LMFDB - Embedded newform 138.2.e.a.133.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(13,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("138.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.e (of order $11$, degree $10$, 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:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			133.1
Root			$0.959493 + 0.281733i$ of defining polynomial
Character	$\chi$	$=$	138.133
Dual form			138.2.e.a.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.455922 - 3.17101i) q^{5} +(0.841254 - 0.540641i) q^{6} +(0.628663 + 1.37658i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.455922 - 3.17101i) q^{5} +(0.841254 - 0.540641i) q^{6} +(0.628663 + 1.37658i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-1.33083 + 2.91411i) q^{10} +(6.27358 - 1.84209i) q^{11} +(-0.959493 + 0.281733i) q^{12} +(1.19894 - 2.62531i) q^{13} +(-0.215370 - 1.49793i) q^{14} +(2.09792 + 2.42113i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-1.00654 + 0.646863i) q^{17} +(-0.142315 + 0.989821i) q^{18} +(0.467362 + 0.300355i) q^{19} +(2.09792 - 2.42113i) q^{20} +(-1.45204 - 0.426356i) q^{21} -6.53843 q^{22} +(-4.66752 - 1.10192i) q^{23} +1.00000 q^{24} +(-5.04996 - 1.48280i) q^{25} +(-1.89001 + 2.18119i) q^{26} +(0.841254 + 0.540641i) q^{27} +(-0.215370 + 1.49793i) q^{28} +(-7.29298 + 4.68691i) q^{29} +(-1.33083 - 2.91411i) q^{30} +(4.41087 + 5.09042i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(-2.71616 + 5.94756i) q^{33} +(1.14801 - 0.337086i) q^{34} +(4.65177 - 1.36588i) q^{35} +(0.415415 - 0.909632i) q^{36} +(0.206897 + 1.43900i) q^{37} +(-0.363811 - 0.419860i) q^{38} +(1.19894 + 2.62531i) q^{39} +(-2.69505 + 1.73201i) q^{40} +(0.262991 - 1.82915i) q^{41} +(1.27310 + 0.818172i) q^{42} +(-1.42353 + 1.64284i) q^{43} +(6.27358 + 1.84209i) q^{44} -3.20362 q^{45} +(4.16801 + 2.37227i) q^{46} -11.4135 q^{47} +(-0.959493 - 0.281733i) q^{48} +(3.08427 - 3.55944i) q^{49} +(4.42765 + 2.84548i) q^{50} +(0.170276 - 1.18430i) q^{51} +(2.42796 - 1.56036i) q^{52} +(5.01045 + 10.9714i) q^{53} +(-0.654861 - 0.755750i) q^{54} +(-2.98101 - 20.7334i) q^{55} +(0.628663 - 1.37658i) q^{56} +(-0.533050 + 0.156518i) q^{57} +(8.31801 - 2.44239i) q^{58} +(1.64562 - 3.60341i) q^{59} +(0.455922 + 3.17101i) q^{60} +(-5.91634 - 6.82782i) q^{61} +(-2.79806 - 6.12691i) q^{62} +(1.27310 - 0.818172i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-7.77825 - 4.99878i) q^{65} +(4.28176 - 4.94141i) q^{66} +(7.35733 + 2.16031i) q^{67} -1.19647 q^{68} +(3.88935 - 2.80588i) q^{69} -4.84815 q^{70} +(9.07303 + 2.66408i) q^{71} +(-0.654861 + 0.755750i) q^{72} +(-0.527969 - 0.339305i) q^{73} +(0.206897 - 1.43900i) q^{74} +(4.42765 - 2.84548i) q^{75} +(0.230786 + 0.505350i) q^{76} +(6.47975 + 7.47803i) q^{77} +(-0.410738 - 2.85675i) q^{78} +(-5.72115 + 12.5276i) q^{79} +(3.07385 - 0.902563i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-0.767668 + 1.68096i) q^{82} +(2.21852 + 15.4302i) q^{83} +(-0.991025 - 1.14370i) q^{84} +(1.59230 + 3.48666i) q^{85} +(1.82871 - 1.17524i) q^{86} +(1.23375 - 8.58094i) q^{87} +(-5.50048 - 3.53494i) q^{88} +(3.67930 - 4.24613i) q^{89} +(3.07385 + 0.902563i) q^{90} +4.36768 q^{91} +(-3.33083 - 3.45045i) q^{92} -6.73559 q^{93} +(10.9512 + 3.21556i) q^{94} +(1.16551 - 1.34507i) q^{95} +(0.841254 + 0.540641i) q^{96} +(1.03139 - 7.17350i) q^{97} +(-3.96215 + 2.54632i) q^{98} +(-2.71616 - 5.94756i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{3} - q^{4} + 8 q^{5} - q^{6} + 8 q^{7} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 - q^3 - q^4 + 8 * q^5 - q^6 + 8 * q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} + 8 q^{5} - q^{6} + 8 q^{7} - q^{8} - q^{9} - 3 q^{10} + 7 q^{11} - q^{12} + 3 q^{13} - 3 q^{14} - 3 q^{15} - q^{16} + 4 q^{17} - q^{18} - 3 q^{20} - 3 q^{21} - 26 q^{22} - 12 q^{23} + 10 q^{24} - 15 q^{25} + 3 q^{26} - q^{27} - 3 q^{28} - 25 q^{29} - 3 q^{30} + 6 q^{31} - q^{32} - 4 q^{33} - 7 q^{34} + 2 q^{35} - q^{36} + 9 q^{37} + 11 q^{38} + 3 q^{39} - 3 q^{40} + 24 q^{41} + 8 q^{42} - 30 q^{43} + 7 q^{44} - 14 q^{45} + 21 q^{46} - 48 q^{47} - q^{48} + 9 q^{49} + 7 q^{50} + 15 q^{51} + 14 q^{52} + 15 q^{53} - q^{54} - 23 q^{55} + 8 q^{56} - 11 q^{57} - 3 q^{58} + 5 q^{59} + 8 q^{60} + 12 q^{61} + 28 q^{62} + 8 q^{63} - q^{64} - 13 q^{65} + 18 q^{66} + 18 q^{67} - 18 q^{68} - q^{69} + 2 q^{70} + 28 q^{71} - q^{72} + 19 q^{73} + 9 q^{74} + 7 q^{75} + 22 q^{76} - 12 q^{77} - 8 q^{78} - 52 q^{79} + 8 q^{80} - q^{81} - 20 q^{82} + 7 q^{83} - 3 q^{84} + 23 q^{85} + 14 q^{86} + 30 q^{87} - 4 q^{88} + 3 q^{89} + 8 q^{90} + 42 q^{91} - 23 q^{92} - 16 q^{93} + 29 q^{94} + 22 q^{95} - q^{96} + 51 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 + 8 * q^5 - q^6 + 8 * q^7 - q^8 - q^9 - 3 * q^10 + 7 * q^11 - q^12 + 3 * q^13 - 3 * q^14 - 3 * q^15 - q^16 + 4 * q^17 - q^18 - 3 * q^20 - 3 * q^21 - 26 * q^22 - 12 * q^23 + 10 * q^24 - 15 * q^25 + 3 * q^26 - q^27 - 3 * q^28 - 25 * q^29 - 3 * q^30 + 6 * q^31 - q^32 - 4 * q^33 - 7 * q^34 + 2 * q^35 - q^36 + 9 * q^37 + 11 * q^38 + 3 * q^39 - 3 * q^40 + 24 * q^41 + 8 * q^42 - 30 * q^43 + 7 * q^44 - 14 * q^45 + 21 * q^46 - 48 * q^47 - q^48 + 9 * q^49 + 7 * q^50 + 15 * q^51 + 14 * q^52 + 15 * q^53 - q^54 - 23 * q^55 + 8 * q^56 - 11 * q^57 - 3 * q^58 + 5 * q^59 + 8 * q^60 + 12 * q^61 + 28 * q^62 + 8 * q^63 - q^64 - 13 * q^65 + 18 * q^66 + 18 * q^67 - 18 * q^68 - q^69 + 2 * q^70 + 28 * q^71 - q^72 + 19 * q^73 + 9 * q^74 + 7 * q^75 + 22 * q^76 - 12 * q^77 - 8 * q^78 - 52 * q^79 + 8 * q^80 - q^81 - 20 * q^82 + 7 * q^83 - 3 * q^84 + 23 * q^85 + 14 * q^86 + 30 * q^87 - 4 * q^88 + 3 * q^89 + 8 * q^90 + 42 * q^91 - 23 * q^92 - 16 * q^93 + 29 * q^94 + 22 * q^95 - q^96 + 51 * q^97 - 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	0.455922	−	3.17101i	0.203895	−	1.41812i	−0.588692	−	0.808358i	$-0.700357\pi$
$5$	0.455922	−	3.17101i	0.203895	−	1.41812i	0.792586	−	0.609760i	$-0.208734\pi$
$6$	0.841254	−	0.540641i	0.343440	−	0.220716i
$7$	0.628663	+	1.37658i	0.237612	+	0.520298i	0.990444	−	0.137915i	$-0.0440399\pi$
$7$	0.628663	+	1.37658i	0.237612	+	0.520298i	−0.752832	+	0.658213i	$0.771313\pi$
$8$	−0.654861	−	0.755750i	−0.231528	−	0.267198i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	−1.33083	+	2.91411i	−0.420845	+	0.921523i
$11$	6.27358	−	1.84209i	1.89155	−	0.555411i	0.898311	−	0.439360i	$-0.144795\pi$
$11$	6.27358	−	1.84209i	1.89155	−	0.555411i	0.993243	−	0.116051i	$-0.0370236\pi$
$12$	−0.959493	+	0.281733i	−0.276982	+	0.0813292i
$13$	1.19894	−	2.62531i	0.332526	−	0.728130i	−0.667336	−	0.744757i	$-0.732565\pi$
$13$	1.19894	−	2.62531i	0.332526	−	0.728130i	0.999862	+	0.0166269i	$0.00529276\pi$
$14$	−0.215370	−	1.49793i	−0.0575601	−	0.400340i
$15$	2.09792	+	2.42113i	0.541681	+	0.625133i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	−1.00654	+	0.646863i	−0.244121	+	0.156887i	−0.656980	−	0.753908i	$-0.728167\pi$
$17$	−1.00654	+	0.646863i	−0.244121	+	0.156887i	0.412859	+	0.910795i	$0.364530\pi$
$18$	−0.142315	+	0.989821i	−0.0335439	+	0.233303i
$19$	0.467362	+	0.300355i	0.107220	+	0.0689062i	0.593152	−	0.805090i	$-0.297883\pi$
$19$	0.467362	+	0.300355i	0.107220	+	0.0689062i	−0.485932	+	0.873997i	$0.661520\pi$
$20$	2.09792	−	2.42113i	0.469110	−	0.541381i
$21$	−1.45204	−	0.426356i	−0.316860	−	0.0930386i
$22$	−6.53843			−1.39400
$23$	−4.66752	−	1.10192i	−0.973246	−	0.229765i
$23$	−4.66752	−	1.10192i	−0.973246	−	0.229765i
$24$	1.00000			0.204124
$25$	−5.04996	−	1.48280i	−1.00999	−	0.296560i
$26$	−1.89001	+	2.18119i	−0.370661	+	0.427766i
$27$	0.841254	+	0.540641i	0.161899	+	0.104046i
$28$	−0.215370	+	1.49793i	−0.0407012	+	0.283083i
$29$	−7.29298	+	4.68691i	−1.35427	+	0.870337i	−0.997948	−	0.0640253i	$-0.979606\pi$
$29$	−7.29298	+	4.68691i	−1.35427	+	0.870337i	−0.356323	+	0.934363i	$0.615970\pi$
$30$	−1.33083	−	2.91411i	−0.242975	−	0.532041i
$31$	4.41087	+	5.09042i	0.792216	+	0.914266i	0.997928	−	0.0643467i	$-0.0204963\pi$
$31$	4.41087	+	5.09042i	0.792216	+	0.914266i	−0.205712	+	0.978613i	$0.565951\pi$
$32$	−0.142315	−	0.989821i	−0.0251579	−	0.174977i
$33$	−2.71616	+	5.94756i	−0.472823	+	1.03534i
$34$	1.14801	−	0.337086i	0.196882	−	0.0578097i
$35$	4.65177	−	1.36588i	0.786292	−	0.230876i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	0.206897	+	1.43900i	0.0340137	+	0.236570i	0.999735	−	0.0230098i	$-0.00732488\pi$
$37$	0.206897	+	1.43900i	0.0340137	+	0.236570i	−0.965722	+	0.259580i	$0.916416\pi$
$38$	−0.363811	−	0.419860i	−0.0590179	−	0.0681103i
$39$	1.19894	+	2.62531i	0.191984	+	0.420386i
$40$	−2.69505	+	1.73201i	−0.426125	+	0.273854i
$41$	0.262991	−	1.82915i	0.0410724	−	0.285665i	−0.958926	−	0.283658i	$-0.908452\pi$
$41$	0.262991	−	1.82915i	0.0410724	−	0.285665i	0.999998	−	0.00200695i	$-0.000638831\pi$
$42$	1.27310	+	0.818172i	0.196444	+	0.126247i
$43$	−1.42353	+	1.64284i	−0.217086	+	0.250531i	−0.853839	−	0.520537i	$-0.825732\pi$
$43$	−1.42353	+	1.64284i	−0.217086	+	0.250531i	0.636753	+	0.771068i	$0.280277\pi$
$44$	6.27358	+	1.84209i	0.945777	+	0.277705i
$45$	−3.20362			−0.477567
$46$	4.16801	+	2.37227i	0.614540	+	0.349773i
$47$	−11.4135			−1.66483			−0.832416	−	0.554152i	$-0.813043\pi$
$47$	−11.4135			−1.66483			−0.832416	+	0.554152i	$0.813043\pi$
$48$	−0.959493	−	0.281733i	−0.138491	−	0.0406646i
$49$	3.08427	−	3.55944i	0.440610	−	0.508491i
$50$	4.42765	+	2.84548i	0.626164	+	0.402411i
$51$	0.170276	−	1.18430i	0.0238434	−	0.165835i
$52$	2.42796	−	1.56036i	0.336698	−	0.216382i
$53$	5.01045	+	10.9714i	0.688238	+	1.50703i	0.853672	+	0.520811i	$0.174370\pi$
$53$	5.01045	+	10.9714i	0.688238	+	1.50703i	−0.165434	+	0.986221i	$0.552902\pi$
$54$	−0.654861	−	0.755750i	−0.0891153	−	0.102844i
$55$	−2.98101	−	20.7334i	−0.401960	−	2.79569i
