042i	0.0294070	+	0.0339489i
$771$	−1.94991	−	6.00120i	−0.0702242	−	0.216128i
$772$	5.38463	+	16.5722i	0.193797	+	0.596446i
$773$	−23.2575	−	16.8976i	−0.836515	−	0.607764i	0.0848801	−	0.996391i	$-0.472949\pi$
$773$	−23.2575	−	16.8976i	−0.836515	−	0.607764i	−0.921395	+	0.388628i	$0.872949\pi$
$774$	10.2394			0.368046
$775$	3.94553	+	7.48360i	0.141728	+	0.268819i
$776$	−1.73974			−0.0624532
$777$	23.1104	+	16.7907i	0.829082	+	0.602364i
$778$	2.56407	+	7.89140i	0.0919264	+	0.282920i
$779$	5.07397	+	15.6161i	0.181794	+	0.559503i
$780$	0.0592111	+	0.690722i	0.00212010	+	0.0247318i
$781$	0.403252	−	1.24108i	0.0144295	−	0.0444094i
$782$	−27.0463			−0.967175
$783$	2.10492	−	6.47829i	0.0752238	−	0.231515i
$784$	−1.27305	+	0.924925i	−0.0454661	+	0.0330330i
$785$	14.3273	−	6.05197i	0.511363	−	0.216004i
$786$	13.4459	+	9.76903i	0.479600	+	0.348450i
$787$	39.9330	−	29.0130i	1.42346	−	1.03420i	0.432269	−	0.901745i	$-0.357713\pi$
$787$	39.9330	−	29.0130i	1.42346	−	1.03420i	0.991189	−	0.132458i	$-0.0422869\pi$
$788$	−12.0885	+	8.78283i	−0.430636	+	0.312875i
$789$	−2.31332	−	1.68073i	−0.0823564	−	0.0598354i
$790$	−0.299898	−	3.49844i	−0.0106699	−	0.124469i
$791$	45.3398	−	32.9413i	1.61210	−	1.17126i
$792$	−0.0588229	+	0.181038i	−0.00209018	+	0.00643292i
$793$	−1.71948			−0.0610603
$794$	9.73897	−	29.9735i	0.345623	−	1.06372i
$795$	11.5175	−	19.0925i	0.408485	−	0.677143i
$796$	−1.51553	−	4.66432i	−0.0537165	−	0.165323i
$797$	0.907289	+	2.79235i	0.0321378	+	0.0989101i	0.965839	−	0.259144i	$-0.0834404\pi$
$797$	0.907289	+	2.79235i	0.0321378	+	0.0989101i	−0.933701	+	0.358054i	$0.883440\pi$
$798$	7.66578	+	5.56951i	0.271366	+	0.197159i
$799$	−64.7804			−2.29176
$800$	−3.48587	+	3.58451i	−0.123244	+	0.126731i
$801$	−9.28381			−0.328027
$802$	−11.0787	−	8.04915i	−0.391203	−	0.284225i
$803$	0.684553	+	2.10684i	0.0241574	+	0.0743487i
$804$	−4.66375	−	14.3535i	−0.164478	−	0.506210i
$805$	28.5186	+	6.63669i	1.00515	+	0.233913i
$806$	0.162103	−	0.498901i	0.00570983	−	0.0175730i
$807$	−9.70617			−0.341673
$808$	0.236456	−	0.727737i	0.00831850	−	0.0256017i
$809$	29.2720	−	21.2674i	1.02915	−	0.747721i	0.0610115	−	0.998137i	$-0.480567\pi$
$809$	29.2720	−	21.2674i	1.02915	−	0.747721i	0.968138	+	0.250416i	$0.0805674\pi$
$810$	−1.15502	+	1.91466i	−0.0405831	+	0.0672744i
$811$	36.5650	+	26.5660i	1.28397	+	0.932858i	0.999665	−	0.0258756i	$-0.00823738\pi$
$811$	36.5650	+	26.5660i	1.28397	+	0.932858i	0.284304	+	0.958734i	$0.408237\pi$
$812$	−16.1359	+	11.7234i	−0.566258	+	0.411411i
$813$	−13.8887	+	10.0908i	−0.487099	+	0.353898i
