LMFDB - Embedded newform 132.2.o.b.59.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [132,2,Mod(47,132)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(132, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 8]))

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

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

chi := DirichletCharacter("132.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 132 = 2^{2} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	132.o (of order $10$, 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:	$1.05402530668$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			59.1
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	132.59
Dual form			132.2.o.b.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.221232 + 1.39680i) q^{2} +(-1.08779 + 1.34786i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(0.951057 + 1.30902i) q^{5} +(-2.12334 - 1.22123i) q^{6} +(-0.224514 + 0.0729490i) q^{7} +(-1.28408 - 2.52015i) q^{8} +(-0.633446 - 2.93236i) q^{9} +O(q^{10})$	\(q+(0.221232 + 1.39680i) q^{2} +(-1.08779 + 1.34786i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(0.951057 + 1.30902i) q^{5} +(-2.12334 - 1.22123i) q^{6} +(-0.224514 + 0.0729490i) q^{7} +(-1.28408 - 2.52015i) q^{8} +(-0.633446 - 2.93236i) q^{9} +(-1.61803 + 1.61803i) q^{10} +(-2.19098 + 2.48990i) q^{11} +(1.23607 - 3.23607i) q^{12} +(0.809017 + 0.587785i) q^{13} +(-0.151565 - 0.297463i) q^{14} +(-2.79892 - 0.142040i) q^{15} +(3.23607 - 2.35114i) q^{16} +(2.99193 + 4.11803i) q^{17} +(3.95579 - 1.53353i) q^{18} +(4.61653 + 1.50000i) q^{19} +(-2.61803 - 1.90211i) q^{20} +(0.145898 - 0.381966i) q^{21} +(-3.96261 - 2.50953i) q^{22} +1.76393 q^{23} +(4.79360 + 1.01062i) q^{24} +(0.736068 - 2.26538i) q^{25} +(-0.642040 + 1.26007i) q^{26} +(4.64146 + 2.33598i) q^{27} +(0.381966 - 0.277515i) q^{28} +(-3.80423 + 1.23607i) q^{29} +(-0.420808 - 3.94095i) q^{30} +(3.44095 - 4.73607i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-0.972712 - 5.66161i) q^{33} +(-5.09017 + 5.09017i) q^{34} +(-0.309017 - 0.224514i) q^{35} +(3.01719 + 5.18619i) q^{36} +(3.16312 + 9.73508i) q^{37} +(-1.07388 + 6.78022i) q^{38} +(-1.67229 + 0.451057i) q^{39} +(2.07768 - 4.07768i) q^{40} +(-9.00854 - 2.92705i) q^{41} +(0.565808 + 0.119288i) q^{42} -6.23607i q^{43} +(2.62866 - 6.09017i) q^{44} +(3.23607 - 3.61803i) q^{45} +(0.390238 + 2.46386i) q^{46} +(2.04508 - 6.29412i) q^{47} +(-0.351141 + 6.91930i) q^{48} +(-5.61803 + 4.08174i) q^{49} +(3.32714 + 0.526966i) q^{50} +(-8.80510 - 0.446842i) q^{51} +(-1.90211 - 0.618034i) q^{52} +(6.96767 - 9.59017i) q^{53} +(-2.23607 + 7.00000i) q^{54} +(-5.34307 - 0.500000i) q^{55} +(0.472136 + 0.472136i) q^{56} +(-7.04358 + 4.59075i) q^{57} +(-2.56816 - 5.04029i) q^{58} +(-0.263932 - 0.812299i) q^{59} +(5.41164 - 1.45965i) q^{60} +(4.92705 - 3.57971i) q^{61} +(7.37660 + 3.75856i) q^{62} +(0.356131 + 0.612147i) q^{63} +(-4.70228 + 6.47214i) q^{64} +1.61803i q^{65} +(7.69296 - 2.61121i) q^{66} -2.85410i q^{67} +(-8.23607 - 5.98385i) q^{68} +(-1.91878 + 2.37753i) q^{69} +(0.245237 - 0.481305i) q^{70} +(4.92705 - 3.57971i) q^{71} +(-6.57659 + 5.36176i) q^{72} +(-2.38197 - 7.33094i) q^{73} +(-12.8982 + 6.57196i) q^{74} +(2.25273 + 3.45637i) q^{75} -9.70820 q^{76} +(0.310271 - 0.718847i) q^{77} +(-1.00000 - 2.23607i) q^{78} +(-10.0984 + 13.8992i) q^{79} +(6.15537 + 2.00000i) q^{80} +(-8.19749 + 3.71499i) q^{81} +(2.09554 - 13.2307i) q^{82} +(-3.66312 + 2.66141i) q^{83} +(-0.0414466 + 0.816712i) q^{84} +(-2.54508 + 7.83297i) q^{85} +(8.71055 - 1.37962i) q^{86} +(2.47214 - 6.47214i) q^{87} +(9.08831 + 2.32437i) q^{88} -7.18034i q^{89} +(5.76960 + 3.71972i) q^{90} +(-0.224514 - 0.0729490i) q^{91} +(-3.35520 + 1.09017i) q^{92} +(2.64053 + 9.78975i) q^{93} +(9.24408 + 1.46412i) q^{94} +(2.42705 + 7.46969i) q^{95} +(-9.74258 + 1.04029i) q^{96} +(-2.69098 - 1.95511i) q^{97} +(-6.94427 - 6.94427i) q^{98} +(8.68915 + 4.84754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 4 q^{3} - 2 q^{6} - 4 q^{8} - 10 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 4 * q^3 - 2 * q^6 - 4 * q^8 - 10 * q^9	$ 8 q + 2 q^{2} - 4 q^{3} - 2 q^{6} - 4 q^{8} - 10 q^{9} - 4 q^{10} - 22 q^{11} - 8 q^{12} + 2 q^{13} + 14 q^{14} + 2 q^{15} + 8 q^{16} - 14 q^{18} - 12 q^{20} + 28 q^{21} - 8 q^{22} + 32 q^{23} + 20 q^{24} - 12 q^{25} - 2 q^{26} + 2 q^{27} + 12 q^{28} + 32 q^{32} - 4 q^{33} + 4 q^{34} + 2 q^{35} + 8 q^{36} - 6 q^{37} - 18 q^{38} - 6 q^{39} - 8 q^{40} - 10 q^{42} + 8 q^{45} - 2 q^{46} - 6 q^{47} + 16 q^{48} - 36 q^{49} + 2 q^{50} + 28 q^{51} - 32 q^{56} - 6 q^{57} - 8 q^{58} - 20 q^{59} + 16 q^{60} + 26 q^{61} + 10 q^{62} - 28 q^{63} - 2 q^{66} - 48 q^{68} - 16 q^{69} + 8 q^{70} + 26 q^{71} - 28 q^{72} - 28 q^{73} + 6 q^{74} + 16 q^{75} - 24 q^{76} - 8 q^{78} - 2 q^{81} + 30 q^{82} + 2 q^{83} - 16 q^{84} + 2 q^{85} + 18 q^{86} - 16 q^{87} + 36 q^{88} + 22 q^{90} - 10 q^{93} + 16 q^{94} + 6 q^{95} + 8 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 4 * q^3 - 2 * q^6 - 4 * q^8 - 10 * q^9 - 4 * q^10 - 22 * q^11 - 8 * q^12 + 2 * q^13 + 14 * q^14 + 2 * q^15 + 8 * q^16 - 14 * q^18 - 12 * q^20 + 28 * q^21 - 8 * q^22 + 32 * q^23 + 20 * q^24 - 12 * q^25 - 2 * q^26 + 2 * q^27 + 12 * q^28 + 32 * q^32 - 4 * q^33 + 4 * q^34 + 2 * q^35 + 8 * q^36 - 6 * q^37 - 18 * q^38 - 6 * q^39 - 8 * q^40 - 10 * q^42 + 8 * q^45 - 2 * q^46 - 6 * q^47 + 16 * q^48 - 36 * q^49 + 2 * q^50 + 28 * q^51 - 32 * q^56 - 6 * q^57 - 8 * q^58 - 20 * q^59 + 16 * q^60 + 26 * q^61 + 10 * q^62 - 28 * q^63 - 2 * q^66 - 48 * q^68 - 16 * q^69 + 8 * q^70 + 26 * q^71 - 28 * q^72 - 28 * q^73 + 6 * q^74 + 16 * q^75 - 24 * q^76 - 8 * q^78 - 2 * q^81 + 30 * q^82 + 2 * q^83 - 16 * q^84 + 2 * q^85 + 18 * q^86 - 16 * q^87 + 36 * q^88 + 22 * q^90 - 10 * q^93 + 16 * q^94 + 6 * q^95 + 8 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/132\mathbb{Z}\right)^\times$.

$n$	$13$	$67$	$89$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.221232	+	1.39680i	0.156434	+	0.987688i
$2$	0.221232	+	1.39680i	0.156434	+	0.987688i
$3$	−1.08779	+	1.34786i	−0.628033	+	0.778187i
$3$	−1.08779	+	1.34786i	−0.628033	+	0.778187i
$4$	−1.90211	+	0.618034i	−0.951057	+	0.309017i
$5$	0.951057	+	1.30902i	0.425325	+	0.585410i	0.966872	−	0.255260i	$-0.0821612\pi$
$5$	0.951057	+	1.30902i	0.425325	+	0.585410i	−0.541547	+	0.840670i	$0.682161\pi$
$6$	−2.12334	−	1.22123i	−0.866852	−	0.498566i
$7$	−0.224514	+	0.0729490i	−0.0848583	+	0.0275721i	−0.351138	−	0.936324i	$-0.614205\pi$
$7$	−0.224514	+	0.0729490i	−0.0848583	+	0.0275721i	0.266280	+	0.963896i	$0.414205\pi$
$8$	−1.28408	−	2.52015i	−0.453990	−	0.891007i
$9$	−0.633446	−	2.93236i	−0.211149	−	0.977454i
$10$	−1.61803	+	1.61803i	−0.511667	+	0.511667i
$11$	−2.19098	+	2.48990i	−0.660606	+	0.750733i
$11$	−2.19098	+	2.48990i	−0.660606	+	0.750733i
$12$	1.23607	−	3.23607i	0.356822	−	0.934172i
$13$	0.809017	+	0.587785i	0.224381	+	0.163022i	0.694297	−	0.719689i	$-0.255716\pi$
$13$	0.809017	+	0.587785i	0.224381	+	0.163022i	−0.469916	+	0.882711i	$0.655716\pi$
$14$	−0.151565	−	0.297463i	−0.0405074	−	0.0795003i
$15$	−2.79892	−	0.142040i	−0.722677	−	0.0366744i
$16$	3.23607	−	2.35114i	0.809017	−	0.587785i
$17$	2.99193	+	4.11803i	0.725649	+	0.998770i	0.999317	+	0.0369459i	$0.0117629\pi$
$17$	2.99193	+	4.11803i	0.725649	+	0.998770i	−0.273668	+	0.961824i	$0.588237\pi$
$18$	3.95579	−	1.53353i	0.932389	−	0.361457i
$19$	4.61653	+	1.50000i	1.05910	+	0.344124i	0.786235	−	0.617928i	$-0.212028\pi$
$19$	4.61653	+	1.50000i	1.05910	+	0.344124i	0.272869	+	0.962051i	$0.412028\pi$
$20$	−2.61803	−	1.90211i	−0.585410	−	0.425325i
$21$	0.145898	−	0.381966i	0.0318376	−	0.0833518i
$22$	−3.96261	−	2.50953i	−0.844831	−	0.535033i
$23$	1.76393			0.367805			0.183903	−	0.982944i	$-0.441127\pi$
$23$	1.76393			0.367805			0.183903	+	0.982944i	$0.441127\pi$
$24$	4.79360	+	1.01062i	0.978490	+	0.206292i
$25$	0.736068	−	2.26538i	0.147214	−	0.453077i
$26$	−0.642040	+	1.26007i	−0.125914	+	0.247121i
$27$	4.64146	+	2.33598i	0.893250	+	0.449560i
$28$	0.381966	−	0.277515i	0.0721848	−	0.0524453i
$29$	−3.80423	+	1.23607i	−0.706427	+	0.229532i	−0.640129	−	0.768268i	$-0.721119\pi$
$29$	−3.80423	+	1.23607i	−0.706427	+	0.229532i	−0.0662984	+	0.997800i	$0.521119\pi$
$30$	−0.420808	−	3.94095i	−0.0768286	−	0.719517i
$31$	3.44095	−	4.73607i	0.618014	−	0.850623i	−0.379193	−	0.925318i	$-0.623798\pi$
$31$	3.44095	−	4.73607i	0.618014	−	0.850623i	0.997206	+	0.0746948i	$0.0237983\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$	−0.972712	−	5.66161i	−0.169327	−	0.985560i
$34$	−5.09017	+	5.09017i	−0.872957	+	0.872957i
$35$	−0.309017	−	0.224514i	−0.0522334	−	0.0379498i
$36$	3.01719	+	5.18619i	0.502864	+	0.864365i
$37$	3.16312	+	9.73508i	0.520014	+	1.60044i	0.773971	+	0.633222i	$0.218268\pi$
$37$	3.16312	+	9.73508i	0.520014	+	1.60044i	−0.253957	+	0.967216i	$0.581732\pi$
$38$	−1.07388	+	6.78022i	−0.174207	+	1.09990i
$39$	−1.67229	+	0.451057i	−0.267780	+	0.0722268i
$40$	2.07768	−	4.07768i	0.328511	−	0.644738i
$41$	−9.00854	−	2.92705i	−1.40690	−	0.457129i	−0.495482	−	0.868618i	$-0.665009\pi$
$41$	−9.00854	−	2.92705i	−1.40690	−	0.457129i	−0.911415	+	0.411489i	$0.865009\pi$
$42$	0.565808	+	0.119288i	0.0873061	+	0.0184065i
$43$		−	6.23607i		−	0.950991i	−0.879718	−	0.475496i	$-0.842269\pi$
$43$		−	6.23607i		−	0.950991i	0.879718	−	0.475496i	$-0.157731\pi$
$44$	2.62866	−	6.09017i	0.396285	−	0.918128i
$45$	3.23607	−	3.61803i	0.482405	−	0.539345i
$46$	0.390238	+	2.46386i	0.0575374	+	0.363277i
$47$	2.04508	−	6.29412i	0.298306	−	0.918092i	−0.683784	−	0.729684i	$-0.739667\pi$
$47$	2.04508	−	6.29412i	0.298306	−	0.918092i	0.982091	−	0.188408i	$-0.0603328\pi$
$48$	−0.351141	+	6.91930i	−0.0506828	+	0.998715i
$49$	−5.61803	+	4.08174i	−0.802576	+	0.583106i