$56$	0.628663	−	1.37658i	0.0840086	−	0.183953i
$57$	−0.533050	+	0.156518i	−0.0706042	+	0.0207313i
$58$	8.31801	−	2.44239i	1.09221	−	0.320701i
$59$	1.64562	−	3.60341i	0.214242	−	0.469125i	−0.771748	−	0.635928i	$-0.780617\pi$
$59$	1.64562	−	3.60341i	0.214242	−	0.469125i	0.985990	+	0.166804i	$0.0533446\pi$
$60$	0.455922	+	3.17101i	0.0588593	+	0.409375i
$61$	−5.91634	−	6.82782i	−0.757510	−	0.874213i	0.237764	−	0.971323i	$-0.423586\pi$
$61$	−5.91634	−	6.82782i	−0.757510	−	0.874213i	−0.995274	+	0.0971102i	$0.969040\pi$
$62$	−2.79806	−	6.12691i	−0.355355	−	0.778118i
$63$	1.27310	−	0.818172i	0.160396	−	0.103080i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	−7.77825	−	4.99878i	−0.964774	−	0.620022i
$66$	4.28176	−	4.94141i	0.527048	−	0.608246i
$67$	7.35733	+	2.16031i	0.898841	+	0.263924i	0.698337	−	0.715769i	$-0.253924\pi$
$67$	7.35733	+	2.16031i	0.898841	+	0.263924i	0.200504	+	0.979693i	$0.435742\pi$
$68$	−1.19647			−0.145094
$69$	3.88935	−	2.80588i	0.468223	−	0.337788i
$70$	−4.84815			−0.579465
$71$	9.07303	+	2.66408i	1.07677	+	0.316168i	0.771586	−	0.636125i	$-0.219464\pi$
$71$	9.07303	+	2.66408i	1.07677	+	0.316168i	0.305184	+	0.952293i	$0.401282\pi$
$72$	−0.654861	+	0.755750i	−0.0771761	+	0.0890659i
$73$	−0.527969	−	0.339305i	−0.0617941	−	0.0397127i	0.509379	−	0.860542i	$-0.329875\pi$
$73$	−0.527969	−	0.339305i	−0.0617941	−	0.0397127i	−0.571173	+	0.820830i	$0.693512\pi$
$74$	0.206897	−	1.43900i	0.0240513	−	0.167281i
$75$	4.42765	−	2.84548i	0.511261	−	0.328567i
$76$	0.230786	+	0.505350i	0.0264729	+	0.0579676i
$77$	6.47975	+	7.47803i	0.738436	+	0.852200i
$78$	−0.410738	−	2.85675i	−0.0465069	−	0.323463i
$79$	−5.72115	+	12.5276i	−0.643680	+	1.40946i	0.253298	+	0.967388i	$0.418485\pi$
$79$	−5.72115	+	12.5276i	−0.643680	+	1.40946i	−0.896978	+	0.442074i	$0.854243\pi$
$80$	3.07385	−	0.902563i	0.343667	−	0.100910i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	−0.767668	+	1.68096i	−0.0847748	+	0.185631i
$83$	2.21852	+	15.4302i	0.243515	+	1.69368i	0.634209	+	0.773161i	$0.281326\pi$
$83$	2.21852	+	15.4302i	0.243515	+	1.69368i	−0.390695	+	0.920520i	$0.627765\pi$
$84$	−0.991025	−	1.14370i	−0.108130	−	0.124788i
$85$	1.59230	+	3.48666i	0.172710	+	0.378181i
$86$	1.82871	−	1.17524i	0.197195	−	0.126729i
$87$	1.23375	−	8.58094i	0.132272	−	0.919973i
$88$	−5.50048	−	3.53494i	−0.586353	−	0.376826i
$89$	3.67930	−	4.24613i	0.390005	−	0.450089i	−0.526463	−	0.850198i	$-0.676482\pi$
$89$	3.67930	−	4.24613i	0.390005	−	0.450089i	0.916468	+	0.400109i	$0.131028\pi$
$90$	3.07385	+	0.902563i	0.324012	+	0.0951385i
$91$	4.36768			0.457857
$92$	−3.33083	−	3.45045i	−0.347263	−	0.359734i
$93$	−6.73559			−0.698448
$94$	10.9512	+	3.21556i	1.12953	+	0.331659i
$95$	1.16551	−	1.34507i	0.119579	−	0.138001i
$96$	0.841254	+	0.540641i	0.0858601	+	0.0551789i
$97$	1.03139	−	7.17350i	0.104722	−	0.728359i	−0.868030	−	0.496512i	$-0.834614\pi$
$97$	1.03139	−	7.17350i	0.104722	−	0.728359i	0.972752	−	0.231847i	$-0.0744769\pi$
$98$	−3.96215	+	2.54632i	−0.400237	+	0.257217i
$99$	−2.71616	−	5.94756i	−0.272985	−	0.597753i
$100$	−3.44663	−	3.97763i	−0.344663	−	0.397763i
$101$	0.145699	+	1.01336i	0.0144976	+	0.100833i	0.995785	−	0.0917137i	$-0.0292345\pi$
$101$	0.145699	+	1.01336i	0.0144976	+	0.100833i	−0.981288	+	0.192546i	$0.938325\pi$
$102$	−0.497033	+	1.08835i	−0.0492136	+	0.107763i
$103$	−4.36497	+	1.28167i	−0.430093	+	0.126287i	−0.489612	−	0.871940i	$-0.662862\pi$
$103$	−4.36497	+	1.28167i	−0.430093	+	0.126287i	0.0595187	+	0.998227i	$0.481043\pi$
$104$	−2.76921	+	0.813115i	−0.271544	+	0.0797325i
$105$	−2.01399	+	4.41003i	−0.196546	+	0.430375i
$106$	−1.71650	−	11.9385i	−0.166722	−	1.15957i
$107$	0.394872	+	0.455707i	0.0381738	+	0.0440549i	0.774515	−	0.632555i	$-0.217994\pi$
$107$	0.394872	+	0.455707i	0.0381738	+	0.0440549i	−0.736342	+	0.676610i	$0.763448\pi$
$108$	0.415415	+	0.909632i	0.0399733	+	0.0875294i
$109$	−4.94301	+	3.17668i	−0.473454	+	0.304271i	−0.755521	−	0.655124i	$-0.772616\pi$
$109$	−4.94301	+	3.17668i	−0.473454	+	0.304271i	0.282067	+	0.959395i	$0.408980\pi$
$110$	−2.98101	+	20.7334i	−0.284229	+	1.97685i
$111$	−1.22301	−	0.785983i	−0.116083	−	0.0746022i
$112$	−0.991025	+	1.14370i	−0.0936431	+	0.108070i
$113$	−11.8091	−	3.46746i	−1.11091	−	0.326191i	−0.325729	−	0.945463i	$-0.605610\pi$
$113$	−11.8091	−	3.46746i	−1.11091	−	0.326191i	−0.785177	+	0.619272i	$0.787428\pi$
$114$	0.555554			0.0520324
$115$	−5.62221	+	14.2984i	−0.524274	+	1.33333i
$116$	−8.66918			−0.804913
$117$	−2.76921	−	0.813115i	−0.256014	−	0.0751725i
$118$	−2.59416	+	2.99382i	−0.238812	+	0.275604i
$119$	−1.52323	−	0.978921i	−0.139634	−	0.0897375i
$120$	0.455922	−	3.17101i	0.0416198	−	0.289472i
$121$	26.7107	−	17.1659i	2.42824	−	1.56054i
$122$	3.75307	+	8.21807i	0.339787	+	0.744029i
$123$	1.21015	+	1.39659i	0.109116	+	0.125926i
$124$	0.958574	+	6.66703i	0.0860825	+	0.598717i
$125$	−0.350212	+	0.766857i	−0.0313239	+	0.0685898i
$126$	−1.45204	+	0.426356i	−0.129358	+	0.0379828i
$127$	−8.51054	+	2.49892i	−0.755188	+	0.221743i	−0.636594	−	0.771199i	$-0.719657\pi$
$127$	−8.51054	+	2.49892i	−0.755188	+	0.221743i	−0.118595	+	0.992943i	$0.537839\pi$
$128$	0.415415	−	0.909632i	0.0367178	−	0.0804009i
$129$	−0.309362	−	2.15166i	−0.0272378	−	0.189443i
$130$	6.05486	+	6.98768i	0.531046	+	0.612860i
$131$	5.20867	+	11.4054i	0.455083	+	0.996493i	0.988581	+	0.150692i	$0.0481501\pi$
$131$	5.20867	+	11.4054i	0.455083	+	0.996493i	−0.533498	+	0.845802i	$0.679123\pi$
$132$	−5.50048	+	3.53494i	−0.478755	+	0.307677i
$133$	−0.119650	+	0.832183i	−0.0103750	+	0.0721594i
$134$	−6.45068	−	4.14560i	−0.557254	−	0.358125i
$135$	2.09792	−	2.42113i	0.180560	−	0.208378i
$136$	1.14801	+	0.337086i	0.0984409	+	0.0289049i
$137$	−13.6483			−1.16606			−0.583028	−	0.812452i	$-0.698132\pi$
$137$	−13.6483			−1.16606			−0.583028	+	0.812452i	$0.698132\pi$
$138$	−4.52231	+	1.59646i	−0.384965	+	0.135900i
$139$	−11.6537			−0.988455			−0.494227	−	0.869333i	$-0.664549\pi$
$139$	−11.6537			−0.988455			−0.494227	+	0.869333i	$0.664549\pi$
$140$	4.65177	+	1.36588i	0.393146	+	0.115438i
$141$	7.47426	−	8.62575i	0.629446	−	0.726420i
$142$	−7.95495	−	5.11234i	−0.667565	−	0.429018i
$143$	2.68558	−	18.6786i	0.224580	−	1.56199i
$144$	0.841254	−	0.540641i	0.0701045	−	0.0450534i
$145$	11.5372	+	25.2629i	0.958112	+	2.09797i
$146$	0.410989	+	0.474307i	0.0340137	+	0.0392539i
$147$	0.670276	+	4.66187i	0.0552834	+	0.384505i
$148$	−0.603930	+	1.32242i	−0.0496428	+	0.108702i
$149$	−16.6025	+	4.87494i	−1.36013	+	0.399371i	−0.878809	−	0.477173i	$-0.841661\pi$
$149$	−16.6025	+	4.87494i	−1.36013	+	0.399371i	−0.481322	+	0.876544i	$0.659843\pi$
$150$	−5.04996	+	1.48280i	−0.412327	+	0.121070i
$151$	−2.00749	+	4.39579i	−0.163367	+	0.357724i	−0.973557	−	0.228443i	$-0.926637\pi$
$151$	−2.00749	+	4.39579i	−0.163367	+	0.357724i	0.810190	+	0.586167i	$0.199364\pi$
$152$	−0.0790636	−	0.549899i	−0.00641291	−	0.0446027i
$153$	0.783524	+	0.904235i	0.0633441	+	0.0731030i
$154$	−4.11047	−	9.00067i	−0.331231	−	0.725295i
$155$	18.1528	−	11.6661i	1.45807	−	0.937042i
$156$	−0.410738	+	2.85675i	−0.0328854	+	0.228723i
$157$	−4.24859	−	2.73040i	−0.339075	−	0.217910i	0.360011	−	0.932948i	$-0.382773\pi$
$157$	−4.24859	−	2.73040i	−0.339075	−	0.217910i	−0.699086	+	0.715038i	$0.746409\pi$
$158$	9.01883	−	10.4083i	0.717500	−	0.828039i
$159$	−11.5727	−	3.39807i	−0.917779	−	0.269484i
$160$	−3.20362			−0.253268
$161$	−1.41742	−	7.11795i	−0.111709	−	0.560973i
$162$	1.00000			0.0785674
$163$	−3.42292	−	1.00506i	−0.268104	−	0.0787225i	0.144917	−	0.989444i	$-0.453708\pi$
$163$	−3.42292	−	1.00506i	−0.268104	−	0.0787225i	−0.413021	+	0.910721i	$0.635527\pi$
$164$	1.21015	−	1.39659i	0.0944971	−	0.109055i
$165$	17.6214	+	11.3246i	1.37183	+	0.881618i
$166$	2.21852	−	15.4302i	0.172191	−	1.19761i
$167$	3.83643	−	2.46553i	0.296872	−	0.190788i	−0.383722	−	0.923449i	$-0.625358\pi$
$167$	3.83643	−	2.46553i	0.296872	−	0.190788i	0.680594	+	0.732660i	$0.261722\pi$
$168$	0.628663	+	1.37658i	0.0485024	+	0.106205i
$169$	3.05839	+	3.52957i	0.235261	+	0.271506i
$170$	−0.545499	−	3.79403i	−0.0418378	−	0.290989i
$171$	0.230786	−	0.505350i	0.0176486	−	0.0386451i
$172$	−2.08574	+	0.612427i	−0.159036	+	0.0466971i
$173$	14.9808	−	4.39875i	1.13897	−	0.334431i	0.342740	−	0.939430i	$-0.388645\pi$
$173$	14.9808	−	4.39875i	1.13897	−	0.334431i	0.796226	+	0.605000i	$0.206827\pi$
$174$	−3.60131	+	7.88576i	−0.273014	+	0.597818i
$175$	−1.13353	−	7.88385i	−0.0856866	−	0.595963i
$176$	4.28176	+	4.94141i	0.322750	+	0.372473i
$177$	1.64562	+	3.60341i	0.123693	+	0.270849i
$178$	−4.72653	+	3.03756i	−0.354269	+	0.227675i
$179$	−0.911557	+	6.34002i	−0.0681330	+	0.473875i	0.926978	+	0.375115i	$0.122397\pi$
$179$	−0.911557	+	6.34002i	−0.0681330	+	0.473875i	−0.995111	+	0.0987602i	$0.968512\pi$
$180$	−2.69505	−	1.73201i	−0.200877	−	0.129096i
$181$	14.4962	−	16.7295i	1.07750	−	1.24350i	0.109112	−	0.994029i	$-0.465199\pi$
$181$	14.4962	−	16.7295i	1.07750	−	1.24350i	0.968383	−	0.249467i	$-0.0802554\pi$
$182$	−4.19075	−	1.23052i	−0.310639	−	0.0912120i
$183$	9.03450			0.667850
$184$	2.22381	+	4.24908i	0.163941	+	0.313246i
$185$	4.65742			0.342420
$186$	6.46275	+	1.89763i	0.473872	+	0.139141i
$187$	−5.12301	+	5.91227i	−0.374632	+	0.432348i
$188$	−9.60165	−	6.17061i	−0.700273	−	0.450038i
$189$	−0.215370	+	1.49793i	−0.0156659	+	0.108959i
$190$	−1.49725	+	0.962223i	−0.108622	+	0.0698070i
$191$	−0.892788	−	1.95493i	−0.0645999	−	0.141454i	0.874578	−	0.484884i	$-0.161138\pi$
$191$	−0.892788	−	1.95493i	−0.0645999	−	0.141454i	−0.939178	+	0.343430i	$0.888411\pi$
$192$	−0.654861	−	0.755750i	−0.0472605	−	0.0545415i
$193$	1.60048	+	11.1316i	0.115205	+	0.801267i	0.962721	+	0.270497i	$0.0871880\pi$
$193$	1.60048	+	11.1316i	0.115205	+	0.801267i	−0.847516	+	0.530770i	$0.821903\pi$
