LMFDB - Embedded newform 150.2.g.c.31.2

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			31.2
Root			$1.31557 + 1.28500i$ of defining polynomial
Character	$\chi$	$=$	150.31
Dual form			150.2.g.c.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.00655751 + 2.23606i) q^{5} +(0.809017 + 0.587785i) q^{6} +2.63925 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.00655751 + 2.23606i) q^{5} +(0.809017 + 0.587785i) q^{6} +2.63925 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +(2.12459 - 0.697217i) q^{10} +(1.93766 + 5.96351i) q^{11} +(0.309017 - 0.951057i) q^{12} +(0.697541 - 2.14681i) q^{13} +(-0.815575 - 2.51008i) q^{14} +(-1.31963 - 1.80515i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.31557 - 0.955821i) q^{17} -1.00000 q^{18} +(1.00000 + 0.726543i) q^{19} +(-1.31963 - 1.80515i) q^{20} +(-2.13520 + 1.55131i) q^{21} +(5.07286 - 3.68565i) q^{22} +(-1.38197 - 4.25325i) q^{23} -1.00000 q^{24} +(-4.99991 + 0.0293259i) q^{25} -2.25729 q^{26} +(0.309017 + 0.951057i) q^{27} +(-2.13520 + 1.55131i) q^{28} +(-5.55164 + 4.03350i) q^{29} +(-1.30902 + 1.81286i) q^{30} +(4.75324 + 3.45343i) q^{31} -1.00000 q^{32} +(-5.07286 - 3.68565i) q^{33} +(-0.502505 + 1.54655i) q^{34} +(0.0173069 + 5.90153i) q^{35} +(0.309017 + 0.951057i) q^{36} +(2.49750 - 7.68650i) q^{37} +(0.381966 - 1.17557i) q^{38} +(0.697541 + 2.14681i) q^{39} +(-1.30902 + 1.81286i) q^{40} +(3.55164 - 10.9308i) q^{41} +(2.13520 + 1.55131i) q^{42} -1.97377 q^{43} +(-5.07286 - 3.68565i) q^{44} +(2.12864 + 0.684743i) q^{45} +(-3.61803 + 2.62866i) q^{46} +(-5.25729 + 3.81964i) q^{47} +(0.309017 + 0.951057i) q^{48} -0.0343355 q^{49} +(1.57295 + 4.74614i) q^{50} +1.62614 q^{51} +(0.697541 + 2.14681i) q^{52} +(5.66298 - 4.11440i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-13.3220 + 4.37183i) q^{55} +(2.13520 + 1.55131i) q^{56} -1.23607 q^{57} +(5.55164 + 4.03350i) q^{58} +(2.79176 - 8.59216i) q^{59} +(2.12864 + 0.684743i) q^{60} +(-0.933608 - 2.87335i) q^{61} +(1.81557 - 5.58776i) q^{62} +(0.815575 - 2.51008i) q^{63} +(0.309017 + 0.951057i) q^{64} +(4.80496 + 1.54566i) q^{65} +(-1.93766 + 5.96351i) q^{66} +(8.12451 + 5.90280i) q^{67} +1.62614 q^{68} +(3.61803 + 2.62866i) q^{69} +(5.60734 - 1.84013i) q^{70} +(7.90966 - 5.74670i) q^{71} +(0.809017 - 0.587785i) q^{72} +(-3.70565 - 11.4048i) q^{73} -8.08206 q^{74} +(4.02778 - 2.96260i) q^{75} -1.23607 q^{76} +(5.11398 + 15.7392i) q^{77} +(1.82618 - 1.32680i) q^{78} +(-3.03853 + 2.20762i) q^{79} +(2.12864 + 0.684743i) q^{80} +(-0.809017 - 0.587785i) q^{81} -11.4934 q^{82} +(6.77446 + 4.92193i) q^{83} +(0.815575 - 2.51008i) q^{84} +(2.12864 - 2.94797i) q^{85} +(0.609928 + 1.87717i) q^{86} +(2.12054 - 6.52635i) q^{87} +(-1.93766 + 5.96351i) q^{88} +(-0.120539 - 0.370980i) q^{89} +(-0.00655751 - 2.23606i) q^{90} +(1.84099 - 5.66598i) q^{91} +(3.61803 + 2.62866i) q^{92} -5.87532 q^{93} +(5.25729 + 3.81964i) q^{94} +(-1.61803 + 2.24082i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-1.21471 + 0.882537i) q^{97} +(0.0106103 + 0.0326550i) q^{98} +6.27040 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 $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.00655751	+	2.23606i	0.00293261	+	0.999996i
$5$	0.00655751	+	2.23606i	0.00293261	+	0.999996i
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	2.63925			0.997544			0.498772	−	0.866733i	$-0.333784\pi$
$7$	2.63925			0.997544			0.498772	+	0.866733i	$0.333784\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	2.12459	−	0.697217i	0.671855	−	0.220479i
$11$	1.93766	+	5.96351i	0.584227	+	1.79807i	0.602353	+	0.798230i	$0.294230\pi$
$11$	1.93766	+	5.96351i	0.584227	+	1.79807i	−0.0181264	+	0.999836i	$0.505770\pi$
$12$	0.309017	−	0.951057i	0.0892055	−	0.274546i
$13$	0.697541	−	2.14681i	0.193463	−	0.595418i	−0.806528	−	0.591196i	$-0.798656\pi$
$13$	0.697541	−	2.14681i	0.193463	−	0.595418i	0.999991	−	0.00422199i	$-0.00134391\pi$
$14$	−0.815575	−	2.51008i	−0.217971	−	0.670847i
$15$	−1.31963	−	1.80515i	−0.340726	−	0.466089i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−1.31557	−	0.955821i	−0.319074	−	0.231821i	0.416706	−	0.909041i	$-0.363184\pi$
$17$	−1.31557	−	0.955821i	−0.319074	−	0.231821i	−0.735780	+	0.677221i	$0.763184\pi$
$18$	−1.00000			−0.235702
$19$	1.00000	+	0.726543i	0.229416	+	0.166680i	0.696555	−	0.717504i	$-0.254715\pi$
$19$	1.00000	+	0.726543i	0.229416	+	0.166680i	−0.467139	+	0.884184i	$0.654715\pi$
$20$	−1.31963	−	1.80515i	−0.295078	−	0.403645i
$21$	−2.13520	+	1.55131i	−0.465939	+	0.338525i
$22$	5.07286	−	3.68565i	1.08154	−	0.785783i
$23$	−1.38197	−	4.25325i	−0.288160	−	0.886865i	−0.985434	−	0.170060i	$-0.945604\pi$
$23$	−1.38197	−	4.25325i	−0.288160	−	0.886865i	0.697274	−	0.716805i	$-0.254396\pi$
$24$	−1.00000			−0.204124
$25$	−4.99991	+	0.0293259i	−0.999983	+	0.00586519i
$26$	−2.25729			−0.442691
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−2.13520	+	1.55131i	−0.403515	+	0.293171i
$29$	−5.55164	+	4.03350i	−1.03091	+	0.749003i	−0.968491	−	0.249047i	$-0.919883\pi$
$29$	−5.55164	+	4.03350i	−1.03091	+	0.749003i	−0.0624227	+	0.998050i	$0.519883\pi$
$30$	−1.30902	+	1.81286i	−0.238993	+	0.330982i
$31$	4.75324	+	3.45343i	0.853706	+	0.620254i	0.926165	−	0.377117i	$-0.123085\pi$
$31$	4.75324	+	3.45343i	0.853706	+	0.620254i	−0.0724591	+	0.997371i	$0.523085\pi$
$32$	−1.00000			−0.176777
$33$	−5.07286	−	3.68565i	−0.883072	−	0.641589i
$34$	−0.502505	+	1.54655i	−0.0861789	+	0.265231i
$35$	0.0173069	+	5.90153i	0.00292540	+	0.997540i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	2.49750	−	7.68650i	0.410586	−	1.26365i	−0.505554	−	0.862795i	$-0.668712\pi$
$37$	2.49750	−	7.68650i	0.410586	−	1.26365i	0.916140	−	0.400858i	$-0.131288\pi$
$38$	0.381966	−	1.17557i	0.0619631	−	0.190703i
$39$	0.697541	+	2.14681i	0.111696	+	0.343765i
$40$	−1.30902	+	1.81286i	−0.206974	+	0.286639i
$41$	3.55164	−	10.9308i	0.554673	−	1.70711i	−0.142131	−	0.989848i	$-0.545395\pi$
$41$	3.55164	−	10.9308i	0.554673	−	1.70711i	0.696804	−	0.717261i	$-0.254605\pi$
$42$	2.13520	+	1.55131i	0.329469	+	0.239373i
$43$	−1.97377			−0.300997			−0.150499	−	0.988610i	$-0.548088\pi$
$43$	−1.97377			−0.300997			−0.150499	+	0.988610i	$0.548088\pi$
$44$	−5.07286	−	3.68565i	−0.764763	−	0.555633i
$45$	2.12864	+	0.684743i	0.317320	+	0.102076i
$46$	−3.61803	+	2.62866i	−0.533450	+	0.387574i
$47$	−5.25729	+	3.81964i	−0.766854	+	0.557152i	−0.901005	−	0.433809i	$-0.857169\pi$
$47$	−5.25729	+	3.81964i	−0.766854	+	0.557152i	0.134151	+	0.990961i	$0.457169\pi$
$48$	0.309017	+	0.951057i	0.0446028	+	0.137273i
$49$	−0.0343355			−0.00490508
$50$	1.57295	+	4.74614i	0.222449	+	0.671205i
$51$	1.62614			0.227705
$52$	0.697541	+	2.14681i	0.0967315	+	0.297709i
$53$	5.66298	−	4.11440i	0.777870	−	0.565156i	−0.126469	−	0.991971i	$-0.540364\pi$
$53$	5.66298	−	4.11440i	0.777870	−	0.565156i	0.904339	+	0.426815i	$0.140364\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	−13.3220	+	4.37183i	−1.79634	+	0.589497i
$56$	2.13520	+	1.55131i	0.285328	+	0.207303i
$57$	−1.23607			−0.163721
$58$	5.55164	+	4.03350i	0.728966	+	0.529625i
$59$	2.79176	−	8.59216i	0.363457	−	1.11860i	−0.587485	−	0.809235i	$-0.699882\pi$
$59$	2.79176	−	8.59216i	0.363457	−	1.11860i	0.950942	−	0.309370i	$-0.100118\pi$
$60$	2.12864	+	0.684743i	0.274807	+	0.0884000i
$61$	−0.933608	−	2.87335i	−0.119536	−	0.367895i	0.873330	−	0.487129i	$-0.161956\pi$
$61$	−0.933608	−	2.87335i	−0.119536	−	0.367895i	−0.992866	+	0.119234i	$0.961956\pi$
$62$	1.81557	−	5.58776i	0.230578	−	0.709647i
$63$	0.815575	−	2.51008i	0.102753	−	0.316240i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	4.80496	+	1.54566i	0.595982	+	0.191716i
$66$	−1.93766	+	5.96351i	−0.238510	+	0.734057i
$67$	8.12451	+	5.90280i	0.992566	+	0.721142i	0.960482	−	0.278344i	$-0.0897854\pi$
$67$	8.12451	+	5.90280i	0.992566	+	0.721142i	0.0320847	+	0.999485i	$0.489785\pi$
$68$	1.62614			0.197198
$69$	3.61803	+	2.62866i	0.435560	+	0.316453i
$70$	5.60734	−	1.84013i	0.670205	−	0.219938i
$71$	7.90966	−	5.74670i	0.938704	−	0.682008i	−0.00940457	−	0.999956i	$-0.502994\pi$
$71$	7.90966	−	5.74670i	0.938704	−	0.682008i	0.948108	+	0.317948i	$0.102994\pi$
$72$	0.809017	−	0.587785i	0.0953436	−	0.0692712i
$73$	−3.70565	−	11.4048i	−0.433713	−	1.33483i	−0.894400	−	0.447269i	$-0.852397\pi$
$73$	−3.70565	−	11.4048i	−0.433713	−	1.33483i	0.460687	−	0.887563i	$-0.347603\pi$
$74$	−8.08206			−0.939521
$75$	4.02778	−	2.96260i	0.465088	−	0.342092i
$76$	−1.23607			−0.141787
$77$	5.11398	+	15.7392i	0.582792	+	1.79365i
$78$	1.82618	−	1.32680i	0.206775	−	0.150231i
$79$	−3.03853	+	2.20762i	−0.341861	+	0.248377i	−0.745447	−	0.666565i	$-0.767764\pi$
$79$	−3.03853	+	2.20762i	−0.341861	+	0.248377i	0.403586	+	0.914942i	$0.367764\pi$
$80$	2.12864	+	0.684743i	0.237990	+	0.0765566i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−11.4934			−1.26923
$83$	6.77446	+	4.92193i	0.743593	+	0.540252i	0.893834	−	0.448397i	$-0.148005\pi$
