LMFDB - Embedded newform 132.2.o.a.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.a.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$2$	−1.39680	+	0.221232i	−0.987688	+	0.156434i
$2$	−1.39680	+	0.221232i	−0.987688	+	0.156434i
$3$	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	$0.682161\pi$
$6$	−1.22123	+	2.12334i	−0.498566	+	0.866852i
$7$	0.224514	−	0.0729490i	0.0848583	−	0.0275721i	−0.266280	−	0.963896i	$-0.585795\pi$
$7$	0.224514	−	0.0729490i	0.0848583	−	0.0275721i	0.351138	+	0.936324i	$0.385795\pi$
$8$	−2.52015	+	1.28408i	−0.891007	+	0.453990i
$9$	−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	$0.655716\pi$
$14$	−0.297463	+	0.151565i	−0.0795003	+	0.0405074i
$15$	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	$0.588237\pi$
$18$	1.53353	+	3.95579i	0.361457	+	0.932389i
$19$	−4.61653	−	1.50000i	−1.05910	−	0.344124i	−0.272869	−	0.962051i	$-0.587972\pi$
$19$	−4.61653	−	1.50000i	−1.05910	−	0.344124i	−0.786235	+	0.617928i	$0.787972\pi$
$20$	2.61803	+	1.90211i	0.585410	+	0.425325i
$21$	0.145898	−	0.381966i	0.0318376	−	0.0833518i
$22$	−2.50953	+	3.96261i	−0.535033	+	0.844831i
$23$	−1.76393			−0.367805			−0.183903	−	0.982944i	$-0.558873\pi$
$23$	−1.76393			−0.367805			−0.183903	+	0.982944i	$0.558873\pi$
$24$	−1.01062	+	4.79360i	−0.206292	+	0.978490i
$25$	0.736068	−	2.26538i	0.147214	−	0.453077i
$26$	−1.26007	−	0.642040i	−0.247121	−	0.125914i
$27$	−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	$0.521119\pi$
$30$	−3.94095	+	0.420808i	−0.719517	+	0.0768286i
$31$	−3.44095	+	4.73607i	−0.618014	+	0.850623i	−0.997206	−	0.0746948i	$-0.976202\pi$
$31$	−3.44095	+	4.73607i	−0.618014	+	0.850623i	0.379193	+	0.925318i	$0.376202\pi$
$32$	−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	$0.581732\pi$
$38$	6.78022	+	1.07388i	1.09990	+	0.174207i
$39$	1.67229	−	0.451057i	0.267780	−	0.0722268i
$40$	−4.07768	−	2.07768i	−0.644738	−	0.328511i
$41$	−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	$0.865009\pi$
$42$	−0.119288	+	0.565808i	−0.0184065	+	0.0873061i
$43$			6.23607i			0.950991i	0.879718	+	0.475496i	$0.157731\pi$
$43$			6.23607i			0.950991i	−0.879718	+	0.475496i	$0.842269\pi$
$44$	2.62866	−	6.09017i	0.396285	−	0.918128i
$45$	3.23607	−	3.61803i	0.482405	−	0.539345i
$46$	2.46386	−	0.390238i	0.363277	−	0.0575374i
$47$	−2.04508	+	6.29412i	−0.298306	+	0.918092i	0.683784	+	0.729684i	$0.260333\pi$
$47$	−2.04508	+	6.29412i	−0.298306	+	0.918092i	−0.982091	+	0.188408i	$0.939667\pi$
$48$	0.351141	−	6.91930i	0.0506828	−	0.998715i
$49$	−5.61803	+	4.08174i	−0.802576	+	0.583106i
$50$	−0.526966	+	3.32714i	−0.0745243	+	0.470528i
$51$	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	$-0.102793\pi$
$54$	7.00000	+	2.23607i	0.952579	+	0.304290i
$55$	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
$58$	5.04029	−	2.56816i	0.661823	−	0.337216i
$59$	0.263932	+	0.812299i	0.0343610	+	0.105752i	0.966766	−	0.255663i	$-0.0822937\pi$
$59$	0.263932	+	0.812299i	0.0343610	+	0.105752i	−0.932405	+	0.361415i	$0.882294\pi$
$60$	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	$0.172515\pi$
$62$	3.75856	−	7.37660i	0.477338	−	0.936829i
$63$	−0.356131	−	0.612147i	−0.0448682	−	0.0771233i
$64$	4.70228	−	6.47214i	0.587785	−	0.809017i
$65$			1.61803i			0.200692i