$194$	−3.01062	+	6.59235i	−0.216150	+	0.473303i
$195$	8.87150	−	2.60491i	0.635301	−	0.186541i
$196$	4.51903	−	1.32691i	0.322788	−	0.0947791i
$197$	4.32551	−	9.47155i	0.308180	−	0.674820i	−0.690650	−	0.723190i	$-0.742675\pi$
$197$	4.32551	−	9.47155i	0.308180	−	0.674820i	0.998830	+	0.0483697i	$0.0154026\pi$
$198$	0.930515	+	6.47188i	0.0661289	+	0.459936i
$199$	−9.88825	−	11.4117i	−0.700960	−	0.808950i	0.287922	−	0.957654i	$-0.407036\pi$
$199$	−9.88825	−	11.4117i	−0.700960	−	0.808950i	−0.988882	+	0.148703i	$0.952490\pi$
$200$	2.18639	+	4.78753i	0.154601	+	0.338530i
$201$	−6.45068	+	4.14560i	−0.454996	+	0.292408i
$202$	0.145699	−	1.01336i	0.0102513	−	0.0712995i
$203$	−11.0367	−	7.09288i	−0.774627	−	0.497822i
$204$	0.783524	−	0.904235i	0.0548576	−	0.0633091i
$205$	−5.68033	−	1.66790i	−0.396732	−	0.116491i
$206$	4.54925			0.316961
$207$	−0.426443	+	4.77683i	−0.0296398	+	0.332013i
$208$	2.88612			0.200117
$209$	3.48531	+	1.02338i	0.241084	+	0.0707887i
$210$	3.17486	−	3.66399i	0.219086	−	0.252839i
$211$	9.65999	+	6.20810i	0.665021	+	0.427383i	0.829127	−	0.559060i	$-0.188838\pi$
$211$	9.65999	+	6.20810i	0.665021	+	0.427383i	−0.164107	+	0.986443i	$0.552474\pi$
$212$	−1.71650	+	11.9385i	−0.117890	+	0.819943i
$213$	−7.95495	+	5.11234i	−0.545064	+	0.350291i
$214$	−0.250490	−	0.548496i	−0.0171231	−	0.0374944i
$215$	4.56044	+	5.26303i	0.311019	+	0.358936i
$216$	−0.142315	−	0.989821i	−0.00968330	−	0.0673488i
$217$	−4.23441	+	9.27207i	−0.287451	+	0.629429i
$218$	5.63776	−	1.65539i	0.381837	−	0.112117i
$219$	0.602176	−	0.176815i	0.0406913	−	0.0119480i
$220$	8.70154	−	19.0537i	0.586658	−	1.28460i
$221$	0.491437	+	3.41802i	0.0330577	+	0.229921i
$222$	0.952036	+	1.09871i	0.0638965	+	0.0737405i
$223$	−6.56619	−	14.3779i	−0.439704	−	0.962818i	−0.991652	−	0.128940i	$-0.958843\pi$
$223$	−6.56619	−	14.3779i	−0.439704	−	0.962818i	0.551948	−	0.833879i	$-0.313885\pi$
$224$	1.27310	−	0.818172i	0.0850626	−	0.0546664i
$225$	−0.749025	+	5.20958i	−0.0499350	+	0.347305i
$226$	10.3538	+	6.65401i	0.688727	+	0.442618i
$227$	1.69916	−	1.96094i	0.112777	−	0.130152i	−0.696554	−	0.717504i	$-0.745284\pi$
$227$	1.69916	−	1.96094i	0.112777	−	0.130152i	0.809331	+	0.587352i	$0.199830\pi$
$228$	−0.533050	−	0.156518i	−0.0353021	−	0.0103656i
$229$	9.99374			0.660405			0.330202	−	0.943910i	$-0.392883\pi$
$229$	9.99374			0.660405			0.330202	+	0.943910i	$0.392883\pi$
$230$	9.42279	−	12.1352i	0.621320	−	0.800173i
$231$	−9.89485			−0.651033
$232$	8.31801	+	2.44239i	0.546104	+	0.160351i
$233$	17.8743	−	20.6280i	1.17098	−	1.35139i	0.246971	−	0.969023i	$-0.420565\pi$
$233$	17.8743	−	20.6280i	1.17098	−	1.35139i	0.924012	−	0.382363i	$-0.124890\pi$
$234$	2.42796	+	1.56036i	0.158721	+	0.102004i
$235$	−5.20367	+	36.1923i	−0.339450	+	2.36093i
$236$	3.33254	−	2.14169i	0.216930	−	0.139412i
$237$	−5.72115	−	12.5276i	−0.371629	−	0.813754i
$238$	1.18574	+	1.36841i	0.0768598	+	0.0887010i
$239$	−2.03776	−	14.1729i	−0.131812	−	0.916771i	−0.943191	−	0.332251i	$-0.892192\pi$
$239$	−2.03776	−	14.1729i	−0.131812	−	0.916771i	0.811379	−	0.584520i	$-0.198717\pi$
$240$	−1.33083	+	2.91411i	−0.0859047	+	0.188105i
$241$	−13.6207	+	3.99940i	−0.877387	+	0.257624i	−0.689254	−	0.724520i	$-0.742062\pi$
$241$	−13.6207	+	3.99940i	−0.877387	+	0.257624i	−0.188133	+	0.982144i	$0.560244\pi$
$242$	−30.4649	+	8.94531i	−1.95836	+	0.575026i
$243$	0.415415	−	0.909632i	0.0266489	−	0.0583529i
$244$	−1.28574	−	8.94254i	−0.0823113	−	0.572488i
$245$	−9.88082	−	11.4031i	−0.631262	−	0.728515i
$246$	−0.767668	−	1.68096i	−0.0489447	−	0.107174i
$247$	1.34886	−	0.866862i	0.0858262	−	0.0551571i
$248$	0.958574	−	6.66703i	0.0608695	−	0.423357i
$249$	−13.1142	−	8.42797i	−0.831077	−	0.534101i
$250$	0.552075	−	0.637128i	0.0349163	−	0.0402955i
$251$	−11.4799	−	3.37080i	−0.724604	−	0.212763i	−0.101426	−	0.994843i	$-0.532341\pi$
$251$	−11.4799	−	3.37080i	−0.724604	−	0.212763i	−0.623178	+	0.782080i	$0.714159\pi$
$252$	1.51334			0.0953313
$253$	−31.3119	+	1.68503i	−1.96856	+	0.105937i
$254$	8.86983			0.556543
$255$	−3.67778	−	1.07989i	−0.230311	−	0.0676255i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	21.8698	+	14.0549i	1.36420	+	0.876720i	0.998539	−	0.0540274i	$-0.0172058\pi$
$257$	21.8698	+	14.0549i	1.36420	+	0.876720i	0.365663	+	0.930747i	$0.380842\pi$
$258$	−0.309362	+	2.15166i	−0.0192601	+	0.133957i
$259$	−1.85083	+	1.18946i	−0.115005	+	0.0739093i
$260$	−3.84094	−	8.41048i	−0.238205	−	0.521596i
$261$	5.67710	+	6.55173i	0.351404	+	0.405542i
$262$	−1.78441	−	12.4108i	−0.110241	−	0.766744i
$263$	2.38558	−	5.22370i	0.147101	−	0.322107i	−0.821710	−	0.569906i	$-0.806980\pi$
$263$	2.38558	−	5.22370i	0.147101	−	0.322107i	0.968812	+	0.247798i	$0.0797070\pi$
$264$	6.27358	−	1.84209i	0.386112	−	0.113373i
$265$	37.0746	−	10.8861i	2.27748	−	0.668727i
$266$	0.349256	−	0.764765i	0.0214143	−	0.0468907i
$267$	0.799587	+	5.56125i	0.0489339	+	0.340343i
$268$	5.02143	+	5.79504i	0.306733	+	0.353988i
$269$	3.39779	+	7.44012i	0.207167	+	0.453632i	0.984483	−	0.175477i	$-0.0561469\pi$
$269$	3.39779	+	7.44012i	0.207167	+	0.453632i	−0.777317	+	0.629110i	$0.783420\pi$
$270$	−2.69505	+	1.73201i	−0.164016	+	0.105406i
$271$	1.92200	−	13.3678i	0.116753	−	0.812036i	−0.844339	−	0.535809i	$-0.820007\pi$
$271$	1.92200	−	13.3678i	0.116753	−	0.812036i	0.961092	−	0.276227i	$-0.0890841\pi$
$272$	−1.00654	−	0.646863i	−0.0610303	−	0.0392218i
$273$	−2.86022	+	3.30087i	−0.173108	+	0.199778i
$274$	13.0955	+	3.84518i	0.791127	+	0.232296i
$275$	−34.4128			−2.07517
$276$	4.78890	−	0.257712i	0.288258	−	0.0155125i
$277$	14.9697			0.899440			0.449720	−	0.893169i	$-0.351524\pi$
$277$	14.9697			0.899440			0.449720	+	0.893169i	$0.351524\pi$
$278$	11.1817	+	3.28323i	0.670631	+	0.196915i
$279$	4.41087	−	5.09042i	0.264072	−	0.304755i
$280$	−4.07852	−	2.62111i	−0.243738	−	0.156641i
$281$	−3.83880	+	26.6994i	−0.229003	+	1.59275i	0.473317	+	0.880892i	$0.343056\pi$
$281$	−3.83880	+	26.6994i	−0.229003	+	1.59275i	−0.702320	+	0.711861i	$0.747853\pi$
$282$	−9.60165	+	6.17061i	−0.571770	+	0.367454i
$283$	5.69920	+	12.4795i	0.338783	+	0.741830i	0.999965	−	0.00839502i	$-0.00267225\pi$
$283$	5.69920	+	12.4795i	0.338783	+	0.741830i	−0.661182	+	0.750225i	$0.729945\pi$
$284$	6.19241	+	7.14642i	0.367452	+	0.424062i
$285$	0.253289	+	1.76167i	0.0150036	+	0.104352i
$286$	−7.83918	+	17.1654i	−0.463540	+	1.01501i
$287$	2.68330	−	0.787887i	0.158390	−	0.0465075i
$288$	−0.959493	+	0.281733i	−0.0565387	+	0.0166013i
$289$	−6.46737	+	14.1616i	−0.380433	+	0.833033i
$290$	−3.95247	−	27.4900i	−0.232097	−	1.61427i
$291$	4.74595	+	5.47712i	0.278213	+	0.321074i
$292$	−0.260714	−	0.570883i	−0.0152571	−	0.0334084i
$293$	7.74373	−	4.97659i	0.452393	−	0.290736i	−0.294534	−	0.955641i	$-0.595165\pi$
$293$	7.74373	−	4.97659i	0.452393	−	0.290736i	0.746928	+	0.664905i	$0.231528\pi$
$294$	0.670276	−	4.66187i	0.0390913	−	0.271886i
$295$	−10.6762	−	6.86116i	−0.621591	−	0.399472i
$296$	0.952036	−	1.09871i	0.0553360	−	0.0638611i
$297$	6.27358	+	1.84209i	0.364030	+	0.106889i
$298$	17.3034			1.00236
$299$	−8.48895	+	10.9326i	−0.490928	+	0.632247i
$300$	5.26315			0.303868
$301$	−3.15642	−	0.926809i	−0.181933	−	0.0534204i
$302$	3.16461	−	3.65215i	0.182103	−	0.210158i
$303$	−0.861256	−	0.553496i	−0.0494779	−	0.0317975i
$304$	−0.0790636	+	0.549899i	−0.00453461	+	0.0315389i
$305$	−24.3485	+	15.6478i	−1.39419	+	0.895991i
$306$	−0.497033	−	1.08835i	−0.0284135	−	0.0622169i
$307$	−1.15044	−	1.32767i	−0.0656588	−	0.0757743i	0.721970	−	0.691924i	$-0.243237\pi$
$307$	−1.15044	−	1.32767i	−0.0656588	−	0.0757743i	−0.787629	+	0.616150i	$0.788691\pi$
$308$	1.40818	+	9.79413i	0.0802387	+	0.558072i
$309$	1.88983	−	4.13814i	0.107508	−	0.235411i
$310$	−20.7042	+	6.07929i	−1.17592	+	0.345281i
$311$	−29.1330	+	8.55421i	−1.65198	+	0.485065i	−0.969347	−	0.245697i	$-0.920983\pi$
$311$	−29.1330	+	8.55421i	−1.65198	+	0.485065i	−0.682632	+	0.730762i	$0.739165\pi$
$312$	1.19894	−	2.62531i	0.0678765	−	0.148629i
$313$	−1.56820	−	10.9071i	−0.0886398	−	0.616503i	−0.984919	−	0.173014i	$-0.944649\pi$
$313$	−1.56820	−	10.9071i	−0.0886398	−	0.616503i	0.896280	−	0.443489i	$-0.146260\pi$
$314$	3.30725	+	3.81677i	0.186639	+	0.215393i
$315$	−2.01399	−	4.41003i	−0.113476	−	0.248477i
$316$	−11.5859	+	7.44578i	−0.651756	+	0.418858i
$317$	1.44409	−	10.0439i	0.0811081	−	0.564119i	−0.908229	−	0.418474i	$-0.862565\pi$
$317$	1.44409	−	10.0439i	0.0811081	−	0.564119i	0.989337	−	0.145645i	$-0.0465258\pi$
$318$	10.1466	+	6.52084i	0.568994	+	0.365670i
$319$	−37.1193	+	42.8380i	−2.07828	+	2.39847i
$320$	3.07385	+	0.902563i	0.171833	+	0.0504548i
$321$	−0.602987			−0.0336554
$322$	−0.645351	+	7.22896i	−0.0359640	+	0.402854i
$323$	−0.664706			−0.0369852
$324$	−0.959493	−	0.281733i	−0.0533052	−	0.0156518i
$325$	−9.94740	+	11.4799i	−0.551783	+	0.636791i
$326$	3.00111	+	1.92870i	0.166216	+	0.106821i
$327$	0.836209	−	5.81596i	0.0462424	−	0.321623i
$328$	−1.55460	+	0.999080i	−0.0858384	+	0.0551650i
$329$	−7.17525	−	15.7116i	−0.395584	−	0.866209i
$330$	−13.7171	−	15.8304i	−0.755102	−	0.871434i
$331$	−4.23799	−	29.4759i	−0.232941	−	1.62014i	−0.685270	−	0.728289i	$-0.740316\pi$
$331$	−4.23799	−	29.4759i	−0.232941	−	1.62014i	0.452329	−	0.891851i	$-0.350593\pi$
$332$	−6.47584	+	14.1801i	−0.355408	+	0.778235i
$333$	1.39491	−	0.409583i	0.0764406	−	0.0224450i
$334$	−4.37565	+	1.28481i	−0.239425	+	0.0703015i
$335$	10.2047	−	22.3452i	0.557544	−	1.22085i
$336$	−0.215370	−	1.49793i	−0.0117494	−	0.0817190i
$337$	12.4809	+	14.4037i	0.679876	+	0.784619i	0.985888	−	0.167409i	$-0.0535400\pi$
$337$	12.4809	+	14.4037i	0.679876	+	0.784619i	−0.306011	+	0.952028i	$0.598995\pi$
$338$	−1.94011	−	4.24825i	−0.105528	−	0.231074i
$339$	10.3538	−	6.65401i	0.562344	−	0.361396i
$340$	−0.545499	+	3.79403i	−0.0295838	+	0.205760i