$50$	3.32714	+	0.526966i	0.470528	+	0.0745243i
$51$	−8.80510	−	0.446842i	−1.23296	−	0.0625704i
$52$	−1.90211	−	0.618034i	−0.263776	−	0.0857059i
$53$	6.96767	−	9.59017i	0.957083	−	1.31731i	0.00877397	−	0.999962i	$-0.497207\pi$
$53$	6.96767	−	9.59017i	0.957083	−	1.31731i	0.948309	−	0.317350i	$-0.102793\pi$
$54$	−2.23607	+	7.00000i	−0.304290	+	0.952579i
$55$	−5.34307	−	0.500000i	−0.720459	−	0.0674200i
$56$	0.472136	+	0.472136i	0.0630918	+	0.0630918i
$57$	−7.04358	+	4.59075i	−0.932944	+	0.608059i
$58$	−2.56816	−	5.04029i	−0.337216	−	0.661823i
$59$	−0.263932	−	0.812299i	−0.0343610	−	0.105752i	0.932405	−	0.361415i	$-0.117706\pi$
$59$	−0.263932	−	0.812299i	−0.0343610	−	0.105752i	−0.966766	+	0.255663i	$0.917706\pi$
$60$	5.41164	−	1.45965i	0.698640	−	0.188440i
$61$	4.92705	−	3.57971i	0.630844	−	0.458335i	−0.225848	−	0.974162i	$-0.572515\pi$
$61$	4.92705	−	3.57971i	0.630844	−	0.458335i	0.856693	+	0.515827i	$0.172515\pi$
$62$	7.37660	+	3.75856i	0.936829	+	0.477338i
$63$	0.356131	+	0.612147i	0.0448682	+	0.0771233i
$64$	−4.70228	+	6.47214i	−0.587785	+	0.809017i
$65$			1.61803i			0.200692i
$66$	7.69296	−	2.61121i	0.946937	−	0.321418i
$67$		−	2.85410i		−	0.348684i	−0.984685	−	0.174342i	$-0.944220\pi$
$67$		−	2.85410i		−	0.348684i	0.984685	−	0.174342i	$-0.0557798\pi$
$68$	−8.23607	−	5.98385i	−0.998770	−	0.725649i
$69$	−1.91878	+	2.37753i	−0.230994	+	0.286221i
$70$	0.245237	−	0.481305i	0.0293115	−	0.0575270i
$71$	4.92705	−	3.57971i	0.584733	−	0.424834i	−0.255694	−	0.966758i	$-0.582304\pi$
$71$	4.92705	−	3.57971i	0.584733	−	0.424834i	0.840427	+	0.541924i	$0.182304\pi$
$72$	−6.57659	+	5.36176i	−0.775058	+	0.631890i
$73$	−2.38197	−	7.33094i	−0.278788	−	0.858021i	−0.988192	−	0.153219i	$-0.951036\pi$
$73$	−2.38197	−	7.33094i	−0.278788	−	0.858021i	0.709404	−	0.704802i	$-0.248964\pi$
$74$	−12.8982	+	6.57196i	−1.49939	+	0.763975i
$75$	2.25273	+	3.45637i	0.260123	+	0.399107i
$76$	−9.70820			−1.11361
$77$	0.310271	−	0.718847i	0.0353586	−	0.0819202i
$78$	−1.00000	−	2.23607i	−0.113228	−	0.253185i
$79$	−10.0984	+	13.8992i	−1.13615	+	1.56378i	−0.360336	+	0.932822i	$0.617338\pi$
$79$	−10.0984	+	13.8992i	−1.13615	+	1.56378i	−0.775817	+	0.630958i	$0.782662\pi$
$80$	6.15537	+	2.00000i	0.688191	+	0.223607i
$81$	−8.19749	+	3.71499i	−0.910832	+	0.412777i
$82$	2.09554	−	13.2307i	0.231413	−	1.46109i
$83$	−3.66312	+	2.66141i	−0.402080	+	0.292128i	−0.770387	−	0.637576i	$-0.779937\pi$
$83$	−3.66312	+	2.66141i	−0.402080	+	0.292128i	0.368308	+	0.929704i	$0.379937\pi$
$84$	−0.0414466	+	0.816712i	−0.00452219	+	0.0891106i
$85$	−2.54508	+	7.83297i	−0.276053	+	0.849604i
$86$	8.71055	−	1.37962i	0.939283	−	0.148768i
$87$	2.47214	−	6.47214i	0.265041	−	0.693886i
$88$	9.08831	+	2.32437i	0.968817	+	0.247779i
$89$		−	7.18034i		−	0.761115i	−0.924757	−	0.380557i	$-0.875732\pi$
$89$		−	7.18034i		−	0.761115i	0.924757	−	0.380557i	$-0.124268\pi$
$90$	5.76960	+	3.71972i	0.608169	+	0.392093i
$91$	−0.224514	−	0.0729490i	−0.0235355	−	0.00764713i
$92$	−3.35520	+	1.09017i	−0.349804	+	0.113658i
$93$	2.64053	+	9.78975i	0.273810	+	1.01515i
$94$	9.24408	+	1.46412i	0.953455	+	0.151012i
$95$	2.42705	+	7.46969i	0.249010	+	0.766375i
$96$	−9.74258	+	1.04029i	−0.994348	+	0.106175i
$97$	−2.69098	−	1.95511i	−0.273228	−	0.198512i	0.442730	−	0.896655i	$-0.354010\pi$
$97$	−2.69098	−	1.95511i	−0.273228	−	0.198512i	−0.715958	+	0.698143i	$0.754010\pi$
$98$	−6.94427	−	6.94427i	−0.701477	−	0.701477i
$99$	8.68915	+	4.84754i	0.873293	+	0.487196i
$100$			4.76393i			0.476393i
$101$	−2.93893	+	4.04508i	−0.292434	+	0.402501i	−0.929803	−	0.368058i	$-0.880023\pi$
$101$	−2.93893	+	4.04508i	−0.292434	+	0.402501i	0.637369	+	0.770559i	$0.280023\pi$
$102$	−1.32382	−	12.3978i	−0.131078	−	1.22757i
$103$	16.5640	−	5.38197i	1.63210	−	0.530301i	0.657346	−	0.753589i	$-0.271679\pi$
$103$	16.5640	−	5.38197i	1.63210	−	0.530301i	0.974752	+	0.223288i	$0.0716791\pi$
$104$	0.442463	−	2.79360i	0.0433871	−	0.273935i
$105$	0.638757	−	0.172288i	0.0623363	−	0.0168136i
$106$	14.9370	+	7.61080i	1.45081	+	0.739226i
$107$	0.0729490	−	0.224514i	0.00705225	−	0.0217046i	−0.947468	−	0.319849i	$-0.896368\pi$
$107$	0.0729490	−	0.224514i	0.00705225	−	0.0217046i	0.954521	+	0.298145i	$0.0963678\pi$
$108$	−10.2723	−	1.57472i	−0.988453	−	0.151528i
$109$	12.7639			1.22256			0.611281	−	0.791413i	$-0.290654\pi$
$109$	12.7639			1.22256			0.611281	+	0.791413i	$0.290654\pi$
$110$	−0.483655	−	7.57383i	−0.0461147	−	0.722136i
$111$	−16.5623	−	6.32624i	−1.57202	−	0.600460i
$112$	−0.555029	+	0.763932i	−0.0524453	+	0.0721848i
$113$	0.951057	+	0.309017i	0.0894679	+	0.0290699i	0.353409	−	0.935469i	$-0.385022\pi$
$113$	0.951057	+	0.309017i	0.0894679	+	0.0290699i	−0.263941	+	0.964539i	$0.585022\pi$
$114$	−7.97063	−	8.82286i	−0.746518	−	0.826337i
$115$	1.67760	+	2.30902i	0.156437	+	0.215317i
$116$	6.47214	−	4.70228i	0.600923	−	0.436596i
$117$	1.21113	−	2.74466i	0.111969	−	0.253744i
$118$	1.07623	−	0.548367i	0.0990751	−	0.0504813i
$119$	−0.972136	−	0.706298i	−0.0891156	−	0.0647462i
$120$	3.23607	+	7.23607i	0.295411	+	0.660560i
$121$	−1.39919	−	10.9106i	−0.127199	−	0.991877i
$122$	6.09017	+	6.09017i	0.551378	+	0.551378i
$123$	13.7446	−	8.95823i	1.23931	−	0.807737i
$124$	−3.61803	+	11.1352i	−0.324909	+	0.999967i
$125$	11.3597	−	3.69098i	1.01604	−	0.330132i
$126$	−0.776261	+	0.632870i	−0.0691548	+	0.0563806i
$127$	4.80828	+	6.61803i	0.426666	+	0.587256i	0.967184	−	0.254077i	$-0.0817717\pi$
$127$	4.80828	+	6.61803i	0.426666	+	0.587256i	−0.540518	+	0.841333i	$0.681772\pi$
$128$	−10.0806	−	5.13632i	−0.891007	−	0.453990i
$129$	8.40534	+	6.78350i	0.740049	+	0.597254i
$130$	−2.26007	+	0.357960i	−0.198222	+	0.0313952i
$131$	−16.6180			−1.45192			−0.725962	−	0.687735i	$-0.758605\pi$
$131$	−16.6180			−1.45192			−0.725962	+	0.687735i	$0.758605\pi$
$132$	5.34928	+	10.1679i	0.465595	+	0.884998i
$133$	−1.14590			−0.0993620
$134$	3.98662	−	0.631418i	0.344391	−	0.0545462i
$135$	1.35645	+	8.29741i	0.116745	+	0.714127i
$136$	6.53618	−	12.8280i	0.560473	−	1.09999i
$137$	5.73910	+	7.89919i	0.490324	+	0.674873i	0.980448	−	0.196780i	$-0.0630484\pi$
$137$	5.73910	+	7.89919i	0.490324	+	0.674873i	−0.490124	+	0.871653i	$0.663048\pi$
$138$	−3.74544	−	2.15417i	−0.318833	−	0.183375i
$139$	−6.74315	+	2.19098i	−0.571947	+	0.185837i	−0.580690	−	0.814125i	$-0.697217\pi$
$139$	−6.74315	+	2.19098i	−0.571947	+	0.185837i	0.00874291	+	0.999962i	$0.497217\pi$
$140$	0.726543	+	0.236068i	0.0614041	+	0.0199514i
$141$	6.25898	+	9.60314i	0.527101	+	0.808730i
$142$	6.09017	+	6.09017i	0.511076	+	0.511076i
$143$	−3.23607	+	0.726543i	−0.270614	+	0.0607565i
$144$	−8.94427	−	8.00000i	−0.745356	−	0.666667i
$145$	−5.23607	−	3.80423i	−0.434832	−	0.315924i
$146$	9.71290	−	4.94897i	0.803846	−	0.409580i
$147$	0.609605	−	12.0124i	0.0502793	−	0.990764i
$148$	−12.0332	−	16.5623i	−0.989125	−	1.36141i
$149$	1.59184	+	2.19098i	0.130409	+	0.179492i	0.869228	−	0.494411i	$-0.164616\pi$
$149$	1.59184	+	2.19098i	0.130409	+	0.179492i	−0.738819	+	0.673904i	$0.764616\pi$
$150$	−4.32949	+	3.91128i	−0.353501	+	0.319355i
$151$	−5.25731	−	1.70820i	−0.427834	−	0.139012i	0.0871818	−	0.996192i	$-0.472214\pi$
$151$	−5.25731	−	1.70820i	−0.427834	−	0.139012i	−0.515016	+	0.857181i	$0.672214\pi$
$152$	−2.14776	−	13.5604i	−0.174207	−	1.09990i
$153$	10.1803	−	11.3820i	0.823032	−	0.920177i
$154$	1.07273	+	0.274355i	0.0864430	+	0.0221082i
$155$	9.47214			0.760820
$156$	2.90211	−	1.89149i	0.232355	−	0.151441i
$157$	0.763932	−	2.35114i	0.0609684	−	0.187641i	−0.915933	−	0.401330i	$-0.868548\pi$
$157$	0.763932	−	2.35114i	0.0609684	−	0.187641i	0.976902	+	0.213689i	$0.0685479\pi$
$158$	−21.6485	−	11.0305i	−1.72226	−	0.877536i
$159$	5.34687	+	19.8235i	0.424034	+	1.57210i
$160$	−1.43184	+	9.04029i	−0.113197	+	0.714698i
$161$	−0.396027	+	0.128677i	−0.0312113	+	0.0101412i
$162$	−7.00265	−	10.6284i	−0.550180	−	0.835046i
$163$	−3.16344	+	4.35410i	−0.247780	+	0.341040i	−0.914732	−	0.404061i	$-0.867598\pi$
$163$	−3.16344	+	4.35410i	−0.247780	+	0.341040i	0.666952	+	0.745100i	$0.267598\pi$
$164$	18.9443			1.47930
$165$	6.48604	−	6.65781i	0.504938	−	0.518310i
$166$	−4.52786	−	4.52786i	−0.351430	−	0.351430i
$167$	4.54508	+	3.30220i	0.351709	+	0.255532i	0.749586	−	0.661907i	$-0.230253\pi$
$167$	4.54508	+	3.30220i	0.351709	+	0.255532i	−0.397876	+	0.917439i	$0.630253\pi$
$168$	−1.14996	+	0.122790i	−0.0887210	+	0.00947346i
$169$	−3.70820	−	11.4127i	−0.285246	−	0.877898i
$170$	−11.5042	−	1.82208i	−0.882329	−	0.139747i
$171$	1.47422	−	14.4875i	0.112736	−	1.10789i
$172$	3.85410	+	11.8617i	0.293873	+	0.904447i
$173$	−3.61247	−	1.17376i	−0.274651	−	0.0892395i	0.168453	−	0.985710i	$-0.446123\pi$
$173$	−3.61247	−	1.17376i	−0.274651	−	0.0892395i	−0.443104	+	0.896470i	$0.646123\pi$
$174$	9.58721	+	2.02124i	0.726804	+	0.153230i
$175$			0.562306i			0.0425063i
$176$	−1.23607	+	13.2088i	−0.0931721	+	0.995650i
$177$	1.38197	+	0.527864i	0.103875	+	0.0396767i
$178$	10.0295	−	1.58852i	0.751744	−	0.119065i
$179$	−2.60081	+	8.00448i	−0.194394	+	0.598283i	0.805589	+	0.592474i	$0.201849\pi$
$179$	−2.60081	+	8.00448i	−0.194394	+	0.598283i	−0.999983	+	0.00580843i	$0.998151\pi$
$180$	−3.91930	+	8.88191i	−0.292127	+	0.662018i
$181$	−10.1353	+	7.36369i	−0.753348	+	0.547339i	−0.896863	−	0.442309i	$-0.854159\pi$
$181$	−10.1353	+	7.36369i	−0.753348	+	0.547339i	0.143515	+	0.989648i	$0.454159\pi$
$182$	0.0522257	−	0.329740i	0.00387123	−	0.0244420i
$183$	−0.534627	+	10.5349i	−0.0395208	+	0.778764i
$184$	−2.26503	−	4.44537i	−0.166980	−	0.327717i
$185$	−9.73508	+	13.3992i	−0.715737	+	0.985128i
$186$	−13.0902	+	5.85410i	−0.959818	+	0.429244i
$187$	−16.8087	−	1.57295i	−1.22918	−	0.115025i
$188$			13.2361i			0.965339i
$189$	−1.21248	−	0.185871i	−0.0881950	−	0.0135201i
$190$	−9.89675	+	5.04264i	−0.717985	+	0.365832i