$814$	−1.50242	−	1.09157i	−0.0526598	−	0.0382596i
$815$	−16.1702	+	26.8053i	−0.566419	+	0.938948i
$816$	−4.89273	+	3.55478i	−0.171280	+	0.124442i
$817$	−10.2394	+	31.5135i	−0.358230	+	1.10252i
$818$	30.0967			1.05231
$819$	0.280525	−	0.863367i	0.00980233	−	0.0301685i
$820$	11.0505	+	2.57160i	0.385899	+	0.0898041i
$821$	−6.03945	−	18.5875i	−0.210778	−	0.648709i	−0.999426	−	0.0338640i	$-0.989219\pi$
$821$	−6.03945	−	18.5875i	−0.210778	−	0.648709i	0.788648	−	0.614845i	$-0.210781\pi$
$822$	3.28742	+	10.1176i	0.114662	+	0.352893i
$823$	14.1755	+	10.2991i	0.494128	+	0.359005i	0.806770	−	0.590866i	$-0.201214\pi$
$823$	14.1755	+	10.2991i	0.494128	+	0.359005i	−0.312642	+	0.949871i	$0.601214\pi$
$824$	−5.63298			−0.196234
$825$	−0.443884	−	0.841928i	−0.0154540	−	0.0293122i
$826$	−21.7451			−0.756608
$827$	20.1268	+	14.6230i	0.699879	+	0.508492i	0.879893	−	0.475172i	$-0.157614\pi$
$827$	20.1268	+	14.6230i	0.699879	+	0.508492i	−0.180014	+	0.983664i	$0.557614\pi$
$828$	1.38197	+	4.25325i	0.0480266	+	0.147811i
$829$	−4.93738	−	15.1957i	−0.171482	−	0.527768i	0.827973	−	0.560768i	$-0.189494\pi$
$829$	−4.93738	−	15.1957i	−0.171482	−	0.527768i	−0.999455	+	0.0329996i	$0.989494\pi$
$830$	−15.0377	+	24.9279i	−0.521967	+	0.865262i
$831$	−0.631532	+	1.94366i	−0.0219076	+	0.0674247i
$832$	0.310033			0.0107485
$833$	2.94079	−	9.05082i	0.101892	−	0.313592i
$834$	18.5199	−	13.4555i	0.641291	−	0.465925i
$835$	0.263064	+	3.06875i	0.00910371	+	0.106199i
$836$	−0.498356	−	0.362077i	−0.0172360	−	0.0125227i
$837$	1.36886	−	0.994532i	0.0473146	−	0.0343761i
$838$	8.60696	−	6.25332i	0.297322	−	0.216017i
$839$	32.7244	+	23.7757i	1.12977	+	0.820827i	0.985662	−	0.168734i	$-0.0539679\pi$
$839$	32.7244	+	23.7757i	1.12977	+	0.820827i	0.144110	+	0.989562i	$0.453968\pi$
$840$	6.03135	−	2.54769i	0.208101	−	0.0879038i
$841$	−14.0760	+	10.2268i	−0.485381	+	0.352650i
$842$	−3.73916	+	11.5080i	−0.128860	+	0.396590i
$843$	5.15881			0.177679
$844$	−0.380710	+	1.17170i	−0.0131046	+	0.0403317i
$845$	−2.46442	−	28.7485i	−0.0847787	−	0.988979i
$846$	3.31003	+	10.1872i	0.113801	+	0.350244i
$847$	−9.92026	−	30.5314i	−0.340864	−	1.04907i
$848$	−8.06731	−	5.86125i	−0.277033	−	0.201276i
$849$	−9.38651			−0.322144
$850$	4.31332	−	29.9295i	0.147946	−	1.02657i
$851$	−43.6299			−1.49561
$852$	−5.54610	−	4.02948i	−0.190006	−	0.138048i
$853$	−13.3509	−	41.0898i	−0.457126	−	1.40689i	−0.868621	−	0.495476i	$-0.834993\pi$
$853$	−13.3509	−	41.0898i	−0.457126	−	1.40689i	0.411496	−	0.911412i	$-0.365007\pi$
$854$	5.01824	+	15.4445i	0.171721	+	0.528501i