$341$	37.0489	+	23.8099i	2.00631	+	1.28938i
$342$	−0.363811	+	0.419860i	−0.0196726	+	0.0227034i
$343$	17.0031	+	4.99255i	0.918080	+	0.269572i
$344$	2.17379			0.117203
$345$	−7.12422	−	13.6124i	−0.383555	−	0.732868i
$346$	−15.6132			−0.839371
$347$	11.6990	+	3.43514i	0.628036	+	0.184408i	0.580235	−	0.814449i	$-0.302961\pi$
$347$	11.6990	+	3.43514i	0.628036	+	0.184408i	0.0478007	+	0.998857i	$0.484779\pi$
$348$	5.67710	−	6.55173i	0.304325	−	0.351209i
$349$	−12.9571	−	8.32704i	−0.693579	−	0.445736i	0.145778	−	0.989317i	$-0.453432\pi$
$349$	−12.9571	−	8.32704i	−0.693579	−	0.445736i	−0.839357	+	0.543581i	$0.817068\pi$
$350$	−1.13353	+	7.88385i	−0.0605896	+	0.421410i
$351$	2.42796	−	1.56036i	0.129595	−	0.0832856i
$352$	−2.71616	−	5.94756i	−0.144772	−	0.317006i
$353$	−12.1351	−	14.0046i	−0.645886	−	0.745392i	0.334518	−	0.942389i	$-0.391426\pi$
$353$	−12.1351	−	14.0046i	−0.645886	−	0.745392i	−0.980404	+	0.196997i	$0.936881\pi$
$354$	−0.563766	−	3.92108i	−0.0299638	−	0.208403i
$355$	12.5844	−	27.5560i	0.667912	−	1.46252i
$356$	5.39085	−	1.58290i	0.285715	−	0.0838934i
$357$	1.73732	−	0.510124i	0.0919489	−	0.0269986i
$358$	2.66082	−	5.82639i	0.140629	−	0.307934i
$359$	1.67363	+	11.6404i	0.0883310	+	0.614356i	0.985116	+	0.171890i	$0.0549873\pi$
$359$	1.67363	+	11.6404i	0.0883310	+	0.614356i	−0.896785	+	0.442466i	$0.854104\pi$
$360$	2.09792	+	2.42113i	0.110570	+	0.127605i
$361$	−7.76467	−	17.0023i	−0.408667	−	0.894856i
$362$	−18.6223	+	11.9678i	−0.978765	+	0.629014i
$363$	−4.51865	+	31.4279i	−0.237167	+	1.64954i
$364$	3.67432	+	2.36134i	0.192587	+	0.123768i
$365$	−1.31665	+	1.51950i	−0.0689167	+	0.0795341i
$366$	−8.66854	−	2.54531i	−0.453112	−	0.133046i
$367$	−7.81907			−0.408152			−0.204076	−	0.978955i	$-0.565419\pi$
$367$	−7.81907			−0.408152			−0.204076	+	0.978955i	$0.565419\pi$
$368$	−0.936621	−	4.70348i	−0.0488247	−	0.245186i
$369$	−1.84796			−0.0962007
$370$	−4.46876	−	1.31215i	−0.232320	−	0.0682152i
$371$	−11.9531	+	13.7946i	−0.620572	+	0.716179i
$372$	−5.66634	−	3.64153i	−0.293786	−	0.188805i
$373$	−0.304293	+	2.11640i	−0.0157557	+	0.109583i	−0.996182	−	0.0873051i	$-0.972175\pi$
$373$	−0.304293	+	2.11640i	−0.0157557	+	0.109583i	0.980426	+	0.196888i	$0.0630836\pi$
$374$	6.58118	−	4.22946i	0.340304	−	0.218700i
$375$	−0.350212	−	0.766857i	−0.0180849	−	0.0396003i
$376$	7.47426	+	8.62575i	0.385455	+	0.444839i
$377$	3.56076	+	24.7656i	0.183389	+	1.27550i
$378$	0.628663	−	1.37658i	0.0323349	−	0.0708036i
$379$	20.7946	−	6.10585i	1.06815	−	0.313636i	0.300019	−	0.953933i	$-0.403007\pi$
$379$	20.7946	−	6.10585i	1.06815	−	0.313636i	0.768128	+	0.640297i	$0.221189\pi$
$380$	1.70769	−	0.501423i	0.0876026	−	0.0257224i
$381$	3.68466	−	8.06828i	0.188771	−	0.413351i
$382$	0.305856	+	2.12727i	0.0156489	+	0.108841i
$383$	−3.28069	−	3.78612i	−0.167635	−	0.193462i	0.665716	−	0.746205i	$-0.268126\pi$
$383$	−3.28069	−	3.78612i	−0.167635	−	0.193462i	−0.833351	+	0.552744i	$0.813581\pi$
$384$	0.415415	+	0.909632i	0.0211991	+	0.0464195i
$385$	26.6671	−	17.1379i	1.35908	−	0.873430i
$386$	1.60048	−	11.1316i	0.0814620	−	0.566581i
$387$	1.82871	+	1.17524i	0.0929584	+	0.0597408i
$388$	4.74595	−	5.47712i	0.240939	−	0.278059i
$389$	5.77784	+	1.69653i	0.292948	+	0.0860174i	0.424905	−	0.905238i	$-0.360308\pi$
$389$	5.77784	+	1.69653i	0.292948	+	0.0860174i	−0.131956	+	0.991256i	$0.542126\pi$
$390$	−9.24603			−0.468191
$391$	5.41083	−	1.91013i	0.273637	−	0.0965992i
$392$	−4.70981			−0.237881
$393$	−12.0306	−	3.53249i	−0.606862	−	0.178191i
$394$	−6.81874	+	7.86925i	−0.343523	+	0.396447i
$395$	37.1166	+	23.8534i	1.86754	+	1.20020i
$396$	0.930515	−	6.47188i	0.0467602	−	0.325224i
$397$	20.1916	−	12.9763i	1.01339	−	0.651263i	0.0751183	−	0.997175i	$-0.476067\pi$
$397$	20.1916	−	12.9763i	1.01339	−	0.651263i	0.938267	+	0.345911i	$0.112430\pi$
$398$	6.27267	+	13.7352i	0.314421	+	0.688485i
$399$	−0.550568	−	0.635389i	−0.0275629	−	0.0318093i
$400$	−0.749025	−	5.20958i	−0.0374512	−	0.260479i
$401$	−6.01379	+	13.1684i	−0.300314	+	0.657596i	−0.998286	−	0.0585293i	$-0.981359\pi$
$401$	−6.01379	+	13.1684i	−0.300314	+	0.657596i	0.697972	+	0.716125i	$0.254086\pi$
$402$	7.35733	−	2.16031i	0.366950	−	0.107746i
$403$	18.6523	−	5.47681i	0.929137	−	0.272819i
$404$	−0.425292	+	0.931260i	−0.0211591	+	0.0463319i
$405$	0.455922	+	3.17101i	0.0226549	+	0.157569i
$406$	8.59137	+	9.91497i	0.426383	+	0.492072i
$407$	3.94875	+	8.64657i	0.195733	+	0.428594i
$408$	−1.00654	+	0.646863i	−0.0498310	+	0.0320245i
$409$	4.64566	−	32.3112i	0.229713	−	1.59769i	−0.469604	−	0.882877i	$-0.655603\pi$
$409$	4.64566	−	32.3112i	0.229713	−	1.59769i	0.699317	−	0.714811i	$-0.253487\pi$
$410$	4.98034	+	3.20067i	0.245961	+	0.158070i
$411$	8.93775	−	10.3147i	0.440867	−	0.508788i
$412$	−4.36497	−	1.28167i	−0.215047	−	0.0631434i
$413$	5.99493			0.294991
$414$	1.75496	−	4.46320i	0.0862515	−	0.219354i
$415$	49.9407			2.45149
$416$	−2.76921	−	0.813115i	−0.135772	−	0.0398662i
$417$	7.63156	−	8.80729i	0.373719	−	0.431295i
$418$	−3.05581	−	1.96385i	−0.149465	−	0.0960551i
$419$	5.15788	−	35.8738i	0.251979	−	1.75255i	−0.334324	−	0.942458i	$-0.608508\pi$
$419$	5.15788	−	35.8738i	0.251979	−	1.75255i	0.586302	−	0.810092i	$-0.300583\pi$
$420$	−4.07852	+	2.62111i	−0.199012	+	0.127897i
$421$	2.90196	+	6.35441i	0.141433	+	0.309695i	0.967072	−	0.254504i	$-0.0819123\pi$
$421$	2.90196	+	6.35441i	0.141433	+	0.309695i	−0.825639	+	0.564199i	$0.809185\pi$
$422$	−7.51967	−	8.67816i	−0.366052	−	0.422446i
$423$	1.62431	+	11.2973i	0.0789767	+	0.549295i
$424$	5.01045	−	10.9714i	0.243329	−	0.532816i
$425$	6.04214	−	1.77413i	0.293087	−	0.0860581i
$426$	9.07303	−	2.66408i	0.439590	−	0.129075i
$427$	5.67966	−	12.4367i	0.274858	−	0.601855i
$428$	0.0858140	+	0.596849i	0.00414798	+	0.0288498i
$429$	12.3577	+	14.2615i	0.596635	+	0.688553i
$430$	−2.89294	−	6.33466i	−0.139510	−	0.305485i
$431$	−28.0183	+	18.0063i	−1.34959	+	0.867331i	−0.997638	−	0.0686858i	$-0.978119\pi$
$431$	−28.0183	+	18.0063i	−1.34959	+	0.867331i	−0.351955	+	0.936017i	$0.614483\pi$
$432$	−0.142315	+	0.989821i	−0.00684713	+	0.0476228i
$433$	−18.1413	−	11.6587i	−0.871816	−	0.560282i	0.0264914	−	0.999649i	$-0.491567\pi$
$433$	−18.1413	−	11.6587i	−0.871816	−	0.560282i	−0.898308	+	0.439367i	$0.855203\pi$
$434$	6.67514	−	7.70352i	0.320417	−	0.369781i
$435$	−26.6477	−	7.82448i	−1.27766	−	0.375155i
$436$	−5.87577			−0.281398
$437$	−1.85046	−	1.91691i	−0.0885193	−	0.0916982i
$438$	−0.627598			−0.0299878
$439$	−16.5410	−	4.85686i	−0.789457	−	0.231805i	−0.137941	−	0.990440i	$-0.544048\pi$
$439$	−16.5410	−	4.85686i	−0.789457	−	0.231805i	−0.651516	+	0.758635i	$0.725867\pi$
$440$	−13.7171	+	15.8304i	−0.653938	+	0.754684i
$441$	−3.96215	−	2.54632i	−0.188674	−	0.121253i
$442$	0.491437	−	3.41802i	0.0233753	−	0.162579i
$443$	15.9136	−	10.2271i	0.756080	−	0.485903i	−0.104937	−	0.994479i	$-0.533464\pi$
$443$	15.9136	−	10.2271i	0.756080	−	0.485903i	0.861017	+	0.508576i	$0.169828\pi$
$444$	−0.603930	−	1.32242i	−0.0286613	−	0.0627594i
$445$	−11.7870	−	13.6030i	−0.558760	−	0.644843i
$446$	2.24948	+	15.6454i	0.106516	+	0.740833i
$447$	7.18810	−	15.7397i	0.339986	−	0.744465i
$448$	−1.45204	+	0.426356i	−0.0686023	+	0.0201434i
$449$	−22.1174	+	6.49424i	−1.04378	+	0.306482i	−0.758303	−	0.651902i	$-0.773971\pi$
$449$	−22.1174	+	6.49424i	−1.04378	+	0.306482i	−0.285480	+	0.958385i	$0.592153\pi$
$450$	2.18639	−	4.78753i	0.103068	−	0.225686i
$451$	−1.71955	−	11.9597i	−0.0809705	−	0.563162i
$452$	−8.05979	−	9.30149i	−0.379101	−	0.437505i
$453$	−2.00749	−	4.39579i	−0.0943200	−	0.206532i
$454$	−2.18279	+	1.40280i	−0.102444	+	0.0658365i
$455$	1.99132	−	13.8499i	0.0933545	−	0.649295i
$456$	0.467362	+	0.300355i	0.0218862	+	0.0140654i
$457$	−9.94760	+	11.4801i	−0.465329	+	0.537019i	−0.939107	−	0.343626i	$-0.888345\pi$
$457$	−9.94760	+	11.4801i	−0.465329	+	0.537019i	0.473777	+	0.880645i	$0.342890\pi$
$458$	−9.58892	−	2.81556i	−0.448061	−	0.131563i
$459$	−1.19647			−0.0558466
$460$	−12.4600	+	8.98895i	−0.580950	+	0.419112i
$461$	19.2440			0.896281			0.448141	−	0.893963i	$-0.352086\pi$
$461$	19.2440			0.896281			0.448141	+	0.893963i	$0.352086\pi$
$462$	9.49404	+	2.78770i	0.441703	+	0.129696i
$463$	1.98580	−	2.29173i	0.0922878	−	0.106506i	−0.707727	−	0.706486i	$-0.750279\pi$
$463$	1.98580	−	2.29173i	0.0922878	−	0.106506i	0.800015	+	0.599980i	$0.204825\pi$
$464$	−7.29298	−	4.68691i	−0.338568	−	0.217584i
$465$	−3.07090	+	21.3586i	−0.142410	+	0.990481i
$466$	−22.9618	+	14.7567i	−1.06369	+	0.683590i
$467$	1.18398	+	2.59256i	0.0547882	+	0.119969i	0.935046	−	0.354526i	$-0.115358\pi$
$467$	1.18398	+	2.59256i	0.0547882	+	0.119969i	−0.880258	+	0.474495i	$0.842631\pi$
$468$	−1.89001	−	2.18119i	−0.0873657	−	0.100825i
$469$	1.65145	+	11.4861i	0.0762567	+	0.530377i
$470$	15.1894	−	33.2602i	0.700637	−	1.53418i
$471$	4.84574	−	1.42284i	0.223280	−	0.0655609i
$472$	−3.80093	+	1.11605i	−0.174952	+	0.0513706i
$473$	−5.90436	+	12.9287i	−0.271483	+	0.594465i
$474$	1.95998	+	13.6320i	0.0900248	+	0.626137i
$475$	−1.91479	−	2.20979i	−0.0878566	−	0.101392i
$476$	−0.752179	−	1.64704i	−0.0344761	−	0.0754920i
$477$	10.1466	−	6.52084i	0.464582	−	0.298569i
$478$	−2.03776	+	14.1729i	−0.0932050	+	0.648255i
$479$	31.3457	+	20.1447i	1.43222	+	0.920433i	0.999824	+	0.0187506i	$0.00596884\pi$
$479$	31.3457	+	20.1447i	1.43222	+	0.920433i	0.432398	+	0.901683i	$0.357668\pi$
$480$	2.09792	−	2.42113i	0.0957566	−	0.110509i
$481$	4.02588	+	1.18211i	0.183564	+	0.0538994i
$482$	14.1957			0.646598
$483$	6.30761	+	3.59005i	0.287006	+	0.163353i
$484$	31.7511			1.44323
$485$	−22.2770	−	6.54111i	−1.01155	−	0.297017i
$486$	−0.654861	+	0.755750i	−0.0297051	+	0.0342815i
$487$	−25.8648	−	16.6223i	−1.17204	−	0.753227i	−0.198137	−	0.980174i	$-0.563489\pi$