$191$	3.21885	+	9.90659i	0.232908	+	0.716816i	0.997392	+	0.0721737i	$0.0229936\pi$
$191$	3.21885	+	9.90659i	0.232908	+	0.716816i	−0.764484	+	0.644642i	$0.777006\pi$
$192$	−3.60845	−	13.3783i	−0.260418	−	0.965496i
$193$	−12.9721	+	9.42481i	−0.933755	+	0.678413i	−0.946909	−	0.321501i	$-0.895813\pi$
$193$	−12.9721	+	9.42481i	−0.933755	+	0.678413i	0.0131545	+	0.999913i	$0.495813\pi$
$194$	2.13558	−	4.19130i	0.153325	−	0.300918i
$195$	−2.18088	−	1.76007i	−0.156176	−	0.126041i
$196$	8.16348	−	11.2361i	0.583106	−	0.802576i
$197$			6.61803i			0.471515i	0.971812	+	0.235758i	$0.0757572\pi$
$197$			6.61803i			0.471515i	−0.971812	+	0.235758i	$0.924243\pi$
$198$	−4.84873	+	13.2095i	−0.344585	+	0.938755i
$199$		−	2.05573i		−	0.145727i	−0.997342	−	0.0728634i	$-0.976786\pi$
$199$		−	2.05573i		−	0.145727i	0.997342	−	0.0728634i	$-0.0232137\pi$
$200$	−6.65427	+	1.05393i	−0.470528	+	0.0745243i
$201$	3.84693	+	3.10465i	0.271341	+	0.218985i
$202$	−6.30037	−	3.21020i	−0.443292	−	0.225869i
$203$	0.763932	−	0.555029i	0.0536175	−	0.0389554i
$204$	17.0245	−	4.59191i	1.19195	−	0.321498i
$205$	−4.73607	−	14.5761i	−0.330781	−	1.01804i
$206$	11.1820	+	21.9460i	0.779088	+	1.52905i
$207$	−1.11736	−	5.17249i	−0.0776616	−	0.359513i
$208$	4.00000			0.277350
$209$	−13.8496	+	8.20820i	−0.957995	+	0.567773i
$210$	0.381966	+	0.854102i	0.0263582	+	0.0589386i
$211$	−6.69015	+	9.20820i	−0.460569	+	0.633919i	−0.974627	−	0.223837i	$-0.928142\pi$
$211$	−6.69015	+	9.20820i	−0.460569	+	0.633919i	0.514058	+	0.857756i	$0.328142\pi$
$212$	−7.32624	+	22.5478i	−0.503168	+	1.54859i
$213$	−0.534627	+	10.5349i	−0.0366320	+	0.721841i
$214$	0.329740	+	0.0522257i	0.0225406	+	0.00357008i
$215$	8.16312	−	5.93085i	0.556720	−	0.404481i
$216$	−0.0729839	−	14.6968i	−0.00496592	−	0.999988i
$217$	−0.427051	+	1.31433i	−0.0289901	+	0.0892224i
$218$	2.82379	+	17.8287i	0.191251	+	1.20751i
$219$	12.4721	+	4.76393i	0.842789	+	0.321917i
$220$	10.4721	−	2.35114i	0.706031	−	0.158514i
$221$			5.09017i			0.342402i
$222$	5.17240	−	24.5338i	0.347148	−	1.64660i
$223$	−19.6947	−	6.39919i	−1.31885	−	0.428521i	−0.436752	−	0.899582i	$-0.643871\pi$
$223$	−19.6947	−	6.39919i	−1.31885	−	0.428521i	−0.882101	+	0.471061i	$0.843871\pi$
$224$	−1.18985	−	0.606260i	−0.0795003	−	0.0405074i
$225$	−7.10919	−	0.723418i	−0.473946	−	0.0482279i
$226$	−0.221232	+	1.39680i	−0.0147161	+	0.0929139i
$227$	−3.21885	−	9.90659i	−0.213642	−	0.657524i	−0.999247	−	0.0387950i	$-0.987648\pi$
$227$	−3.21885	−	9.90659i	−0.213642	−	0.657524i	0.785605	−	0.618729i	$-0.212352\pi$
$228$	10.5604	−	13.0853i	0.699382	−	0.866594i
$229$	10.8541	+	7.88597i	0.717259	+	0.521119i	0.885507	−	0.464625i	$-0.153811\pi$
$229$	10.8541	+	7.88597i	0.717259	+	0.521119i	−0.168248	+	0.985745i	$0.553811\pi$
$230$	−2.85410	+	2.85410i	−0.188194	+	0.188194i
$231$	0.631396	+	1.20015i	0.0415428	+	0.0789642i
$232$	8.00000	+	8.00000i	0.525226	+	0.525226i
$233$	10.9106	−	15.0172i	0.714780	−	0.983811i	−0.284901	−	0.958557i	$-0.591961\pi$
$233$	10.9106	−	15.0172i	0.714780	−	0.983811i	0.999681	−	0.0252538i	$-0.00803939\pi$
$234$	4.10169	+	1.08450i	0.268136	+	0.0708962i
$235$	10.1841	−	3.30902i	0.664338	−	0.215856i
$236$	1.00406	+	1.38197i	0.0653585	+	0.0899583i
$237$	−7.74930	−	28.7305i	−0.503371	−	1.86625i
$238$	0.771491	−	1.51414i	0.0500084	−	0.0981469i
$239$	5.95492	−	18.3273i	0.385191	−	1.18550i	−0.551150	−	0.834406i	$-0.685811\pi$
$239$	5.95492	−	18.3273i	0.385191	−	1.18550i	0.936341	−	0.351091i	$-0.114189\pi$
$240$	−9.39144	+	6.12099i	−0.606215	+	0.395109i
$241$	5.41641			0.348902			0.174451	−	0.984666i	$-0.444185\pi$
$241$	5.41641			0.348902			0.174451	+	0.984666i	$0.444185\pi$
$242$	14.9305	−	4.36817i	0.959767	−	0.280797i
$243$	3.90983	−	15.0902i	0.250816	−	0.968035i
$244$	−7.15942	+	9.85410i	−0.458335	+	0.630844i
$245$	−10.6861	−	3.47214i	−0.682712	−	0.221827i
$246$	15.5536	+	17.2166i	0.991663	+	1.09769i
$247$	2.85317	+	3.92705i	0.181543	+	0.249872i
$248$	−16.3540	−	2.59023i	−1.03848	−	0.164480i
$249$	0.397480	−	7.83241i	0.0251893	−	0.496359i
$250$	7.66869	+	15.0507i	0.485011	+	0.951887i
$251$	−18.0623	−	13.1230i	−1.14008	−	0.828319i	−0.152952	−	0.988234i	$-0.548878\pi$
$251$	−18.0623	−	13.1230i	−1.14008	−	0.828319i	−0.987131	+	0.159915i	$0.948878\pi$
$252$	−1.05573	−	0.944272i	−0.0665046	−	0.0594835i
$253$	−3.86475	+	4.39201i	−0.242974	+	0.276123i
$254$	−8.18034	+	8.18034i	−0.513280	+	0.513280i
$255$	−7.78923	−	11.9510i	−0.487780	−	0.748401i
$256$	4.94427	−	15.2169i	0.309017	−	0.951057i
$257$	13.8496	−	4.50000i	0.863913	−	0.280702i	0.156651	−	0.987654i	$-0.449930\pi$
$257$	13.8496	−	4.50000i	0.863913	−	0.280702i	0.707262	+	0.706952i	$0.249930\pi$
$258$	−7.61568	+	13.2413i	−0.474132	+	0.824369i
$259$	−1.42033	−	1.95492i	−0.0882549	−	0.121473i
$260$	−1.00000	−	3.07768i	−0.0620174	−	0.190870i
$261$	6.03437	+	10.3724i	0.373518	+	0.642034i
$262$	−3.67644	−	23.2121i	−0.227131	−	1.43405i
$263$	4.85410			0.299317			0.149658	−	0.988738i	$-0.452183\pi$
$263$	4.85410			0.299317			0.149658	+	0.988738i	$0.452183\pi$
$264$	−13.0191	+	9.72133i	−0.801267	+	0.598307i
$265$	19.1803			1.17824
$266$	−0.253509	−	1.60059i	−0.0155436	−	0.0981387i
$267$	9.67808	+	7.81067i	0.592289	+	0.478005i
$268$	1.76393	+	5.42882i	0.107749	+	0.331618i
$269$	−11.8617	−	16.3262i	−0.723221	−	0.995428i	−0.999411	−	0.0343252i	$-0.989072\pi$
$269$	−11.8617	−	16.3262i	−0.723221	−	0.995428i	0.276190	−	0.961103i	$-0.410928\pi$
$270$	−11.2897	+	3.73034i	−0.687072	+	0.227022i
$271$	12.9515	−	4.20820i	0.786749	−	0.255630i	0.112030	−	0.993705i	$-0.464265\pi$
$271$	12.9515	−	4.20820i	0.786749	−	0.255630i	0.674719	+	0.738075i	$0.264265\pi$
$272$	19.3642	+	6.29180i	1.17412	+	0.381496i
$273$	0.342548	−	0.223260i	0.0207319	−	0.0135123i
$274$	−9.76393	+	9.76393i	−0.589861	+	0.589861i
$275$	4.02786	+	6.79615i	0.242889	+	0.409823i
$276$	2.18034	−	5.70820i	0.131241	−	0.343594i
$277$	−13.4443	−	9.76784i	−0.807788	−	0.586892i	0.105400	−	0.994430i	$-0.466388\pi$
$277$	−13.4443	−	9.76784i	−0.807788	−	0.586892i	−0.913188	+	0.407538i	$0.866388\pi$
$278$	−4.55217	−	8.93414i	−0.273021	−	0.535834i
$279$	−16.0675	−	7.09008i	−0.961938	−	0.424472i
$280$	−0.169006	+	1.06706i	−0.0101000	+	0.0637691i
$281$	−3.63271	−	5.00000i	−0.216709	−	0.298275i	0.686797	−	0.726849i	$-0.259016\pi$
$281$	−3.63271	−	5.00000i	−0.216709	−	0.298275i	−0.903507	+	0.428574i	$0.859016\pi$
$282$	−12.0290	+	10.8671i	−0.716317	+	0.647125i
$283$	21.0948	+	6.85410i	1.25395	+	0.407434i	0.859336	−	0.511412i	$-0.170877\pi$
$283$	21.0948	+	6.85410i	1.25395	+	0.407434i	0.394617	+	0.918846i	$0.370877\pi$
$284$	−7.15942	+	9.85410i	−0.424834	+	0.584733i
$285$	−12.7082	−	4.85410i	−0.752769	−	0.287532i
$286$	−1.73076	−	4.35941i	−0.102342	−	0.257777i
$287$	2.23607			0.131991
$288$	9.19566	−	14.2632i	0.541860	−	0.840469i
$289$	−2.75329	+	8.47375i	−0.161958	+	0.498456i
$290$	4.15537	−	8.15537i	0.244012	−	0.478900i
$291$	5.56243	−	1.50032i	0.326075	−	0.0879504i
$292$	9.06154	+	12.4721i	0.530286	+	0.729877i
$293$	−4.20025	+	1.36475i	−0.245381	+	0.0797293i	−0.429126	−	0.903245i	$-0.641178\pi$
$293$	−4.20025	+	1.36475i	−0.245381	+	0.0797293i	0.183744	+	0.982974i	$0.441178\pi$
$294$	16.9138	−	1.80602i	0.986431	−	0.105329i
$295$	0.812299	−	1.11803i	0.0472939	−	0.0650945i
$296$	20.4721	−	20.4721i	1.18992	−	1.18992i
$297$	−15.9857	+	6.43867i	−0.927586	+	0.373610i
$298$	−2.70820	+	2.70820i	−0.156882	+	0.156882i
$299$	1.42705	+	1.03681i	0.0825285	+	0.0599605i
$300$	−6.42111	−	5.18213i	−0.370723	−	0.299191i
$301$	0.454915	+	1.40008i	0.0262209	+	0.0806995i
$302$	1.22294	−	7.72133i	0.0703722	−	0.444313i
$303$	−2.25528	−	8.36144i	−0.129563	−	0.480352i
$304$	18.4661	−	6.00000i	1.05910	−	0.344124i
$305$	9.37181	+	3.04508i	0.536628	+	0.174361i
$306$	18.1506	+	11.7019i	1.03760	+	0.668951i
$307$		−	0.618034i		−	0.0352731i	−0.999844	−	0.0176365i	$-0.994386\pi$
$307$		−	0.618034i		−	0.0352731i	0.999844	−	0.0176365i	$-0.00561417\pi$
$308$	−0.145898	+	1.55909i	−0.00831331	+	0.0888372i
$309$	−10.7639	+	28.1803i	−0.612339	+	1.60312i
$310$	2.09554	+	13.2307i	0.119019	+	0.751453i
$311$	8.54508	−	26.2991i	0.484547	−	1.49128i	−0.348088	−	0.937462i	$-0.613169\pi$
$311$	8.54508	−	26.2991i	0.484547	−	1.49128i	0.832635	−	0.553821i	$-0.186831\pi$
$312$	3.28408	+	3.63522i	0.185924	+	0.205804i
$313$	8.04508	−	5.84510i	0.454735	−	0.330384i	−0.336727	−	0.941602i	$-0.609320\pi$
$313$	8.04508	−	5.84510i	0.454735	−	0.330384i	0.791462	+	0.611218i	$0.209320\pi$
$314$	3.45309	+	0.546915i	0.194869	+	0.0308642i
$315$	−0.462611	+	1.04837i	−0.0260651	+	0.0590688i
$316$	10.6180	−	32.6789i	0.597311	−	1.83833i
$317$	−7.74721	+	10.6631i	−0.435127	+	0.598900i	−0.969120	−	0.246588i	$-0.920691\pi$
$317$	−7.74721	+	10.6631i	−0.435127	+	0.598900i	0.533994	+	0.845488i	$0.320691\pi$
$318$	−26.5066	+	11.8541i	−1.48642	+	0.664745i
$319$	5.25731	−	12.1803i	0.294353	−	0.681968i
$320$	−12.9443			−0.723607
$321$	0.223260	+	0.342548i	0.0124612	+	0.0191192i
$322$	−0.267350	−	0.524705i	−0.0148989	−	0.0292406i
$323$	7.63525	+	23.4989i	0.424837	+	1.30751i
$324$	13.2966	−	12.1327i	0.738698	−	0.674036i
$325$	1.92705	−	1.40008i	0.106894	−	0.0776627i
$326$	−6.78167	−	3.45543i	−0.375602	−	0.191379i
$327$	−13.8844	+	17.2040i	−0.767810	+	0.951382i
$328$	4.19107	+	26.4614i	0.231413	+	1.46109i
$329$			1.56231i			0.0861327i
$330$	10.7346	+	7.58680i	0.590918	+	0.417639i
$331$			13.2918i			0.730583i	0.930893	+	0.365292i	$0.119031\pi$
$331$			13.2918i			0.730583i	−0.930893	+	0.365292i	$0.880969\pi$
$332$	5.32282	−	7.32624i	0.292128	−	0.402080i
$333$	26.5431	−	15.4421i	1.45455	−	0.846220i
$334$	−3.60700	+	7.07914i	−0.197366	+	0.387353i
$335$	3.73607	−	2.71441i	0.204123	−	0.148304i
$336$	−0.425920	−	1.57909i	−0.0232358	−	0.0861467i