$83$	6.77446	+	4.92193i	0.743593	+	0.540252i	−0.150241	+	0.988649i	$0.548005\pi$
$84$	0.815575	−	2.51008i	0.0889865	−	0.273872i
$85$	2.12864	−	2.94797i	0.230884	−	0.319752i
$86$	0.609928	+	1.87717i	0.0657703	+	0.202420i
$87$	2.12054	−	6.52635i	0.227346	−	0.699698i
$88$	−1.93766	+	5.96351i	−0.206555	+	0.635712i
$89$	−0.120539	−	0.370980i	−0.0127771	−	0.0393238i	0.944465	−	0.328613i	$-0.106581\pi$
$89$	−0.120539	−	0.370980i	−0.0127771	−	0.0393238i	−0.957242	+	0.289289i	$0.906581\pi$
$90$	−0.00655751	−	2.23606i	−0.000691222	−	0.235701i
$91$	1.84099	−	5.66598i	0.192988	−	0.593956i
$92$	3.61803	+	2.62866i	0.377206	+	0.274056i
$93$	−5.87532			−0.609243
$94$	5.25729	+	3.81964i	0.542248	+	0.393966i
$95$	−1.61803	+	2.24082i	−0.166007	+	0.229904i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	−1.21471	+	0.882537i	−0.123335	+	0.0896081i	−0.647743	−	0.761859i	$-0.724287\pi$
$97$	−1.21471	+	0.882537i	−0.123335	+	0.0896081i	0.524408	+	0.851467i	$0.324287\pi$
$98$	0.0106103	+	0.0326550i	0.00107180	+	0.00329866i
$99$	6.27040			0.630199
$100$	4.02778	−	2.96260i	0.402778	−	0.296260i
$101$	4.68671			0.466345			0.233172	−	0.972435i	$-0.425089\pi$
$101$	4.68671			0.466345			0.233172	+	0.972435i	$0.425089\pi$
$102$	−0.502505	−	1.54655i	−0.0497554	−	0.153131i
$103$	3.46161	−	2.51501i	0.341083	−	0.247811i	−0.404036	−	0.914743i	$-0.632393\pi$
$103$	3.46161	−	2.51501i	0.341083	−	0.247811i	0.745119	+	0.666932i	$0.232393\pi$
$104$	1.82618	−	1.32680i	0.179072	−	0.130104i
$105$	−3.48283	−	4.76426i	−0.339890	−	0.464944i
$106$	−5.66298	−	4.11440i	−0.550037	−	0.399625i
$107$	−18.7850			−1.81601			−0.908006	−	0.418956i	$-0.862396\pi$
$107$	−18.7850			−1.81601			−0.908006	+	0.418956i	$0.862396\pi$
$108$	−0.809017	−	0.587785i	−0.0778477	−	0.0565597i
$109$	−4.94982	+	15.2340i	−0.474107	+	1.45915i	0.373052	+	0.927810i	$0.378311\pi$
$109$	−4.94982	+	15.2340i	−0.474107	+	1.45915i	−0.847159	+	0.531340i	$0.821689\pi$
$110$	8.27460	+	11.3190i	0.788952	+	1.07923i
$111$	2.49750	+	7.68650i	0.237052	+	0.729570i
$112$	0.815575	−	2.51008i	0.0770645	−	0.237180i
$113$	−2.98776	+	9.19537i	−0.281064	+	0.865027i	0.706486	+	0.707727i	$0.250279\pi$
$113$	−2.98776	+	9.19537i	−0.281064	+	0.865027i	−0.987551	+	0.157301i	$0.949721\pi$
$114$	0.381966	+	1.17557i	0.0357744	+	0.110102i
$115$	9.50146	−	3.11805i	0.886016	−	0.290759i
$116$	2.12054	−	6.52635i	0.196887	−	0.605956i
$117$	−1.82618	−	1.32680i	−0.168831	−	0.122663i
$118$	−9.03434			−0.831678
$119$	−3.47214	−	2.52265i	−0.318290	−	0.231251i
$120$	−0.00655751	−	2.23606i	−0.000598616	−	0.204123i
$121$	−22.9097	+	16.6449i	−2.08270	+	1.51317i
$122$	−2.44422	+	1.77583i	−0.221289	+	0.160776i
$123$	3.55164	+	10.9308i	0.320241	+	0.985600i
$124$	−5.87532			−0.527620
$125$	−0.0983615	−	11.1799i	−0.00879772	−	0.999961i
$126$	−2.63925			−0.235123
$127$	2.30651	+	7.09871i	0.204670	+	0.629909i	0.999727	+	0.0233743i	$0.00744093\pi$
$127$	2.30651	+	7.09871i	0.204670	+	0.629909i	−0.795057	+	0.606535i	$0.792559\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	1.59681	−	1.16015i	0.140592	−	0.102146i
$130$	−0.0148022	−	5.04743i	−0.00129824	−	0.442689i
$131$	−16.5966	−	12.0582i	−1.45006	−	1.05353i	−0.985818	−	0.167816i	$-0.946329\pi$
$131$	−16.5966	−	12.0582i	−1.45006	−	1.05353i	−0.464237	−	0.885711i	$-0.653671\pi$
$132$	6.27040			0.545769
$133$	2.63925	+	1.91753i	0.228852	+	0.166271i
$134$	3.10328	−	9.55093i	0.268083	−	0.825075i
$135$	−2.12459	+	0.697217i	−0.182856	+	0.0600069i
$136$	−0.502505	−	1.54655i	−0.0430894	−	0.132616i
$137$	−0.946724	+	2.91372i	−0.0808840	+	0.248936i	−0.983319	−	0.181891i	$-0.941778\pi$
$137$	−0.946724	+	2.91372i	−0.0808840	+	0.248936i	0.902435	+	0.430827i	$0.141778\pi$
$138$	1.38197	−	4.25325i	0.117641	−	0.362061i
$139$	−5.15400	−	15.8624i	−0.437157	−	1.34543i	−0.890860	−	0.454278i	$-0.849897\pi$
$139$	−5.15400	−	15.8624i	−0.437157	−	1.34543i	0.453703	−	0.891153i	$-0.350103\pi$
$140$	−3.48283	−	4.76426i	−0.294353	−	0.402654i
$141$	2.00811	−	6.18031i	0.169113	−	0.520476i
$142$	−7.90966	−	5.74670i	−0.663764	−	0.482253i
$143$	14.1541			1.18363
$144$	−0.809017	−	0.587785i	−0.0674181	−	0.0489821i
$145$	−9.05556	−	12.3873i	−0.752023	−	1.02871i
$146$	−9.70151	+	7.04856i	−0.802902	+	0.583343i
$147$	0.0277780	−	0.0201819i	0.00229109	−	0.00166458i
$148$	2.49750	+	7.68650i	0.205293	+	0.631826i
$149$	14.4853			1.18668			0.593339	−	0.804953i	$-0.297809\pi$
$149$	14.4853			1.18668			0.593339	+	0.804953i	$0.297809\pi$
$150$	−4.06225	−	2.91515i	−0.331682	−	0.238021i
$151$	10.3050			0.838610			0.419305	−	0.907845i	$-0.362274\pi$
$151$	10.3050			0.838610			0.419305	+	0.907845i	$0.362274\pi$
$152$	0.381966	+	1.17557i	0.0309815	+	0.0953514i
$153$	−1.31557	+	0.955821i	−0.106358	+	0.0772735i
$154$	13.3886	−	9.72737i	1.07888	−	0.783854i
$155$	−7.69090	+	10.6512i	−0.617748	+	0.855522i
$156$	−1.82618	−	1.32680i	−0.146212	−	0.106229i
$157$	−7.58370			−0.605245			−0.302623	−	0.953110i	$-0.597862\pi$
$157$	−7.58370			−0.605245			−0.302623	+	0.953110i	$0.597862\pi$
$158$	3.03853	+	2.20762i	0.241732	+	0.175629i
$159$	−2.16307	+	6.65723i	−0.171542	+	0.527953i
$160$	−0.00655751	−	2.23606i	−0.000518416	−	0.176776i
$161$	−3.64736	−	11.2254i	−0.287452	−	0.884687i
$162$	−0.309017	+	0.951057i	−0.0242787	+	0.0747221i
$163$	−4.32624	+	13.3148i	−0.338857	+	1.04289i	0.625934	+	0.779876i	$0.284718\pi$
$163$	−4.32624	+	13.3148i	−0.338857	+	1.04289i	−0.964791	+	0.263019i	$0.915282\pi$
$164$	3.55164	+	10.9308i	0.277337	+	0.853555i
$165$	8.20806	−	11.3674i	0.638997	−	0.884950i
$166$	2.58761	−	7.96385i	0.200838	−	0.618115i
$167$	−14.0210	−	10.1869i	−1.08498	−	0.788285i	−0.106437	−	0.994319i	$-0.533944\pi$
$167$	−14.0210	−	10.1869i	−1.08498	−	0.788285i	−0.978545	+	0.206034i	$0.933944\pi$
$168$	−2.63925			−0.203623
$169$	6.39500	+	4.64624i	0.491923	+	0.357403i
$170$	−3.46147	−	1.11349i	−0.265483	−	0.0854007i
$171$	1.00000	−	0.726543i	0.0764719	−	0.0555601i
$172$	1.59681	−	1.16015i	0.121756	−	0.0884608i
$173$	1.17528	+	3.61713i	0.0893547	+	0.275005i	0.985741	−	0.168268i	$-0.0538172\pi$
$173$	1.17528	+	3.61713i	0.0893547	+	0.275005i	−0.896387	+	0.443273i	$0.853817\pi$
$174$	−6.86221			−0.520223
$175$	−13.1960	+	0.0773986i	−0.997527	+	0.00585078i
$176$	6.27040			0.472649
$177$	2.79176	+	8.59216i	0.209842	+	0.645827i
$178$	−0.315575	+	0.229278i	−0.0236533	+	0.0171851i
$179$	−0.100866	+	0.0732836i	−0.00753909	+	0.00547747i	−0.591548	−	0.806269i	$-0.701483\pi$
$179$	−0.100866	+	0.0732836i	−0.00753909	+	0.00547747i	0.584009	+	0.811747i	$0.301483\pi$
$180$	−2.12459	+	0.697217i	−0.158358	+	0.0519675i
$181$	7.53853	+	5.47706i	0.560334	+	0.407107i	0.831581	−	0.555403i	$-0.187436\pi$
$181$	7.53853	+	5.47706i	0.560334	+	0.407107i	−0.271247	+	0.962510i	$0.587436\pi$
$182$	−5.95756			−0.441604
$183$	2.44422	+	1.77583i	0.180682	+	0.131273i
$184$	1.38197	−	4.25325i	0.101880	−	0.313554i
$185$	17.2038	+	5.53414i	1.26485	+	0.406878i
$186$	1.81557	+	5.58776i	0.133124	+	0.409715i
$187$	3.15091	−	9.69750i	0.230417	−	0.709151i
$188$	2.00811	−	6.18031i	0.146456	−	0.450746i
$189$	0.815575	+	2.51008i	0.0593243	+	0.182581i
$190$	2.63115	+	0.846389i	0.190884	+	0.0614035i
$191$	1.00000	−	3.07768i	0.0723575	−	0.222693i	−0.908337	−	0.418239i	$-0.862648\pi$
$191$	1.00000	−	3.07768i	0.0723575	−	0.222693i	0.980695	+	0.195545i	$0.0626476\pi$
$192$	−0.809017	−	0.587785i	−0.0583858	−	0.0424197i
$193$	−10.8641			−0.782017			−0.391008	−	0.920387i	$-0.627874\pi$
$193$	−10.8641			−0.782017			−0.391008	+	0.920387i	$0.627874\pi$
$194$	1.21471	+	0.882537i	0.0872110	+	0.0633625i
$195$	−4.79582	+	1.57382i	−0.343436	+	0.112704i
$196$	0.0277780	−	0.0201819i	0.00198415	−	0.00144157i
$197$	7.34335	−	5.33526i	0.523192	−	0.380121i	−0.294613	−	0.955617i	$-0.595191\pi$
$197$	7.34335	−	5.33526i	0.523192	−	0.380121i	0.817805	+	0.575495i	$0.195191\pi$
$198$	−1.93766	−	5.96351i	−0.137704	−	0.423808i
$199$	26.0735			1.84830			0.924151	−	0.382027i	$-0.124774\pi$
$199$	26.0735			1.84830			0.924151	+	0.382027i	$0.124774\pi$
$200$	−4.06225	−	2.91515i	−0.287245	−	0.206132i
$201$	−10.0424			−0.708339
$202$	−1.44827	−	4.45732i	−0.101900	−	0.313616i
$203$	−14.6522	+	10.6454i	−1.02838	+	0.747164i
$204$	−1.31557	+	0.955821i	−0.0921086	+	0.0669208i
$205$	24.4653	+	7.87000i	1.70873	+	0.549665i
$206$	−3.46161	−	2.51501i	−0.241182	−	0.175229i
$207$	−4.47214			−0.310835
$208$	−1.82618	−	1.32680i	−0.126623	−	0.0919971i
$209$	−2.39508	+	7.37130i	−0.165671	+	0.509884i
$210$	−3.45483	+	4.78461i	−0.238406	+	0.330169i
$211$	4.79016	+	14.7426i	0.329768	+	1.01492i	0.969242	+	0.246110i	$0.0791523\pi$
$211$	4.79016	+	14.7426i	0.329768	+	1.01492i	−0.639474	+	0.768813i	$0.720848\pi$
$212$	−2.16307	+	6.65723i	−0.148560	+	0.457221i
$213$	−3.02122	+	9.29836i	−0.207011	+	0.637113i
$214$	5.80488	+	17.8656i	0.396813	+	1.22127i
$215$	−0.0129430	−	4.41346i	−0.000882706	−	0.300996i
$216$	−0.309017	+	0.951057i	−0.0210259	+	0.0647112i
$217$	12.5450	+	9.11448i	0.851610	+	0.618731i