$487$	−25.8648	−	16.6223i	−1.17204	−	0.753227i	−0.973907	+	0.226947i	$0.927126\pi$
$488$	−1.28574	+	8.94254i	−0.0582029	+	0.404810i
$489$	3.00111	−	1.92870i	0.135715	−	0.0872188i
$490$	6.26796	+	13.7249i	0.283157	+	0.620028i
$491$	−5.11770	−	5.90614i	−0.230959	−	0.266540i	0.628427	−	0.777869i	$-0.283699\pi$
$491$	−5.11770	−	5.90614i	−0.230959	−	0.266540i	−0.859386	+	0.511328i	$0.829154\pi$
$492$	0.262991	+	1.82915i	0.0118566	+	0.0824643i
$493$	4.30887	−	9.43510i	0.194062	−	0.424936i
$494$	−1.53845	+	0.451729i	−0.0692181	+	0.0203243i
$495$	−20.0981	+	5.90134i	−0.903344	+	0.265246i
$496$	−2.79806	+	6.12691i	−0.125637	+	0.275106i
$497$	2.03656	+	14.1646i	0.0913520	+	0.635367i
$498$	10.2085	+	11.7813i	0.457455	+	0.527931i
$499$	5.38364	+	11.7885i	0.241005	+	0.527727i	0.991023	−	0.133690i	$-0.0426827\pi$
$499$	5.38364	+	11.7885i	0.241005	+	0.527727i	−0.750018	+	0.661417i	$0.769955\pi$
$500$	−0.709211	+	0.455783i	−0.0317169	+	0.0203832i
$501$	−0.649009	+	4.51396i	−0.0289956	+	0.201669i
$502$	10.0652	+	6.46851i	0.449232	+	0.288704i
$503$	−12.8552	+	14.8357i	−0.573184	+	0.661489i	−0.966125	−	0.258074i	$-0.916912\pi$
$503$	−12.8552	+	14.8357i	−0.573184	+	0.661489i	0.392941	+	0.919564i	$0.371458\pi$
$504$	−1.45204	−	0.426356i	−0.0646788	−	0.0189914i
$505$	3.27979			0.145949
$506$	30.5183	+	7.20480i	1.35670	+	0.320293i
$507$	−4.67030			−0.207415
$508$	−8.51054	−	2.49892i	−0.377594	−	0.110872i
$509$	−4.09448	+	4.72528i	−0.181484	+	0.209444i	−0.839201	−	0.543821i	$-0.816977\pi$
$509$	−4.09448	+	4.72528i	−0.181484	+	0.209444i	0.657717	+	0.753265i	$0.271522\pi$
$510$	3.22456	+	2.07230i	0.142786	+	0.0917629i
$511$	0.135166	−	0.940100i	0.00597939	−	0.0415876i
$512$	0.841254	−	0.540641i	0.0371785	−	0.0238932i
$513$	0.230786	+	0.505350i	0.0101894	+	0.0223117i
$514$	−17.0242	−	19.6470i	−0.750907	−	0.866592i
$515$	2.07410	+	14.4257i	0.0913958	+	0.635672i
$516$	0.903025	−	1.97735i	0.0397534	−	0.0870479i
$517$	−71.6035	+	21.0247i	−3.14912	+	0.924665i
$518$	2.11097	−	0.619837i	0.0927507	−	0.0272341i
$519$	−6.48596	+	14.2023i	−0.284702	+	0.623410i
$520$	1.31585	+	9.15192i	0.0577037	+	0.401338i
$521$	−15.7103	−	18.1307i	−0.688283	−	0.794321i	0.298837	−	0.954304i	$-0.403401\pi$
$521$	−15.7103	−	18.1307i	−0.688283	−	0.794321i	−0.987120	+	0.159984i	$0.948856\pi$
$522$	−3.60131	−	7.88576i	−0.157625	−	0.345150i
$523$	−6.24846	+	4.01564i	−0.273226	+	0.175592i	−0.670077	−	0.742291i	$-0.733739\pi$
$523$	−6.24846	+	4.01564i	−0.273226	+	0.175592i	0.396852	+	0.917883i	$0.370103\pi$
$524$	−1.78441	+	12.4108i	−0.0779523	+	0.542170i
$525$	6.70052	+	4.30616i	0.292435	+	0.187936i
$526$	−3.76064	+	4.34001i	−0.163972	+	0.189233i
$527$	−7.73251	−	2.27047i	−0.336833	−	0.0989032i
$528$	−6.53843			−0.284549
$529$	20.5716	+	10.2864i	0.894416	+	0.447237i
$530$	−38.6398			−1.67841
$531$	−3.80093	−	1.11605i	−0.164946	−	0.0484327i
$532$	−0.550568	+	0.635389i	−0.0238702	+	0.0275476i
$533$	−4.48676	−	2.88347i	−0.194343	−	0.124897i
$534$	0.799587	−	5.56125i	0.0346015	−	0.240659i
$535$	1.62508	−	1.04438i	0.0702584	−	0.0451523i
$536$	−3.18538	−	6.97500i	−0.137587	−	0.301274i
$537$	−4.19452	−	4.84074i	−0.181007	−	0.208893i
$538$	−1.16403	−	8.09601i	−0.0501849	−	0.349044i
$539$	12.7926	−	28.0119i	0.551017	−	1.20656i
$540$	3.07385	−	0.902563i	0.132277	−	0.0388401i
$541$	−19.6113	+	5.75840i	−0.843157	+	0.247573i	−0.674660	−	0.738129i	$-0.735710\pi$
$541$	−19.6113	+	5.75840i	−0.843157	+	0.247573i	−0.168497	+	0.985702i	$0.553891\pi$
$542$	−5.61029	+	12.2848i	−0.240982	+	0.527678i
$543$	3.15033	+	21.9110i	0.135194	+	0.940292i
$544$	0.783524	+	0.904235i	0.0335933	+	0.0387687i
$545$	7.81964	+	17.1226i	0.334957	+	0.733453i
$546$	3.67432	−	2.36134i	0.157247	−	0.101056i
$547$	1.32499	−	9.21550i	0.0566524	−	0.394026i	−0.941690	−	0.336481i	$-0.890763\pi$
$547$	1.32499	−	9.21550i	0.0566524	−	0.394026i	0.998343	−	0.0575459i	$-0.0183275\pi$
$548$	−11.4817	−	7.37884i	−0.490474	−	0.315209i
$549$	−5.91634	+	6.82782i	−0.252503	+	0.291404i
$550$	33.0188	+	9.69519i	1.40793	+	0.413404i
$551$	−4.81620			−0.205177
$552$	−4.66752	−	1.10192i	−0.198663	−	0.0469007i
$553$	−20.8419			−0.886287
$554$	−14.3633	−	4.21744i	−0.610238	−	0.179182i
$555$	−3.04996	+	3.51984i	−0.129464	+	0.149409i
$556$	−9.80372	−	6.30047i	−0.415771	−	0.267199i
$557$	4.54281	−	31.5960i	0.192485	−	1.33876i	−0.632917	−	0.774219i	$-0.718143\pi$
$557$	4.54281	−	31.5960i	0.192485	−	1.33876i	0.825402	−	0.564545i	$-0.190948\pi$
$558$	−5.66634	+	3.64153i	−0.239875	+	0.154158i
$559$	2.60624	+	5.70687i	0.110232	+	0.241375i
$560$	3.17486	+	3.66399i	0.134162	+	0.154832i
$561$	−1.11334	−	7.74343i	−0.0470051	−	0.326928i
$562$	11.2054	−	24.5364i	0.472671	−	1.03500i
$563$	16.1686	−	4.74754i	0.681427	−	0.200085i	0.0773416	−	0.997005i	$-0.475357\pi$
$563$	16.1686	−	4.74754i	0.681427	−	0.200085i	0.604085	+	0.796920i	$0.293539\pi$
$564$	10.9512	−	3.21556i	0.461128	−	0.135399i
$565$	−16.3794	+	35.8658i	−0.689085	+	1.50889i
$566$	−1.95246	−	13.5797i	−0.0820680	−	0.570796i
$567$	−0.991025	−	1.14370i	−0.0416191	−	0.0480310i
$568$	−3.92819	−	8.60154i	−0.164823	−	0.360913i
$569$	−1.83549	+	1.17960i	−0.0769478	+	0.0494513i	−0.578549	−	0.815648i	$-0.696381\pi$
$569$	−1.83549	+	1.17960i	−0.0769478	+	0.0494513i	0.501601	+	0.865099i	$0.332744\pi$
$570$	0.253289	−	1.76167i	0.0106091	−	0.0737881i
$571$	−7.55227	−	4.85355i	−0.316053	−	0.203115i	0.372990	−	0.927835i	$-0.378332\pi$
$571$	−7.55227	−	4.85355i	−0.316053	−	0.203115i	−0.689043	+	0.724721i	$0.741969\pi$
$572$	12.3577	−	14.2615i	0.516701	−	0.596305i
$573$	2.06209	+	0.605485i	0.0861451	+	0.0252945i
$574$	−2.79658			−0.116727
$575$	21.9369	+	12.4856i	0.914831	+	0.520687i
$576$	1.00000			0.0416667
$577$	39.5160	+	11.6029i	1.64507	+	0.483037i	0.967595	−	0.252508i	$-0.0812553\pi$
$577$	39.5160	+	11.6029i	1.64507	+	0.483037i	0.677477	+	0.735544i	$0.263073\pi$
$578$	10.1952	−	11.7658i	0.424063	−	0.489395i
$579$	−9.46075	−	6.08006i	−0.393175	−	0.252679i
$580$	−3.95247	+	27.4900i	−0.164117	+	1.14146i
$581$	−19.8462	+	12.7544i	−0.823358	+	0.529140i
$582$	−3.01062	−	6.59235i	−0.124794	−	0.273262i
$583$	51.6437	+	59.6000i	2.13886	+	2.46838i
$584$	0.0893165	+	0.621210i	0.00369594	+	0.0257059i
$585$	−3.84094	+	8.41048i	−0.158803	+	0.347731i
$586$	−8.83212	+	2.59334i	−0.364851	+	0.107130i
$587$	−9.22184	+	2.70778i	−0.380626	+	0.111762i	−0.466448	−	0.884549i	$-0.654467\pi$
$587$	−9.22184	+	2.70778i	−0.380626	+	0.111762i	0.0858220	+	0.996310i	$0.472648\pi$
$588$	−1.95653	+	4.28419i	−0.0806858	+	0.176677i
$589$	0.532540	+	3.70390i	0.0219429	+	0.152616i
$590$	8.31070	+	9.59106i	0.342146	+	0.394858i
$591$	4.32551	+	9.47155i	0.177928	+	0.389607i
$592$	−1.22301	+	0.785983i	−0.0502656	+	0.0323037i
$593$	5.18844	−	36.0864i	0.213064	−	1.48189i	−0.549781	−	0.835309i	$-0.685289\pi$
$593$	5.18844	−	36.0864i	0.213064	−	1.48189i	0.762845	−	0.646581i	$-0.223802\pi$
$594$	−5.50048	−	3.53494i	−0.225687	−	0.145040i
$595$	−3.79864	+	4.38386i	−0.155729	+	0.179721i
$596$	−16.6025	−	4.87494i	−0.680066	−	0.199685i
$597$	15.0998			0.617993
$598$	11.2251	−	8.09811i	0.459030	−	0.331156i
$599$	−6.93439			−0.283331			−0.141666	−	0.989915i	$-0.545246\pi$
$599$	−6.93439			−0.283331			−0.141666	+	0.989915i	$0.545246\pi$
$600$	−5.04996	−	1.48280i	−0.206164	−	0.0605351i
$601$	−10.9824	+	12.6744i	−0.447983	+	0.517000i	−0.934157	−	0.356862i	$-0.883847\pi$
$601$	−10.9824	+	12.6744i	−0.447983	+	0.517000i	0.486174	+	0.873862i	$0.338392\pi$
$602$	2.76745	+	1.77853i	0.112793	+	0.0724876i
$603$	1.09126	−	7.58989i	0.0444396	−	0.309084i
$604$	−4.06535	+	2.61264i	−0.165417	+	0.106307i
$605$	−42.2553	−	92.5261i	−1.71792	−	3.76172i
$606$	0.670431	+	0.773719i	0.0272344	+	0.0314302i
$607$	1.54717	+	10.7608i	0.0627977	+	0.436768i	0.996829	+	0.0795759i	$0.0253566\pi$
$607$	1.54717	+	10.7608i	0.0627977	+	0.436768i	−0.934031	+	0.357192i	$0.883734\pi$
$608$	0.230786	−	0.505350i	0.00935959	−	0.0204946i
$609$	12.5880	−	3.69616i	0.510090	−	0.149776i
$610$	27.7707	−	8.15420i	1.12440	−	0.330154i
$611$	−13.6841	+	29.9640i	−0.553599	+	1.21221i
$612$	0.170276	+	1.18430i	0.00688300	+	0.0478723i
$613$	−13.5856	−	15.6786i	−0.548717	−	0.633253i	0.411867	−	0.911244i	$-0.364877\pi$
$613$	−13.5856	−	15.6786i	−0.548717	−	0.633253i	−0.960584	+	0.277991i	$0.910331\pi$
$614$	0.729786	+	1.59801i	0.0294518	+	0.0644903i
$615$	4.98034	−	3.20067i	0.200827	−	0.129063i
$616$	1.40818	−	9.79413i	0.0567373	−	0.394617i
$617$	2.60245	+	1.67249i	0.104771	+	0.0673321i	0.591977	−	0.805955i	$-0.298348\pi$
$617$	2.60245	+	1.67249i	0.104771	+	0.0673321i	−0.487206	+	0.873287i	$0.661984\pi$
$618$	−2.97912	+	3.43809i	−0.119838	+	0.138300i
$619$	12.4859	+	3.66620i	0.501851	+	0.147357i	0.522853	−	0.852423i	$-0.324868\pi$
$619$	12.4859	+	3.66620i	0.501851	+	0.147357i	−0.0210022	+	0.999779i	$0.506686\pi$
$620$	21.5782			0.866603
$621$	−3.33083	−	3.45045i	−0.133662	−	0.138462i
$622$	30.3629			1.21744
$623$	8.15818	+	2.39546i	0.326850	+	0.0959720i
$624$	−1.89001	+	2.18119i	−0.0756609	+	0.0873173i
$625$	−19.8662	−	12.7672i	−0.794648	−	0.510689i
$626$	−1.56820	+	10.9071i	−0.0626778	+	0.435934i
$627$	−3.05581	+	1.96385i	−0.122037	+	0.0784287i
$628$	−2.09798	−	4.59393i	−0.0837183	−	0.183318i
$629$	−1.13909	−	1.31458i	−0.0454184	−	0.0524156i
$630$	0.689964	+	4.79880i	0.0274888	+	0.191189i
$631$	4.08060	−	8.93527i	0.162446	−	0.355707i	−0.810852	−	0.585251i	$-0.800996\pi$
$631$	4.08060	−	8.93527i	0.162446	−	0.355707i	0.973298	+	0.229544i	$0.0737233\pi$
$632$	13.2143	−	3.88006i	0.525635	−	0.154340i
$633$	−11.0177	+	3.23509i	−0.437915	+	0.128583i
$634$	−4.21527	+	9.23016i	−0.167410	+	0.366577i
$635$	4.04395	+	28.1263i	0.160479	+	1.11616i
$636$	−7.89848	−	9.11533i	−0.313195	−	0.361446i
$637$	−5.64677	−	12.3647i	−0.223733	−	0.489908i