$337$	9.90983	+	30.4993i	0.539823	+	1.66140i	0.732991	+	0.680238i	$0.238124\pi$
$337$	9.90983	+	30.4993i	0.539823	+	1.66140i	−0.193168	+	0.981166i	$0.561876\pi$
$338$	15.1209	−	7.70447i	0.822468	−	0.419068i
$339$	−1.45106	+	0.945746i	−0.0788106	+	0.0513659i
$340$		−	16.4721i		−	0.893327i
$341$	4.25325	+	18.9443i	0.230327	+	1.02589i
$342$	20.5623	−	1.14590i	1.11188	−	0.0619631i
$343$	1.93487	−	2.66312i	0.104473	−	0.143795i
$344$	−15.7158	+	8.00760i	−0.847340	+	0.431741i
$345$	−4.93710	−	0.250548i	−0.265804	−	0.0134891i
$346$	0.840321	−	5.30558i	0.0451759	−	0.285230i
$347$	−26.7984	+	19.4702i	−1.43861	+	1.04521i	−0.450282	+	0.892886i	$0.648676\pi$
$347$	−26.7984	+	19.4702i	−1.43861	+	1.04521i	−0.988330	+	0.152326i	$0.951324\pi$
$348$	−0.702282	+	13.8386i	−0.0376463	+	0.741827i
$349$	7.72542	−	23.7764i	0.413533	−	1.27272i	−0.500024	−	0.866011i	$-0.666676\pi$
$349$	7.72542	−	23.7764i	0.413533	−	1.27272i	0.913557	−	0.406711i	$-0.133324\pi$
$350$	−0.785430	+	0.124400i	−0.0419830	+	0.00664946i
$351$	2.38197	+	4.61803i	0.127140	+	0.246492i
$352$	−18.7235	+	1.19566i	−0.997967	+	0.0637290i
$353$		−	15.7082i		−	0.836063i	−0.908432	−	0.418032i	$-0.862720\pi$
$353$		−	15.7082i		−	0.836063i	0.908432	−	0.418032i	$-0.137280\pi$
$354$	−0.431587	+	2.04711i	−0.0229386	+	0.108803i
$355$	9.37181	+	3.04508i	0.497404	+	0.161616i
$356$	4.43769	+	13.6578i	0.235197	+	0.723863i
$357$	2.00947	−	0.542001i	0.106352	−	0.0286858i
$358$	−11.7561	−	1.86198i	−0.621327	−	0.0984085i
$359$	5.52786	+	17.0130i	0.291750	+	0.897913i	0.984294	+	0.176537i	$0.0564897\pi$
$359$	5.52786	+	17.0130i	0.291750	+	0.897913i	−0.692544	+	0.721375i	$0.743510\pi$
$360$	−13.2733	−	3.50953i	−0.699567	−	0.184968i
$361$	3.69098	+	2.68166i	0.194262	+	0.141140i
$362$	−12.5279	−	12.5279i	−0.658450	−	0.658450i
$363$	16.2280	+	9.98254i	0.851751	+	0.523947i
$364$	0.472136			0.0247466
$365$	7.33094	−	10.0902i	0.383719	−	0.528144i
$366$	−14.8335	+	1.58389i	−0.775359	+	0.0827914i
$367$	−12.6740	+	4.11803i	−0.661578	+	0.214960i	−0.620512	−	0.784197i	$-0.713075\pi$
$367$	−12.6740	+	4.11803i	−0.661578	+	0.214960i	−0.0410655	+	0.999156i	$0.513075\pi$
$368$	5.70820	−	4.14725i	0.297561	−	0.216191i
$369$	−2.87675	+	28.2704i	−0.149757	+	1.47170i
$370$	−20.8697	−	10.6337i	−1.08497	−	0.552817i
$371$	−0.864745	+	2.66141i	−0.0448953	+	0.138174i
$372$	−11.0730	−	16.9893i	−0.574107	−	0.880852i
$373$	−25.4721			−1.31890			−0.659449	−	0.751750i	$-0.729210\pi$
$373$	−25.4721			−1.31890			−0.659449	+	0.751750i	$0.729210\pi$
$374$	−1.52153	−	23.8265i	−0.0786764	−	1.23204i
$375$	−7.38197	+	19.3262i	−0.381203	+	0.998003i
$376$	−18.4882	+	2.92824i	−0.953455	+	0.151012i
$377$	−3.80423	−	1.23607i	−0.195928	−	0.0636607i
$378$	−0.00861458	−	1.73472i	−0.000443086	−	0.0892242i
$379$	−13.7966	−	18.9894i	−0.708682	−	0.975418i	−0.999824	−	0.0187379i	$-0.994035\pi$
$379$	−13.7966	−	18.9894i	−0.708682	−	0.975418i	0.291142	−	0.956680i	$-0.405965\pi$
$380$	−9.23305	−	12.7082i	−0.473646	−	0.651917i
$381$	−14.1506	−	0.718113i	−0.724955	−	0.0367901i
$382$	−13.1254	+	6.68775i	−0.671556	+	0.342175i
$383$	20.6074	+	14.9721i	1.05299	+	0.765041i	0.972778	−	0.231737i	$-0.0744409\pi$
$383$	20.6074	+	14.9721i	1.05299	+	0.765041i	0.0802100	+	0.996778i	$0.474441\pi$
$384$	17.8885	−	8.00000i	0.912871	−	0.408248i
$385$	1.23607	−	0.277515i	0.0629959	−	0.0141435i
$386$	−16.0344	−	16.0344i	−0.816132	−	0.816132i
$387$	−18.2864	+	3.95022i	−0.929550	+	0.200801i
$388$	6.32688	+	2.05573i	0.321199	+	0.104364i
$389$	28.6705	−	9.31559i	1.45365	−	0.472319i	0.527526	−	0.849539i	$-0.323120\pi$
$389$	28.6705	−	9.31559i	1.45365	−	0.472319i	0.926124	+	0.377220i	$0.123120\pi$
$390$	1.97599	−	3.43564i	0.100058	−	0.173971i
$391$	5.27756	+	7.26393i	0.266897	+	0.367353i
$392$	17.5006	+	8.91699i	0.883913	+	0.450376i
$393$	18.0769	−	22.3988i	0.911857	−	1.12987i
$394$	−9.24408	+	1.46412i	−0.465710	+	0.0737613i
$395$	−27.7984			−1.39869
$396$	−19.5237	−	3.85037i	−0.981103	−	0.193488i
$397$	−1.47214			−0.0738844			−0.0369422	−	0.999317i	$-0.511762\pi$
$397$	−1.47214			−0.0738844			−0.0369422	+	0.999317i	$0.511762\pi$
$398$	2.87145	−	0.454792i	0.143933	−	0.0227967i
$399$	1.24649	−	1.54451i	0.0624026	−	0.0773221i
$400$	−2.94427	−	9.06154i	−0.147214	−	0.453077i
$401$	−7.07367	−	9.73607i	−0.353242	−	0.486196i	0.595008	−	0.803720i	$-0.297149\pi$
$401$	−7.07367	−	9.73607i	−0.353242	−	0.486196i	−0.948250	+	0.317524i	$0.897149\pi$
$402$	−3.48552	+	6.06024i	−0.173842	+	0.302257i
$403$	5.56758	−	1.80902i	0.277341	−	0.0901136i
$404$	3.09017	−	9.51057i	0.153742	−	0.473168i
$405$	−12.6593	−	7.19749i	−0.629044	−	0.357646i
$406$	0.944272	+	0.944272i	0.0468634	+	0.0468634i
$407$	−31.1697	−	13.4535i	−1.54502	−	0.666868i
$408$	10.1803	+	22.7639i	0.504002	+	1.12698i
$409$	25.6525	+	18.6376i	1.26843	+	0.921571i	0.999139	−	0.0414872i	$-0.0132096\pi$
$409$	25.6525	+	18.6376i	1.26843	+	0.921571i	0.269294	+	0.963058i	$0.413210\pi$
$410$	19.3122	−	9.84005i	0.953761	−	0.485965i
$411$	−16.8899	−	0.857129i	−0.833117	−	0.0422791i
$412$	−28.1803	+	20.4742i	−1.38835	+	1.00869i
$413$	0.118513	+	0.163119i	0.00583164	+	0.00802656i
$414$	6.97775	−	2.70504i	0.342938	−	0.132946i
$415$	−6.96767	−	2.26393i	−0.342029	−	0.111132i
$416$	0.884927	+	5.58721i	0.0433871	+	0.273935i
$417$	4.38197	−	11.4721i	0.214586	−	0.561793i
$418$	−14.5292	−	17.5292i	−0.710647	−	0.857381i
$419$	7.03444			0.343655			0.171827	−	0.985127i	$-0.445033\pi$
$419$	7.03444			0.343655			0.171827	+	0.985127i	$0.445033\pi$
$420$	−1.10851	+	0.722485i	−0.0540897	+	0.0352537i
$421$	−1.02786	+	3.16344i	−0.0500950	+	0.154177i	−0.972975	−	0.230912i	$-0.925829\pi$
$421$	−1.02786	+	3.16344i	−0.0500950	+	0.154177i	0.922880	+	0.385089i	$0.125829\pi$
$422$	−14.3421	−	7.30767i	−0.698163	−	0.355732i
$423$	−19.7521	−	2.00994i	−0.960380	−	0.0977265i
$424$	−33.1157	−	5.24501i	−1.60824	−	0.254720i
$425$	11.5312	−	3.74671i	0.559345	−	0.181742i
$426$	−14.8335	+	1.58389i	−0.718685	+	0.0767398i
$427$	−0.845055	+	1.16312i	−0.0408951	+	0.0562873i
$428$			0.472136i			0.0228216i
$429$	2.54087	−	5.15208i	0.122674	−	0.248745i
$430$	10.0902	+	10.0902i	0.486591	+	0.486591i
$431$	11.7361	+	8.52675i	0.565307	+	0.410719i	0.833397	−	0.552674i	$-0.186393\pi$
$431$	11.7361	+	8.52675i	0.565307	+	0.410719i	−0.268091	+	0.963394i	$0.586393\pi$
$432$	20.5123	−	3.35333i	0.986899	−	0.161337i
$433$	3.79837	+	11.6902i	0.182538	+	0.561795i	0.999897	−	0.0143338i	$-0.00456274\pi$
$433$	3.79837	+	11.6902i	0.182538	+	0.561795i	−0.817359	+	0.576129i	$0.804563\pi$
$434$	−1.93033	−	0.305735i	−0.0926590	−	0.0146757i
$435$	10.8233	−	2.91930i	0.518936	−	0.139970i
$436$	−24.2784	+	7.88854i	−1.16273	+	0.377793i
$437$	8.14324	+	2.64590i	0.389544	+	0.126570i
$438$	−3.89504	+	18.4750i	−0.186112	+	0.882772i
$439$		−	23.3607i		−	1.11494i	−0.830196	−	0.557472i	$-0.811771\pi$
$439$		−	23.3607i		−	1.11494i	0.830196	−	0.557472i	$-0.188229\pi$
$440$	5.60085	+	14.1074i	0.267010	+	0.672542i
$441$	15.5279	+	13.8885i	0.739422	+	0.661359i
$442$	−7.10996	+	1.12611i	−0.338186	+	0.0535635i
$443$	−4.61803	+	14.2128i	−0.219409	+	0.675273i	0.779402	+	0.626525i	$0.215523\pi$
$443$	−4.61803	+	14.2128i	−0.219409	+	0.675273i	−0.998811	+	0.0487482i	$0.984477\pi$
$444$	35.4132	+	1.79715i	1.68064	+	0.0852890i
$445$	9.39919	−	6.82891i	0.445564	−	0.323721i
$446$	4.58131	−	28.9253i	0.216931	−	1.36965i
$447$	−4.68472	−	0.237740i	−0.221580	−	0.0112447i
$448$	0.583592	−	1.79611i	0.0275721	−	0.0848583i
$449$	3.73871	−	5.14590i	0.176441	−	0.242850i	−0.711632	−	0.702552i	$-0.752044\pi$
$449$	3.73871	−	5.14590i	0.176441	−	0.242850i	0.888073	+	0.459702i	$0.152044\pi$
$450$	−0.562306	−	10.0902i	−0.0265074	−	0.475655i
$451$	27.0256	−	16.0172i	1.27259	−	0.754221i
$452$	−2.00000			−0.0940721
$453$	8.02124	−	5.22795i	0.376871	−	0.245631i
$454$	13.1254	−	6.68775i	0.616007	−	0.313871i
$455$	−0.118034	−	0.363271i	−0.00553352	−	0.0170304i
$456$	20.6139	+	11.8560i	0.965333	+	0.555207i
$457$	6.35410	−	4.61653i	0.297232	−	0.215952i	−0.429166	−	0.903225i	$-0.641193\pi$
$457$	6.35410	−	4.61653i	0.297232	−	0.215952i	0.726399	+	0.687274i	$0.241193\pi$
$458$	−8.61386	+	16.9057i	−0.402499	+	0.789950i
$459$	4.26726	+	26.1028i	0.199179	+	1.21837i
$460$	−4.61803	−	3.35520i	−0.215317	−	0.156437i
$461$			19.1459i			0.891713i	0.895104	+	0.445857i	$0.147101\pi$
$461$			19.1459i			0.891713i	−0.895104	+	0.445857i	$0.852899\pi$
$462$	−1.53669	+	1.14745i	−0.0714933	+	0.0533841i
$463$			3.56231i			0.165554i	0.996568	+	0.0827772i	$0.0263790\pi$
$463$			3.56231i			0.165554i	−0.996568	+	0.0827772i	$0.973621\pi$
$464$	−9.40456	+	12.9443i	−0.436596	+	0.600923i
$465$	−10.3036	+	12.7671i	−0.477820	+	0.592060i
$466$	23.3899	+	11.9177i	1.08351	+	0.552078i
$467$	2.04508	−	1.48584i	0.0946352	−	0.0687565i	−0.539461	−	0.842010i	$-0.681372\pi$
$467$	2.04508	−	1.48584i	0.0946352	−	0.0687565i	0.634097	+	0.773254i	$0.281372\pi$
$468$	−0.607412	+	5.96917i	−0.0280776	+	0.275925i
$469$	0.208204	+	0.640786i	0.00961396	+	0.0295887i
$470$	6.87509	+	13.4931i	0.317124	+	0.622391i
$471$	2.33801	+	3.58721i	0.107730	+	0.165290i
$472$	−1.70820	+	1.70820i	−0.0786265	+	0.0786265i
$473$	15.5272	+	13.6631i	0.713940	+	0.628231i
$474$	38.4164	−	17.1803i	1.76452	−	0.789119i
$475$	6.79615	−	9.35410i	0.311829	−	0.429196i
$476$	2.28563	+	0.742646i	0.104762	+	0.0340391i
$477$	−32.5355	−	14.3569i	−1.48970	−	0.657355i
$478$	26.9171	+	4.26325i	1.23116	+	0.194996i
$479$	1.97214	−	1.43284i	0.0901092	−	0.0654682i	−0.541818	−	0.840496i	$-0.682264\pi$
$479$	1.97214	−	1.43284i	0.0901092	−	0.0654682i	0.631928	+	0.775027i	$0.282264\pi$
$480$	−10.6275	−	11.7638i	−0.485077	−	0.536942i
$481$	−3.16312	+	9.73508i	−0.144226	+	0.443881i
$482$	1.19828	+	7.56565i	0.0545802	+	0.344606i
$483$	0.257354	−	0.673762i	0.0117100	−	0.0306572i