$218$	16.0180			1.08487
$219$	9.70151	+	7.04856i	0.655567	+	0.476297i
$220$	8.20806	−	11.3674i	0.553388	−	0.766389i
$221$	−2.96963	+	2.15756i	−0.199759	+	0.145133i
$222$	6.53853	−	4.75052i	0.438837	−	0.318834i
$223$	0.555695	+	1.71025i	0.0372121	+	0.114527i	0.967937	−	0.251193i	$-0.0808228\pi$
$223$	0.555695	+	1.71025i	0.0372121	+	0.114527i	−0.930725	+	0.365720i	$0.880823\pi$
$224$	−2.63925			−0.176343
$225$	−1.51717	+	4.76426i	−0.101145	+	0.317618i
$226$	9.66858			0.643144
$227$	−0.319627	−	0.983712i	−0.0212144	−	0.0652912i	0.939889	−	0.341481i	$-0.110928\pi$
$227$	−0.319627	−	0.983712i	−0.0212144	−	0.0652912i	−0.961103	+	0.276189i	$0.910928\pi$
$228$	1.00000	−	0.726543i	0.0662266	−	0.0481165i
$229$	2.21626	−	1.61020i	0.146454	−	0.106405i	−0.512145	−	0.858899i	$-0.671149\pi$
$229$	2.21626	−	1.61020i	0.146454	−	0.106405i	0.658600	+	0.752493i	$0.271149\pi$
$230$	−5.90155	−	8.07290i	−0.389137	−	0.532311i
$231$	−13.3886	−	9.72737i	−0.880904	−	0.640014i
$232$	−6.86221			−0.450526
$233$	−14.5768	−	10.5907i	−0.954960	−	0.693819i	−0.00298513	−	0.999996i	$-0.500950\pi$
$233$	−14.5768	−	10.5907i	−0.954960	−	0.693819i	−0.951975	+	0.306177i	$0.900950\pi$
$234$	−0.697541	+	2.14681i	−0.0455996	+	0.140341i
$235$	−8.57542	−	11.7306i	−0.559399	−	0.765217i
$236$	2.79176	+	8.59216i	0.181728	+	0.559302i
$237$	1.16061	−	3.57200i	0.0753900	−	0.232027i
$238$	−1.32624	+	4.08174i	−0.0859672	+	0.264580i
$239$	−0.840987	−	2.58829i	−0.0543989	−	0.167423i	0.920166	−	0.391529i	$-0.128054\pi$
$239$	−0.840987	−	2.58829i	−0.0543989	−	0.167423i	−0.974565	+	0.224106i	$0.928054\pi$
$240$	−2.12459	+	0.697217i	−0.137142	+	0.0450051i
$241$	0.463977	−	1.42798i	0.0298874	−	0.0919840i	−0.935000	−	0.354647i	$-0.884601\pi$
$241$	0.463977	−	1.42798i	0.0298874	−	0.0919840i	0.964888	+	0.262663i	$0.0846009\pi$
$242$	22.9097	+	16.6449i	1.47269	+	1.06997i
$243$	1.00000			0.0641500
$244$	2.44422	+	1.77583i	0.156475	+	0.113686i
$245$	−0.000225156	−	0.0767763i	−1.43847e−5	−	0.00490506i
$246$	9.29832	−	6.75563i	0.592839	−	0.430723i
$247$	2.25729	−	1.64002i	0.143628	−	0.104352i
$248$	1.81557	+	5.58776i	0.115289	+	0.354823i
$249$	−8.37369			−0.530661
$250$	−10.6023	+	3.54833i	−0.670550	+	0.224416i
$251$	−0.957281			−0.0604230			−0.0302115	−	0.999544i	$-0.509618\pi$
$251$	−0.957281			−0.0604230			−0.0302115	+	0.999544i	$0.509618\pi$
$252$	0.815575	+	2.51008i	0.0513764	+	0.158120i
$253$	22.6865	−	16.4827i	1.42629	−	1.03626i
$254$	6.03853	−	4.38725i	0.378891	−	0.275280i
$255$	0.0106634	+	3.63614i	0.000667769	+	0.227704i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−8.25729			−0.515076			−0.257538	−	0.966268i	$-0.582911\pi$
$257$	−8.25729			−0.515076			−0.257538	+	0.966268i	$0.582911\pi$
$258$	−1.59681	−	1.16015i	−0.0994133	−	0.0722280i
$259$	6.59153	−	20.2866i	0.409577	−	1.26055i
$260$	−4.79582	+	1.57382i	−0.297424	+	0.0976041i
$261$	2.12054	+	6.52635i	0.131258	+	0.403971i
$262$	−6.33935	+	19.5105i	−0.391647	+	1.20536i
$263$	−0.467126	+	1.43767i	−0.0288043	+	0.0886504i	−0.964425	−	0.264356i	$-0.914841\pi$
$263$	−0.467126	+	1.43767i	−0.0288043	+	0.0886504i	0.935621	+	0.353006i	$0.114841\pi$
$264$	−1.93766	−	5.96351i	−0.119255	−	0.367029i
$265$	9.23716	+	12.6358i	0.567434	+	0.776209i
$266$	1.00811	−	3.10263i	0.0618109	−	0.190234i
$267$	0.315575	+	0.229278i	0.0193128	+	0.0140316i
$268$	−10.0424			−0.613440
$269$	−7.96139	−	5.78429i	−0.485414	−	0.352674i	0.318004	−	0.948089i	$-0.396988\pi$
$269$	−7.96139	−	5.78429i	−0.485414	−	0.352674i	−0.803418	+	0.595415i	$0.796988\pi$
$270$	1.31963	+	1.80515i	0.0803100	+	0.109858i
$271$	−6.96808	+	5.06261i	−0.423281	+	0.307532i	−0.778957	−	0.627078i	$-0.784251\pi$
$271$	−6.96808	+	5.06261i	−0.423281	+	0.307532i	0.355676	+	0.934609i	$0.384251\pi$
$272$	−1.31557	+	0.955821i	−0.0797684	+	0.0579552i
$273$	1.84099	+	5.66598i	0.111422	+	0.342920i
$274$	3.06366			0.185083
$275$	−9.86303	−	29.7602i	−0.594763	−	1.79461i
$276$	−4.47214			−0.269191
$277$	4.52373	+	13.9226i	0.271804	+	0.836528i	0.990047	+	0.140735i	$0.0449466\pi$
$277$	4.52373	+	13.9226i	0.271804	+	0.836528i	−0.718243	+	0.695792i	$0.755053\pi$
$278$	−13.4934	+	9.80350i	−0.809278	+	0.587975i
$279$	4.75324	−	3.45343i	0.284569	−	0.206751i
$280$	−3.45483	+	4.78461i	−0.206466	+	0.285935i
$281$	1.56890	+	1.13987i	0.0935925	+	0.0679989i	0.633597	−	0.773663i	$-0.281578\pi$
$281$	1.56890	+	1.13987i	0.0935925	+	0.0679989i	−0.540005	+	0.841662i	$0.681578\pi$
$282$	−6.49837			−0.386972
$283$	−1.69481	−	1.23135i	−0.100746	−	0.0731963i	0.536272	−	0.844045i	$-0.319832\pi$
$283$	−1.69481	−	1.23135i	−0.100746	−	0.0731963i	−0.637018	+	0.770849i	$0.719832\pi$
$284$	−3.02122	+	9.29836i	−0.179276	+	0.551756i
$285$	−0.00810552	−	2.76392i	−0.000480130	−	0.163720i
$286$	−4.37386	−	13.4614i	−0.258632	−	0.795987i
$287$	9.37369	−	28.8492i	0.553311	−	1.70292i
$288$	−0.309017	+	0.951057i	−0.0182090	+	0.0560415i
$289$	−4.43615	−	13.6531i	−0.260950	−	0.803121i
$290$	−8.98275	+	12.4402i	−0.527485	+	0.730516i
$291$	0.463977	−	1.42798i	0.0271988	−	0.0837094i
$292$	9.70151	+	7.04856i	0.567738	+	0.412486i
$293$	24.1031			1.40812			0.704059	−	0.710141i	$-0.251369\pi$
$293$	24.1031			1.40812			0.704059	+	0.710141i	$0.251369\pi$
$294$	−0.0277780	−	0.0201819i	−0.00162005	−	0.00117703i
$295$	19.2309	+	6.18620i	1.11967	+	0.360175i
$296$	6.53853	−	4.75052i	0.380044	−	0.276118i
$297$	−5.07286	+	3.68565i	−0.294357	+	0.213863i
$298$	−4.47619	−	13.7763i	−0.259299	−	0.798039i
$299$	−10.0949			−0.583803
$300$	−1.51717	+	4.76426i	−0.0875937	+	0.275065i
$301$	−5.20928			−0.300258
$302$	−3.18443	−	9.80065i	−0.183243	−	0.563964i
$303$	−3.79162	+	2.75478i	−0.217823	+	0.158258i
$304$	1.00000	−	0.726543i	0.0573539	−	0.0416701i
$305$	6.41886	−	2.10645i	0.367543	−	0.120615i
$306$	1.31557	+	0.955821i	0.0752064	+	0.0546406i
$307$	−14.5670			−0.831385			−0.415692	−	0.909505i	$-0.636461\pi$
$307$	−14.5670			−0.831385			−0.415692	+	0.909505i	$0.636461\pi$
$308$	−13.3886	−	9.72737i	−0.762885	−	0.554268i
$309$	−1.32222	+	4.06937i	−0.0752184	+	0.231498i
$310$	12.5065	+	4.02309i	0.710320	+	0.228496i
$311$	2.37696	+	7.31552i	0.134785	+	0.414825i	0.995556	−	0.0941662i	$-0.0300185\pi$
$311$	2.37696	+	7.31552i	0.134785	+	0.414825i	−0.860772	+	0.508991i	$0.830019\pi$
$312$	−0.697541	+	2.14681i	−0.0394905	+	0.121539i
$313$	7.42601	−	22.8549i	0.419743	−	1.29184i	−0.488196	−	0.872734i	$-0.662345\pi$
$313$	7.42601	−	22.8549i	0.419743	−	1.29184i	0.907939	−	0.419102i	$-0.137655\pi$
$314$	2.34349	+	7.21253i	0.132251	+	0.407026i
$315$	5.61803	+	1.80721i	0.316540	+	0.101825i
$316$	1.16061	−	3.57200i	0.0652897	−	0.200941i
$317$	9.53161	+	6.92512i	0.535348	+	0.388953i	0.822355	−	0.568975i	$-0.192660\pi$
$317$	9.53161	+	6.92512i	0.535348	+	0.388953i	−0.287006	+	0.957929i	$0.592660\pi$
$318$	6.99983			0.392531
$319$	−34.8110	−	25.2917i	−1.94904	−	1.41606i
$320$	−2.12459	+	0.697217i	−0.118768	+	0.0389756i
$321$	15.1974	−	11.0415i	0.848234	−	0.616278i
$322$	−9.54891	+	6.93769i	−0.532140	+	0.386622i
$323$	−0.621130	−	1.91164i	−0.0345606	−	0.106367i
$324$	1.00000			0.0555556
$325$	−3.42469	+	10.7543i	−0.189967	+	0.596542i
$326$	14.0000			0.775388
$327$	−4.94982	−	15.2340i	−0.273726	−	0.842441i
$328$	9.29832	−	6.75563i	0.513414	−	0.373017i
$329$	−13.8753	+	10.0810i	−0.764971	+	0.555784i
$330$	−13.3475	−	4.29362i	−0.734753	−	0.236356i
$331$	10.9228	+	7.93586i	0.600370	+	0.436194i	0.846010	−	0.533167i	$-0.178998\pi$
$331$	10.9228	+	7.93586i	0.600370	+	0.436194i	−0.245640	+	0.969361i	$0.578998\pi$
$332$	−8.37369			−0.459566
$333$	−6.53853	−	4.75052i	−0.358309	−	0.260327i
$334$	−5.35556	+	16.4827i	−0.293043	+	0.901895i
$335$	−13.1457	+	18.2056i	−0.718228	+	0.994677i
$336$	0.815575	+	2.51008i	0.0444932	+	0.136936i
$337$	7.91075	−	24.3468i	0.430926	−	1.32625i	−0.466278	−	0.884638i	$-0.654405\pi$
$337$	7.91075	−	24.3468i	0.430926	−	1.32625i	0.897204	−	0.441616i	$-0.145595\pi$
$338$	2.44267	−	7.51777i	0.132864	−	0.408913i
$339$	−2.98776	−	9.19537i	−0.162273	−	0.499424i
$340$	0.0106634	+	3.63614i	0.000578305	+	0.197198i
$341$	−11.3844	+	35.0375i	−0.616499	+	1.89739i
$342$	−1.00000	−	0.726543i	−0.0540738	−	0.0392869i
$343$	−18.5654			−1.00244
$344$	−1.59681	−	1.16015i	−0.0860944	−	0.0625513i
$345$	−5.85410	+	8.10737i	−0.315174	+	0.436486i
$346$	3.07692	−	2.23551i	0.165416	−	0.120182i
$347$	0.205646	−	0.149411i	0.0110397	−	0.00802078i	−0.582252	−	0.813009i	$-0.697828\pi$
$347$	0.205646	−	0.149411i	0.0110397	−	0.00802078i	0.593291	+	0.804988i	$0.297828\pi$
$348$	2.12054	+	6.52635i	0.113673	+	0.349849i
$349$	−31.6783			−1.69570			−0.847849	−	0.530238i	$-0.822103\pi$
$349$	−31.6783			−1.69570			−0.847849	+	0.530238i	$0.822103\pi$
$350$	4.15141	+	12.5263i	0.221902	+	0.669557i
$351$	2.25729			0.120485
$352$	−1.93766	−	5.96351i	−0.103278	−	0.317856i
$353$	−23.4295	+	17.0225i	−1.24703	+	0.906019i	−0.998046	−	0.0624895i	$-0.980096\pi$
$353$	−23.4295	+	17.0225i	−1.24703	+	0.906019i	−0.248982	+	0.968508i	$0.580096\pi$