$638$	47.6846	−	30.6450i	1.88785	−	1.21325i
$639$	1.34574	−	9.35982i	0.0532366	−	0.370269i
$640$	−2.69505	−	1.73201i	−0.106531	−	0.0684635i
$641$	−8.92969	+	10.3054i	−0.352702	+	0.407039i	−0.904181	−	0.427149i	$-0.859518\pi$
$641$	−8.92969	+	10.3054i	−0.352702	+	0.407039i	0.551480	+	0.834188i	$0.314063\pi$
$642$	0.578562	+	0.169881i	0.0228340	+	0.00670467i
$643$	3.57857			0.141125			0.0705626	−	0.997507i	$-0.477521\pi$
$643$	3.57857			0.141125			0.0705626	+	0.997507i	$0.477521\pi$
$644$	2.65584	−	6.75432i	0.104655	−	0.266158i
$645$	−6.96398			−0.274207
$646$	0.637781	+	0.187269i	0.0250931	+	0.00736801i
$647$	17.1896	−	19.8379i	0.675793	−	0.779906i	−0.309478	−	0.950907i	$-0.600154\pi$
$647$	17.1896	−	19.8379i	0.675793	−	0.779906i	0.985271	+	0.171000i	$0.0546999\pi$
$648$	0.841254	+	0.540641i	0.0330476	+	0.0212384i
$649$	3.68614	−	25.6377i	0.144694	−	1.00637i
$650$	12.7787	−	8.21239i	0.501223	−	0.322116i
$651$	−4.23441	−	9.27207i	−0.165960	−	0.363401i
$652$	−2.33617	−	2.69608i	−0.0914915	−	0.105587i
$653$	−3.66305	−	25.4771i	−0.143346	−	0.996994i	−0.926803	−	0.375548i	$-0.877454\pi$
$653$	−3.66305	−	25.4771i	−0.143346	−	0.996994i	0.783457	−	0.621446i	$-0.213455\pi$
$654$	−2.44088	+	5.34478i	−0.0954460	+	0.208998i
$655$	38.5413	−	11.3167i	1.50593	−	0.442182i
$656$	1.77310	−	0.520629i	0.0692279	−	0.0203272i
$657$	−0.260714	+	0.570883i	−0.0101714	+	0.0222723i
$658$	2.45813	+	17.0967i	0.0958279	+	0.666498i
$659$	6.67928	+	7.70831i	0.260188	+	0.300273i	0.870780	−	0.491672i	$-0.163614\pi$
$659$	6.67928	+	7.70831i	0.260188	+	0.300273i	−0.610592	+	0.791945i	$0.709069\pi$
$660$	8.70154	+	19.0537i	0.338707	+	0.741665i
$661$	−25.1993	+	16.1946i	−0.980140	+	0.629897i	−0.929501	−	0.368820i	$-0.879762\pi$
$661$	−25.1993	+	16.1946i	−0.980140	+	0.629897i	−0.0506386	+	0.998717i	$0.516126\pi$
$662$	−4.23799	+	29.4759i	−0.164714	+	1.14561i
$663$	−2.90499	−	1.86692i	−0.112821	−	0.0725053i
$664$	10.2085	−	11.7813i	0.396168	−	0.457202i
$665$	2.58431	+	0.758821i	0.100215	+	0.0294258i
$666$	−1.45380			−0.0563336
$667$	39.2047	−	13.8400i	1.51801	−	0.535888i
$668$	4.56038			0.176446
$669$	15.1661	+	4.45316i	0.586354	+	0.172169i
$670$	−16.0867	+	18.5651i	−0.621485	+	0.717232i
$671$	−49.6941	−	31.9364i	−1.91842	−	1.23289i
$672$	−0.215370	+	1.49793i	−0.00830809	+	0.0577840i
$673$	−1.70536	+	1.09597i	−0.0657367	+	0.0422464i	−0.573096	−	0.819488i	$-0.694258\pi$
$673$	−1.70536	+	1.09597i	−0.0657367	+	0.0422464i	0.507360	+	0.861734i	$0.330622\pi$
$674$	−7.91732	−	17.3365i	−0.304964	−	0.667777i
$675$	−3.44663	−	3.97763i	−0.132661	−	0.153099i
$676$	0.664652	+	4.62276i	0.0255636	+	0.177798i
$677$	1.02323	−	2.24056i	0.0393259	−	0.0861116i	−0.888950	−	0.458005i	$-0.848564\pi$
$677$	1.02323	−	2.24056i	0.0393259	−	0.0861116i	0.928275	+	0.371894i	$0.121291\pi$
$678$	−11.8091	+	3.46746i	−0.453525	+	0.133167i
$679$	10.5233	−	3.08992i	0.403847	−	0.118580i
$680$	1.59230	−	3.48666i	0.0610620	−	0.133707i
$681$	0.369263	+	2.56828i	0.0141502	+	0.0984168i
$682$	−28.8402	−	33.2833i	−1.10435	−	1.27448i
$683$	−12.5872	−	27.5621i	−0.481635	−	1.05463i	−0.982011	−	0.188825i	$-0.939532\pi$
$683$	−12.5872	−	27.5621i	−0.481635	−	1.05463i	0.500376	−	0.865808i	$-0.333195\pi$
$684$	0.467362	−	0.300355i	0.0178700	−	0.0114844i
$685$	−6.22257	+	43.2790i	−0.237752	+	1.65360i
$686$	−14.9078	−	9.58064i	−0.569181	−	0.365790i
$687$	−6.54451	+	7.55276i	−0.249689	+	0.288156i
$688$	−2.08574	−	0.612427i	−0.0795179	−	0.0233486i
$689$	34.8104			1.32617
$690$	3.00057	+	15.0681i	0.114230	+	0.573635i
$691$	−1.71993			−0.0654294			−0.0327147	−	0.999465i	$-0.510415\pi$
$691$	−1.71993			−0.0654294			−0.0327147	+	0.999465i	$0.510415\pi$
$692$	14.9808	+	4.39875i	0.569483	+	0.167215i
$693$	6.47975	−	7.47803i	0.246145	−	0.284067i
$694$	−10.2573	−	6.59199i	−0.389363	−	0.250228i
$695$	−5.31318	+	36.9540i	−0.201541	+	1.40175i
$696$	−7.29298	+	4.68691i	−0.276440	+	0.177657i
$697$	0.918495	+	2.01122i	0.0347905	+	0.0761805i
$698$	10.0863	+	11.6402i	0.381771	+	0.440587i
$699$	3.88445	+	27.0170i	0.146923	+	1.02188i
$700$	3.30875	−	7.24515i	0.125059	−	0.273841i
$701$	0.709124	−	0.208218i	0.0267833	−	0.00786427i	−0.268313	−	0.963332i	$-0.586466\pi$
$701$	0.709124	−	0.208218i	0.0267833	−	0.00786427i	0.295097	+	0.955467i	$0.404648\pi$
$702$	−2.76921	+	0.813115i	−0.104517	+	0.0306890i
$703$	−0.335516	+	0.734677i	−0.0126542	+	0.0277089i
$704$	0.930515	+	6.47188i	0.0350701	+	0.243918i
$705$	−23.9447	−	27.6336i	−0.901808	−	1.04074i
$706$	7.69797	+	16.8562i	0.289717	+	0.634392i
$707$	−1.30337	+	0.837626i	−0.0490183	+	0.0315022i
$708$	−0.563766	+	3.92108i	−0.0211876	+	0.147363i
$709$	18.9971	+	12.2087i	0.713451	+	0.458507i	0.846353	−	0.532622i	$-0.178793\pi$
$709$	18.9971	+	12.2087i	0.713451	+	0.458507i	−0.132902	+	0.991129i	$0.542430\pi$
$710$	−19.8381	+	22.8944i	−0.744510	+	0.859211i
$711$	13.2143	+	3.88006i	0.495574	+	0.145514i
$712$	−5.61844			−0.210560
$713$	−14.9786	−	28.6201i	−0.560954	−	1.07183i
$714$	−1.81067			−0.0677626
$715$	−58.0057	−	17.0320i	−2.16929	−	0.636961i
$716$	−4.19452	+	4.84074i	−0.156757	+	0.180907i
$717$	12.0456	+	7.74126i	0.449853	+	0.289103i
$718$	1.67363	−	11.6404i	0.0624595	−	0.434415i
$719$	9.21249	−	5.92051i	0.343568	−	0.220798i	−0.357465	−	0.933926i	$-0.616359\pi$
$719$	9.21249	−	5.92051i	0.343568	−	0.220798i	0.701033	+	0.713129i	$0.252723\pi$
$720$	−1.33083	−	2.91411i	−0.0495971	−	0.108603i
$721$	−4.50842	−	5.20299i	−0.167902	−	0.193769i
$722$	2.66006	+	18.5011i	0.0989971	+	0.688540i
$723$	5.89712	−	12.9129i	0.219316	−	0.480236i
$724$	21.2397	−	6.23653i	0.789366	−	0.231779i
$725$	43.7790	−	12.8547i	1.62591	−	0.477410i
$726$	13.1899	−	28.8818i	0.489522	−	1.07190i
$727$	−5.30540	−	36.8999i	−0.196766	−	1.36854i	−0.813590	−	0.581439i	$-0.802490\pi$
$727$	−5.30540	−	36.8999i	−0.196766	−	1.36854i	0.616824	−	0.787101i	$-0.288419\pi$
$728$	−2.86022	−	3.30087i	−0.106007	−	0.122338i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	1.69141	−	1.08700i	0.0626019	−	0.0402318i
$731$	0.370144	−	2.57441i	0.0136903	−	0.0952179i
$732$	7.60031	+	4.88442i	0.280915	+	0.180533i
$733$	−21.0216	+	24.2602i	−0.776449	+	0.896070i	−0.996848	−	0.0793401i	$-0.974719\pi$
$733$	−21.0216	+	24.2602i	−0.776449	+	0.896070i	0.220399	+	0.975410i	$0.429264\pi$
$734$	7.50235	+	2.20289i	0.276917	+	0.0813101i
$735$	15.0884			0.556545
$736$	−0.426443	+	4.77683i	−0.0157189	+	0.176076i
$737$	50.1363			1.84679
$738$	1.77310	+	0.520629i	0.0652687	+	0.0191646i
$739$	−24.5623	+	28.3464i	−0.903537	+	1.04274i	0.0953439	+	0.995444i	$0.469605\pi$
$739$	−24.5623	+	28.3464i	−0.903537	+	1.04274i	−0.998881	+	0.0472931i	$0.984941\pi$
$740$	3.91807	+	2.51799i	0.144031	+	0.0925631i
$741$	−0.228187	+	1.58708i	−0.00838267	+	0.0583027i
$742$	15.3553	−	9.86823i	0.563709	−	0.362274i
$743$	13.2431	+	28.9983i	0.485841	+	1.06384i	0.980816	+	0.194936i	$0.0624501\pi$
$743$	13.2431	+	28.9983i	0.485841	+	1.06384i	−0.494975	+	0.868907i	$0.664823\pi$
$744$	4.41087	+	5.09042i	0.161710	+	0.186624i
$745$	7.88901	+	54.8693i	0.289031	+	2.01026i
$746$	0.888226	−	1.94494i	0.0325203	−	0.0712094i
$747$	14.9574	−	4.39189i	0.547262	−	0.160691i
$748$	−7.50617	+	2.20401i	−0.274453	+	0.0805866i
$749$	−0.379076	+	0.830060i	−0.0138511	+	0.0303297i
$750$	0.119977	+	0.834460i	0.00438095	+	0.0304702i
$751$	11.7544	+	13.5652i	0.428923	+	0.495003i	0.928534	−	0.371246i	$-0.121069\pi$
$751$	11.7544	+	13.5652i	0.428923	+	0.495003i	−0.499612	+	0.866249i	$0.666524\pi$
$752$	−4.74134	−	10.3821i	−0.172899	−	0.378596i
$753$	10.0652	−	6.46851i	0.366796	−	0.235726i
$754$	3.56076	−	24.7656i	0.129675	−	0.901911i
$755$	13.0238	+	8.36990i	0.473985	+	0.304612i
$756$	−0.991025	+	1.14370i	−0.0360432	+	0.0415961i
$757$	10.5177	+	3.08827i	0.382271	+	0.112245i	0.467222	−	0.884140i	$-0.345255\pi$
$757$	10.5177	+	3.08827i	0.382271	+	0.112245i	−0.0849504	+	0.996385i	$0.527073\pi$
$758$	−21.6725			−0.787180
$759$	19.2315	−	24.7674i	0.698058	−	0.899000i
$760$	−1.77978			−0.0645595
$761$	0.351035	+	0.103073i	0.0127250	+	0.00373640i	0.288089	−	0.957604i	$-0.406980\pi$
$761$	0.351035	+	0.103073i	0.0127250	+	0.00373640i	−0.275364	+	0.961340i	$0.588798\pi$
$762$	−5.80850	+	6.70337i	−0.210420	+	0.242838i
$763$	−7.48044	−	4.80739i	−0.270810	−	0.174039i
$764$	0.305856	−	2.12727i	0.0110655	−	0.0769620i
$765$	3.22456	−	2.07230i	0.116584	−	0.0749241i
$766$	2.08113	+	4.55703i	0.0751942	+	0.164652i
$767$	−7.48708	−	8.64055i	−0.270343	−	0.311992i
$768$	−0.142315	−	0.989821i	−0.00513534	−	0.0357171i
$769$	0.127106	−	0.278324i	0.00458358	−	0.0100366i	−0.907326	−	0.420427i	$-0.861880\pi$
$769$	0.127106	−	0.278324i	0.00458358	−	0.0100366i	0.911910	+	0.410390i	$0.134608\pi$
$770$	−30.4152	+	8.93072i	−1.09609	+	0.321841i
$771$	−24.9437	+	7.32412i	−0.898324	+	0.263772i
$772$	−4.67176	+	10.2297i	−0.168140	+	0.368176i
$773$	0.502419	+	3.49440i	0.0180708	+	0.125685i	0.996860	−	0.0791853i	$-0.0252319\pi$
$773$	0.502419	+	3.49440i	0.0180708	+	0.125685i	−0.978789	+	0.204870i	$0.934323\pi$
$774$	−1.42353	−	1.64284i	−0.0511677	−	0.0590507i
$775$	−14.7266	−	32.2468i	−0.528997	−	1.15834i
$776$	−6.09679	+	3.91817i	−0.218862	+	0.140654i
$777$	0.313105	−	2.17770i	0.0112326	−	0.0781244i
$778$	−5.06583	−	3.25561i	−0.181619	−	0.116719i
$779$	0.672306	−	0.775882i	0.0240879	−	0.0277989i
$780$	8.87150	+	2.60491i	0.317651	+	0.0932706i
$781$	61.8278			2.21237
$782$	−5.72980	+	0.308346i	−0.204897	+	0.0110264i
$783$	−8.66918			−0.309811
$784$	4.51903	+	1.32691i	0.161394	+	0.0473895i
$785$	−10.5952	+	12.2275i	−0.378157	+	0.436417i
$786$	10.5480	+	6.77880i	0.376236	+	0.241792i
$787$	0.320128	−	2.22654i	0.0114113	−	0.0793675i	−0.983320	−	0.181884i	$-0.941780\pi$
$787$	0.320128	−	2.22654i	0.0114113	−	0.0793675i	0.994731	+	0.102517i	$0.0326895\pi$