$855$	−4.73771	−	5.46944i	−0.162026	−	0.187051i
$856$	2.72257	−	8.37921i	0.0930555	−	0.286395i
$857$	21.6193			0.738501			0.369250	−	0.929330i	$-0.379614\pi$
$857$	21.6193			0.738501			0.369250	+	0.929330i	$0.379614\pi$
$858$	−0.0182371	+	0.0561279i	−0.000622603	+	0.00191617i
$859$	31.5871	−	22.9494i	1.07774	−	0.783023i	0.100451	−	0.994942i	$-0.467971\pi$
$859$	31.5871	−	22.9494i	1.07774	−	0.783023i	0.977287	+	0.211919i	$0.0679713\pi$
$860$	14.9908	+	17.3060i	0.511181	+	0.590131i
$861$	−12.0195	−	8.73267i	−0.409623	−	0.297609i
$862$	−0.883610	+	0.641980i	−0.0300959	+	0.0218659i
$863$	17.3283	−	12.5897i	0.589861	−	0.428559i	−0.252405	−	0.967622i	$-0.581221\pi$
$863$	17.3283	−	12.5897i	0.589861	−	0.428559i	0.842266	+	0.539063i	$0.181221\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	−8.97930	−	2.08961i	−0.305305	−	0.0710489i
$866$	9.81035	−	7.12763i	0.333369	−	0.242207i
$867$	6.04908	−	18.6171i	0.205437	−	0.632271i
$868$	−4.95429			−0.168159
$869$	0.0923690	−	0.284283i	0.00313340	−	0.00964362i
$870$	14.0310	−	5.92680i	0.475694	−	0.200937i
$871$	−1.44592	−	4.45007i	−0.0489930	−	0.150785i
$872$	−4.90623	−	15.0998i	−0.166146	−	0.511344i
$873$	−1.40748	−	1.02260i	−0.0476361	−	0.0346096i
$874$	−14.4721			−0.489527
$875$	−11.8923	+	30.5003i	−0.402033	+	1.03110i
$876$	11.6375			0.393196
$877$	−37.9859	−	27.5984i	−1.28269	−	0.931930i	−0.283061	−	0.959102i	$-0.591350\pi$
$877$	−37.9859	−	27.5984i	−1.28269	−	0.931930i	−0.999631	+	0.0271718i	$0.991350\pi$
$878$	−4.29363	−	13.2144i	−0.144903	−	0.445966i
$879$	−2.52825	−	7.78116i	−0.0852758	−	0.262452i
$880$	−0.392101	+	0.165627i	−0.0132177	+	0.00558327i
$881$	0.100961	−	0.310727i	0.00340147	−	0.0104687i	−0.949341	−	0.314247i	$-0.898248\pi$
$881$	0.100961	−	0.310727i	0.00340147	−	0.0104687i	0.952743	+	0.303778i	$0.0982481\pi$
$882$	−1.57358			−0.0529851
$883$	−4.29257	+	13.2112i	−0.144457	+	0.444592i	−0.996941	−	0.0781615i	$-0.975095\pi$
$883$	−4.29257	+	13.2112i	−0.144457	+	0.444592i	0.852484	+	0.522753i	$0.175095\pi$
$884$	−1.51691	+	1.10210i	−0.0510191	+	0.0370676i
$885$	16.1738	+	3.76388i	0.543677	+	0.126521i
$886$	−30.9082	−	22.4561i	−1.03838	−	0.754429i
$887$	4.39488	−	3.19307i	0.147566	−	0.107213i	−0.511553	−	0.859252i	$-0.670930\pi$
$887$	4.39488	−	3.19307i	0.147566	−	0.107213i	0.659119	+	0.752039i	$0.270930\pi$
$888$	−7.89273	+	5.73440i	−0.264863	+	0.192434i
$889$	19.2775	+	14.0060i	0.646548	+	0.469745i
$890$	−13.5918	−	15.6910i	−0.455599	−	0.525965i
$891$	−0.154000	+	0.111888i	−0.00515921	+	0.00374838i