$354$	7.30893	−	5.31025i	0.388465	−	0.282237i
$355$	12.9018	+	17.6488i	0.684758	+	0.936700i
$356$	0.315575	+	0.229278i	0.0167254	+	0.0121517i
$357$	4.29180			0.227146
$358$	0.100866	+	0.0732836i	0.00533095	+	0.00387316i
$359$	−2.47715	+	7.62387i	−0.130739	+	0.402372i	−0.994903	−	0.100838i	$-0.967848\pi$
$359$	−2.47715	+	7.62387i	−0.130739	+	0.402372i	0.864164	+	0.503210i	$0.167848\pi$
$360$	1.31963	+	1.80515i	0.0695505	+	0.0951400i
$361$	−5.39919	−	16.6170i	−0.284168	−	0.874578i
$362$	2.87946	−	8.86207i	0.151341	−	0.465780i
$363$	8.75073	−	26.9320i	0.459294	−	1.41356i
$364$	1.84099	+	5.66598i	0.0964939	+	0.296978i
$365$	25.4775	−	8.36083i	1.33355	−	0.437626i
$366$	0.933608	−	2.87335i	0.0488005	−	0.150192i
$367$	−12.4056	−	9.01320i	−0.647567	−	0.470485i	0.214874	−	0.976642i	$-0.431066\pi$
$367$	−12.4056	−	9.01320i	−0.647567	−	0.470485i	−0.862442	+	0.506157i	$0.831066\pi$
$368$	−4.47214			−0.233126
$369$	−9.29832	−	6.75563i	−0.484051	−	0.351684i
$370$	−0.0529982	−	18.0720i	−0.00275524	−	0.939517i
$371$	14.9460	−	10.8589i	0.775960	−	0.563768i
$372$	4.75324	−	3.45343i	0.246444	−	0.179052i
$373$	5.13261	+	15.7966i	0.265757	+	0.817914i	0.991518	+	0.129968i	$0.0414875\pi$
$373$	5.13261	+	15.7966i	0.265757	+	0.817914i	−0.725762	+	0.687946i	$0.758512\pi$
$374$	−10.1966			−0.527251
$375$	6.65096	+	8.98692i	0.343454	+	0.464083i
$376$	−6.49837			−0.335128
$377$	4.78667	+	14.7318i	0.246526	+	0.758729i
$378$	2.13520	−	1.55131i	0.109823	−	0.0797910i
$379$	−15.8539	+	11.5186i	−0.814362	+	0.591668i	−0.915092	−	0.403245i	$-0.867882\pi$
$379$	−15.8539	+	11.5186i	−0.814362	+	0.591668i	0.100730	+	0.994914i	$0.467882\pi$
$380$	−0.00810552	−	2.76392i	−0.000415805	−	0.141786i
$381$	−6.03853	−	4.38725i	−0.309363	−	0.224765i
$382$	−3.23607			−0.165572
$383$	15.5620	+	11.3065i	0.795182	+	0.577734i	0.909497	−	0.415711i	$-0.136467\pi$
$383$	15.5620	+	11.3065i	0.795182	+	0.577734i	−0.114314	+	0.993445i	$0.536467\pi$
$384$	−0.309017	+	0.951057i	−0.0157695	+	0.0485334i
$385$	−35.1603	+	11.5384i	−1.79193	+	0.588050i
$386$	3.35720	+	10.3324i	0.170877	+	0.525905i
$387$	−0.609928	+	1.87717i	−0.0310044	+	0.0954218i
$388$	0.463977	−	1.42798i	0.0235549	−	0.0724945i
$389$	−0.510524	−	1.57123i	−0.0258846	−	0.0796646i	0.937280	−	0.348578i	$-0.113335\pi$
$389$	−0.510524	−	1.57123i	−0.0258846	−	0.0796646i	−0.963164	+	0.268914i	$0.913335\pi$
$390$	2.97878	+	4.07476i	0.150836	+	0.206333i
$391$	−2.24727	+	6.91638i	−0.113649	+	0.349777i
$392$	−0.0277780	−	0.0201819i	−0.00140300	−	0.00101934i
$393$	20.5146			1.03482
$394$	−7.34335	−	5.33526i	−0.369953	−	0.268786i
$395$	−4.95629	−	6.77985i	−0.249378	−	0.341131i
$396$	−5.07286	+	3.68565i	−0.254921	+	0.185211i
$397$	6.55392	−	4.76170i	0.328932	−	0.238983i	−0.411045	−	0.911615i	$-0.634836\pi$
$397$	6.55392	−	4.76170i	0.328932	−	0.238983i	0.739977	+	0.672632i	$0.234836\pi$
$398$	−8.05716	−	24.7974i	−0.403869	−	1.24298i
$399$	−3.26230			−0.163319
$400$	−1.51717	+	4.76426i	−0.0758584	+	0.238213i
$401$	−24.0079			−1.19890			−0.599449	−	0.800413i	$-0.704614\pi$
$401$	−24.0079			−1.19890			−0.599449	+	0.800413i	$0.704614\pi$
$402$	3.10328	+	9.55093i	0.154778	+	0.476357i
$403$	10.7294	−	7.79538i	0.534471	−	0.388316i
$404$	−3.79162	+	2.75478i	−0.188640	+	0.137055i
$405$	1.30902	−	1.81286i	0.0650456	−	0.0900819i
$406$	14.6522	+	10.6454i	0.727176	+	0.528325i
$407$	50.6778			2.51201
$408$	1.31557	+	0.955821i	0.0651306	+	0.0473202i
$409$	−3.50101	+	10.7750i	−0.173114	+	0.532789i	−0.999542	−	0.0302522i	$-0.990369\pi$
$409$	−3.50101	+	10.7750i	−0.173114	+	0.532789i	0.826429	+	0.563042i	$0.190369\pi$
$410$	−0.0753678	−	25.6998i	−0.00372215	−	1.26922i
$411$	−0.946724	−	2.91372i	−0.0466984	−	0.143723i
$412$	−1.32222	+	4.06937i	−0.0651410	+	0.200483i
$413$	7.36817	−	22.6769i	0.362564	−	1.11586i
$414$	1.38197	+	4.25325i	0.0679199	+	0.209036i
$415$	−10.9613	+	15.1804i	−0.538069	+	0.745174i
$416$	−0.697541	+	2.14681i	−0.0341997	+	0.105256i
$417$	13.4934	+	9.80350i	0.660773	+	0.480079i
$418$	7.75065			0.379096
$419$	18.5382	+	13.4688i	0.905651	+	0.657994i	0.939911	−	0.341419i	$-0.110907\pi$
$419$	18.5382	+	13.4688i	0.905651	+	0.657994i	−0.0342601	+	0.999413i	$0.510907\pi$
$420$	5.61803	+	1.80721i	0.274132	+	0.0881829i
$421$	−23.7532	+	17.2577i	−1.15766	+	0.841089i	−0.989480	−	0.144667i	$-0.953789\pi$
$421$	−23.7532	+	17.2577i	−1.15766	+	0.841089i	−0.168180	+	0.985756i	$0.553789\pi$
$422$	12.5408	−	9.11143i	0.610477	−	0.443537i
$423$	2.00811	+	6.18031i	0.0976374	+	0.300497i
$424$	6.99983			0.339942
$425$	6.60579	+	4.74044i	0.320428	+	0.229945i
$426$	9.77688			0.473691
$427$	−2.46403	−	7.58351i	−0.119243	−	0.366992i
$428$	15.1974	−	11.0415i	0.734593	−	0.533713i
$429$	−11.4509	+	8.31958i	−0.552855	+	0.401673i
$430$	−4.19345	+	1.37615i	−0.202226	+	0.0663636i
$431$	−3.20173	−	2.32619i	−0.154222	−	0.112049i	0.507998	−	0.861358i	$-0.330386\pi$
$431$	−3.20173	−	2.32619i	−0.154222	−	0.112049i	−0.662220	+	0.749309i	$0.730386\pi$
$432$	1.00000			0.0481125
$433$	−0.328915	−	0.238970i	−0.0158066	−	0.0114842i	0.579854	−	0.814720i	$-0.303110\pi$
$433$	−0.328915	−	0.238970i	−0.0158066	−	0.0114842i	−0.595661	+	0.803236i	$0.703110\pi$
$434$	4.79176	−	14.7475i	0.230012	−	0.707904i
$435$	14.6072	+	4.69885i	0.700362	+	0.225293i
$436$	−4.94982	−	15.2340i	−0.237053	−	0.729575i
$437$	1.70820	−	5.25731i	0.0817145	−	0.251491i
$438$	3.70565	−	11.4048i	0.177063	−	0.544943i
$439$	−1.76233	−	5.42390i	−0.0841115	−	0.258868i	0.900152	−	0.435576i	$-0.143455\pi$
$439$	−1.76233	−	5.42390i	−0.0841115	−	0.258868i	−0.984263	+	0.176708i	$0.943455\pi$
$440$	−13.3475	−	4.29362i	−0.636315	−	0.204690i
$441$	−0.0106103	+	0.0326550i	−0.000505251	+	0.00155500i
$442$	2.96963	+	2.15756i	0.141251	+	0.102625i
$443$	−22.7666			−1.08167			−0.540836	−	0.841128i	$-0.681892\pi$
$443$	−22.7666			−1.08167			−0.540836	+	0.841128i	$0.681892\pi$
$444$	−6.53853	−	4.75052i	−0.310305	−	0.225450i
$445$	0.828743	−	0.271964i	0.0392862	−	0.0128923i
$446$	1.45483	−	1.05700i	0.0688882	−	0.0500502i
$447$	−11.7188	+	8.51422i	−0.554281	+	0.402709i
$448$	0.815575	+	2.51008i	0.0385323	+	0.118590i
$449$	34.7078			1.63796			0.818980	−	0.573822i	$-0.194540\pi$
$449$	34.7078			1.63796			0.818980	+	0.573822i	$0.194540\pi$
$450$	4.99991	−	0.0293259i	0.235698	−	0.00138244i
$451$	72.0680			3.39355
$452$	−2.98776	−	9.19537i	−0.140532	−	0.432514i
$453$	−8.33693	+	6.05714i	−0.391703	+	0.284589i
$454$	−0.836795	+	0.607967i	−0.0392727	+	0.0285333i
$455$	12.6815	+	4.07940i	0.594519	+	0.191245i
$456$	−1.00000	−	0.726543i	−0.0468293	−	0.0340235i
$457$	36.5194			1.70831			0.854153	−	0.520022i	$-0.174076\pi$
$457$	36.5194			1.70831			0.854153	+	0.520022i	$0.174076\pi$
$458$	−2.21626	−	1.61020i	−0.103559	−	0.0752399i
$459$	0.502505	−	1.54655i	0.0234549	−	0.0721868i
$460$	−5.85410	+	8.10737i	−0.272949	+	0.378008i
$461$	9.21772	+	28.3692i	0.429312	+	1.32129i	0.898804	+	0.438350i	$0.144437\pi$
$461$	9.21772	+	28.3692i	0.429312	+	1.32129i	−0.469492	+	0.882936i	$0.655563\pi$
$462$	−5.11398	+	15.7392i	−0.237924	+	0.732255i
$463$	−11.3555	+	34.9485i	−0.527733	+	1.62419i	0.231115	+	0.972927i	$0.425763\pi$
$463$	−11.3555	+	34.9485i	−0.527733	+	1.62419i	−0.758848	+	0.651268i	$0.774237\pi$
$464$	2.12054	+	6.52635i	0.0984435	+	0.302978i
$465$	−0.0385275	−	13.1376i	−0.00178667	−	0.609240i
$466$	−5.56785	+	17.1361i	−0.257926	+	0.793814i
$467$	−17.7336	−	12.8842i	−0.820614	−	0.596211i	0.0962744	−	0.995355i	$-0.469307\pi$
$467$	−17.7336	−	12.8842i	−0.820614	−	0.596211i	−0.916888	+	0.399144i	$0.869307\pi$
$468$	2.25729			0.104343
$469$	21.4426	+	15.5790i	0.990129	+	0.719371i
$470$	−8.50647	+	11.7807i	−0.392374	+	0.543401i
$471$	6.13534	−	4.45759i	0.282702	−	0.205395i
$472$	7.30893	−	5.31025i	0.336421	−	0.244424i
$473$	−3.82450	−	11.7706i	−0.175851	−	0.541212i
$474$	−3.75583			−0.172511
$475$	−5.02122	−	3.60332i	−0.230389	−	0.165332i
$476$	4.29180			0.196714
$477$	−2.16307	−	6.65723i	−0.0990400	−	0.304814i
$478$	−2.20173	+	1.59965i	−0.100705	+	0.0731664i
$479$	5.88844	−	4.27820i	0.269050	−	0.195476i	−0.445077	−	0.895492i	$-0.646824\pi$
$479$	5.88844	−	4.27820i	0.269050	−	0.195476i	0.714127	+	0.700016i	$0.246824\pi$
$480$	1.31963	+	1.80515i	0.0602325	+	0.0823937i
$481$	−14.7593	−	10.7233i	−0.672968	−	0.488940i
$482$	−1.50146			−0.0683897
$483$	9.54891	+	6.93769i	0.434491	+	0.315676i
$484$	8.75073	−	26.9320i	0.397761	−	1.22418i
$485$	−1.98137	−	2.71037i	−0.0899694	−	0.123072i
$486$	−0.309017	−	0.951057i	−0.0140173	−	0.0431408i
$487$	−9.70333	+	29.8638i	−0.439700	+	1.35326i	0.448493	+	0.893787i	$0.351961\pi$
$487$	−9.70333	+	29.8638i	−0.439700	+	1.35326i	−0.888193	+	0.459471i	$0.848039\pi$
$488$	0.933608	−	2.87335i	0.0422625	−	0.130071i
$489$	−4.32624	−	13.3148i	−0.195639	−	0.602116i
$490$	−0.0729490	+	0.0239393i	−0.00329550	+	0.00108147i
$491$	−8.18133	+	25.1795i	−0.369218	+	1.13634i	0.578079	+	0.815981i	$0.303803\pi$