$66$	2.61121	+	7.69296i	0.321418	+	0.946937i
$67$			2.85410i			0.348684i	0.984685	+	0.174342i	$0.0557798\pi$
$67$			2.85410i			0.348684i	−0.984685	+	0.174342i	$0.944220\pi$
$68$	8.23607	+	5.98385i	0.998770	+	0.725649i
$69$	−1.91878	+	2.37753i	−0.230994	+	0.286221i
$70$	−0.481305	−	0.245237i	−0.0575270	−	0.0293115i
$71$	−4.92705	+	3.57971i	−0.584733	+	0.424834i	−0.840427	−	0.541924i	$-0.817696\pi$
$71$	−4.92705	+	3.57971i	−0.584733	+	0.424834i	0.255694	+	0.966758i	$0.417696\pi$
$72$	5.36176	+	6.57659i	0.631890	+	0.775058i
$73$	−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	$-0.248964\pi$
$74$	−6.57196	−	12.8982i	−0.763975	−	1.49939i
$75$	−2.25273	−	3.45637i	−0.260123	−	0.399107i
$76$	−9.70820			−1.11361
$77$	0.310271	−	0.718847i	0.0353586	−	0.0819202i
$78$	−2.23607	+	1.00000i	−0.253185	+	0.113228i
$79$	10.0984	−	13.8992i	1.13615	−	1.56378i	0.360336	−	0.932822i	$-0.382662\pi$
$79$	10.0984	−	13.8992i	1.13615	−	1.56378i	0.775817	−	0.630958i	$-0.217338\pi$
$80$	6.15537	+	2.00000i	0.688191	+	0.223607i
$81$	−8.19749	+	3.71499i	−0.910832	+	0.412777i
$82$	13.2307	+	2.09554i	1.46109	+	0.231413i
$83$	3.66312	−	2.66141i	0.402080	−	0.292128i	−0.368308	−	0.929704i	$-0.620063\pi$
$83$	3.66312	−	2.66141i	0.402080	−	0.292128i	0.770387	+	0.637576i	$0.220063\pi$
$84$	0.0414466	−	0.816712i	0.00452219	−	0.0891106i
$85$	−2.54508	+	7.83297i	−0.276053	+	0.849604i
$86$	−1.37962	−	8.71055i	−0.148768	−	0.939283i
$87$	−2.47214	+	6.47214i	−0.265041	+	0.693886i
$88$	−2.32437	+	9.08831i	−0.247779	+	0.968817i
$89$		−	7.18034i		−	0.761115i	−0.924757	−	0.380557i	$-0.875732\pi$
$89$		−	7.18034i		−	0.761115i	0.924757	−	0.380557i	$-0.124268\pi$
$90$	−3.71972	+	5.76960i	−0.392093	+	0.608169i
$91$	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
$94$	1.46412	−	9.24408i	0.151012	−	0.953455i
$95$	−2.42705	−	7.46969i	−0.249010	−	0.766375i
$96$	1.04029	+	9.74258i	0.106175	+	0.994348i
$97$	−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	$0.280023\pi$
$102$	−12.3978	+	1.32382i	−1.22757	+	0.131078i
$103$	−16.5640	+	5.38197i	−1.63210	+	0.530301i	−0.974752	−	0.223288i	$-0.928321\pi$
$103$	−16.5640	+	5.38197i	−1.63210	+	0.530301i	−0.657346	+	0.753589i	$0.728321\pi$
$104$	−2.79360	−	0.442463i	−0.273935	−	0.0433871i
$105$	0.638757	−	0.172288i	0.0623363	−	0.0168136i
$106$	−7.61080	+	14.9370i	−0.739226	+	1.45081i
$107$	−0.0729490	+	0.224514i	−0.00705225	+	0.0217046i	−0.954521	−	0.298145i	$-0.903632\pi$
$107$	−0.0729490	+	0.224514i	−0.00705225	+	0.0217046i	0.947468	+	0.319849i	$0.103632\pi$
$108$	−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	$0.290654\pi$
$110$	−7.57383	+	0.483655i	−0.722136	+	0.0461147i
$111$	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	$0.585022\pi$
$114$	8.82286	−	7.97063i	0.826337	−	0.746518i
$115$	−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
$118$	−0.548367	−	1.07623i	−0.0504813	−	0.0990751i
$119$	0.972136	+	0.706298i	0.0891156	+	0.0647462i
$120$	−7.23607	+	3.23607i	−0.660560	+	0.295411i
$121$	−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
$126$	0.632870	+	0.776261i	0.0563806	+	0.0691548i
$127$	−4.80828	−	6.61803i	−0.426666	−	0.587256i	0.540518	−	0.841333i	$-0.318228\pi$
$127$	−4.80828	−	6.61803i	−0.426666	−	0.587256i	−0.967184	+	0.254077i	$0.918228\pi$