$484$	9.40456	+	19.8885i	0.427480	+	0.904025i
$485$		−	5.38197i		−	0.244382i
$486$	21.9430	+	2.12283i	0.995353	+	0.0962937i
$487$	12.9843	+	4.21885i	0.588374	+	0.191174i	0.588048	−	0.808826i	$-0.299896\pi$
$487$	12.9843	+	4.21885i	0.588374	+	0.191174i	0.000325311		1.00000i	$0.499896\pi$
$488$	−15.3481	−	7.82026i	−0.694777	−	0.354007i
$489$	−2.42757	−	9.00020i	−0.109779	−	0.407003i
$490$	2.48577	−	15.6946i	0.112296	−	0.709008i
$491$	−12.0451	−	37.0710i	−0.543587	−	1.67299i	−0.724326	−	0.689458i	$-0.757849\pi$
$491$	−12.0451	−	37.0710i	−0.543587	−	1.67299i	0.180739	−	0.983531i	$-0.442151\pi$
$492$	−20.6073	+	25.5342i	−0.929049	+	1.15117i
$493$	−16.4721	−	11.9677i	−0.741868	−	0.538998i
$494$	−4.85410	+	4.85410i	−0.218396	+	0.218396i
$495$	1.91837	+	15.9845i	0.0862242	+	0.718451i
$496$		−	23.4164i		−	1.05143i
$497$	−0.845055	+	1.16312i	−0.0379059	+	0.0521730i
$498$	11.0283	−	1.17758i	0.494188	−	0.0527685i
$499$	−2.99193	+	0.972136i	−0.133937	+	0.0435188i	−0.375218	−	0.926936i	$-0.622432\pi$
$499$	−2.99193	+	0.972136i	−0.133937	+	0.0435188i	0.241281	+	0.970455i	$0.422432\pi$
$500$	−19.3262	+	14.0413i	−0.864296	+	0.627948i
$501$	−9.39497	+	2.53405i	−0.419736	+	0.113213i
$502$	14.3343	−	28.1327i	0.639772	−	1.25562i
$503$	9.20163	−	28.3197i	0.410280	−	1.26271i	−0.506125	−	0.862460i	$-0.668922\pi$
$503$	9.20163	−	28.3197i	0.410280	−	1.26271i	0.916405	−	0.400252i	$-0.131078\pi$
$504$	1.08540	−	1.68355i	0.0483476	−	0.0749911i
$505$	−8.09017			−0.360008
$506$	−6.98978	−	4.42663i	−0.310733	−	0.196788i
$507$	19.4164	+	7.41641i	0.862313	+	0.329374i
$508$	−13.2361	−	9.61657i	−0.587256	−	0.426666i
$509$	−32.9237	−	10.6976i	−1.45932	−	0.474161i	−0.531456	−	0.847086i	$-0.678355\pi$
$509$	−32.9237	−	10.6976i	−1.45932	−	0.474161i	−0.927862	+	0.372925i	$0.878355\pi$
$510$	14.9700	−	13.5239i	0.662881	−	0.598851i
$511$	1.06957	+	1.47214i	0.0473150	+	0.0651235i
$512$	22.3488	+	3.53971i	0.987688	+	0.156434i
$513$	17.9235	+	17.7463i	0.791340	+	0.783519i
$514$	9.34958	+	18.3496i	0.412392	+	0.809365i
$515$	22.7984	+	16.5640i	1.00462	+	0.729897i
$516$	−20.1803	−	7.70820i	−0.888390	−	0.339335i
$517$	11.1910	+	18.8824i	0.492179	+	0.830446i
$518$	2.41641	−	2.41641i	0.106171	−	0.106171i
$519$	5.51166	−	3.59230i	0.241935	−	0.157684i
$520$	4.07768	−	2.07768i	0.178818	−	0.0911125i
$521$	−32.7849	+	10.6525i	−1.43633	+	0.466693i	−0.920753	−	0.390147i	$-0.872424\pi$
$521$	−32.7849	+	10.6525i	−1.43633	+	0.466693i	−0.515582	+	0.856840i	$0.672424\pi$
$522$	−13.1532	+	10.7235i	−0.575699	+	0.469356i
$523$	9.66183	+	13.2984i	0.422483	+	0.581497i	0.966207	−	0.257766i	$-0.0829865\pi$
$523$	9.66183	+	13.2984i	0.422483	+	0.581497i	−0.543725	+	0.839264i	$0.682986\pi$
$524$	31.6094	−	10.2705i	1.38086	−	0.448669i
$525$	−0.757909	−	0.611668i	−0.0330779	−	0.0266954i
$526$	1.07388	+	6.78022i	0.0468235	+	0.295632i
$527$	29.7984			1.29804
$528$	−16.4590	−	16.0344i	−0.716286	−	0.697806i
$529$	−19.8885			−0.864719
$530$	4.24330	+	26.7911i	0.184317	+	1.16373i
$531$	−2.21477	+	1.28849i	−0.0961128	+	0.0559158i
$532$	2.17963	−	0.708204i	0.0944988	−	0.0307045i
$533$	−5.56758	−	7.66312i	−0.241159	−	0.331927i
$534$	−8.76886	+	15.2463i	−0.379466	+	0.659774i
$535$	0.363271	−	0.118034i	0.0157056	−	0.00510305i
$536$	−7.19276	+	3.66489i	−0.310680	+	0.158299i
$537$	−7.95978	−	12.2127i	−0.343490	−	0.527016i
$538$	20.1803	−	20.1803i	0.870036	−	0.870036i
$539$	2.14590	−	22.9314i	0.0924304	−	0.987723i
$540$	−7.70820	−	14.9443i	−0.331708	−	0.643099i
$541$	−5.39919	−	3.92274i	−0.232129	−	0.168652i	0.465640	−	0.884974i	$-0.345824\pi$
$541$	−5.39919	−	3.92274i	−0.232129	−	0.168652i	−0.697770	+	0.716322i	$0.745824\pi$
$542$	8.74332	+	17.1597i	0.375558	+	0.737073i
$543$	1.09976	−	21.6710i	0.0471953	−	0.929992i
$544$	−4.50443	+	28.4398i	−0.193126	+	1.21935i
$545$	12.1392	+	16.7082i	0.519987	+	0.715701i
$546$	0.387633	+	0.429080i	0.0165892	+	0.0183629i
$547$	−24.8662	−	8.07953i	−1.06320	−	0.345456i	−0.275366	−	0.961339i	$-0.588799\pi$
$547$	−24.8662	−	8.07953i	−1.06320	−	0.345456i	−0.787837	+	0.615884i	$0.788799\pi$
$548$	−15.7984	−	11.4782i	−0.674873	−	0.490324i
$549$	−13.6180	−	12.1803i	−0.581204	−	0.519844i
$550$	−8.60179	+	7.12965i	−0.366782	+	0.304009i
$551$	−19.4164			−0.827167
$552$	8.45559	+	1.78267i	0.359894	+	0.0758754i
$553$	1.25329	−	3.85723i	0.0532953	−	0.164026i
$554$	10.6694	−	20.9399i	0.453301	−	0.889653i
$555$	−7.47054	−	27.6969i	−0.317107	−	1.17567i
$556$	11.4721	−	8.33499i	0.486527	−	0.353483i
$557$	−8.42075	+	2.73607i	−0.356799	+	0.115931i	−0.481931	−	0.876209i	$-0.660064\pi$
$557$	−8.42075	+	2.73607i	−0.356799	+	0.115931i	0.125132	+	0.992140i	$0.460064\pi$
$558$	6.34879	−	24.0117i	0.268766	−	1.01650i
$559$	3.66547	−	5.04508i	0.155033	−	0.213384i
$560$	−1.52786			−0.0645640
$561$	20.4044	−	20.9448i	0.861475	−	0.884290i
$562$	6.18034	−	6.18034i	0.260702	−	0.260702i
$563$	5.80902	+	4.22050i	0.244821	+	0.177873i	0.703428	−	0.710766i	$-0.251652\pi$
$563$	5.80902	+	4.22050i	0.244821	+	0.177873i	−0.458607	+	0.888639i	$0.651652\pi$
$564$	−17.8404	−	14.3980i	−0.751214	−	0.606265i
$565$	0.500000	+	1.53884i	0.0210352	+	0.0647396i
$566$	−4.90700	+	30.9815i	−0.206256	+	1.30225i
$567$	1.56945	−	1.43207i	0.0659106	−	0.0601411i
$568$	−15.3481	−	7.82026i	−0.643993	−	0.328131i
$569$	−17.4620	−	5.67376i	−0.732047	−	0.237856i	−0.0808085	−	0.996730i	$-0.525750\pi$
$569$	−17.4620	−	5.67376i	−0.732047	−	0.237856i	−0.651238	+	0.758873i	$0.725750\pi$
$570$	3.96876	−	18.8247i	0.166233	−	0.788481i
$571$			32.5623i			1.36269i	0.731962	+	0.681345i	$0.238605\pi$
$571$			32.5623i			1.36269i	−0.731962	+	0.681345i	$0.761395\pi$
$572$	5.70634	−	3.38197i	0.238594	−	0.141407i
$573$	−16.8541	−	6.43769i	−0.704090	−	0.268939i
$574$	0.494689	+	3.12334i	0.0206479	+	0.130366i
$575$	1.29837	−	3.99598i	0.0541459	−	0.166644i
$576$	21.9573	+	9.68904i	0.914887	+	0.403710i
$577$	8.32624	−	6.04937i	0.346626	−	0.251838i	−0.400826	−	0.916154i	$-0.631277\pi$
$577$	8.32624	−	6.04937i	0.346626	−	0.251838i	0.747452	+	0.664316i	$0.231277\pi$
$578$	−12.4453	−	1.97114i	−0.517655	−	0.0819885i
$579$	1.40759	−	27.7368i	0.0584973	−	1.15270i
$580$	12.3107	+	4.00000i	0.511175	+	0.166091i
$581$	0.628274	−	0.864745i	0.0260652	−	0.0358757i
$582$	3.32624	+	7.43769i	0.137877	+	0.308302i
$583$	8.61251	+	38.3607i	0.356694	+	1.58874i
$584$	−15.4164	+	15.4164i	−0.637935	+	0.637935i
$585$	4.74466	−	1.02494i	0.196168	−	0.0423760i
$586$	−2.83551	−	5.56500i	−0.117134	−	0.229888i
$587$	1.12868	+	3.47371i	0.0465855	+	0.143375i	0.971644	−	0.236450i	$-0.0759840\pi$
$587$	1.12868	+	3.47371i	0.0465855	+	0.143375i	−0.925058	+	0.379826i	$0.875984\pi$
$588$	6.26452	+	23.2256i	0.258344	+	0.957810i
$589$	22.9894	−	16.7027i	0.947260	−	0.688225i
$590$	1.74138	+	0.887277i	0.0716914	+	0.0365286i
$591$	−8.92018	−	7.19900i	−0.366927	−	0.296127i
$592$	33.1246	+	24.0664i	1.36141	+	0.989125i
$593$			9.61803i			0.394965i	0.980306	+	0.197483i	$0.0632766\pi$
$593$			9.61803i			0.394965i	−0.980306	+	0.197483i	$0.936723\pi$
$594$	−12.5301	−	20.9045i	−0.514116	−	0.857721i
$595$		−	1.94427i		−	0.0797074i
$596$	−4.38197	−	3.18368i	−0.179492	−	0.130409i
$597$	2.77083	+	2.23619i	0.113403	+	0.0915212i
$598$	−1.13251	+	2.22268i	−0.0463119	+	0.0908923i
$599$	−17.0344	+	12.3762i	−0.696008	+	0.505680i	−0.878630	−	0.477504i	$-0.841542\pi$
$599$	−17.0344	+	12.3762i	−0.696008	+	0.505680i	0.182621	+	0.983183i	$0.441542\pi$
$600$	5.81787	−	10.1155i	0.237513	−	0.412962i
$601$	4.39919	+	13.5393i	0.179447	+	0.552280i	0.999809	−	0.0195648i	$-0.00622805\pi$
$601$	4.39919	+	13.5393i	0.179447	+	0.552280i	−0.820362	+	0.571845i	$0.806228\pi$
$602$	−1.85500	+	0.945169i	−0.0756041	+	0.0385222i
$603$	−8.36926	+	1.80792i	−0.340823	+	0.0736242i
$604$	11.0557			0.449851
$605$	12.9515	−	12.2082i	0.526554	−	0.496334i
$606$	11.1803	−	5.00000i	0.454170	−	0.203111i
$607$	18.2743	−	25.1525i	0.741733	−	1.02091i	−0.256784	−	0.966469i	$-0.582663\pi$
$607$	18.2743	−	25.1525i	0.741733	−	1.02091i	0.998517	−	0.0544388i	$-0.0173370\pi$
$608$	12.4661	+	24.4661i	0.505567	+	0.992231i
$609$	−0.0828931	+	1.63342i	−0.00335900	+	0.0661897i
$610$	−2.18004	+	13.7642i	−0.0882672	+	0.557297i
$611$	5.35410	−	3.88998i	0.216604	−	0.157372i
$612$	−12.3297	+	27.9416i	−0.498399	+	1.12947i
$613$	1.43769	−	4.42477i	0.0580679	−	0.178715i	−0.917815	−	0.397007i	$-0.870049\pi$
$613$	1.43769	−	4.42477i	0.0580679	−	0.178715i	0.975883	+	0.218293i	$0.0700487\pi$
$614$	0.863271	−	0.136729i	0.0348388	−	0.00551792i
$615$	24.7984	+	9.47214i	0.999967	+	0.381953i
$616$	−2.21001	+	0.141129i	−0.0890439	+	0.00568624i
$617$		−	24.2361i		−	0.975707i	−0.872925	−	0.487854i	$-0.837780\pi$
$617$		−	24.2361i		−	0.975707i	0.872925	−	0.487854i	$-0.162220\pi$
$618$	−41.7437	−	8.80070i	−1.67918	−	0.354016i
$619$	−25.4665	−	8.27458i	−1.02359	−	0.332583i	−0.251335	−	0.967900i	$-0.580869\pi$
$619$	−25.4665	−	8.27458i	−1.02359	−	0.332583i	−0.772251	+	0.635317i	$0.780869\pi$
$620$	−18.0171	+	5.85410i	−0.723583	+	0.235106i
$621$	8.18723	+	4.12052i	0.328542	+	0.165351i
$622$	38.6250	+	6.11761i	1.54872	+	0.245294i
$623$	0.523799	+	1.61209i	0.0209856	+	0.0645869i
$624$	−4.35114	+	5.39144i	−0.174185	+	0.215830i
$625$	6.00000	+	4.35926i	0.240000	+	0.174370i
$626$	9.94427	+	9.94427i	0.397453	+	0.397453i
$627$	4.00186	−	27.5960i	0.159819	−	1.10208i
$628$			4.94427i			0.197298i
$629$	−30.6256	+	42.1525i	−1.22112	+	1.68073i
$630$	−1.56671	−	0.414243i	−0.0624191	−	0.0165038i
$631$	−35.7239	+	11.6074i	−1.42215	+	0.462083i	−0.916283	−	0.400531i	$-0.868826\pi$
$631$	−35.7239	+	11.6074i	−1.42215	+	0.462083i	−0.505862	+	0.862614i	$0.668826\pi$
$632$	47.9951	+	7.60167i	1.90914	+	0.302378i
$633$	−5.13391	−	19.0339i	−0.204055	−	0.756531i
$634$	−16.6082	−	8.46230i	−0.659596	−	0.336081i