$491$	−8.18133	+	25.1795i	−0.369218	+	1.13634i	−0.947297	+	0.320356i	$0.896197\pi$
$492$	−9.29832	−	6.75563i	−0.419201	−	0.304567i
$493$	11.1589			0.502572
$494$	−2.25729	−	1.64002i	−0.101560	−	0.0737878i
$495$	0.0411182	+	14.0210i	0.00184813	+	0.630197i
$496$	4.75324	−	3.45343i	0.213427	−	0.155063i
$497$	20.8756	−	15.1670i	0.936399	−	0.680333i
$498$	2.58761	+	7.96385i	0.115954	+	0.356869i
$499$	−28.1904			−1.26197			−0.630987	−	0.775793i	$-0.717350\pi$
$499$	−28.1904			−1.26197			−0.630987	+	0.775793i	$0.717350\pi$
$500$	6.65096	+	8.98692i	0.297440	+	0.401907i
$501$	17.3310			0.774291
$502$	0.295816	+	0.910428i	0.0132029	+	0.0406344i
$503$	−5.76421	+	4.18794i	−0.257013	+	0.186731i	−0.708829	−	0.705380i	$-0.750776\pi$
$503$	−5.76421	+	4.18794i	−0.257013	+	0.186731i	0.451816	+	0.892111i	$0.350776\pi$
$504$	2.13520	−	1.55131i	0.0951094	−	0.0691011i
$505$	0.0307331	+	10.4797i	0.00136760	+	0.466343i
$506$	−22.6865	−	16.4827i	−1.00854	−	0.732747i
$507$	−7.90465			−0.351058
$508$	−6.03853	−	4.38725i	−0.267916	−	0.194653i
$509$	−2.61038	+	8.03393i	−0.115703	+	0.356097i	−0.992093	−	0.125505i	$-0.959945\pi$
$509$	−2.61038	+	8.03393i	−0.115703	+	0.356097i	0.876390	+	0.481602i	$0.159945\pi$
$510$	3.45488	−	1.13377i	0.152985	−	0.0502042i
$511$	−9.78014	−	30.1002i	−0.432648	−	1.33155i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−0.381966	+	1.17557i	−0.0168642	+	0.0519027i
$514$	2.55164	+	7.85315i	0.112548	+	0.346388i
$515$	5.64640	+	7.72387i	0.248810	+	0.340355i
$516$	−0.609928	+	1.87717i	−0.0268506	+	0.0826377i
$517$	−32.9653	−	23.9507i	−1.44981	−	1.05335i
$518$	−21.3306			−0.937214
$519$	−3.07692	−	2.23551i	−0.135062	−	0.0981280i
$520$	2.97878	+	4.07476i	0.130628	+	0.178690i
$521$	11.4788	−	8.33986i	0.502897	−	0.365376i	−0.307226	−	0.951637i	$-0.599401\pi$
$521$	11.4788	−	8.33986i	0.502897	−	0.365376i	0.810122	+	0.586261i	$0.199401\pi$
$522$	5.55164	−	4.03350i	0.242989	−	0.176542i
$523$	−5.88343	−	18.1073i	−0.257264	−	0.791778i	−0.993375	−	0.114917i	$-0.963340\pi$
$523$	−5.88343	−	18.1073i	−0.257264	−	0.791778i	0.736111	−	0.676861i	$-0.236660\pi$
$524$	20.5146			0.896183
$525$	10.6303	−	7.81906i	0.463946	−	0.341252i
$526$	1.51165			0.0659112
$527$	−2.95238	−	9.08648i	−0.128608	−	0.395813i
$528$	−5.07286	+	3.68565i	−0.220768	+	0.160397i
$529$	2.42705	−	1.76336i	0.105524	−	0.0766676i
$530$	9.16289	−	12.6897i	0.398011	−	0.551207i
$531$	−7.30893	−	5.31025i	−0.317181	−	0.230445i
$532$	−3.26230			−0.141439
$533$	−20.9890	−	15.2494i	−0.909134	−	0.660525i
$534$	0.120539	−	0.370980i	0.00521622	−	0.0160539i
$535$	−0.123183	−	42.0043i	−0.00532565	−	1.81600i
$536$	3.10328	+	9.55093i	0.134041	+	0.412537i
$537$	0.0385275	−	0.118575i	0.00166258	−	0.00511690i
$538$	−3.04098	+	9.35917i	−0.131106	+	0.403503i
$539$	−0.0665307	−	0.204760i	−0.00286568	−	0.00881965i
$540$	1.30902	−	1.81286i	0.0563311	−	0.0780132i
$541$	4.88256	−	15.0270i	0.209918	−	0.646060i	−0.789558	−	0.613676i	$-0.789690\pi$
$541$	4.88256	−	15.0270i	0.209918	−	0.646060i	0.999476	−	0.0323838i	$-0.0103099\pi$
$542$	6.96808	+	5.06261i	0.299305	+	0.217458i
$543$	−9.31813			−0.399879
$544$	1.31557	+	0.955821i	0.0564048	+	0.0409805i
$545$	−34.0965	−	10.9682i	−1.46053	−	0.469826i
$546$	4.81977	−	3.50177i	0.206267	−	0.149862i
$547$	−17.0558	+	12.3918i	−0.729255	+	0.529835i	−0.889328	−	0.457271i	$-0.848827\pi$
$547$	−17.0558	+	12.3918i	−0.729255	+	0.529835i	0.160073	+	0.987105i	$0.448827\pi$
$548$	−0.946724	−	2.91372i	−0.0404420	−	0.124468i
$549$	−3.02122			−0.128943
$550$	−25.2558	+	18.5767i	−1.07691	+	0.792113i
$551$	−8.48215			−0.361352
$552$	1.38197	+	4.25325i	0.0588204	+	0.181031i
$553$	−8.01945	+	5.82647i	−0.341022	+	0.247767i
$554$	11.8433	−	8.60464i	0.503172	−	0.365576i
$555$	−17.1711	+	5.63495i	−0.728872	+	0.239190i
$556$	13.4934	+	9.80350i	0.572246	+	0.415761i
$557$	10.1705			0.430938			0.215469	−	0.976511i	$-0.430872\pi$
$557$	10.1705			0.430938			0.215469	+	0.976511i	$0.430872\pi$
$558$	−4.75324	−	3.45343i	−0.201221	−	0.146195i
$559$	−1.37678	+	4.23731i	−0.0582318	+	0.179219i
$560$	5.61803	+	1.80721i	0.237405	+	0.0763687i
$561$	3.15091	+	9.69750i	0.133031	+	0.409429i
$562$	0.599265	−	1.84435i	0.0252785	−	0.0777991i
$563$	−6.12049	+	18.8369i	−0.257948	+	0.793881i	0.735287	+	0.677756i	$0.237047\pi$
$563$	−6.12049	+	18.8369i	−0.257948	+	0.793881i	−0.993235	+	0.116125i	$0.962953\pi$
$564$	2.00811	+	6.18031i	0.0845565	+	0.260238i
$565$	−20.5810	−	6.62050i	−0.865848	−	0.278526i
$566$	−0.647360	+	1.99237i	−0.0272106	+	0.0837455i
$567$	−2.13520	−	1.55131i	−0.0896700	−	0.0651491i
$568$	9.77688			0.410229
$569$	−8.34991	−	6.06656i	−0.350046	−	0.254324i	0.398842	−	0.917020i	$-0.369412\pi$
$569$	−8.34991	−	6.06656i	−0.350046	−	0.254324i	−0.748889	+	0.662696i	$0.769412\pi$
$570$	−2.62614	+	0.861807i	−0.109997	+	0.0360971i
$571$	−9.50146	+	6.90322i	−0.397624	+	0.288891i	−0.768572	−	0.639763i	$-0.779033\pi$
$571$	−9.50146	+	6.90322i	−0.397624	+	0.288891i	0.370949	+	0.928653i	$0.379033\pi$
$572$	−11.4509	+	8.31958i	−0.478787	+	0.347859i
$573$	1.00000	+	3.07768i	0.0417756	+	0.128572i
$574$	−30.3339			−1.26611
$575$	7.03444	+	21.2254i	0.293357	+	0.885159i
$576$	1.00000			0.0416667
$577$	3.30910	+	10.1844i	0.137760	+	0.423981i	0.996009	−	0.0892521i	$-0.0284477\pi$
$577$	3.30910	+	10.1844i	0.137760	+	0.423981i	−0.858249	+	0.513233i	$0.828448\pi$
$578$	−11.6140	+	8.43805i	−0.483078	+	0.350977i
$579$	8.78926	−	6.38577i	0.365269	−	0.265384i
$580$	14.6072	+	4.69885i	0.606531	+	0.195109i
$581$	17.8795	+	12.9902i	0.741767	+	0.538925i
$582$	−1.50146			−0.0622376
$583$	35.5092	+	25.7989i	1.47064	+	1.06848i
$584$	3.70565	−	11.4048i	0.153341	−	0.471934i
$585$	2.95483	−	4.09216i	0.122167	−	0.169190i
$586$	−7.44827	−	22.9234i	−0.307685	−	0.946958i
$587$	−11.4736	+	35.3122i	−0.473567	+	1.45749i	0.374313	+	0.927303i	$0.377879\pi$
$587$	−11.4736	+	35.3122i	−0.473567	+	1.45749i	−0.847880	+	0.530188i	$0.822121\pi$
$588$	−0.0106103	+	0.0326550i	−0.000437560	+	0.00134667i
$589$	2.24417	+	6.90686i	0.0924696	+	0.284592i
$590$	−0.0592427	−	20.2013i	−0.00243898	−	0.831674i
$591$	−2.80491	+	8.63263i	−0.115379	+	0.355099i
$592$	−6.53853	−	4.75052i	−0.268732	−	0.195245i
$593$	−16.5966			−0.681542			−0.340771	−	0.940146i	$-0.610688\pi$
$593$	−16.5966			−0.681542			−0.340771	+	0.940146i	$0.610688\pi$
$594$	5.07286	+	3.68565i	0.208142	+	0.151224i
$595$	5.61803	−	7.78044i	0.230317	−	0.318967i
$596$	−11.7188	+	8.51422i	−0.480021	+	0.348756i
$597$	−21.0939	+	15.3256i	−0.863316	+	0.627236i
$598$	3.11950	+	9.60082i	0.127566	+	0.392607i
$599$	45.8295			1.87254			0.936272	−	0.351275i	$-0.114252\pi$
$599$	45.8295			1.87254			0.936272	+	0.351275i	$0.114252\pi$
$600$	4.99991	−	0.0293259i	0.204121	−	0.00119723i
$601$	−23.3609			−0.952909			−0.476455	−	0.879199i	$-0.658078\pi$
$601$	−23.3609			−0.952909			−0.476455	+	0.879199i	$0.658078\pi$
$602$	1.60976	+	4.95432i	0.0656088	+	0.201923i
$603$	8.12451	−	5.90280i	0.330855	−	0.240381i
$604$	−8.33693	+	6.05714i	−0.339225	+	0.246461i
$605$	−37.3692	−	51.1183i	−1.51927	−	2.07825i
$606$	3.79162	+	2.75478i	0.154024	+	0.111905i
$607$	21.3526			0.866674			0.433337	−	0.901232i	$-0.357336\pi$
$607$	21.3526			0.866674			0.433337	+	0.901232i	$0.357336\pi$
$608$	−1.00000	−	0.726543i	−0.0405554	−	0.0294652i
$609$	5.59664	−	17.2247i	0.226787	−	0.697980i
$610$	−3.98688	−	5.45377i	−0.161424	−	0.220817i
$611$	4.53287	+	13.9508i	0.183380	+	0.564387i
$612$	0.502505	−	1.54655i	0.0203126	−	0.0625156i
$613$	10.4761	−	32.2421i	0.423126	−	1.30225i	−0.481652	−	0.876363i	$-0.659963\pi$
$613$	10.4761	−	32.2421i	0.423126	−	1.30225i	0.904777	−	0.425885i	$-0.140037\pi$
$614$	4.50146	+	13.8541i	0.181664	+	0.559105i
$615$	−24.4187	+	8.01336i	−0.984657	+	0.323130i
$616$	−5.11398	+	15.7392i	−0.206048	+	0.634151i
$617$	−5.59850	−	4.06755i	−0.225387	−	0.163753i	0.469361	−	0.883006i	$-0.344484\pi$
$617$	−5.59850	−	4.06755i	−0.225387	−	0.163753i	−0.694748	+	0.719253i	$0.744484\pi$
$618$	4.27879			0.172118
$619$	11.1538	+	8.10373i	0.448310	+	0.325717i	0.788928	−	0.614485i	$-0.210636\pi$
$619$	11.1538	+	8.10373i	0.448310	+	0.325717i	−0.340618	+	0.940202i	$0.610636\pi$
$620$	−0.0385275	−	13.1376i	−0.00154730	−	0.527617i
$621$	3.61803	−	2.62866i	0.145187	−	0.105484i
$622$	6.22295	−	4.52124i	0.249518	−	0.181285i
$623$	−0.318132	−	0.979111i	−0.0127457	−	0.0392272i
$624$	2.25729			0.0903639
$625$	24.9983	−	0.293254i	0.999931	−	0.0117302i
$626$	−24.0311			−0.960475
$627$	−2.39508	−	7.37130i	−0.0956503	−	0.294381i
$628$	6.13534	−	4.45759i	0.244827	−	0.177877i
$629$	−10.6326	+	7.72501i	−0.423948	+	0.308016i
$630$	−0.0173069	−	5.90153i	−0.000689525	−	0.235122i
$631$	−9.03461	−	6.56403i	−0.359662	−	0.261310i	0.393249	−	0.919432i	$-0.371351\pi$
$631$	−9.03461	−	6.56403i	−0.359662	−	0.261310i	−0.752911	+	0.658122i	$0.771351\pi$
$632$	−3.75583			−0.149399
$633$	−12.5408	−	9.11143i	−0.498452	−	0.362147i
$634$	3.64075	−	11.2051i	0.144593	−	0.445010i