$892$	1.44079	−	4.43429i	0.0482412	−	0.148471i
$893$	−34.6631			−1.15996
$894$	−0.435153	+	1.33926i	−0.0145537	+	0.0447917i
$895$	−6.30706	−	7.28117i	−0.210822	−	0.243383i
$896$	−0.904822	−	2.78476i	−0.0302280	−	0.0930322i
$897$	0.428455	+	1.31865i	0.0143057	+	0.0440284i
$898$	11.9809	+	8.70461i	0.399807	+	0.290477i
$899$	−11.5254			−0.384392
$900$	−4.92705	+	0.850981i	−0.164235	+	0.0283660i
$901$	60.3066			2.00910
$902$	0.781393	+	0.567715i	0.0260175	+	0.0189028i
$903$	−9.26480	−	28.5141i	−0.308313	−	0.948891i
$904$	5.91457	+	18.2032i	0.196716	+	0.605428i
$905$	2.48125	+	28.9449i	0.0824797	+	0.962160i
$906$	2.43269	−	7.48704i	0.0808206	−	0.248740i
$907$	−48.3381			−1.60504			−0.802521	−	0.596624i	$-0.796508\pi$
$907$	−48.3381			−1.60504			−0.802521	+	0.596624i	$0.796508\pi$
$908$	0.177245	−	0.545504i	0.00588208	−	0.0181032i
$909$	0.619050	−	0.449766i	0.0205326	−	0.0149178i
$910$	1.86992	−	0.789869i	0.0619872	−	0.0261839i
$911$	−6.80839	−	4.94658i	−0.225572	−	0.163888i	0.469259	−	0.883060i	$-0.344521\pi$
$911$	−6.80839	−	4.94658i	−0.225572	−	0.163888i	−0.694831	+	0.719173i	$0.744521\pi$
$912$	−2.61803	+	1.90211i	−0.0866918	+	0.0629853i
$913$	−2.00501	+	1.45672i	−0.0663561	+	0.0482105i
$914$	3.93414	+	2.85832i	0.130130	+	0.0945448i
$915$	−1.05921	−	12.3561i	−0.0350164	−	0.408481i
$916$	−24.0545	+	17.4766i	−0.794784	+	0.577444i
$917$	15.0382	−	46.2829i	0.496605	−	1.52839i
$918$	−6.04775			−0.199605
$919$	8.87108	−	27.3024i	0.292630	−	0.900623i	−0.691377	−	0.722494i	$-0.742996\pi$
$919$	8.87108	−	27.3024i	0.292630	−	0.900623i	0.984007	−	0.178129i	$-0.0570043\pi$
$920$	−5.16539	+	8.56264i	−0.170298	+	0.282302i
$921$	1.81042	+	5.57190i	0.0596554	+	0.183600i
$922$	6.27484	+	19.3120i	0.206651	+	0.636006i
$923$	−1.71948	−	1.24927i	−0.0565972	−	0.0411203i
$924$	0.557372			0.0183362
$925$	6.95806	−	48.2809i	0.228779	−	1.58747i
$926$	−39.9825			−1.31391
$927$	−4.55718	−	3.31098i	−0.149677	−	0.108747i
$928$	−2.10492	−	6.47829i	−0.0690975	−	0.212660i
$929$	−2.14735	−	6.60886i	−0.0704522	−	0.216830i	0.909631	−	0.415417i	$-0.136364\pi$
$929$	−2.14735	−	6.60886i	−0.0704522	−	0.216830i	−0.980083	+	0.198588i	$0.936364\pi$
$930$	3.68496	+	0.857543i	0.120835	+	0.0281199i
$931$	1.57358	−	4.84297i	0.0515719	−	0.158722i
$932$	−13.8769			−0.454552
$933$	−5.88361	+	18.1079i	−0.192621	+	0.592826i
$934$	−12.8970	+	9.37024i	−0.422004	+	0.306604i
$935$	1.32968	−	2.20420i	0.0434851	−	0.0720849i
$936$	0.250822	+	0.182233i	0.00819838	+	0.00595647i
$937$	−20.1124	+	14.6125i	−0.657043	+	0.477370i	−0.865663	−	0.500627i	$-0.833103\pi$