$788$	8.75956	−	5.62943i	0.312046	−	0.200540i
$789$	2.38558	+	5.22370i	0.0849291	+	0.185969i
$790$	−28.8929	−	33.3442i	−1.02796	−	1.18633i
$791$	−2.65070	−	18.4360i	−0.0942480	−	0.655510i
$792$	−2.71616	+	5.94756i	−0.0965146	+	0.211337i
$793$	−25.0185	+	7.34609i	−0.888432	+	0.260867i
$794$	−23.0295	+	6.76208i	−0.817287	+	0.239977i
$795$	−16.0516	+	35.1480i	−0.569290	+	1.24657i
$796$	−2.14892	−	14.9461i	−0.0761665	−	0.529750i
$797$	25.9779	+	29.9801i	0.920185	+	1.06195i	0.997887	+	0.0649735i	$0.0206963\pi$
$797$	25.9779	+	29.9801i	0.920185	+	1.06195i	−0.0777020	+	0.996977i	$0.524758\pi$
$798$	0.349256	+	0.764765i	0.0123635	+	0.0270724i
$799$	11.4881	−	7.38297i	0.406421	−	0.261191i
$800$	−0.749025	+	5.20958i	−0.0264820	+	0.184187i
$801$	−4.72653	−	3.03756i	−0.167004	−	0.107327i
$802$	9.48014	−	10.9407i	0.334755	−	0.386328i
$803$	−3.93728	−	1.15609i	−0.138944	−	0.0407976i
$804$	−7.66794			−0.270427
$805$	−23.2173	+	1.24943i	−0.818303	+	0.0440366i
$806$	−19.4397			−0.684735
$807$	−7.84795	−	2.30437i	−0.276261	−	0.0811175i
$808$	0.670431	−	0.773719i	0.0235857	−	0.0272193i
$809$	−32.3796	−	20.8091i	−1.13841	−	0.731610i	−0.171110	−	0.985252i	$-0.554735\pi$
$809$	−32.3796	−	20.8091i	−1.13841	−	0.731610i	−0.967298	+	0.253642i	$0.918372\pi$
$810$	0.455922	−	3.17101i	0.0160195	−	0.111418i
$811$	−12.1468	+	7.80630i	−0.426533	+	0.274116i	−0.736246	−	0.676714i	$-0.763403\pi$
$811$	−12.1468	+	7.80630i	−0.426533	+	0.274116i	0.309713	+	0.950830i	$0.399767\pi$
$812$	−5.44999	−	11.9338i	−0.191257	−	0.418795i
$813$	8.84406	+	10.2066i	0.310175	+	0.357961i
$814$	−1.35278	−	9.40881i	−0.0474150	−	0.329779i
$815$	−4.74764	+	10.3959i	−0.166303	+	0.364152i
$816$	1.14801	−	0.337086i	0.0401883	−	0.0118004i
$817$	−1.15874	+	0.340236i	−0.0405391	+	0.0119034i
$818$	−13.5606	+	29.6936i	−0.474135	+	1.03821i
$819$	−0.621585	−	4.32322i	−0.0217199	−	0.151066i
$820$	−3.87687	−	4.47414i	−0.135386	−	0.156244i
$821$	12.1602	+	26.6271i	0.424393	+	0.929291i	0.994203	+	0.107515i	$0.0342894\pi$
$821$	12.1602	+	26.6271i	0.424393	+	0.929291i	−0.569810	+	0.821776i	$0.692983\pi$
$822$	−11.4817	+	7.37884i	−0.400470	+	0.257367i
$823$	2.37652	−	16.5290i	0.0828401	−	0.576166i	−0.905551	−	0.424237i	$-0.860542\pi$
$823$	2.37652	−	16.5290i	0.0828401	−	0.576166i	0.988391	−	0.151929i	$-0.0485485\pi$
$824$	3.82707	+	2.45951i	0.133322	+	0.0856810i
$825$	22.5356	−	26.0074i	0.784587	−	0.905462i
$826$	−5.75209	−	1.68897i	−0.200141	−	0.0587667i
$827$	−20.3196			−0.706582			−0.353291	−	0.935514i	$-0.614937\pi$
$827$	−20.3196			−0.706582			−0.353291	+	0.935514i	$0.614937\pi$
$828$	−2.94130	+	3.78798i	−0.102217	+	0.131641i
$829$	0.285271			0.00990788			0.00495394	−	0.999988i	$-0.498423\pi$
$829$	0.285271			0.00990788			0.00495394	+	0.999988i	$0.498423\pi$
$830$	−47.9177	−	14.0699i	−1.66325	−	0.488374i
$831$	−9.80305	+	11.3133i	−0.340064	+	0.392455i
$832$	2.42796	+	1.56036i	0.0841744	+	0.0540956i
$833$	−0.801968	+	5.57781i	−0.0277865	+	0.193260i
$834$	−9.80372	+	6.30047i	−0.339475	+	0.218167i
$835$	−6.06909	−	13.2894i	−0.210029	−	0.459900i
$836$	2.37875	+	2.74522i	0.0822708	+	0.0949456i
$837$	0.958574	+	6.66703i	0.0331332	+	0.230446i
$838$	−15.0558	+	32.9675i	−0.520093	+	1.13884i
$839$	23.4619	−	6.88905i	0.809996	−	0.237836i	0.149593	−	0.988748i	$-0.452204\pi$
$839$	23.4619	−	6.88905i	0.809996	−	0.237836i	0.660403	+	0.750911i	$0.270385\pi$
$840$	4.65177	−	1.36588i	0.160501	−	0.0471274i
$841$	19.1733	−	41.9837i	0.661149	−	1.44771i
$842$	−0.994168	−	6.91459i	−0.0342613	−	0.238293i
$843$	−17.6642	−	20.3856i	−0.608387	−	0.702116i
$844$	4.77015	+	10.4452i	0.164195	+	0.359537i
$845$	12.5867	−	8.08898i	0.432995	−	0.278269i
$846$	1.62431	−	11.2973i	0.0558450	−	0.388410i
$847$	40.4223	+	25.9778i	1.38893	+	0.892608i
$848$	−7.89848	+	9.11533i	−0.271235	+	0.313022i
$849$	−13.1636	−	3.86517i	−0.451773	−	0.132652i
$850$	−6.29722			−0.215993
$851$	0.619962	−	6.94456i	0.0212520	−	0.238056i
$852$	−9.45607			−0.323960
$853$	−27.7862	−	8.15876i	−0.951381	−	0.279351i	−0.231019	−	0.972949i	$-0.574206\pi$
$853$	−27.7862	−	8.15876i	−0.951381	−	0.279351i	−0.720362	+	0.693599i	$0.756024\pi$
$854$	−8.95342	+	10.3328i	−0.306380	+	0.353581i
$855$	−1.49725	−	0.962223i	−0.0512048	−	0.0329073i
$856$	0.0858140	−	0.596849i	0.00293306	−	0.0203999i
$857$	−25.6181	+	16.4638i	−0.875099	+	0.562392i	−0.899308	−	0.437315i	$-0.855929\pi$
$857$	−25.6181	+	16.4638i	−0.875099	+	0.562392i	0.0242097	+	0.999707i	$0.492293\pi$
$858$	−7.83918	−	17.1654i	−0.267625	−	0.586017i
$859$	−27.7481	−	32.0230i	−0.946753	−	1.09261i	−0.995591	−	0.0938044i	$-0.970097\pi$
$859$	−27.7481	−	32.0230i	−0.946753	−	1.09261i	0.0488378	−	0.998807i	$-0.484448\pi$
$860$	0.991078	+	6.89310i	0.0337955	+	0.235053i
$861$	−1.16174	+	2.54386i	−0.0395920	+	0.0866945i
$862$	31.9563	−	9.38322i	1.08844	−	0.319594i
$863$	47.6728	−	13.9980i	1.62280	−	0.476497i	0.661031	−	0.750358i	$-0.270119\pi$
$863$	47.6728	−	13.9980i	1.62280	−	0.476497i	0.961769	+	0.273861i	$0.0883008\pi$
$864$	0.415415	−	0.909632i	0.0141327	−	0.0309463i
$865$	−7.11840	−	49.5096i	−0.242033	−	1.68338i
$866$	14.1218	+	16.2975i	0.479879	+	0.553810i
$867$	−6.46737	−	14.1616i	−0.219643	−	0.480952i
$868$	−8.57508	+	5.51087i	−0.291057	+	0.187051i
$869$	−12.8152	+	89.1316i	−0.434725	+	3.02358i
$870$	23.3639	+	15.0151i	0.792110	+	0.509058i
$871$	14.4925	−	16.7252i	0.491059	−	0.566712i
$872$	5.63776	+	1.65539i	0.190918	+	0.0560587i
$873$	−7.24727			−0.245283
$874$	1.23544	+	2.36059i	0.0417895	+	0.0798483i
$875$	−1.27581			−0.0431301
$876$	0.602176	+	0.176815i	0.0203456	+	0.00597402i
$877$	−3.26487	+	3.76787i	−0.110247	+	0.127232i	−0.808191	−	0.588921i	$-0.799553\pi$
$877$	−3.26487	+	3.76787i	−0.110247	+	0.127232i	0.697944	+	0.716152i	$0.254098\pi$
$878$	14.5026	+	9.32025i	0.489439	+	0.314543i
$879$	−1.31001	+	9.11129i	−0.0441854	+	0.307316i
$880$	17.6214	−	11.3246i	0.594018	−	0.381752i
$881$	20.4593	+	44.7996i	0.689291	+	1.50934i	0.852490	+	0.522744i	$0.175092\pi$
$881$	20.4593	+	44.7996i	0.689291	+	1.50934i	−0.163198	+	0.986593i	$0.552181\pi$
$882$	3.08427	+	3.55944i	0.103853	+	0.119852i
$883$	4.15048	+	28.8672i	0.139675	+	0.971459i	0.932284	+	0.361728i	$0.117813\pi$
$883$	4.15048	+	28.8672i	0.139675	+	0.971459i	−0.792609	+	0.609730i	$0.791278\pi$
$884$	−1.43450	+	3.14111i	−0.0482474	+	0.105647i
$885$	12.1767	−	3.57541i	0.409316	−	0.120186i
$886$	−18.1503	+	5.32942i	−0.609772	+	0.179045i
$887$	2.53121	−	5.54257i	0.0849897	−	0.186101i	−0.862365	−	0.506287i	$-0.831018\pi$
$887$	2.53121	−	5.54257i	0.0849897	−	0.186101i	0.947355	+	0.320185i	$0.103745\pi$
$888$	0.206897	+	1.43900i	0.00694302	+	0.0482897i
$889$	−8.79022	−	10.1445i	−0.294815	−	0.340234i
$890$	7.47719	+	16.3728i	0.250636	+	0.548816i
$891$	−5.50048	+	3.53494i	−0.184273	+	0.118425i
$892$	2.24948	−	15.6454i	0.0753180	−	0.523848i
$893$	−5.33424	−	3.42811i	−0.178504	−	0.114717i
$894$	−11.3313	+	13.0771i	−0.378977	+	0.437362i
$895$	19.6886	+	5.78111i	0.658119	+	0.193241i
$896$	1.51334			0.0505570
$897$	−2.70320	−	13.5748i	−0.0902573	−	0.453250i
$898$	23.0511			0.769225
$899$	−56.0267	−	16.4509i	−1.86860	−	0.548669i
$900$	−3.44663	+	3.97763i	−0.114888	+	0.132588i
$901$	−12.1402	−	7.80201i	−0.404448	−	0.259923i
$902$	−1.71955	+	11.9597i	−0.0572548	+	0.398216i
$903$	2.76745	−	1.77853i	0.0920950	−	0.0591859i
$904$	5.11278	+	11.1954i	0.170048	+	0.372354i
$905$	−46.4403	−	53.5950i	−1.54373	−	1.78156i
$906$	0.687735	+	4.78330i	0.0228485	+	0.158915i
$907$	−1.02214	+	2.23817i	−0.0339396	+	0.0743173i	−0.925842	−	0.377910i	$-0.876643\pi$
$907$	−1.02214	+	2.23817i	−0.0339396	+	0.0743173i	0.891903	+	0.452227i	$0.149370\pi$
$908$	2.48959	−	0.731009i	0.0826199	−	0.0242594i
$909$	0.982307	−	0.288431i	0.0325811	−	0.00956666i
$910$	−5.81264	+	12.7279i	−0.192687	+	0.421926i
$911$	7.45933	+	51.8808i	0.247139	+	1.71889i	0.614593	+	0.788845i	$0.289320\pi$
$911$	7.45933	+	51.8808i	0.247139	+	1.71889i	−0.367454	+	0.930042i	$0.619771\pi$
$912$	−0.363811	−	0.419860i	−0.0120470	−	0.0139029i
$913$	42.3418	+	92.7157i	1.40131	+	3.06844i
$914$	12.7790	−	8.21256i	0.422691	−	0.271647i
$915$	4.11903	−	28.6485i	0.136171	−	0.947089i
$916$	8.40727	+	5.40302i	0.277784	+	0.178521i
$917$	−12.4259	+	14.3403i	−0.410340	+	0.473558i
$918$	1.14801	+	0.337086i	0.0378899	+	0.0111255i
$919$	−12.0132			−0.396280			−0.198140	−	0.980174i	$-0.563490\pi$
$919$	−12.0132			−0.396280			−0.198140	+	0.980174i	$0.563490\pi$
$920$	14.4877	−	5.11445i	0.477647	−	0.168619i
$921$	1.75676			0.0578873
$922$	−18.4645	−	5.42165i	−0.608095	−	0.178553i
$923$	17.8720	−	20.6254i	0.588266	−	0.678895i
$924$	−8.32407	−	5.34956i	−0.273842	−	0.175988i
$925$	1.08893	−	7.57369i	0.0358039	−	0.249021i
$926$	−2.55101	+	1.63944i	−0.0838315	+	0.0538752i
$927$	1.88983	+	4.13814i	0.0620700	+	0.135914i
$928$	5.67710	+	6.55173i	0.186360	+	0.215071i
$929$	2.45403	+	17.0682i	0.0805142	+	0.559989i	0.989651	+	0.143492i	$0.0458331\pi$
$929$	2.45403	+	17.0682i	0.0805142	+	0.559989i	−0.909137	+	0.416497i	$0.863258\pi$
$930$	8.96392	−	19.6283i	0.293939	−	0.643636i
$931$	2.51057	−	0.737169i	0.0822805	−	0.0241597i
$932$	26.1891	−	7.68983i	0.857854	−	0.251889i
$933$	12.6132	−	27.6190i	0.412937	−	0.904207i
$934$	−0.405614	−	2.82111i	−0.0132721	−	0.0923095i
$935$	16.4122	+	18.9407i	0.536735	+	0.619426i
$936$	1.19894	+	2.62531i	0.0391885	+	0.0858109i
$937$	16.7304	−	10.7520i	0.546559	−	0.351252i	−0.238040	−	0.971255i	$-0.576505\pi$
$937$	16.7304	−	10.7520i	0.546559	−	0.351252i	0.784599	+	0.620003i	$0.212869\pi$
$938$	1.65145	−	11.4861i	0.0539216	−	0.375033i
$939$	9.26995	+	5.95744i	0.302513	+	0.194414i
$940$	−23.9447	+	27.6336i	−0.780988	+	0.901309i
$941$	14.1949	+	4.16801i	0.462742	+	0.135873i	0.504790	−	0.863242i	$-0.331570\pi$