$635$	−15.8580	+	5.20405i	−0.629306	+	0.206516i
$636$	−2.16307	−	6.65723i	−0.0857711	−	0.263976i
$637$	−0.0239504	+	0.0737119i	−0.000948951	+	0.00292057i
$638$	−13.2966	+	40.9228i	−0.526419	+	1.62015i
$639$	−3.02122	−	9.29836i	−0.119518	−	0.367837i
$640$	1.31963	+	1.80515i	0.0521628	+	0.0713550i
$641$	4.97551	−	15.3130i	0.196521	−	0.604829i	−0.803435	−	0.595393i	$-0.796996\pi$
$641$	4.97551	−	15.3130i	0.196521	−	0.604829i	0.999955	−	0.00943607i	$-0.00300364\pi$
$642$	−15.1974	−	11.0415i	−0.599792	−	0.435775i
$643$	−2.52460			−0.0995603			−0.0497802	−	0.998760i	$-0.515852\pi$
$643$	−2.52460			−0.0995603			−0.0497802	+	0.998760i	$0.515852\pi$
$644$	9.54891	+	6.93769i	0.376280	+	0.273383i
$645$	2.60464	+	3.56296i	0.102558	+	0.140291i
$646$	−1.62614	+	1.18146i	−0.0639796	+	0.0464839i
$647$	0.896543	−	0.651377i	0.0352467	−	0.0256083i	−0.570022	−	0.821629i	$-0.693065\pi$
$647$	0.896543	−	0.651377i	0.0352467	−	0.0256083i	0.605269	+	0.796021i	$0.293065\pi$
$648$	−0.309017	−	0.951057i	−0.0121393	−	0.0373610i
$649$	56.6489			2.22366
$650$	11.2862	−	0.0661971i	0.442683	−	0.00259646i
$651$	−15.5065			−0.607747
$652$	−4.32624	−	13.3148i	−0.169429	−	0.521447i
$653$	−26.1323	+	18.9862i	−1.02264	+	0.742988i	−0.966822	−	0.255453i	$-0.917775\pi$
$653$	−26.1323	+	18.9862i	−1.02264	+	0.742988i	−0.0558144	+	0.998441i	$0.517775\pi$
$654$	−12.9588	+	9.41512i	−0.506729	+	0.368160i
$655$	26.8539	−	37.1901i	1.04927	−	1.45314i
$656$	−9.29832	−	6.75563i	−0.363038	−	0.263763i
$657$	−11.9917			−0.467842
$658$	13.8753	+	10.0810i	0.540916	+	0.392999i
$659$	−0.654648	+	2.01480i	−0.0255015	+	0.0784854i	−0.962997	−	0.269511i	$-0.913138\pi$
$659$	−0.654648	+	2.01480i	−0.0255015	+	0.0784854i	0.937496	+	0.347997i	$0.113138\pi$
$660$	0.0411182	+	14.0210i	0.00160052	+	0.545766i
$661$	−15.3606	−	47.2750i	−0.597457	−	1.83878i	−0.542095	−	0.840317i	$-0.682369\pi$
$661$	−15.3606	−	47.2750i	−0.597457	−	1.83878i	−0.0553624	−	0.998466i	$-0.517631\pi$
$662$	4.17213	−	12.8405i	0.162154	−	0.499060i
$663$	1.13430	−	3.49101i	0.0440525	−	0.135580i
$664$	2.58761	+	7.96385i	0.100419	+	0.309057i
$665$	−4.27040	+	5.91410i	−0.165599	+	0.229339i
$666$	−2.49750	+	7.68650i	−0.0967760	+	0.297846i
$667$	24.8277	+	18.0384i	0.961332	+	0.698449i
$668$	17.3310			0.670555
$669$	−1.45483	−	1.05700i	−0.0562469	−	0.0408658i
$670$	21.3768	+	6.87650i	0.825857	+	0.265662i
$671$	15.3262	−	11.1352i	0.591663	−	0.429868i
$672$	2.13520	−	1.55131i	0.0823672	−	0.0598433i
$673$	−2.85916	−	8.79960i	−0.110213	−	0.339200i	0.880706	−	0.473664i	$-0.157069\pi$
$673$	−2.85916	−	8.79960i	−0.110213	−	0.339200i	−0.990918	+	0.134464i	$0.957069\pi$
$674$	−25.5997			−0.986065
$675$	−1.57295	−	4.74614i	−0.0605428	−	0.182679i
$676$	−7.90465			−0.304025
$677$	−10.8742	−	33.4674i	−0.417930	−	1.28626i	−0.909603	−	0.415478i	$-0.863614\pi$
$677$	−10.8742	−	33.4674i	−0.417930	−	1.28626i	0.491673	−	0.870780i	$-0.336386\pi$
$678$	−7.82205	+	5.68305i	−0.300404	+	0.218256i
$679$	−3.20592	+	2.32924i	−0.123032	+	0.0893880i
$680$	3.45488	−	1.13377i	0.132489	−	0.0434782i
$681$	0.836795	+	0.607967i	0.0320661	+	0.0232974i
$682$	36.8406			1.41070
$683$	−16.1761	−	11.7527i	−0.618963	−	0.449703i	0.233596	−	0.972334i	$-0.424951\pi$
$683$	−16.1761	−	11.7527i	−0.618963	−	0.449703i	−0.852559	+	0.522631i	$0.824951\pi$
$684$	−0.381966	+	1.17557i	−0.0146048	+	0.0449491i
$685$	−6.52145	−	2.09782i	−0.249172	−	0.0801537i
$686$	5.73702	+	17.6567i	0.219041	+	0.674138i
$687$	−0.846535	+	2.60537i	−0.0322973	+	0.0994009i
$688$	−0.609928	+	1.87717i	−0.0232533	+	0.0715663i
$689$	−4.88266	−	15.0273i	−0.186015	−	0.572494i
$690$	9.51959	+	3.06227i	0.362404	+	0.116578i
$691$	4.81448	−	14.8174i	0.183151	−	0.563682i	−0.816760	−	0.576977i	$-0.804232\pi$
$691$	4.81448	−	14.8174i	0.183151	−	0.563682i	0.999912	+	0.0132952i	$0.00423212\pi$
$692$	−3.07692	−	2.23551i	−0.116967	−	0.0849813i
$693$	16.5492			0.628652
$694$	−0.205646	−	0.149411i	−0.00780622	−	0.00567155i
$695$	35.4354	−	11.6287i	1.34414	−	0.441101i
$696$	5.55164	−	4.03350i	0.210434	−	0.152890i
$697$	−15.1204	+	10.9856i	−0.572725	+	0.416109i
$698$	9.78912	+	30.1278i	0.370524	+	1.14035i
$699$	18.0180			0.681502
$700$	10.6303	−	7.81906i	0.401789	−	0.295533i
$701$	−28.2932			−1.06862			−0.534310	−	0.845289i	$-0.679428\pi$
$701$	−28.2932			−1.06862			−0.534310	+	0.845289i	$0.679428\pi$
$702$	−0.697541	−	2.14681i	−0.0263270	−	0.0810261i
$703$	8.08206	−	5.87196i	0.304821	−	0.221465i
$704$	−5.07286	+	3.68565i	−0.191191	+	0.138908i
$705$	13.8327	+	4.44971i	0.520970	+	0.167586i
$706$	23.4295	+	17.0225i	0.881782	+	0.640652i
$707$	12.3694			0.465199
$708$	−7.30893	−	5.31025i	−0.274686	−	0.199571i
$709$	4.10591	−	12.6367i	0.154201	−	0.474581i	−0.843878	−	0.536534i	$-0.819733\pi$
$709$	4.10591	−	12.6367i	0.154201	−	0.474581i	0.998079	+	0.0619537i	$0.0197331\pi$
$710$	12.7981	−	17.7241i	0.480304	−	0.665175i
$711$	1.16061	+	3.57200i	0.0435264	+	0.133961i
$712$	0.120539	−	0.370980i	0.00451738	−	0.0139031i
$713$	8.11950	−	24.9892i	0.304078	−	0.935854i
$714$	−1.32624	−	4.08174i	−0.0496332	−	0.152755i
$715$	0.0928157	+	31.6494i	0.00347111	+	1.18362i
$716$	0.0385275	−	0.118575i	0.00143984	−	0.00443137i
$717$	2.20173	+	1.59965i	0.0822252	+	0.0597401i
$718$	8.01621			0.299162
$719$	38.2407	+	27.7835i	1.42614	+	1.03615i	0.990719	+	0.135923i	$0.0433999\pi$
$719$	38.2407	+	27.7835i	1.42614	+	1.03615i	0.435419	+	0.900228i	$0.356600\pi$
$720$	1.30902	−	1.81286i	0.0487842	−	0.0675614i
$721$	9.13607	−	6.63775i	0.340245	−	0.247203i
$722$	−14.1353	+	10.2699i	−0.526060	+	0.382205i
$723$	0.463977	+	1.42798i	0.0172555	+	0.0531070i
$724$	−9.31813			−0.346306
$725$	27.6394	−	20.3300i	1.02650	−	0.755037i
$726$	−28.3180			−1.05098
$727$	−4.33935	−	13.3552i	−0.160938	−	0.495315i	0.837776	−	0.546014i	$-0.183855\pi$
$727$	−4.33935	−	13.3552i	−0.160938	−	0.495315i	−0.998714	+	0.0506983i	$0.983855\pi$
$728$	4.81977	−	3.50177i	0.178632	−	0.129784i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−15.8246	−	21.6469i	−0.585695	−	0.801188i
$731$	2.59664	+	1.88657i	0.0960403	+	0.0697773i
$732$	−3.02122			−0.111668
$733$	37.7288	+	27.4116i	1.39355	+	1.01247i	0.995466	+	0.0951187i	$0.0303231\pi$
$733$	37.7288	+	27.4116i	1.39355	+	1.01247i	0.398079	+	0.917351i	$0.369677\pi$
$734$	−4.73852	+	14.5837i	−0.174902	+	0.538293i
$735$	0.0453101	+	0.0619810i	0.00167129	+	0.00228620i
$736$	1.38197	+	4.25325i	0.0509399	+	0.156777i
$737$	−19.4588	+	59.8882i	−0.716776	+	2.20601i
$738$	−3.55164	+	10.9308i	−0.130738	+	0.402369i
$739$	2.84791	+	8.76497i	0.104762	+	0.322424i	0.989675	−	0.143333i	$-0.0457820\pi$
$739$	2.84791	+	8.76497i	0.104762	+	0.322424i	−0.884912	+	0.465757i	$0.845782\pi$
$740$	−17.1711	+	5.63495i	−0.631222	+	0.207145i
$741$	−0.862207	+	2.65360i	−0.0316740	+	0.0974825i
$742$	−14.9460	−	10.8589i	−0.548687	−	0.398644i
$743$	17.7239			0.650225			0.325113	−	0.945675i	$-0.394598\pi$
$743$	17.7239			0.650225			0.325113	+	0.945675i	$0.394598\pi$
$744$	−4.75324	−	3.45343i	−0.174262	−	0.126609i
$745$	0.0949871	+	32.3899i	0.00348006	+	1.18667i
$746$	13.4374	−	9.76281i	0.491976	−	0.357442i
$747$	6.77446	−	4.92193i	0.247864	−	0.180084i
$748$	3.15091	+	9.69750i	0.115209	+	0.354576i
$749$	−49.5783			−1.81155
$750$	6.49181	−	9.10255i	0.237047	−	0.332378i
$751$	−24.1305			−0.880535			−0.440268	−	0.897867i	$-0.645116\pi$
$751$	−24.1305			−0.880535			−0.440268	+	0.897867i	$0.645116\pi$
$752$	2.00811	+	6.18031i	0.0732281	+	0.225373i
$753$	0.774456	−	0.562675i	0.0282228	−	0.0205050i
$754$	12.5317	−	9.10478i	0.456376	−	0.331577i
$755$	0.0675752	+	23.0426i	0.00245931	+	0.838607i
$756$	−2.13520	−	1.55131i	−0.0776565	−	0.0564208i
$757$	−46.8140			−1.70148			−0.850741	−	0.525585i	$-0.823847\pi$
$757$	−46.8140			−1.70148			−0.850741	+	0.525585i	$0.823847\pi$
$758$	15.8539	+	11.5186i	0.575841	+	0.418373i
$759$	−8.66548	+	26.6696i	−0.314537	+	0.968046i
$760$	−2.62614	+	0.861807i	−0.0952601	+	0.0312610i
$761$	−14.3023	−	44.0179i	−0.518458	−	1.59565i	−0.776902	−	0.629622i	$-0.783210\pi$
$761$	−14.3023	−	44.0179i	−0.518458	−	1.59565i	0.258444	−	0.966026i	$-0.416790\pi$
$762$	−2.30651	+	7.09871i	−0.0835561	+	0.257159i
$763$	−13.0638	+	40.2063i	−0.472943	+	1.45557i
$764$	1.00000	+	3.07768i	0.0361787	+	0.111347i
$765$	−2.14590	−	2.93543i	−0.0775851	−	0.106131i
$766$	5.94417	−	18.2943i	0.214771	−	0.660999i
$767$	−16.4984	−	11.9868i	−0.595721	−	0.432817i
$768$	1.00000			0.0360844
$769$	30.7054	+	22.3088i	1.10727	+	0.804476i	0.982231	−	0.187676i	$-0.0600955\pi$
$769$	30.7054	+	22.3088i	1.10727	+	0.804476i	0.125036	+	0.992152i	$0.460096\pi$
$770$	21.8388	+	29.8739i	0.787014	+	1.07658i
$771$	6.68029	−	4.85351i	0.240585	−	0.174795i
$772$	8.78926	−	6.38577i	0.316332	−	0.229829i
$773$	16.3878	+	50.4363i	0.589427	+	1.81407i	0.580715	+	0.814107i	$0.302773\pi$
$773$	16.3878	+	50.4363i	0.589427	+	1.81407i	0.00871188	+	0.999962i	$0.497227\pi$
$774$	1.97377			0.0709457
$775$	−23.8670	−	17.1274i	−0.857330	−	0.615236i