$937$	−20.1124	+	14.6125i	−0.657043	+	0.477370i	0.208620	+	0.977997i	$0.433103\pi$
$938$	−35.7513	+	25.9748i	−1.16732	+	0.848108i
$939$	9.70542	+	7.05140i	0.316724	+	0.230114i
$940$	−12.3720	+	20.5089i	−0.403529	+	0.668927i
$941$	0.380637	−	0.276549i	0.0124084	−	0.00901524i	−0.581564	−	0.813501i	$-0.697559\pi$
$941$	0.380637	−	0.276549i	0.0124084	−	0.00901524i	0.593972	+	0.804486i	$0.297559\pi$
$942$	2.14938	−	6.61511i	0.0700306	−	0.215532i
$943$	22.6915			0.738936
$944$	2.29489	−	7.06295i	0.0746923	−	0.229879i
$945$	6.37696	+	1.48401i	0.207442	+	0.0482749i
$946$	0.602309	+	1.85372i	0.0195828	+	0.0602695i
$947$	−10.1511	−	31.2420i	−0.329868	−	1.01523i	−0.969195	−	0.246294i	$-0.920787\pi$
$947$	−10.1511	−	31.2420i	−0.329868	−	1.01523i	0.639327	−	0.768935i	$-0.279213\pi$
$948$	−1.27039	−	0.922993i	−0.0412604	−	0.0299774i
$949$	3.60802			0.117121
$950$	2.30800	−	16.0149i	0.0748814	−	0.519591i
$951$	32.6126			1.05753
$952$	14.3262	+	10.4086i	0.464316	+	0.337345i
$953$	−13.5051	−	41.5645i	−0.437474	−	1.34641i	−0.890530	−	0.454924i	$-0.849666\pi$
$953$	−13.5051	−	41.5645i	−0.437474	−	1.34641i	0.453056	−	0.891482i	$-0.350334\pi$
$954$	−3.08144	−	9.48370i	−0.0997653	−	0.307046i
$955$	−1.42768	+	2.36665i	−0.0461986	+	0.0765831i
$956$	−0.662491	+	2.03894i	−0.0214265	+	0.0659440i
$957$	1.29664			0.0419143
$958$	2.42768	−	7.47163i	0.0784347	−	0.241397i
$959$	25.2006	−	18.3093i	0.813770	−	0.591239i
$960$	0.190983	+	2.22790i	0.00616395	+	0.0719051i
$961$	22.7634	+	16.5386i	0.734304	+	0.533503i
$962$	−2.44701	+	1.77785i	−0.0788947	+	0.0573203i
$963$	7.12778	−	5.17864i	0.229690	−	0.166879i
$964$	−1.40748	−	1.02260i	−0.0453320	−	0.0329356i
$965$	−35.8927	+	15.1614i	−1.15543	+	0.488063i
$966$	10.5938	−	7.69688i	0.340851	−	0.247643i
$967$	−13.3952	+	41.2262i	−0.430760	+	1.32574i	0.466609	+	0.884464i	$0.345476\pi$
$967$	−13.3952	+	41.2262i	−0.430760	+	1.32574i	−0.897369	+	0.441281i	$0.854524\pi$
$968$	10.9638			0.352389
$969$	6.04775	−	18.6130i	0.194282	−	0.597937i
$970$	−0.332262	−	3.87597i	−0.0106683	−	0.124450i
$971$	−9.30580	−	28.6403i	−0.298637	−	0.919111i	−0.981975	−	0.189009i	$-0.939472\pi$
$971$	−9.30580	−	28.6403i	−0.298637	−	0.919111i	0.683338	−	0.730102i	$-0.260528\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	−54.2275	−	39.3986i	−1.73845	−	1.26306i
$974$	40.9465			1.31201
$975$	−1.52755	+	0.263832i	−0.0489207	+	0.00844940i
$976$	−5.54610			−0.177526
$977$	1.14178	+	0.829555i	0.0365289	+	0.0265398i	0.605900	−	0.795541i	$-0.292813\pi$