$635$	−4.09017	+	12.5882i	−0.162313	+	0.499549i
$636$	−22.4219	−	34.4019i	−0.889087	−	1.36413i
$637$	−6.94427			−0.275142
$638$	18.1766	+	4.64875i	0.719619	+	0.184046i
$639$	−13.6180	−	12.1803i	−0.538721	−	0.481847i
$640$	−2.86368	−	18.0806i	−0.113197	−	0.714698i
$641$	21.0745	+	6.84752i	0.832393	+	0.270461i	0.694053	−	0.719924i	$-0.255823\pi$
$641$	21.0745	+	6.84752i	0.832393	+	0.270461i	0.138340	+	0.990385i	$0.455823\pi$
$642$	−0.429080	+	0.387633i	−0.0169344	+	0.0152987i
$643$	−15.4742	−	21.2984i	−0.610242	−	0.839926i	0.386355	−	0.922350i	$-0.373734\pi$
$643$	−15.4742	−	21.2984i	−0.610242	−	0.839926i	−0.996597	+	0.0824241i	$0.973734\pi$
$644$	0.673762	−	0.489517i	0.0265499	−	0.0192897i
$645$	−0.885768	+	17.4542i	−0.0348771	+	0.687259i
$646$	−31.1342	+	15.8636i	−1.22496	+	0.624147i
$647$	−5.02786	−	3.65296i	−0.197666	−	0.143613i	0.484550	−	0.874764i	$-0.338983\pi$
$647$	−5.02786	−	3.65296i	−0.197666	−	0.143613i	−0.682216	+	0.731151i	$0.738983\pi$
$648$	19.8885	+	15.8885i	0.781296	+	0.624161i
$649$	2.60081	+	1.12257i	0.102091	+	0.0440647i
$650$	2.38197	+	2.38197i	0.0934284	+	0.0934284i
$651$	−1.30699	−	2.00531i	−0.0512249	−	0.0785943i
$652$	3.32624	−	10.2371i	0.130266	−	0.400916i
$653$	−1.76336	+	0.572949i	−0.0690054	+	0.0224212i	−0.343316	−	0.939220i	$-0.611550\pi$
$653$	−1.76336	+	0.572949i	−0.0690054	+	0.0224212i	0.274311	+	0.961641i	$0.411550\pi$
$654$	−27.1022	−	15.5877i	−1.05978	−	0.609528i
$655$	−15.8047	−	21.7533i	−0.617540	−	0.849971i
$656$	−36.0341	+	11.7082i	−1.40690	+	0.457129i
$657$	−19.9881	+	11.6285i	−0.779811	+	0.453673i
$658$	−2.18223	+	0.345632i	−0.0850723	+	0.0134741i
$659$	−13.4164			−0.522629			−0.261315	−	0.965254i	$-0.584156\pi$
$659$	−13.4164			−0.522629			−0.261315	+	0.965254i	$0.584156\pi$
$660$	−8.22243	+	16.6725i	−0.320058	+	0.648976i
$661$	−46.2148			−1.79755			−0.898773	−	0.438414i	$-0.855541\pi$
$661$	−46.2148			−1.79755			−0.898773	+	0.438414i	$0.855541\pi$
$662$	−18.5660	+	2.94057i	−0.721588	+	0.114288i
$663$	−6.86083	−	5.53701i	−0.266453	−	0.215040i
$664$	11.4109	+	5.81414i	0.442828	+	0.225632i
$665$	−1.08981	−	1.50000i	−0.0422612	−	0.0581675i
$666$	27.4417	+	33.6592i	1.06334	+	1.30427i
$667$	−6.71040	+	2.18034i	−0.259828	+	0.0844231i
$668$	−10.6861	−	3.47214i	−0.413459	−	0.134341i
$669$	30.0488	−	19.5847i	1.16175	−	0.757188i
$670$	4.61803	+	4.61803i	0.178410	+	0.178410i
$671$	−1.88197	+	20.1109i	−0.0726525	+	0.776374i
$672$	2.11146	−	0.944272i	0.0814512	−	0.0364261i
$673$	6.13525	+	4.45752i	0.236497	+	0.171825i	0.699721	−	0.714416i	$-0.253308\pi$
$673$	6.13525	+	4.45752i	0.236497	+	0.171825i	−0.463224	+	0.886241i	$0.653308\pi$
$674$	−40.4092	+	20.5895i	−1.55650	+	0.793078i
$675$	8.70833	−	8.79526i	0.335184	−	0.338530i
$676$	14.1068	+	19.4164i	0.542571	+	0.746785i
$677$	2.17963	+	3.00000i	0.0837699	+	0.115299i	0.848845	−	0.528641i	$-0.177298\pi$
$677$	2.17963	+	3.00000i	0.0837699	+	0.115299i	−0.765075	+	0.643941i	$0.777298\pi$
$678$	−1.64204	−	1.81761i	−0.0630621	−	0.0698049i
$679$	0.746787	+	0.242646i	0.0286591	+	0.00931189i
$680$	23.0083	−	3.64416i	0.882329	−	0.139747i
$681$	16.8541	+	6.43769i	0.645851	+	0.246693i
$682$	−25.5204	+	10.1320i	−0.977228	+	0.387975i
$683$	22.4164			0.857740			0.428870	−	0.903366i	$-0.358912\pi$
$683$	22.4164			0.857740			0.428870	+	0.903366i	$0.358912\pi$
$684$	6.14963	+	28.4680i	0.235137	+	1.08850i
$685$	−4.88197	+	15.0251i	−0.186530	+	0.574081i
$686$	4.14791	+	2.11346i	0.158368	+	0.0806924i
$687$	−22.4361	+	6.05156i	−0.855991	+	0.230881i
$688$	−14.6619	−	20.1803i	−0.558979	−	0.769368i
$689$	11.2739	−	3.66312i	0.429502	−	0.139554i
$690$	−0.742276	−	6.95158i	−0.0282580	−	0.264642i
$691$	−1.00406	+	1.38197i	−0.0381961	+	0.0525725i	−0.827688	−	0.561189i	$-0.810344\pi$
$691$	−1.00406	+	1.38197i	−0.0381961	+	0.0525725i	0.789492	+	0.613761i	$0.210344\pi$
$692$	7.59675			0.288785
$693$	−2.30446	−	0.454475i	−0.0875392	−	0.0172641i
$694$	−33.1246	−	33.1246i	−1.25739	−	1.25739i
$695$	−9.28115	−	6.74315i	−0.352054	−	0.255782i
$696$	−19.4852	+	2.08059i	−0.738583	+	0.0788645i
$697$	−14.8992	−	45.8550i	−0.564347	−	1.73688i
$698$	34.9201	+	5.53079i	1.32174	+	0.209344i
$699$	8.37265	+	31.0415i	0.316683	+	1.17410i
$700$	−0.347524	−	1.06957i	−0.0131352	−	0.0404259i
$701$	−22.0786	−	7.17376i	−0.833896	−	0.270949i	−0.139211	−	0.990263i	$-0.544456\pi$
$701$	−22.0786	−	7.17376i	−0.833896	−	0.270949i	−0.694686	+	0.719314i	$0.744456\pi$
$702$	−5.92351	+	4.34879i	−0.223569	+	0.164135i
$703$			49.6869i			1.87398i
$704$	−5.81234	−	25.8885i	−0.219061	−	0.975711i
$705$	−6.61803	+	17.3262i	−0.249250	+	0.652544i
$706$	21.9413	−	3.47515i	0.825770	−	0.130789i
$707$	0.364745	−	1.12257i	0.0137177	−	0.0422186i
$708$	−2.95489	−	0.149955i	−0.111052	−	0.00563566i
$709$	31.7705	−	23.0826i	1.19317	−	0.866886i	0.199571	−	0.979883i	$-0.436045\pi$
$709$	31.7705	−	23.0826i	1.19317	−	0.866886i	0.993595	+	0.112997i	$0.0360451\pi$
$710$	−2.18004	+	13.7642i	−0.0818154	+	0.516562i
$711$	47.1542	+	20.8076i	1.76842	+	0.780347i
$712$	−18.0955	+	9.22012i	−0.678158	+	0.345539i
$713$	6.06961	−	8.35410i	0.227309	−	0.312864i
$714$	1.20163	+	2.68692i	0.0449697	+	0.100555i
$715$	−4.02874	−	3.54508i	−0.150666	−	0.132579i
$716$		−	16.8328i		−	0.629072i
$717$	18.2250	+	27.9626i	0.680625	+	1.04428i
$718$	−22.5409	+	11.4852i	−0.841218	+	0.428622i
$719$	9.10739	+	28.0297i	0.339648	+	1.04533i	0.964387	+	0.264496i	$0.0852056\pi$
$719$	9.10739	+	28.0297i	0.339648	+	1.04533i	−0.624738	+	0.780834i	$0.714794\pi$
$720$	1.96563	−	19.3167i	0.0732546	−	0.719889i
$721$	−3.32624	+	2.41665i	−0.123876	+	0.0900009i
$722$	−2.92918	+	5.74884i	−0.109013	+	0.213950i
$723$	−5.89189	+	7.30055i	−0.219122	+	0.271510i
$724$	14.7274	−	20.2705i	0.547339	−	0.753348i
$725$			9.52786i			0.353856i
$726$	−10.3535	+	24.8758i	−0.384254	+	0.923228i
$727$			26.2148i			0.972252i	0.873889	+	0.486126i	$0.161590\pi$
$727$			26.2148i			0.972252i	−0.873889	+	0.486126i	$0.838410\pi$
$728$	0.104451	+	0.659481i	0.00387123	+	0.0244420i
$729$	16.0864	+	21.6848i	0.595791	+	0.803139i
$730$	15.7158	+	8.00760i	0.581668	+	0.296375i
$731$	25.6803	−	18.6579i	0.949822	−	0.690086i
$732$	−5.49402	−	20.3690i	−0.203065	−	0.752861i
$733$	−3.23607	−	9.95959i	−0.119527	−	0.367866i	0.873337	−	0.487116i	$-0.161951\pi$
$733$	−3.23607	−	9.95959i	−0.119527	−	0.367866i	−0.992864	+	0.119250i	$0.961951\pi$
$734$	−8.55597	−	16.7920i	−0.315807	−	0.619805i
$735$	16.3042	−	10.6265i	0.601388	−	0.391963i
$736$	7.05573	+	7.05573i	0.260078	+	0.260078i
$737$	7.10642	+	6.25329i	0.261768	+	0.230343i
$738$	−40.1246	+	2.23607i	−1.47701	+	0.0823108i
$739$	9.30630	−	12.8090i	0.342338	−	0.471187i	−0.602785	−	0.797904i	$-0.705942\pi$
$739$	9.30630	−	12.8090i	0.342338	−	0.471187i	0.945122	+	0.326717i	$0.105942\pi$
$740$	10.2361	−	31.5034i	0.376285	−	1.15809i
$741$	−8.39675	−	0.426119i	−0.308462	−	0.0156539i
$742$	−3.90877	−	0.619089i	−0.143496	−	0.0227275i
$743$	−15.8992	+	11.5514i	−0.583285	+	0.423781i	−0.839907	−	0.542731i	$-0.817390\pi$
$743$	−15.8992	+	11.5514i	−0.583285	+	0.423781i	0.256622	+	0.966512i	$0.417390\pi$
$744$	21.2809	−	19.2253i	0.780197	−	0.704835i
$745$	−1.35410	+	4.16750i	−0.0496105	+	0.152685i
$746$	−5.63525	−	35.5795i	−0.206321	−	1.30266i
$747$	10.1246	+	9.05573i	0.370440	+	0.331332i
$748$	32.9443	−	7.39645i	1.20456	−	0.270441i
$749$			0.0557281i			0.00203626i
$750$	−28.6281	−	6.03557i	−1.04535	−	0.220388i
$751$	19.4499	+	6.31966i	0.709737	+	0.230608i	0.641568	−	0.767066i	$-0.278284\pi$
$751$	19.4499	+	6.31966i	0.709737	+	0.230608i	0.0681694	+	0.997674i	$0.478284\pi$
$752$	−8.18034	−	25.1765i	−0.298306	−	0.918092i
$753$	37.3359	−	10.0704i	1.36060	−	0.366986i
$754$	0.884927	−	5.58721i	0.0322271	−	0.203474i
$755$	−2.76393	−	8.50651i	−0.100590	−	0.309584i
$756$	2.42115	−	0.395807i	0.0880564	−	0.0143954i
$757$	−19.6631	−	14.2861i	−0.714668	−	0.519237i	0.170008	−	0.985443i	$-0.445621\pi$
$757$	−19.6631	−	14.2861i	−0.714668	−	0.519237i	−0.884676	+	0.466206i	$0.845621\pi$
$758$	23.4721	−	23.4721i	0.852546	−	0.852546i
$759$	−1.71580	−	9.98670i	−0.0622795	−	0.362494i
$760$	15.7082	−	15.7082i	0.569796	−	0.569796i
$761$	17.7068	−	24.3713i	0.641871	−	0.883460i	−0.356843	−	0.934165i	$-0.616147\pi$
$761$	17.7068	−	24.3713i	0.641871	−	0.883460i	0.998714	+	0.0507048i	$0.0161468\pi$
$762$	−2.12749	−	19.9244i	−0.0770708	−	0.721785i
$763$	−2.86568	+	0.931116i	−0.103745	+	0.0337087i
$764$	−12.2452	−	16.8541i	−0.443017	−	0.609760i
$765$	24.5813	+	2.50134i	0.888738	+	0.0904363i
$766$	−16.3541	+	32.0968i	−0.590898	+	1.15970i
$767$	0.263932	−	0.812299i	0.00953003	−	0.0293304i
$768$	15.1319	+	23.2169i	0.546027	+	0.837768i
$769$	−24.9230			−0.898746			−0.449373	−	0.893344i	$-0.648353\pi$
$769$	−24.9230			−0.898746			−0.449373	+	0.893344i	$0.648353\pi$
$770$	0.661090	+	1.66515i	0.0238240	+	0.0600078i
$771$	−9.00000	+	23.5623i	−0.324127	+	0.848576i
$772$	18.8496	−	25.9443i	0.678413	−	0.933755i
$773$	14.0943	+	4.57953i	0.506938	+	0.164714i	0.551309	−	0.834301i	$-0.314128\pi$
$773$	14.0943	+	4.57953i	0.506938	+	0.164714i	−0.0443713	+	0.999015i	$0.514128\pi$
$774$	−9.56320	−	24.6686i	−0.343742	−	0.886694i
$775$	−8.19624	−	11.2812i	−0.294418	−	0.405231i
$776$	−1.47174	+	9.29219i	−0.0528323	+	0.333570i
$777$	4.17996	+	0.212125i	0.149955	+	0.00760994i
$778$	19.3549	+	37.9860i	0.693905	+	1.36187i
$779$	−37.1976	−	27.0256i	−1.33274	−	0.968293i
$780$	5.23607	+	2.00000i	0.187481	+	0.0716115i
$781$	−1.88197	+	20.1109i	−0.0673420	+	0.719626i
$782$	−8.97871	+	8.97871i	−0.321078	+	0.321078i
$783$	−20.5446	−	3.14945i	−0.734204	−	0.112552i
$784$	−8.58359	+	26.4176i	−0.306557	+	0.943485i
$785$	3.80423	−	1.23607i	0.135779	−	0.0441172i
$786$	35.2858	+	20.2945i	1.25860	+	0.723880i
$787$	1.79611	+	2.47214i	0.0640245	+	0.0881221i	0.839829	−	0.542852i	$-0.182655\pi$