$776$	−1.50146			−0.0538993
$777$	6.59153	+	20.2866i	0.236470	+	0.727779i
$778$	−1.33657	+	0.971075i	−0.0479184	+	0.0348147i
$779$	11.4934	−	8.35041i	0.411792	−	0.299185i
$780$	2.95483	−	4.09216i	0.105800	−	0.146523i
$781$	49.5967	+	36.0341i	1.77471	+	1.28940i
$782$	7.27232			0.260058
$783$	−5.55164	−	4.03350i	−0.198400	−	0.144146i
$784$	−0.0106103	+	0.0326550i	−0.000378938	+	0.00116625i
$785$	−0.0497302	−	16.9576i	−0.00177495	−	0.605242i
$786$	−6.33935	−	19.5105i	−0.226117	−	0.695917i
$787$	3.52776	−	10.8573i	0.125751	−	0.387022i	−0.868286	−	0.496064i	$-0.834778\pi$
$787$	3.52776	−	10.8573i	0.125751	−	0.387022i	0.994037	+	0.109042i	$0.0347783\pi$
$788$	−2.80491	+	8.63263i	−0.0999208	+	0.307525i
$789$	−0.467126	−	1.43767i	−0.0166301	−	0.0511823i
$790$	−4.91644	+	6.80880i	−0.174919	+	0.242246i
$791$	−7.88545	+	24.2689i	−0.280374	+	0.862903i
$792$	5.07286	+	3.68565i	0.180256	+	0.130964i
$793$	−6.81977			−0.242177
$794$	−6.55392	−	4.76170i	−0.232590	−	0.168987i
$795$	−14.9001	−	4.79309i	−0.528454	−	0.169993i
$796$	−21.0939	+	15.3256i	−0.747654	+	0.543202i
$797$	−20.1910	+	14.6696i	−0.715200	+	0.519623i	−0.884847	−	0.465882i	$-0.845737\pi$
$797$	−20.1910	+	14.6696i	−0.715200	+	0.519623i	0.169647	+	0.985505i	$0.445737\pi$
$798$	1.00811	+	3.10263i	0.0356865	+	0.109832i
$799$	10.5672			0.373842
$800$	4.99991	−	0.0293259i	0.176774	−	0.00103683i
$801$	−0.390072			−0.0137825
$802$	7.41886	+	22.8329i	0.261969	+	0.806258i
$803$	60.8324	−	44.1973i	2.14673	−	1.55969i
$804$	8.12451	−	5.90280i	0.286529	−	0.208176i
$805$	25.0768	−	8.22932i	0.883840	−	0.290045i
$806$	−10.7294	−	7.79538i	−0.377928	−	0.274581i
$807$	9.84081			0.346413
$808$	3.79162	+	2.75478i	0.133389	+	0.0969127i
$809$	6.13985	−	18.8965i	0.215865	−	0.664366i	−0.783226	−	0.621738i	$-0.786427\pi$
$809$	6.13985	−	18.8965i	0.215865	−	0.664366i	0.999091	−	0.0426279i	$-0.0135730\pi$
$810$	−2.12864	−	0.684743i	−0.0747929	−	0.0240594i
$811$	−1.19554	−	3.67949i	−0.0419811	−	0.129205i	0.927869	−	0.372906i	$-0.121638\pi$
$811$	−1.19554	−	3.67949i	−0.0419811	−	0.129205i	−0.969850	+	0.243701i	$0.921638\pi$
$812$	5.59664	−	17.2247i	0.196404	−	0.604468i
$813$	2.66157	−	8.19147i	0.0933454	−	0.287288i
$814$	−15.6603	−	48.1975i	−0.548893	−	1.68932i
$815$	−29.8010	−	9.58641i	−1.04388	−	0.335797i
$816$	0.502505	−	1.54655i	0.0175912	−	0.0541401i
$817$	−1.97377	−	1.43403i	−0.0690535	−	0.0501703i
$818$	11.3295			0.396127
$819$	−4.81977	−	3.50177i	−0.168416	−	0.122362i
$820$	−24.4187	+	8.01336i	−0.852738	+	0.279839i
$821$	8.80907	−	6.40016i	0.307439	−	0.223367i	−0.423358	−	0.905962i	$-0.639149\pi$
$821$	8.80907	−	6.40016i	0.307439	−	0.223367i	0.730797	+	0.682595i	$0.239149\pi$
$822$	−2.47855	+	1.80078i	−0.0864495	+	0.0628092i
$823$	−3.17874	−	9.78315i	−0.110804	−	0.341019i	0.880245	−	0.474520i	$-0.157378\pi$
$823$	−3.17874	−	9.78315i	−0.110804	−	0.341019i	−0.991049	+	0.133500i	$0.957378\pi$
$824$	4.27879			0.149059
$825$	25.4720	+	18.2792i	0.886820	+	0.636399i
$826$	−23.8439			−0.829636
$827$	5.23497	+	16.1116i	0.182038	+	0.560255i	0.999885	−	0.0151810i	$-0.00483246\pi$
$827$	5.23497	+	16.1116i	0.182038	+	0.560255i	−0.817847	+	0.575436i	$0.804832\pi$
$828$	3.61803	−	2.62866i	0.125735	−	0.0913521i
$829$	12.2855	−	8.92593i	0.426692	−	0.310010i	−0.353633	−	0.935384i	$-0.615054\pi$
$829$	12.2855	−	8.92593i	0.426692	−	0.310010i	0.780325	+	0.625374i	$0.215054\pi$
$830$	17.8246	+	5.73383i	0.618701	+	0.199024i
$831$	−11.8433	−	8.60464i	−0.410838	−	0.298492i
$832$	2.25729			0.0782574
$833$	0.0451710	+	0.0328186i	0.00156508	+	0.00113710i
$834$	5.15400	−	15.8624i	0.178469	−	0.549270i
$835$	22.6865	−	31.4187i	0.785100	−	1.08729i
$836$	−2.39508	−	7.37130i	−0.0828356	−	0.254942i
$837$	−1.81557	+	5.58776i	−0.0627554	+	0.193141i
$838$	7.08097	−	21.7930i	0.244608	−	0.752826i
$839$	1.70827	+	5.25751i	0.0589760	+	0.181510i	0.976204	−	0.216852i	$-0.0695789\pi$
$839$	1.70827	+	5.25751i	0.0589760	+	0.181510i	−0.917228	+	0.398362i	$0.869579\pi$
$840$	−0.0173069	−	5.90153i	−0.000597146	−	0.203622i
$841$	5.59008	−	17.2045i	0.192762	−	0.593259i
$842$	23.7532	+	17.2577i	0.818589	+	0.594740i
$843$	−1.93926			−0.0667917
$844$	−12.5408	−	9.11143i	−0.431672	−	0.313628i
$845$	−10.3473	+	14.3300i	−0.355959	+	0.492969i
$846$	5.25729	−	3.81964i	0.180749	−	0.131322i
$847$	−60.4646	+	43.9301i	−2.07759	+	1.50946i
$848$	−2.16307	−	6.65723i	−0.0742800	−	0.228610i
$849$	2.09490			0.0718968
$850$	2.46713	−	7.74736i	0.0846217	−	0.265732i
$851$	−36.1441			−1.23900
$852$	−3.02122	−	9.29836i	−0.103505	−	0.318557i
$853$	−11.5422	+	8.38591i	−0.395198	+	0.287128i	−0.767582	−	0.640951i	$-0.778540\pi$
$853$	−11.5422	+	8.38591i	−0.395198	+	0.287128i	0.372384	+	0.928079i	$0.378540\pi$
$854$	−6.45092	+	4.68686i	−0.220746	+	0.160381i
$855$	1.63115	+	2.23129i	0.0557841	+	0.0763086i
$856$	−15.1974	−	11.0415i	−0.519435	−	0.377392i
$857$	9.45919			0.323120			0.161560	−	0.986863i	$-0.448347\pi$
$857$	9.45919			0.323120			0.161560	+	0.986863i	$0.448347\pi$
$858$	11.4509	+	8.31958i	0.390928	+	0.284026i
$859$	−7.59355	+	23.3705i	−0.259088	+	0.797392i	0.733908	+	0.679249i	$0.237694\pi$
$859$	−7.59355	+	23.3705i	−0.259088	+	0.797392i	−0.992997	+	0.118143i	$0.962306\pi$
$860$	2.60464	+	3.56296i	0.0888175	+	0.121496i
$861$	9.37369	+	28.8492i	0.319454	+	0.983180i
$862$	−1.22295	+	3.76386i	−0.0416539	+	0.128198i
$863$	7.80637	−	24.0255i	0.265732	−	0.817839i	−0.725792	−	0.687914i	$-0.758526\pi$
$863$	7.80637	−	24.0255i	0.265732	−	0.817839i	0.991524	−	0.129925i	$-0.0414736\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	−8.08041	+	2.65171i	−0.274742	+	0.0901608i
$866$	−0.125634	+	0.386662i	−0.00426922	+	0.0131393i
$867$	11.6140	+	8.43805i	0.394431	+	0.286571i
$868$	−15.5065			−0.526324
$869$	−19.0528	−	13.8427i	−0.646322	−	0.469580i
$870$	−0.0449990	−	15.3443i	−0.00152561	−	0.520220i
$871$	18.3394	−	13.3243i	0.621405	−	0.451477i
$872$	−12.9588	+	9.41512i	−0.438840	+	0.318836i
$873$	0.463977	+	1.42798i	0.0157033	+	0.0483296i
$874$	−5.52786			−0.186983
$875$	−0.259601	−	29.5066i	−0.00877611	−	0.997506i
$876$	−11.9917			−0.405163
$877$	−10.6956	−	32.9178i	−0.361166	−	1.11155i	−0.952347	−	0.305015i	$-0.901338\pi$
$877$	−10.6956	−	32.9178i	−0.361166	−	1.11155i	0.591182	−	0.806538i	$-0.298662\pi$
$878$	−4.61384	+	3.35215i	−0.155710	+	0.113130i
$879$	−19.4998	+	14.1675i	−0.657713	+	0.477856i
$880$	0.0411182	+	14.0210i	0.00138609	+	0.472647i
$881$	33.4160	+	24.2781i	1.12581	+	0.817950i	0.985080	−	0.172097i	$-0.0550543\pi$
$881$	33.4160	+	24.2781i	1.12581	+	0.817950i	0.140732	+	0.990048i	$0.455054\pi$
$882$	0.0343355			0.00115614
$883$	−33.7636	−	24.5307i	−1.13624	−	0.825523i	−0.149645	−	0.988740i	$-0.547813\pi$
$883$	−33.7636	−	24.5307i	−1.13624	−	0.825523i	−0.986590	+	0.163217i	$0.947813\pi$
$884$	1.13430	−	3.49101i	0.0381506	−	0.117415i
$885$	−19.1943	+	6.29889i	−0.645208	+	0.211735i
$886$	7.03526	+	21.6523i	0.236354	+	0.727423i
$887$	−7.17533	+	22.0834i	−0.240924	+	0.741488i	0.755356	+	0.655315i	$0.227464\pi$
$887$	−7.17533	+	22.0834i	−0.240924	+	0.741488i	−0.996280	+	0.0861734i	$0.972536\pi$
$888$	−2.49750	+	7.68650i	−0.0838105	+	0.257942i
$889$	6.08747	+	18.7353i	0.204167	+	0.628362i
$890$	−0.514749	−	0.704140i	−0.0172544	−	0.0236028i
$891$	1.93766	−	5.96351i	0.0649141	−	0.199785i
$892$	−1.45483	−	1.05700i	−0.0487113	−	0.0353908i
$893$	−8.03242			−0.268795
$894$	11.7188	+	8.51422i	0.391936	+	0.284758i
$895$	−0.164528	−	0.225062i	−0.00549956	−	0.00752300i
$896$	2.13520	−	1.55131i	0.0713321	−	0.0518258i
$897$	8.16695	−	5.93363i	0.272686	−	0.198118i
$898$	−10.7253	−	33.0090i	−0.357907	−	1.10153i
$899$	−40.3177			−1.34467
$900$	−1.57295	−	4.74614i	−0.0524316	−	0.158205i
$901$	−11.3827			−0.379213
$902$	−22.2702	−	68.5407i	−0.741518	−	2.28216i
$903$	4.21440	−	3.06194i	0.140246	−	0.101895i
$904$	−7.82205	+	5.68305i	−0.260157	+	0.189015i
$905$	−12.1976	+	16.8925i	−0.405462	+	0.561526i
$906$	8.33693	+	6.05714i	0.276976	+	0.201235i
$907$	33.4166			1.10958			0.554790	−	0.831990i	$-0.312798\pi$
$907$	33.4166			1.10958			0.554790	+	0.831990i	$0.312798\pi$
$908$	0.836795	+	0.607967i	0.0277700	+	0.0201761i
$909$	1.44827	−	4.45732i	0.0480361	−	0.147840i
$910$	−0.0390667	−	13.3214i	−0.00129505	−	0.441602i
$911$	−10.6524	−	32.7846i	−0.352929	−	1.08620i	−0.957201	−	0.289425i	$-0.906536\pi$
$911$	−10.6524	−	32.7846i	−0.352929	−	1.08620i	0.604272	−	0.796778i	$-0.293464\pi$
$912$	−0.381966	+	1.17557i	−0.0126482	+	0.0389270i
$913$	−16.2254	+	49.9366i	−0.536981	+	1.65266i
$914$	−11.2851	−	34.7320i	−0.373279	−	1.14883i
$915$	−3.95483	+	5.47706i	−0.130743	+	0.181066i
$916$	−0.846535	+	2.60537i	−0.0279703	+	0.0860837i
$917$	−43.8028	−	31.8246i	−1.44649	−	1.05094i
$918$	−1.62614			−0.0536706
$919$	0.617756	+	0.448826i	0.0203779	+	0.0148054i	0.597928	−	0.801550i	$-0.295991\pi$
$919$	0.617756	+	0.448826i	0.0203779	+	0.0148054i	−0.577550	+	0.816356i	$0.695991\pi$