$977$	1.14178	+	0.829555i	0.0365289	+	0.0265398i	−0.569371	+	0.822081i	$0.692813\pi$
$978$	4.32624	+	13.3148i	0.138338	+	0.425760i
$979$	−0.546101	−	1.68073i	−0.0174535	−	0.0537162i
$980$	−2.30377	−	2.65958i	−0.0735912	−	0.0849572i
$981$	4.90623	−	15.0998i	0.156644	−	0.482100i
$982$	7.51824			0.239917
$983$	3.00251	−	9.24078i	0.0957653	−	0.294735i	−0.891687	−	0.452652i	$-0.850478\pi$
$983$	3.00251	−	9.24078i	0.0957653	−	0.294735i	0.987452	+	0.157917i	$0.0504779\pi$
$984$	4.10492	−	2.98240i	0.130860	−	0.0950755i
$985$	−21.8759	−	25.2546i	−0.697025	−	0.804679i
$986$	33.3277	+	24.2140i	1.06137	+	0.771130i
$987$	25.3740	−	18.4353i	0.807663	−	0.586801i
$988$	−0.811677	+	0.589718i	−0.0258229	+	0.0187614i
$989$	37.0463	+	26.9157i	1.17801	+	0.855871i
$990$	−0.414569	−	0.0964762i	−0.0131759	−	0.00306621i
$991$	−15.3838	+	11.1770i	−0.488683	+	0.355049i	−0.804677	−	0.593712i	$-0.797662\pi$
$991$	−15.3838	+	11.1770i	−0.488683	+	0.355049i	0.315995	+	0.948761i	$0.397662\pi$
$992$	0.522856	−	1.60919i	0.0166007	−	0.0510917i
$993$	3.23200			0.102565
$994$	−6.20288	+	19.0905i	−0.196743	+	0.605514i
$995$	10.1022	−	4.26725i	0.320261	−	0.135281i
$996$	4.02324	+	12.3823i	0.127481	+	0.392347i
$997$	−3.41070	−	10.4970i	−0.108018	−	0.332445i	0.882409	−	0.470483i	$-0.155920\pi$
$997$	−3.41070	−	10.4970i	−0.108018	−	0.332445i	−0.990427	+	0.138038i	$0.955920\pi$
$998$	12.7430	+	9.25836i	0.403374	+	0.293068i
$999$	−9.75595			−0.308665

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.g.c.91.1	yes	8
3.2	odd	2		450.2.h.d.91.2		8
5.2	odd	4		750.2.h.e.49.2		16
5.3	odd	4		750.2.h.e.49.3		16
5.4	even	2		750.2.g.d.451.1		8
25.2	odd	20		750.2.h.e.199.4		16
25.6	even	5		3750.2.a.l.1.4		4
25.8	odd	20		3750.2.c.h.1249.5		8
25.11	even	5	inner	150.2.g.c.61.1	✓	8
25.14	even	10		750.2.g.d.301.1		8
25.17	odd	20		3750.2.c.h.1249.4		8
25.19	even	10		3750.2.a.q.1.1		4
25.23	odd	20		750.2.h.e.199.1		16
75.11	odd	10		450.2.h.d.361.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.c.61.1	✓	8	25.11	even	5	inner
150.2.g.c.91.1	yes	8	1.1	even	1	trivial
450.2.h.d.91.2		8	3.2	odd	2
450.2.h.d.361.2		8	75.11	odd	10
750.2.g.d.301.1		8	25.14	even	10
750.2.g.d.451.1		8	5.4	even	2
750.2.h.e.49.2		16	5.2	odd	4
750.2.h.e.49.3		16	5.3	odd	4
750.2.h.e.199.1		16	25.23	odd	20
750.2.h.e.199.4		16	25.2	odd	20
3750.2.a.l.1.4		4	25.6	even	5
3750.2.a.q.1.1		4	25.19	even	10
3750.2.c.h.1249.4		8	25.17	odd	20
3750.2.c.h.1249.5		8	25.8	odd	20