$787$	1.79611	+	2.47214i	0.0640245	+	0.0881221i	−0.775804	+	0.630974i	$0.782655\pi$
$788$	−4.09017	−	12.5882i	−0.145706	−	0.448438i
$789$	−5.28022	+	6.54264i	−0.187981	+	0.232924i
$790$	−6.14988	−	38.8288i	−0.218803	−	1.38147i
$791$	−0.236068			−0.00839361
$792$	1.05895	−	28.1226i	0.0376281	−	0.999292i
$793$	6.09017			0.216268
$794$	−0.325683	−	2.05628i	−0.0115581	−	0.0729747i
$795$	−20.8641	+	25.8524i	−0.739973	+	0.916890i
$796$	1.27051	+	3.91023i	0.0450320	+	0.138594i
$797$	27.3156	+	37.5967i	0.967569	+	1.33175i	0.943265	+	0.332041i	$0.107737\pi$
$797$	27.3156	+	37.5967i	0.967569	+	1.33175i	0.0243044	+	0.999705i	$0.492263\pi$
$798$	2.43314	+	1.39941i	0.0861321	+	0.0495385i
$799$	32.0382	−	10.4098i	1.13343	−	0.368273i
$800$	12.0058	−	6.11727i	0.424469	−	0.216278i
$801$	−21.0554	+	4.54836i	−0.743954	+	0.160708i
$802$	12.0344	−	12.0344i	0.424951	−	0.424951i
$803$	23.4721	+	10.1311i	0.828314	+	0.357519i
$804$	−9.23607	−	3.52786i	−0.325731	−	0.124418i
$805$	−0.545085	−	0.396027i	−0.0192117	−	0.0139581i
$806$	3.75856	+	7.37660i	0.132390	+	0.259830i
$807$	34.9085	+	1.77154i	1.22884	+	0.0623610i
$808$	13.9680	+	2.21232i	0.491393	+	0.0778291i
$809$	13.1558	+	18.1074i	0.462533	+	0.636622i	0.975032	−	0.222066i	$-0.0712801\pi$
$809$	13.1558	+	18.1074i	0.462533	+	0.636622i	−0.512499	+	0.858688i	$0.671280\pi$
$810$	7.25284	−	19.2748i	0.254839	−	0.677247i
$811$	−4.56352	−	1.48278i	−0.160247	−	0.0520674i	0.227795	−	0.973709i	$-0.426848\pi$
$811$	−4.56352	−	1.48278i	−0.160247	−	0.0520674i	−0.388042	+	0.921642i	$0.626848\pi$
$812$	−1.11006	+	1.52786i	−0.0389554	+	0.0536175i
$813$	−8.41641	+	22.0344i	−0.295176	+	0.772782i
$814$	11.8962	−	46.5143i	0.416962	−	1.63032i
$815$	−8.70820			−0.305035
$816$	−29.5445	+	19.2560i	−1.03426	+	0.674096i
$817$	9.35410	−	28.7890i	0.327259	−	1.00720i
$818$	−20.3579	+	39.9547i	−0.711798	+	1.39698i
$819$	−0.0716953	+	0.704566i	−0.00250524	+	0.0246195i
$820$	18.0171	+	24.7984i	0.629183	+	0.865997i
$821$	39.7854	−	12.9271i	1.38852	−	0.451157i	0.483059	−	0.875588i	$-0.339526\pi$
$821$	39.7854	−	12.9271i	1.38852	−	0.451157i	0.905460	+	0.424431i	$0.139526\pi$
$822$	−2.53934	−	23.7815i	−0.0885697	−	0.829474i
$823$	−21.4455	+	29.5172i	−0.747544	+	1.02891i	0.250605	+	0.968089i	$0.419370\pi$
$823$	−21.4455	+	29.5172i	−0.747544	+	1.02891i	−0.998149	+	0.0608163i	$0.980630\pi$
$824$	−34.8328	−	34.8328i	−1.21346	−	1.21346i
$825$	−13.5417	−	1.96376i	−0.471462	−	0.0683695i
$826$	−0.201626	+	0.201626i	−0.00701547	+	0.00701547i
$827$	−14.5623	−	10.5801i	−0.506381	−	0.367907i	0.305068	−	0.952331i	$-0.401321\pi$
$827$	−14.5623	−	10.5801i	−0.506381	−	0.367907i	−0.811449	+	0.584423i	$0.801321\pi$
$828$	5.32211	+	9.14809i	0.184956	+	0.317918i
$829$	−3.31559	−	10.2044i	−0.115155	−	0.354412i	0.876824	−	0.480811i	$-0.159658\pi$
$829$	−3.31559	−	10.2044i	−0.115155	−	0.354412i	−0.991979	+	0.126400i	$0.959658\pi$
$830$	1.62080	−	10.2333i	0.0562587	−	0.355203i
$831$	27.7901	−	7.49567i	0.964029	−	0.260022i
$832$	−7.60845	+	2.47214i	−0.263776	+	0.0857059i
$833$	−33.6175	−	10.9230i	−1.16478	−	0.378459i
$834$	16.9937	+	3.58274i	0.588445	+	0.124060i
$835$			9.09017i			0.314578i
$836$	21.2705	−	24.1724i	0.735656	−	0.836021i
$837$	27.0344	−	13.9443i	0.934447	−	0.481985i
$838$	1.55624	+	9.82572i	0.0537595	+	0.339424i
$839$	4.51064	−	13.8823i	0.155725	−	0.479271i	−0.842509	−	0.538682i	$-0.818922\pi$
$839$	4.51064	−	13.8823i	0.155725	−	0.479271i	0.998234	+	0.0594111i	$0.0189223\pi$
$840$	−1.25441	−	1.38853i	−0.0432811	−	0.0479089i
$841$	−10.5172	+	7.64121i	−0.362663	+	0.263490i
$842$	−4.64610	−	0.735869i	−0.160115	−	0.0253597i
$843$	10.6909	+	0.542543i	0.368214	+	0.0186862i
$844$	7.03444	−	21.6498i	0.242135	−	0.745216i
$845$	11.4127	−	15.7082i	0.392608	−	0.540379i
$846$	−1.56231	−	28.0344i	−0.0537132	−	0.963844i
$847$	1.11006	+	2.34752i	0.0381421	+	0.0806619i
$848$		−	47.4164i		−	1.62829i
$849$	−32.1849	+	20.9770i	−1.10458	+	0.719927i
$850$	7.78448	+	15.2779i	0.267005	+	0.524028i
$851$	5.57953	+	17.1720i	0.191264	+	0.588649i
$852$	−5.49402	−	20.3690i	−0.188222	−	0.697832i
$853$	−31.5517	+	22.9236i	−1.08031	+	0.784890i	−0.977737	−	0.209836i	$-0.932707\pi$
$853$	−31.5517	+	22.9236i	−1.08031	+	0.784890i	−0.102572	+	0.994726i	$0.532707\pi$
$854$	−1.81160	−	0.923056i	−0.0619917	−	0.0315863i
$855$	20.3664	−	11.8486i	0.696518	−	0.405215i
$856$	−0.659481	+	0.104451i	−0.0225406	+	0.00357008i
$857$			5.11146i			0.174604i	0.996182	+	0.0873020i	$0.0278245\pi$
$857$			5.11146i			0.174604i	−0.996182	+	0.0873020i	$0.972175\pi$
$858$	7.75856	+	2.40929i	0.264873	+	0.0822518i
$859$		−	51.6525i		−	1.76236i	−0.472781	−	0.881180i	$-0.656750\pi$
$859$		−	51.6525i		−	1.76236i	0.472781	−	0.881180i	$-0.343250\pi$
$860$	−11.8617	+	16.3262i	−0.404481	+	0.556720i
$861$	−2.43236	+	3.01390i	−0.0828947	+	0.102714i
$862$	−9.31380	+	18.2794i	−0.317229	+	0.622597i
$863$	−31.6525	+	22.9969i	−1.07746	+	0.782823i	−0.977239	−	0.212142i	$-0.931956\pi$
$863$	−31.6525	+	22.9969i	−1.07746	+	0.782823i	−0.100224	+	0.994965i	$0.531956\pi$
$864$	9.22192	+	27.9098i	0.313736	+	0.949510i
$865$	−1.89919	−	5.84510i	−0.0645743	−	0.198739i
$866$	−15.4886	+	7.89182i	−0.526323	+	0.268175i
$867$	−8.42643	−	12.9287i	−0.286177	−	0.439081i
$868$		−	2.76393i		−	0.0938140i
$869$	−12.4822	−	55.5967i	−0.423431	−	1.88599i
$870$	6.47214	+	14.4721i	0.219426	+	0.490651i
$871$	1.67760	−	2.30902i	0.0568433	−	0.0782381i
$872$	−16.3899	−	32.1670i	−0.555032	−	1.08931i
$873$	−4.02851	+	9.12940i	−0.136344	+	0.308983i
$874$	−1.89425	+	11.9598i	−0.0640741	+	0.404548i
$875$	−2.28115	+	1.65735i	−0.0771170	+	0.0560288i
$876$	−26.6677	−	1.35333i	−0.901018	−	0.0457249i
$877$	−2.36475	+	7.27794i	−0.0798518	+	0.245758i	−0.983011	−	0.183548i	$-0.941242\pi$
$877$	−2.36475	+	7.27794i	−0.0798518	+	0.245758i	0.903159	+	0.429306i	$0.141242\pi$
$878$	32.6302	−	5.16812i	1.10122	−	0.174416i
$879$	2.72949	−	7.14590i	0.0920634	−	0.241025i
$880$	−18.4661	+	10.9443i	−0.622492	+	0.368931i
$881$			15.8541i			0.534138i	0.963677	+	0.267069i	$0.0860552\pi$
$881$			15.8541i			0.534138i	−0.963677	+	0.267069i	$0.913945\pi$
$882$	−15.9643	+	24.7619i	−0.537546	+	0.833778i
$883$	29.6013	+	9.61803i	0.996162	+	0.323673i	0.761331	−	0.648364i	$-0.224546\pi$
$883$	29.6013	+	9.61803i	0.996162	+	0.323673i	0.234831	+	0.972036i	$0.424546\pi$
$884$	−3.14590	−	9.68208i	−0.105808	−	0.325644i
$885$	0.623345	+	2.31105i	0.0209535	+	0.0776849i
$886$	−20.8742	−	3.30615i	−0.701282	−	0.111072i
$887$	8.16312	+	25.1235i	0.274091	+	0.843564i	0.989459	+	0.144816i	$0.0462592\pi$
$887$	8.16312	+	25.1235i	0.274091	+	0.843564i	−0.715368	+	0.698748i	$0.753741\pi$
$888$	5.32426	+	49.8628i	0.178670	+	1.67329i
$889$	−1.56231	−	1.13508i	−0.0523981	−	0.0380694i
$890$	11.6180	+	11.6180i	0.389437	+	0.389437i
$891$	8.71062	−	28.5504i	0.291817	−	0.956474i
$892$	41.4164			1.38672
$893$	18.8824	−	25.9894i	0.631875	−	0.869701i
$894$	−0.704332	−	6.59622i	−0.0235564	−	0.220611i
$895$	−12.9515	+	4.20820i	−0.432922	+	0.140665i
$896$	2.63792	+	0.417806i	0.0881268	+	0.0139579i
$897$	−2.94980	+	0.795633i	−0.0984910	+	0.0265654i
$898$	8.01492	+	4.08381i	0.267461	+	0.136278i
$899$	−7.23607	+	22.2703i	−0.241336	+	0.742757i
$900$	13.9696	−	3.01770i	0.465652	−	0.100590i
$901$	60.3394			2.01020
$902$	28.3518	+	34.2059i	0.944012	+	1.13893i
$903$	−2.38197	−	0.909830i	−0.0792669	−	0.0302772i
$904$	−0.442463	−	2.79360i	−0.0147161	−	0.0929139i
$905$	−19.2784	−	6.26393i	−0.640836	−	0.208220i
$906$	9.07697	+	10.0475i	0.301562	+	0.333806i
$907$	31.4504	+	43.2877i	1.04429	+	1.43735i	0.893654	+	0.448757i	$0.148133\pi$
$907$	31.4504	+	43.2877i	1.04429	+	1.43735i	0.150639	+	0.988589i	$0.451867\pi$
$908$	12.2452	+	16.8541i	0.406372	+	0.559323i
$909$	13.7233	+	6.05565i	0.455173	+	0.200853i
$910$	0.481305	−	0.245237i	0.0159551	−	0.00812954i
$911$	7.42705	+	5.39607i	0.246069	+	0.178780i	0.703983	−	0.710217i	$-0.251403\pi$
$911$	7.42705	+	5.39607i	0.246069	+	0.178780i	−0.457914	+	0.888997i	$0.651403\pi$
$912$	−12.0000	+	31.4164i	−0.397360	+	1.04030i
$913$	1.39919	−	14.9519i	0.0463063	−	0.494836i
$914$	7.85410	+	7.85410i	0.259791	+	0.259791i
$915$	−14.2989	+	9.31947i	−0.472706	+	0.308092i
$916$	−25.5195	−	8.29180i	−0.843189	−	0.273969i
$917$	3.73098	−	1.21227i	0.123208	−	0.0400327i
$918$	−35.5164	+	11.7353i	−1.17222	+	0.387322i
$919$	−28.8015	−	39.6418i	−0.950073	−	1.30766i	−0.951495	−	0.307664i	$-0.900453\pi$
$919$	−28.8015	−	39.6418i	−0.950073	−	1.30766i	0.00142186	−	0.999999i	$-0.499547\pi$
$920$	3.66489	−	7.19276i	0.120828	−	0.237138i
$921$	0.833023	+	0.672288i	0.0274490	+	0.0221527i
$922$	−26.7430	+	4.23568i	−0.880735	+	0.139495i
$923$	6.09017			0.200460
$924$	−1.94272	−	1.89260i	−0.0639109	−	0.0622620i
$925$	24.3820			0.801674
$926$	−4.97584	+	0.788095i	−0.163516	+	0.0258984i
$927$	−26.2743	−	45.1624i	−0.862960	−	1.48333i
$928$	−20.1612	−	10.2726i	−0.661823	−	0.337216i
$929$	−2.66141	−	3.66312i	−0.0873181	−	0.120183i	0.763123	−	0.646253i	$-0.223665\pi$
$929$	−2.66141	−	3.66312i	−0.0873181	−	0.120183i	−0.850441	+	0.526070i	$0.823665\pi$
$930$	−20.1126	−	11.5677i	−0.659518	−	0.379319i
$931$	−32.0584	+	10.4164i	−1.05067	+	0.341384i
$932$	−11.4721	+	35.3076i	−0.375782	+	1.15654i
$933$	26.1522	+	40.1253i	0.856185	+	1.31364i
$934$	2.52786	+	2.52786i	0.0827142	+	0.0827142i
$935$	−13.9271	−	23.4989i	−0.455463	−	0.768496i
$936$	−8.47214	+	0.472136i	−0.276920	+	0.0154322i
$937$	5.66312	+	4.11450i	0.185006	+	0.134415i	0.676433	−	0.736504i	$-0.263525\pi$
$937$	5.66312	+	4.11450i	0.185006	+	0.134415i	−0.491427	+	0.870919i	$0.663525\pi$
$938$	−0.848990	+	0.432582i	−0.0277205	+	0.0141243i
$939$	−0.872960	+	17.2018i	−0.0284880	+	0.561361i
$940$	−17.3262	+	12.5882i	−0.565120	+	0.410583i