$920$	9.51959	+	3.06227i	0.313851	+	0.100960i
$921$	11.7850	−	8.56229i	0.388328	−	0.282137i
$922$	24.1323	−	17.5331i	0.794755	−	0.577423i
$923$	−6.81977	−	20.9891i	−0.224475	−	0.690864i
$924$	16.5492			0.544428
$925$	−12.2618	+	38.5051i	−0.403167	+	1.26604i
$926$	36.7470			1.20758
$927$	−1.32222	−	4.06937i	−0.0434273	−	0.133656i
$928$	5.55164	−	4.03350i	0.182242	−	0.132406i
$929$	12.2680	−	8.91319i	0.402498	−	0.292432i	−0.368059	−	0.929802i	$-0.619978\pi$
$929$	12.2680	−	8.91319i	0.402498	−	0.292432i	0.770558	+	0.637370i	$0.219978\pi$
$930$	−12.4827	+	4.09637i	−0.409323	+	0.134325i
$931$	−0.0343355	−	0.0249462i	−0.00112530	−	0.000817580i
$932$	18.0180			0.590198
$933$	−6.22295	−	4.52124i	−0.203730	−	0.148019i
$934$	−6.77364	+	20.8471i	−0.221640	+	0.682138i
$935$	21.7048	+	6.98202i	0.709824	+	0.228337i
$936$	−0.697541	−	2.14681i	−0.0227998	−	0.0701706i
$937$	−8.61798	+	26.5234i	−0.281537	+	0.866482i	0.705878	+	0.708333i	$0.250553\pi$
$937$	−8.61798	+	26.5234i	−0.281537	+	0.866482i	−0.987415	+	0.158149i	$0.949447\pi$
$938$	8.19036	−	25.2073i	0.267425	−	0.823049i
$939$	7.42601	+	22.8549i	0.242339	+	0.745842i
$940$	13.8327	+	4.44971i	0.451173	+	0.145134i
$941$	11.4347	−	35.1922i	0.372759	−	1.14723i	−0.572219	−	0.820101i	$-0.693917\pi$
$941$	11.4347	−	35.1922i	0.372759	−	1.14723i	0.944978	−	0.327133i	$-0.106083\pi$
$942$	−6.13534	−	4.45759i	−0.199900	−	0.145236i
$943$	−51.3999			−1.67381
$944$	−7.30893	−	5.31025i	−0.237885	−	0.172834i
$945$	−5.60734	+	1.84013i	−0.182407	+	0.0598595i
$946$	−10.0127	+	7.27463i	−0.325540	+	0.236519i
$947$	31.1403	−	22.6248i	1.01192	−	0.735206i	0.0473125	−	0.998880i	$-0.484934\pi$
$947$	31.1403	−	22.6248i	1.01192	−	0.735206i	0.964612	+	0.263674i	$0.0849343\pi$
$948$	1.16061	+	3.57200i	0.0376950	+	0.116013i
$949$	−27.0688			−0.878690
$950$	−1.87532	+	5.88895i	−0.0608435	+	0.191063i
$951$	−11.7817			−0.382048
$952$	−1.32624	−	4.08174i	−0.0429836	−	0.132290i
$953$	3.38452	−	2.45900i	0.109635	−	0.0796548i	−0.531617	−	0.846985i	$-0.678415\pi$
$953$	3.38452	−	2.45900i	0.109635	−	0.0796548i	0.641252	+	0.767330i	$0.278415\pi$
$954$	−5.66298	+	4.11440i	−0.183346	+	0.133208i
$955$	6.88844	+	2.21588i	0.222905	+	0.0717041i
$956$	2.20173	+	1.59965i	0.0712091	+	0.0517365i
$957$	43.0288			1.39092
$958$	−5.88844	−	4.27820i	−0.190247	−	0.138222i
$959$	−2.49864	+	7.69004i	−0.0806854	+	0.248324i
$960$	1.30902	−	1.81286i	0.0422483	−	0.0585099i
$961$	1.08756	+	3.34716i	0.0350825	+	0.107973i
$962$	−5.63757	+	17.3506i	−0.181762	+	0.559407i
$963$	−5.80488	+	17.8656i	−0.187060	+	0.575710i
$964$	0.463977	+	1.42798i	0.0149437	+	0.0459920i
$965$	−0.0712415	−	24.2928i	−0.00229335	−	0.782013i
$966$	3.64736	−	11.2254i	0.117352	−	0.361172i
$967$	10.0583	+	7.30775i	0.323452	+	0.235001i	0.737647	−	0.675187i	$-0.235937\pi$
$967$	10.0583	+	7.30775i	0.323452	+	0.235001i	−0.414195	+	0.910188i	$0.635937\pi$
$968$	−28.3180			−0.910174
$969$	1.62614	+	1.18146i	0.0522391	+	0.0379539i
$970$	−1.96544	+	2.72195i	−0.0631065	+	0.0873964i
$971$	−13.0873	+	9.50848i	−0.419991	+	0.305142i	−0.777634	−	0.628717i	$-0.783580\pi$
$971$	−13.0873	+	9.50848i	−0.419991	+	0.305142i	0.357643	+	0.933858i	$0.383580\pi$
$972$	−0.809017	+	0.587785i	−0.0259492	+	0.0188532i
$973$	−13.6027	−	41.8649i	−0.436083	−	1.34213i
$974$	31.4007			1.00614
$975$	−3.55060	−	10.7134i	−0.113710	−	0.343104i
$976$	−3.02122			−0.0967069
$977$	9.00047	+	27.7006i	0.287951	+	0.886221i	0.985499	+	0.169683i	$0.0542744\pi$
$977$	9.00047	+	27.7006i	0.287951	+	0.886221i	−0.697548	+	0.716538i	$0.745726\pi$
$978$	−11.3262	+	8.22899i	−0.362173	+	0.263134i
$979$	1.97878	−	1.43767i	0.0632421	−	0.0459481i
$980$	0.0453101	+	0.0619810i	0.00144738	+	0.00197991i
$981$	12.9588	+	9.41512i	0.413743	+	0.300602i
$982$	26.4753			0.844862
$983$	−16.8455	−	12.2390i	−0.537289	−	0.390364i	0.285788	−	0.958293i	$-0.407745\pi$
$983$	−16.8455	−	12.2390i	−0.537289	−	0.390364i	−0.823077	+	0.567929i	$0.807745\pi$
$984$	−3.55164	+	10.9308i	−0.113222	+	0.348462i
$985$	11.9781	+	16.3852i	0.381654	+	0.522075i
$986$	−3.44829	−	10.6128i	−0.109816	−	0.337979i
$987$	5.29990	−	16.3114i	0.168698	−	0.519198i
$988$	−0.862207	+	2.65360i	−0.0274305	+	0.0844223i
$989$	2.72768	+	8.39495i	0.0867353	+	0.266944i
$990$	13.3220	−	4.37183i	0.423402	−	0.138946i
$991$	−4.52367	+	13.9224i	−0.143699	+	0.442261i	−0.996841	−	0.0794178i	$-0.974694\pi$
$991$	−4.52367	+	13.9224i	−0.143699	+	0.442261i	0.853142	+	0.521678i	$0.174694\pi$
$992$	−4.75324	−	3.45343i	−0.150915	−	0.109646i
$993$	−13.5013			−0.428450
$994$	−20.8756	−	15.1670i	−0.662134	−	0.481068i
$995$	0.170977	+	58.3019i	0.00542034	+	1.84829i
$996$	6.77446	−	4.92193i	0.214657	−	0.155957i
$997$	3.36030	−	2.44140i	0.106422	−	0.0773198i	−0.533302	−	0.845925i	$-0.679049\pi$
$997$	3.36030	−	2.44140i	0.106422	−	0.0773198i	0.639723	+	0.768605i	$0.279049\pi$
$998$	8.71130	+	26.8106i	0.275751	+	0.848675i
$999$	8.08206			0.255705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.g.c.31.2	✓	8
3.2	odd	2		450.2.h.d.181.1		8
5.2	odd	4		750.2.h.e.349.4		16
5.3	odd	4		750.2.h.e.349.1		16
5.4	even	2		750.2.g.d.151.1		8
25.2	odd	20		3750.2.c.h.1249.3		8
25.3	odd	20		750.2.h.e.649.3		16
25.4	even	10		750.2.g.d.601.1		8
25.11	even	5		3750.2.a.l.1.3		4
25.14	even	10		3750.2.a.q.1.2		4
25.21	even	5	inner	150.2.g.c.121.2	yes	8
25.22	odd	20		750.2.h.e.649.2		16
25.23	odd	20		3750.2.c.h.1249.6		8
75.71	odd	10		450.2.h.d.271.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.c.31.2	✓	8	1.1	even	1	trivial
150.2.g.c.121.2	yes	8	25.21	even	5	inner
450.2.h.d.181.1		8	3.2	odd	2
450.2.h.d.271.1		8	75.71	odd	10
750.2.g.d.151.1		8	5.4	even	2
750.2.g.d.601.1		8	25.4	even	10
750.2.h.e.349.1		16	5.3	odd	4
750.2.h.e.349.4		16	5.2	odd	4
750.2.h.e.649.2		16	25.22	odd	20
750.2.h.e.649.3		16	25.3	odd	20
3750.2.a.l.1.3		4	25.11	even	5
3750.2.a.q.1.2		4	25.14	even	10
3750.2.c.h.1249.3		8	25.2	odd	20
3750.2.c.h.1249.6		8	25.23	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)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.00655751 + 2.23606i) q^{5} +(0.809017 + 0.587785i) q^{6} +2.63925 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.00655751 + 2.23606i) q^{5} +(0.809017 + 0.587785i) q^{6} +2.63925 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +(2.12459 - 0.697217i) q^{10} +(1.93766 + 5.96351i) q^{11} +(0.309017 - 0.951057i) q^{12} +(0.697541 - 2.14681i) q^{13} +(-0.815575 - 2.51008i) q^{14} +(-1.31963 - 1.80515i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.31557 - 0.955821i) q^{17} -1.00000 q^{18} +(1.00000 + 0.726543i) q^{19} +(-1.31963 - 1.80515i) q^{20} +(-2.13520 + 1.55131i) q^{21} +(5.07286 - 3.68565i) q^{22} +(-1.38197 - 4.25325i) q^{23} -1.00000 q^{24} +(-4.99991 + 0.0293259i) q^{25} -2.25729 q^{26} +(0.309017 + 0.951057i) q^{27} +(-2.13520 + 1.55131i) q^{28} +(-5.55164 + 4.03350i) q^{29} +(-1.30902 + 1.81286i) q^{30} +(4.75324 + 3.45343i) q^{31} -1.00000 q^{32} +(-5.07286 - 3.68565i) q^{33} +(-0.502505 + 1.54655i) q^{34} +(0.0173069 + 5.90153i) q^{35} +(0.309017 + 0.951057i) q^{36} +(2.49750 - 7.68650i) q^{37} +(0.381966 - 1.17557i) q^{38} +(0.697541 + 2.14681i) q^{39} +(-1.30902 + 1.81286i) q^{40} +(3.55164 - 10.9308i) q^{41} +(2.13520 + 1.55131i) q^{42} -1.97377 q^{43} +(-5.07286 - 3.68565i) q^{44} +(2.12864 + 0.684743i) q^{45} +(-3.61803 + 2.62866i) q^{46} +(-5.25729 + 3.81964i) q^{47} +(0.309017 + 0.951057i) q^{48} -0.0343355 q^{49} +(1.57295 + 4.74614i) q^{50} +1.62614 q^{51} +(0.697541 + 2.14681i) q^{52} +(5.66298 - 4.11440i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-13.3220 + 4.37183i) q^{55} +(2.13520 + 1.55131i) q^{56} -1.23607 q^{57} +(5.55164 + 4.03350i) q^{58} +(2.79176 - 8.59216i) q^{59} +(2.12864 + 0.684743i) q^{60} +(-0.933608 - 2.87335i) q^{61} +(1.81557 - 5.58776i) q^{62} +(0.815575 - 2.51008i) q^{63} +(0.309017 + 0.951057i) q^{64} +(4.80496 + 1.54566i) q^{65} +(-1.93766 + 5.96351i) q^{66} +(8.12451 + 5.90280i) q^{67} +1.62614 q^{68} +(3.61803 + 2.62866i) q^{69} +(5.60734 - 1.84013i) q^{70} +(7.90966 - 5.74670i) q^{71} +(0.809017 - 0.587785i) q^{72} +(-3.70565 - 11.4048i) q^{73} -8.08206 q^{74} +(4.02778 - 2.96260i) q^{75} -1.23607 q^{76} +(5.11398 + 15.7392i) q^{77} +(1.82618 - 1.32680i) q^{78} +(-3.03853 + 2.20762i) q^{79} +(2.12864 + 0.684743i) q^{80} +(-0.809017 - 0.587785i) q^{81} -11.4934 q^{82} +(6.77446 + 4.92193i) q^{83} +(0.815575 - 2.51008i) q^{84} +(2.12864 - 2.94797i) q^{85} +(0.609928 + 1.87717i) q^{86} +(2.12054 - 6.52635i) q^{87} +(-1.93766 + 5.96351i) q^{88} +(-0.120539 - 0.370980i) q^{89} +(-0.00655751 - 2.23606i) q^{90} +(1.84099 - 5.66598i) q^{91} +(3.61803 + 2.62866i) q^{92} -5.87532 q^{93} +(5.25729 + 3.81964i) q^{94} +(-1.61803 + 2.24082i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-1.21471 + 0.882537i) q^{97} +(0.0106103 + 0.0326550i) q^{98} +6.27040 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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