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.05984 + 0.870094i) q^{5} +(-0.309017 + 0.951057i) q^{6} +2.92807 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.05984 + 0.870094i) q^{5} +(-0.309017 + 0.951057i) q^{6} +2.92807 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-2.17787 - 0.506822i) q^{10} +(-0.154000 - 0.111888i) q^{11} +(-0.809017 + 0.587785i) q^{12} +(-0.250822 + 0.182233i) q^{13} +(2.36886 + 1.72107i) q^{14} +(-1.46403 - 1.69015i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.86886 - 5.75175i) q^{17} -1.00000 q^{18} +(1.00000 - 3.07768i) q^{19} +(-1.46403 - 1.69015i) q^{20} +(0.904822 + 2.78476i) q^{21} +(-0.0588229 - 0.181038i) q^{22} +(-3.61803 - 2.62866i) q^{23} -1.00000 q^{24} +(3.48587 - 3.58451i) q^{25} -0.310033 q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.904822 + 2.78476i) q^{28} +(2.10492 + 6.47829i) q^{29} +(-0.190983 - 2.22790i) q^{30} +(-0.522856 + 1.60919i) q^{31} -1.00000 q^{32} +(0.0588229 - 0.181038i) q^{33} +(4.89273 - 3.55478i) q^{34} +(-6.03135 + 2.54769i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(7.89273 - 5.73440i) q^{37} +(2.61803 - 1.90211i) q^{38} +(-0.250822 - 0.182233i) q^{39} +(-0.190983 - 2.22790i) q^{40} +(-4.10492 + 2.98240i) q^{41} +(-0.904822 + 2.78476i) q^{42} -10.2394 q^{43} +(0.0588229 - 0.181038i) q^{44} +(1.15502 - 1.91466i) q^{45} +(-1.38197 - 4.25325i) q^{46} +(-3.31003 - 10.1872i) q^{47} +(-0.809017 - 0.587785i) q^{48} +1.57358 q^{49} +(4.92705 - 0.850981i) q^{50} +6.04775 q^{51} +(-0.250822 - 0.182233i) q^{52} +(3.08144 + 9.48370i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(0.414569 + 0.0964762i) q^{55} +(-0.904822 + 2.78476i) q^{56} +3.23607 q^{57} +(-2.10492 + 6.47829i) q^{58} +(-6.00810 + 4.36514i) q^{59} +(1.15502 - 1.91466i) q^{60} +(4.48689 + 3.25992i) q^{61} +(-1.36886 + 0.994532i) q^{62} +(-2.36886 + 1.72107i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.358093 - 0.593609i) q^{65} +(0.154000 - 0.111888i) q^{66} +(-4.66375 + 14.3535i) q^{67} +6.04775 q^{68} +(1.38197 - 4.25325i) q^{69} +(-6.37696 - 1.48401i) q^{70} +(2.11842 + 6.51983i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(-9.41496 - 6.84037i) q^{73} +9.75595 q^{74} +(4.48626 + 2.20759i) q^{75} +3.23607 q^{76} +(-0.450924 - 0.327615i) q^{77} +(-0.0958055 - 0.294859i) q^{78} +(0.485246 + 1.49343i) q^{79} +(1.15502 - 1.91466i) q^{80} +(0.309017 - 0.951057i) q^{81} -5.07397 q^{82} +(4.02324 - 12.3823i) q^{83} +(-2.36886 + 1.72107i) q^{84} +(1.15502 + 13.4738i) q^{85} +(-8.28381 - 6.01854i) q^{86} +(-5.51076 + 4.00380i) q^{87} +(0.154000 - 0.111888i) q^{88} +(7.51076 + 5.45689i) q^{89} +(2.05984 - 0.870094i) q^{90} +(-0.734424 + 0.533590i) q^{91} +(1.38197 - 4.25325i) q^{92} -1.69200 q^{93} +(3.31003 - 10.1872i) q^{94} +(0.618034 + 7.20963i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(0.537611 + 1.65460i) q^{97} +(1.27305 + 0.924925i) q^{98} +0.190355 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 4 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 4 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 4 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 4 q^{10} - 5 q^{11} - 2 q^{12} + 6 q^{13} + 2 q^{14} + q^{15} - 2 q^{16} - 2 q^{17} - 8 q^{18} + 8 q^{19} + q^{20} + 3 q^{21} - 20 q^{23} - 8 q^{24} + 14 q^{25} + 14 q^{26} - 2 q^{27} + 3 q^{28} - 18 q^{29} - 6 q^{30} + 9 q^{31} - 8 q^{32} - 3 q^{34} - 4 q^{35} - 2 q^{36} + 21 q^{37} + 12 q^{38} + 6 q^{39} - 6 q^{40} + 2 q^{41} - 3 q^{42} - 32 q^{43} + q^{45} - 20 q^{46} - 10 q^{47} - 2 q^{48} + 22 q^{49} + 26 q^{50} - 2 q^{51} + 6 q^{52} + 7 q^{53} + 2 q^{54} - 40 q^{55} - 3 q^{56} + 8 q^{57} + 18 q^{58} - 25 q^{59} + q^{60} + 10 q^{61} + 6 q^{62} - 2 q^{63} - 2 q^{64} + 37 q^{65} + 5 q^{66} - 2 q^{67} - 2 q^{68} + 20 q^{69} - 11 q^{70} + 2 q^{72} - 24 q^{73} - 26 q^{74} + 14 q^{75} + 8 q^{76} + 35 q^{77} - q^{78} - 6 q^{79} + q^{80} - 2 q^{81} - 42 q^{82} + 11 q^{83} - 2 q^{84} + q^{85} + 2 q^{86} + 7 q^{87} + 5 q^{88} + 9 q^{89} + 4 q^{90} - 4 q^{91} + 20 q^{92} - 6 q^{93} + 10 q^{94} - 4 q^{95} + 2 q^{96} + q^{97} - 7 q^{98} + 10 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 4 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 4 * q^10 - 5 * q^11 - 2 * q^12 + 6 * q^13 + 2 * q^14 + q^15 - 2 * q^16 - 2 * q^17 - 8 * q^18 + 8 * q^19 + q^20 + 3 * q^21 - 20 * q^23 - 8 * q^24 + 14 * q^25 + 14 * q^26 - 2 * q^27 + 3 * q^28 - 18 * q^29 - 6 * q^30 + 9 * q^31 - 8 * q^32 - 3 * q^34 - 4 * q^35 - 2 * q^36 + 21 * q^37 + 12 * q^38 + 6 * q^39 - 6 * q^40 + 2 * q^41 - 3 * q^42 - 32 * q^43 + q^45 - 20 * q^46 - 10 * q^47 - 2 * q^48 + 22 * q^49 + 26 * q^50 - 2 * q^51 + 6 * q^52 + 7 * q^53 + 2 * q^54 - 40 * q^55 - 3 * q^56 + 8 * q^57 + 18 * q^58 - 25 * q^59 + q^60 + 10 * q^61 + 6 * q^62 - 2 * q^63 - 2 * q^64 + 37 * q^65 + 5 * q^66 - 2 * q^67 - 2 * q^68 + 20 * q^69 - 11 * q^70 + 2 * q^72 - 24 * q^73 - 26 * q^74 + 14 * q^75 + 8 * q^76 + 35 * q^77 - q^78 - 6 * q^79 + q^80 - 2 * q^81 - 42 * q^82 + 11 * q^83 - 2 * q^84 + q^85 + 2 * q^86 + 7 * q^87 + 5 * q^88 + 9 * q^89 + 4 * q^90 - 4 * q^91 + 20 * q^92 - 6 * q^93 + 10 * q^94 - 4 * q^95 + 2 * q^96 + q^97 - 7 * q^98 + 10 * q^99

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