$941$	−4.44501	−	6.11803i	−0.144903	−	0.199442i	0.730396	−	0.683024i	$-0.239336\pi$
$941$	−4.44501	−	6.11803i	−0.144903	−	0.199442i	−0.875299	+	0.483582i	$0.839336\pi$
$942$	−4.49338	+	4.05934i	−0.146402	+	0.132261i
$943$	−15.8904	−	5.16312i	−0.517464	−	0.168134i
$944$	−2.76393	−	2.00811i	−0.0899583	−	0.0653585i
$945$	−0.909830	−	1.76393i	−0.0295968	−	0.0573807i
$946$	−15.6496	+	24.7111i	−0.508811	+	0.803427i
$947$	50.8115			1.65115			0.825576	−	0.564290i	$-0.190850\pi$
$947$	50.8115			1.65115			0.825576	+	0.564290i	$0.190850\pi$
$948$	32.4965	+	49.8593i	1.05544	+	1.61935i
$949$	2.38197	−	7.33094i	0.0773219	−	0.237972i
$950$	14.5694	+	7.42346i	0.472692	+	0.240849i
$951$	−5.94508	−	22.0413i	−0.192782	−	0.714739i
$952$	−0.531676	+	3.35687i	−0.0172317	+	0.108797i
$953$	−50.2470	+	16.3262i	−1.62766	+	0.528859i	−0.973732	−	0.227698i	$-0.926880\pi$
$953$	−50.2470	+	16.3262i	−1.62766	+	0.528859i	−0.653928	+	0.756557i	$0.726880\pi$
$954$	12.8558	−	48.6218i	0.416222	−	1.57419i
$955$	−9.90659	+	13.6353i	−0.320570	+	0.441226i
$956$			38.5410i			1.24651i
$957$	10.6986	+	20.3357i	0.345835	+	0.657360i
$958$	2.43769	+	2.43769i	0.0787583	+	0.0787583i
$959$	−1.86475	−	1.35482i	−0.0602158	−	0.0437493i
$960$	14.0806	−	17.4471i	0.454449	−	0.563101i
$961$	−1.01064	−	3.11044i	−0.0326014	−	0.100337i
$962$	−14.2978	−	2.26454i	−0.460978	−	0.0730118i
$963$	−0.704566	−	0.0716953i	−0.0227043	−	0.00231035i
$964$	−10.3026	+	3.34752i	−0.331825	+	0.107816i
$965$	−24.6745	−	8.01722i	−0.794299	−	0.258083i
$966$	0.998047	+	0.210415i	0.0321116	+	0.00677000i
$967$		−	39.6869i		−	1.27625i	−0.769935	−	0.638123i	$-0.779711\pi$
$967$		−	39.6869i		−	1.27625i	0.769935	−	0.638123i	$-0.220289\pi$
$968$	−25.6998	+	17.5363i	−0.826022	+	0.563638i
$969$	−39.9787	−	15.2705i	−1.28430	−	0.490559i
$970$	7.51754	−	1.19066i	0.241374	−	0.0382298i
$971$	−8.65248	+	26.6296i	−0.277671	+	0.854584i	0.710829	+	0.703365i	$0.248320\pi$
$971$	−8.65248	+	26.6296i	−0.277671	+	0.854584i	−0.988500	+	0.151219i	$0.951680\pi$
$972$	1.88930	+	31.1196i	0.0605993	+	0.998162i
$973$	1.35410	−	0.983813i	0.0434105	−	0.0315396i
$974$	−3.02036	+	19.0698i	−0.0967786	+	0.611036i
$975$	−0.209101	+	4.12038i	−0.00669661	+	0.131958i
$976$	7.52786	−	23.1684i	0.240961	−	0.741602i
$977$	−7.12667	+	9.80902i	−0.228002	+	0.313818i	−0.907656	−	0.419715i	$-0.862130\pi$
$977$	−7.12667	+	9.80902i	−0.228002	+	0.313818i	0.679654	+	0.733533i	$0.262130\pi$
$978$	12.0344	−	5.38197i	0.384819	−	0.172096i
$979$	17.8783	+	15.7320i	0.571393	+	0.502797i
$980$	22.4721			0.717846
$981$	−8.08527	−	37.4285i	−0.258143	−	1.19500i
$982$	49.1160	−	25.0259i	1.56736	−	0.798608i
$983$	−14.7426	−	45.3732i	−0.470217	−	1.44718i	−0.852301	−	0.523052i	$-0.824793\pi$
$983$	−14.7426	−	45.3732i	−0.470217	−	1.44718i	0.382083	−	0.924128i	$-0.375207\pi$
$984$	−40.2252	−	23.1353i	−1.28233	−	0.737528i
$985$	−8.66312	+	6.29412i	−0.276030	+	0.200547i
$986$	13.0724	−	25.6560i	0.416309	−	0.817052i
$987$	−2.10577	−	1.69945i	−0.0670273	−	0.0540942i
$988$	−7.85410	−	5.70634i	−0.249872	−	0.181543i
$989$		−	11.0000i		−	0.349780i
$990$	−21.9028	+	6.21586i	−0.696117	+	0.197553i
$991$			25.3262i			0.804514i	0.915527	+	0.402257i	$0.131774\pi$
$991$			25.3262i			0.804514i	−0.915527	+	0.402257i	$0.868226\pi$
$992$	32.7081	−	5.18045i	1.03848	−	0.164480i
$993$	−17.9155	−	14.4586i	−0.568530	−	0.458830i
$994$	−1.81160	−	0.923056i	−0.0574605	−	0.0292776i
$995$	2.69098	−	1.95511i	0.0853099	−	0.0619813i
$996$	4.08465	+	15.1438i	0.129427	+	0.479849i
$997$	10.2984	+	31.6951i	0.326153	+	1.00380i	0.970918	+	0.239414i	$0.0769553\pi$
$997$	10.2984	+	31.6951i	0.326153	+	1.00380i	−0.644765	+	0.764381i	$0.723045\pi$
$998$	−2.01979	−	3.96406i	−0.0639354	−	0.125480i
$999$	−8.05948	+	52.5740i	−0.254991	+	1.66337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	132.2.o.b.59.1	yes	8
3.2	odd	2		132.2.o.a.59.2	yes	8
4.3	odd	2		132.2.o.a.59.1	yes	8
11.3	even	5	inner	132.2.o.b.47.2	yes	8
12.11	even	2	inner	132.2.o.b.59.2	yes	8
33.14	odd	10		132.2.o.a.47.1	✓	8
44.3	odd	10		132.2.o.a.47.2	yes	8
132.47	even	10	inner	132.2.o.b.47.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.o.a.47.1	✓	8	33.14	odd	10
132.2.o.a.47.2	yes	8	44.3	odd	10
132.2.o.a.59.1	yes	8	4.3	odd	2
132.2.o.a.59.2	yes	8	3.2	odd	2
132.2.o.b.47.1	yes	8	132.47	even	10	inner
132.2.o.b.47.2	yes	8	11.3	even	5	inner
132.2.o.b.59.1	yes	8	1.1	even	1	trivial
132.2.o.b.59.2	yes	8	12.11	even	2	inner

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:	\( N \)	\(=\)	\( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	132.o (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.221232 + 1.39680i) q^{2} +(-1.08779 + 1.34786i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(0.951057 + 1.30902i) q^{5} +(-2.12334 - 1.22123i) q^{6} +(-0.224514 + 0.0729490i) q^{7} +(-1.28408 - 2.52015i) q^{8} +(-0.633446 - 2.93236i) q^{9} +O(q^{10})\)	\(q+(0.221232 + 1.39680i) q^{2} +(-1.08779 + 1.34786i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(0.951057 + 1.30902i) q^{5} +(-2.12334 - 1.22123i) q^{6} +(-0.224514 + 0.0729490i) q^{7} +(-1.28408 - 2.52015i) q^{8} +(-0.633446 - 2.93236i) q^{9} +(-1.61803 + 1.61803i) q^{10} +(-2.19098 + 2.48990i) q^{11} +(1.23607 - 3.23607i) q^{12} +(0.809017 + 0.587785i) q^{13} +(-0.151565 - 0.297463i) q^{14} +(-2.79892 - 0.142040i) q^{15} +(3.23607 - 2.35114i) q^{16} +(2.99193 + 4.11803i) q^{17} +(3.95579 - 1.53353i) q^{18} +(4.61653 + 1.50000i) q^{19} +(-2.61803 - 1.90211i) q^{20} +(0.145898 - 0.381966i) q^{21} +(-3.96261 - 2.50953i) q^{22} +1.76393 q^{23} +(4.79360 + 1.01062i) q^{24} +(0.736068 - 2.26538i) q^{25} +(-0.642040 + 1.26007i) q^{26} +(4.64146 + 2.33598i) q^{27} +(0.381966 - 0.277515i) q^{28} +(-3.80423 + 1.23607i) q^{29} +(-0.420808 - 3.94095i) q^{30} +(3.44095 - 4.73607i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-0.972712 - 5.66161i) q^{33} +(-5.09017 + 5.09017i) q^{34} +(-0.309017 - 0.224514i) q^{35} +(3.01719 + 5.18619i) q^{36} +(3.16312 + 9.73508i) q^{37} +(-1.07388 + 6.78022i) q^{38} +(-1.67229 + 0.451057i) q^{39} +(2.07768 - 4.07768i) q^{40} +(-9.00854 - 2.92705i) q^{41} +(0.565808 + 0.119288i) q^{42} -6.23607i q^{43} +(2.62866 - 6.09017i) q^{44} +(3.23607 - 3.61803i) q^{45} +(0.390238 + 2.46386i) q^{46} +(2.04508 - 6.29412i) q^{47} +(-0.351141 + 6.91930i) q^{48} +(-5.61803 + 4.08174i) q^{49} +(3.32714 + 0.526966i) q^{50} +(-8.80510 - 0.446842i) q^{51} +(-1.90211 - 0.618034i) q^{52} +(6.96767 - 9.59017i) q^{53} +(-2.23607 + 7.00000i) q^{54} +(-5.34307 - 0.500000i) q^{55} +(0.472136 + 0.472136i) q^{56} +(-7.04358 + 4.59075i) q^{57} +(-2.56816 - 5.04029i) q^{58} +(-0.263932 - 0.812299i) q^{59} +(5.41164 - 1.45965i) q^{60} +(4.92705 - 3.57971i) q^{61} +(7.37660 + 3.75856i) q^{62} +(0.356131 + 0.612147i) q^{63} +(-4.70228 + 6.47214i) q^{64} +1.61803i q^{65} +(7.69296 - 2.61121i) q^{66} -2.85410i q^{67} +(-8.23607 - 5.98385i) q^{68} +(-1.91878 + 2.37753i) q^{69} +(0.245237 - 0.481305i) q^{70} +(4.92705 - 3.57971i) q^{71} +(-6.57659 + 5.36176i) q^{72} +(-2.38197 - 7.33094i) q^{73} +(-12.8982 + 6.57196i) q^{74} +(2.25273 + 3.45637i) q^{75} -9.70820 q^{76} +(0.310271 - 0.718847i) q^{77} +(-1.00000 - 2.23607i) q^{78} +(-10.0984 + 13.8992i) q^{79} +(6.15537 + 2.00000i) q^{80} +(-8.19749 + 3.71499i) q^{81} +(2.09554 - 13.2307i) q^{82} +(-3.66312 + 2.66141i) q^{83} +(-0.0414466 + 0.816712i) q^{84} +(-2.54508 + 7.83297i) q^{85} +(8.71055 - 1.37962i) q^{86} +(2.47214 - 6.47214i) q^{87} +(9.08831 + 2.32437i) q^{88} -7.18034i q^{89} +(5.76960 + 3.71972i) q^{90} +(-0.224514 - 0.0729490i) q^{91} +(-3.35520 + 1.09017i) q^{92} +(2.64053 + 9.78975i) q^{93} +(9.24408 + 1.46412i) q^{94} +(2.42705 + 7.46969i) q^{95} +(-9.74258 + 1.04029i) q^{96} +(-2.69098 - 1.95511i) q^{97} +(-6.94427 - 6.94427i) q^{98} +(8.68915 + 4.84754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 4 q^{3} - 2 q^{6} - 4 q^{8} - 10 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 4 * q^3 - 2 * q^6 - 4 * q^8 - 10 * q^9	\( 8 q + 2 q^{2} - 4 q^{3} - 2 q^{6} - 4 q^{8} - 10 q^{9} - 4 q^{10} - 22 q^{11} - 8 q^{12} + 2 q^{13} + 14 q^{14} + 2 q^{15} + 8 q^{16} - 14 q^{18} - 12 q^{20} + 28 q^{21} - 8 q^{22} + 32 q^{23} + 20 q^{24} - 12 q^{25} - 2 q^{26} + 2 q^{27} + 12 q^{28} + 32 q^{32} - 4 q^{33} + 4 q^{34} + 2 q^{35} + 8 q^{36} - 6 q^{37} - 18 q^{38} - 6 q^{39} - 8 q^{40} - 10 q^{42} + 8 q^{45} - 2 q^{46} - 6 q^{47} + 16 q^{48} - 36 q^{49} + 2 q^{50} + 28 q^{51} - 32 q^{56} - 6 q^{57} - 8 q^{58} - 20 q^{59} + 16 q^{60} + 26 q^{61} + 10 q^{62} - 28 q^{63} - 2 q^{66} - 48 q^{68} - 16 q^{69} + 8 q^{70} + 26 q^{71} - 28 q^{72} - 28 q^{73} + 6 q^{74} + 16 q^{75} - 24 q^{76} - 8 q^{78} - 2 q^{81} + 30 q^{82} + 2 q^{83} - 16 q^{84} + 2 q^{85} + 18 q^{86} - 16 q^{87} + 36 q^{88} + 22 q^{90} - 10 q^{93} + 16 q^{94} + 6 q^{95} + 8 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 4 * q^3 - 2 * q^6 - 4 * q^8 - 10 * q^9 - 4 * q^10 - 22 * q^11 - 8 * q^12 + 2 * q^13 + 14 * q^14 + 2 * q^15 + 8 * q^16 - 14 * q^18 - 12 * q^20 + 28 * q^21 - 8 * q^22 + 32 * q^23 + 20 * q^24 - 12 * q^25 - 2 * q^26 + 2 * q^27 + 12 * q^28 + 32 * q^32 - 4 * q^33 + 4 * q^34 + 2 * q^35 + 8 * q^36 - 6 * q^37 - 18 * q^38 - 6 * q^39 - 8 * q^40 - 10 * q^42 + 8 * q^45 - 2 * q^46 - 6 * q^47 + 16 * q^48 - 36 * q^49 + 2 * q^50 + 28 * q^51 - 32 * q^56 - 6 * q^57 - 8 * q^58 - 20 * q^59 + 16 * q^60 + 26 * q^61 + 10 * q^62 - 28 * q^63 - 2 * q^66 - 48 * q^68 - 16 * q^69 + 8 * q^70 + 26 * q^71 - 28 * q^72 - 28 * q^73 + 6 * q^74 + 16 * q^75 - 24 * q^76 - 8 * q^78 - 2 * q^81 + 30 * q^82 + 2 * q^83 - 16 * q^84 + 2 * q^85 + 18 * q^86 - 16 * q^87 + 36 * q^88 + 22 * q^90 - 10 * q^93 + 16 * q^94 + 6 * q^95 + 8 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

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