$941$	14.1949	+	4.16801i	0.462742	+	0.135873i	−0.0420478	+	0.999116i	$0.513388\pi$
$942$	−5.05031			−0.164548
$943$	−3.24308	+	8.24779i	−0.105609	+	0.268585i
$944$	3.96140			0.128933
$945$	4.65177	+	1.36588i	0.151322	+	0.0444321i
$946$	9.30764	−	10.7416i	0.302618	−	0.349239i
$947$	−15.2688	−	9.81269i	−0.496171	−	0.318869i	0.268512	−	0.963276i	$-0.413468\pi$
$947$	−15.2688	−	9.81269i	−0.496171	−	0.318869i	−0.764683	+	0.644407i	$0.777104\pi$
$948$	1.95998	−	13.6320i	0.0636572	−	0.442745i
$949$	−1.52378	+	0.979276i	−0.0494641	+	0.0317886i
$950$	1.21466	+	2.65973i	0.0394088	+	0.0862932i
$951$	6.64496	+	7.66870i	0.215478	+	0.248675i
$952$	0.257685	+	1.79224i	0.00835162	+	0.0580868i
$953$	−10.8698	+	23.8016i	−0.352108	+	0.771008i	0.647850	+	0.761768i	$0.275668\pi$
$953$	−10.8698	+	23.8016i	−0.352108	+	0.771008i	−0.999957	+	0.00923998i	$0.997059\pi$
$954$	−11.5727	+	3.39807i	−0.374682	+	0.110016i
$955$	−6.60615	+	1.93974i	−0.213770	+	0.0627685i
$956$	5.94819	−	13.0247i	0.192378	−	0.421250i
$957$	−8.06680	−	56.1058i	−0.260763	−	1.81364i
$958$	−24.4006	−	28.1598i	−0.788347	−	0.909801i
$959$	−8.58020	−	18.7880i	−0.277069	−	0.606697i
$960$	−2.69505	+	1.73201i	−0.0869825	+	0.0559002i
$961$	−2.04480	+	14.2219i	−0.0659613	+	0.458771i
$962$	−3.52977	−	2.26844i	−0.113804	−	0.0731376i
$963$	0.394872	−	0.455707i	0.0127246	−	0.0146850i
$964$	−13.6207	−	3.99940i	−0.438694	−	0.128812i
$965$	36.0279			1.15978
$966$	−5.04067	−	5.22169i	−0.162181	−	0.168005i
$967$	−22.8164			−0.733726			−0.366863	−	0.930275i	$-0.619568\pi$
$967$	−22.8164			−0.733726			−0.366863	+	0.930275i	$0.619568\pi$
$968$	−30.4649	−	8.94531i	−0.979179	−	0.287513i
$969$	0.435290	−	0.502351i	0.0139835	−	0.0161378i
$970$	19.5318	+	12.5523i	0.627127	+	0.403030i
$971$	0.323393	−	2.24925i	0.0103782	−	0.0721818i	−0.983974	−	0.178311i	$-0.942937\pi$
$971$	0.323393	−	2.24925i	0.0103782	−	0.0721818i	0.994352	+	0.106129i	$0.0338458\pi$
$972$	0.841254	−	0.540641i	0.0269832	−	0.0173411i
$973$	−7.32626	−	16.0423i	−0.234869	−	0.514291i
$974$	20.1340	+	23.2359i	0.645136	+	0.744526i
$975$	−2.16178	−	15.0355i	−0.0692323	−	0.481521i
$976$	3.75307	−	8.21807i	0.120133	−	0.263054i
$977$	36.2549	−	10.6454i	1.15990	−	0.340577i	0.355505	−	0.934674i	$-0.384309\pi$
$977$	36.2549	−	10.6454i	1.15990	−	0.340577i	0.804393	+	0.594098i	$0.202491\pi$
$978$	−3.42292	+	1.00506i	−0.109453	+	0.0321383i
$979$	15.2606	−	33.4160i	0.487731	−	1.06798i
$980$	−2.14731	−	14.9348i	−0.0685932	−	0.477076i
$981$	3.84781	+	4.44061i	0.122851	+	0.141778i
$982$	3.24644	+	7.10872i	0.103598	+	0.226848i
$983$	−44.8441	+	28.8196i	−1.43031	+	0.919202i	−0.430444	+	0.902617i	$0.641643\pi$
$983$	−44.8441	+	28.8196i	−1.43031	+	0.919202i	−0.999862	+	0.0165844i	$0.994721\pi$
$984$	0.262991	−	1.82915i	0.00838386	−	0.0583110i
$985$	−28.0623	−	18.0345i	−0.894138	−	0.574627i
$986$	−6.79250	+	7.83897i	−0.216317	+	0.249644i
$987$	16.5728	+	4.86622i	0.527519	+	0.154894i
$988$	1.60340			0.0510109
$989$	8.45463	−	6.09939i	0.268842	−	0.193949i
$990$	20.9466			0.665727
$991$	−16.4716	−	4.83651i	−0.523238	−	0.153637i	0.00943830	−	0.999955i	$-0.496996\pi$
$991$	−16.4716	−	4.83651i	−0.523238	−	0.153637i	−0.532677	+	0.846319i	$0.678814\pi$
$992$	4.41087	−	5.09042i	0.140045	−	0.161621i
$993$	25.0517	+	16.0997i	0.794991	+	0.510910i
$994$	2.03656	−	14.1646i	0.0645956	−	0.449273i
$995$	−40.6947	+	26.1529i	−1.29011	+	0.829103i
$996$	−6.47584	−	14.1801i	−0.205195	−	0.449314i
$997$	18.9102	+	21.8236i	0.598893	+	0.691160i	0.971557	−	0.236807i	$-0.0761009\pi$
$997$	18.9102	+	21.8236i	0.598893	+	0.691160i	−0.372664	+	0.927967i	$0.621555\pi$
$998$	−1.84435	−	12.8278i	−0.0583820	−	0.406055i
$999$	−0.603930	+	1.32242i	−0.0191075	+	0.0418396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.e.a.133.1	yes	10
3.2	odd	2		414.2.i.d.271.1		10
23.3	even	11		3174.2.a.bc.1.1		5
23.9	even	11	inner	138.2.e.a.55.1	✓	10
23.20	odd	22		3174.2.a.bd.1.5		5
69.20	even	22		9522.2.a.bq.1.1		5
69.26	odd	22		9522.2.a.bt.1.5		5
69.32	odd	22		414.2.i.d.55.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.a.55.1	✓	10	23.9	even	11	inner
138.2.e.a.133.1	yes	10	1.1	even	1	trivial
414.2.i.d.55.1		10	69.32	odd	22
414.2.i.d.271.1		10	3.2	odd	2
3174.2.a.bc.1.1		5	23.3	even	11
3174.2.a.bd.1.5		5	23.20	odd	22
9522.2.a.bq.1.1		5	69.20	even	22
9522.2.a.bt.1.5		5	69.26	odd	22

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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.455922 - 3.17101i) q^{5} +(0.841254 - 0.540641i) q^{6} +(0.628663 + 1.37658i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.455922 - 3.17101i) q^{5} +(0.841254 - 0.540641i) q^{6} +(0.628663 + 1.37658i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-1.33083 + 2.91411i) q^{10} +(6.27358 - 1.84209i) q^{11} +(-0.959493 + 0.281733i) q^{12} +(1.19894 - 2.62531i) q^{13} +(-0.215370 - 1.49793i) q^{14} +(2.09792 + 2.42113i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-1.00654 + 0.646863i) q^{17} +(-0.142315 + 0.989821i) q^{18} +(0.467362 + 0.300355i) q^{19} +(2.09792 - 2.42113i) q^{20} +(-1.45204 - 0.426356i) q^{21} -6.53843 q^{22} +(-4.66752 - 1.10192i) q^{23} +1.00000 q^{24} +(-5.04996 - 1.48280i) q^{25} +(-1.89001 + 2.18119i) q^{26} +(0.841254 + 0.540641i) q^{27} +(-0.215370 + 1.49793i) q^{28} +(-7.29298 + 4.68691i) q^{29} +(-1.33083 - 2.91411i) q^{30} +(4.41087 + 5.09042i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(-2.71616 + 5.94756i) q^{33} +(1.14801 - 0.337086i) q^{34} +(4.65177 - 1.36588i) q^{35} +(0.415415 - 0.909632i) q^{36} +(0.206897 + 1.43900i) q^{37} +(-0.363811 - 0.419860i) q^{38} +(1.19894 + 2.62531i) q^{39} +(-2.69505 + 1.73201i) q^{40} +(0.262991 - 1.82915i) q^{41} +(1.27310 + 0.818172i) q^{42} +(-1.42353 + 1.64284i) q^{43} +(6.27358 + 1.84209i) q^{44} -3.20362 q^{45} +(4.16801 + 2.37227i) q^{46} -11.4135 q^{47} +(-0.959493 - 0.281733i) q^{48} +(3.08427 - 3.55944i) q^{49} +(4.42765 + 2.84548i) q^{50} +(0.170276 - 1.18430i) q^{51} +(2.42796 - 1.56036i) q^{52} +(5.01045 + 10.9714i) q^{53} +(-0.654861 - 0.755750i) q^{54} +(-2.98101 - 20.7334i) q^{55} +(0.628663 - 1.37658i) q^{56} +(-0.533050 + 0.156518i) q^{57} +(8.31801 - 2.44239i) q^{58} +(1.64562 - 3.60341i) q^{59} +(0.455922 + 3.17101i) q^{60} +(-5.91634 - 6.82782i) q^{61} +(-2.79806 - 6.12691i) q^{62} +(1.27310 - 0.818172i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-7.77825 - 4.99878i) q^{65} +(4.28176 - 4.94141i) q^{66} +(7.35733 + 2.16031i) q^{67} -1.19647 q^{68} +(3.88935 - 2.80588i) q^{69} -4.84815 q^{70} +(9.07303 + 2.66408i) q^{71} +(-0.654861 + 0.755750i) q^{72} +(-0.527969 - 0.339305i) q^{73} +(0.206897 - 1.43900i) q^{74} +(4.42765 - 2.84548i) q^{75} +(0.230786 + 0.505350i) q^{76} +(6.47975 + 7.47803i) q^{77} +(-0.410738 - 2.85675i) q^{78} +(-5.72115 + 12.5276i) q^{79} +(3.07385 - 0.902563i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-0.767668 + 1.68096i) q^{82} +(2.21852 + 15.4302i) q^{83} +(-0.991025 - 1.14370i) q^{84} +(1.59230 + 3.48666i) q^{85} +(1.82871 - 1.17524i) q^{86} +(1.23375 - 8.58094i) q^{87} +(-5.50048 - 3.53494i) q^{88} +(3.67930 - 4.24613i) q^{89} +(3.07385 + 0.902563i) q^{90} +4.36768 q^{91} +(-3.33083 - 3.45045i) q^{92} -6.73559 q^{93} +(10.9512 + 3.21556i) q^{94} +(1.16551 - 1.34507i) q^{95} +(0.841254 + 0.540641i) q^{96} +(1.03139 - 7.17350i) q^{97} +(-3.96215 + 2.54632i) q^{98} +(-2.71616 - 5.94756i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{3} - q^{4} + 8 q^{5} - q^{6} + 8 q^{7} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 - q^3 - q^4 + 8 * q^5 - q^6 + 8 * q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} + 8 q^{5} - q^{6} + 8 q^{7} - q^{8} - q^{9} - 3 q^{10} + 7 q^{11} - q^{12} + 3 q^{13} - 3 q^{14} - 3 q^{15} - q^{16} + 4 q^{17} - q^{18} - 3 q^{20} - 3 q^{21} - 26 q^{22} - 12 q^{23} + 10 q^{24} - 15 q^{25} + 3 q^{26} - q^{27} - 3 q^{28} - 25 q^{29} - 3 q^{30} + 6 q^{31} - q^{32} - 4 q^{33} - 7 q^{34} + 2 q^{35} - q^{36} + 9 q^{37} + 11 q^{38} + 3 q^{39} - 3 q^{40} + 24 q^{41} + 8 q^{42} - 30 q^{43} + 7 q^{44} - 14 q^{45} + 21 q^{46} - 48 q^{47} - q^{48} + 9 q^{49} + 7 q^{50} + 15 q^{51} + 14 q^{52} + 15 q^{53} - q^{54} - 23 q^{55} + 8 q^{56} - 11 q^{57} - 3 q^{58} + 5 q^{59} + 8 q^{60} + 12 q^{61} + 28 q^{62} + 8 q^{63} - q^{64} - 13 q^{65} + 18 q^{66} + 18 q^{67} - 18 q^{68} - q^{69} + 2 q^{70} + 28 q^{71} - q^{72} + 19 q^{73} + 9 q^{74} + 7 q^{75} + 22 q^{76} - 12 q^{77} - 8 q^{78} - 52 q^{79} + 8 q^{80} - q^{81} - 20 q^{82} + 7 q^{83} - 3 q^{84} + 23 q^{85} + 14 q^{86} + 30 q^{87} - 4 q^{88} + 3 q^{89} + 8 q^{90} + 42 q^{91} - 23 q^{92} - 16 q^{93} + 29 q^{94} + 22 q^{95} - q^{96} + 51 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 + 8 * q^5 - q^6 + 8 * q^7 - q^8 - q^9 - 3 * q^10 + 7 * q^11 - q^12 + 3 * q^13 - 3 * q^14 - 3 * q^15 - q^16 + 4 * q^17 - q^18 - 3 * q^20 - 3 * q^21 - 26 * q^22 - 12 * q^23 + 10 * q^24 - 15 * q^25 + 3 * q^26 - q^27 - 3 * q^28 - 25 * q^29 - 3 * q^30 + 6 * q^31 - q^32 - 4 * q^33 - 7 * q^34 + 2 * q^35 - q^36 + 9 * q^37 + 11 * q^38 + 3 * q^39 - 3 * q^40 + 24 * q^41 + 8 * q^42 - 30 * q^43 + 7 * q^44 - 14 * q^45 + 21 * q^46 - 48 * q^47 - q^48 + 9 * q^49 + 7 * q^50 + 15 * q^51 + 14 * q^52 + 15 * q^53 - q^54 - 23 * q^55 + 8 * q^56 - 11 * q^57 - 3 * q^58 + 5 * q^59 + 8 * q^60 + 12 * q^61 + 28 * q^62 + 8 * q^63 - q^64 - 13 * q^65 + 18 * q^66 + 18 * q^67 - 18 * q^68 - q^69 + 2 * q^70 + 28 * q^71 - q^72 + 19 * q^73 + 9 * q^74 + 7 * q^75 + 22 * q^76 - 12 * q^77 - 8 * q^78 - 52 * q^79 + 8 * q^80 - q^81 - 20 * q^82 + 7 * q^83 - 3 * q^84 + 23 * q^85 + 14 * q^86 + 30 * q^87 - 4 * q^88 + 3 * q^89 + 8 * q^90 + 42 * q^91 - 23 * q^92 - 16 * q^93 + 29 * q^94 + 22 * q^95 - q^96 + 51 * q^97 - 2 * q^98 - 4 * q^99

Introduction

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