$128$	−5.13632	+	10.0806i	−0.453990	+	0.891007i
$129$	8.40534	+	6.78350i	0.740049	+	0.597254i
$130$	−0.357960	−	2.26007i	−0.0313952	−	0.198222i
$131$	16.6180			1.45192			0.725962	−	0.687735i	$-0.241395\pi$
$131$	16.6180			1.45192			0.725962	+	0.687735i	$0.241395\pi$
$132$	−5.34928	−	10.1679i	−0.465595	−	0.884998i
$133$	−1.14590			−0.0993620
$134$	−0.631418	−	3.98662i	−0.0545462	−	0.344391i
$135$	−1.35645	−	8.29741i	−0.116745	−	0.714127i
$136$	−12.8280	−	6.53618i	−1.09999	−	0.560473i
$137$	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	$0.663048\pi$
$138$	2.15417	−	3.74544i	0.183375	−	0.318833i
$139$	6.74315	−	2.19098i	0.571947	−	0.185837i	−0.00874291	−	0.999962i	$-0.502783\pi$
$139$	6.74315	−	2.19098i	0.571947	−	0.185837i	0.580690	+	0.814125i	$0.302783\pi$
$140$	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
$146$	4.94897	+	9.71290i	0.409580	+	0.803846i
$147$	−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	$0.764616\pi$
$150$	3.91128	+	4.32949i	0.319355	+	0.353501i
$151$	5.25731	+	1.70820i	0.427834	+	0.139012i	0.515016	−	0.857181i	$-0.327786\pi$
$151$	5.25731	+	1.70820i	0.427834	+	0.139012i	−0.0871818	+	0.996192i	$0.527786\pi$
$152$	13.5604	−	2.14776i	1.09990	−	0.174207i
$153$	10.1803	−	11.3820i	0.823032	−	0.920177i
$154$	−0.274355	+	1.07273i	−0.0221082	+	0.0864430i
$155$	−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	$0.0685479\pi$
$158$	−11.0305	+	21.6485i	−0.877536	+	1.72226i
$159$	−5.34687	−	19.8235i	−0.424034	−	1.57210i
$160$	−9.04029	−	1.43184i	−0.714698	−	0.113197i
$161$	−0.396027	+	0.128677i	−0.0312113	+	0.0101412i
$162$	10.6284	−	7.00265i	0.835046	−	0.550180i
$163$	3.16344	−	4.35410i	0.247780	−	0.341040i	−0.666952	−	0.745100i	$-0.732402\pi$
$163$	3.16344	−	4.35410i	0.247780	−	0.341040i	0.914732	+	0.404061i	$0.132402\pi$
$164$	−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	0.397876	−	0.917439i	$-0.369747\pi$
$167$	−4.54508	−	3.30220i	−0.351709	−	0.255532i	−0.749586	+	0.661907i	$0.769747\pi$
$168$	0.122790	+	1.14996i	0.00947346	+	0.0887210i
$169$	−3.70820	−	11.4127i	−0.285246	−	0.877898i
$170$	1.82208	−	11.5042i	0.139747	−	0.882329i
$171$	−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	$0.646123\pi$
$174$	2.02124	−	9.58721i	0.153230	−	0.726804i
$175$		−	0.562306i		−	0.0425063i
$176$	1.23607	−	13.2088i	0.0931721	−	0.995650i
$177$	1.38197	+	0.527864i	0.103875	+	0.0396767i
$178$	1.58852	+	10.0295i	0.119065	+	0.751744i
$179$	2.60081	−	8.00448i	0.194394	−	0.598283i	−0.805589	−	0.592474i	$-0.798151\pi$
$179$	2.60081	−	8.00448i	0.194394	−	0.598283i	0.999983	−	0.00580843i	$-0.00184889\pi$
$180$	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	$0.454159\pi$
$182$	−0.329740	−	0.0522257i	−0.0244420	−	0.00387123i
$183$	0.534627	−	10.5349i	0.0395208	−	0.778764i
$184$	4.44537	−	2.26503i	0.327717	−	0.166980i
$185$	−9.73508	+	13.3992i	−0.715737	+	0.985128i
$186$	−5.85410	−	13.0902i	−0.429244	−	0.959818i
$187$	16.8087	+	1.57295i	1.22918	+	0.115025i
$188$			13.2361i			0.965339i
$189$	−1.21248	−	0.185871i	−0.0881950	−	0.0135201i
$190$	5.04264	+	9.89675i	0.365832	+	0.717985i
$191$	−3.21885	−	9.90659i	−0.232908	−	0.716816i	−0.997392	−	0.0721737i	$-0.977006\pi$
$191$	−3.21885	−	9.90659i	−0.232908	−	0.716816i	0.764484	−	0.644642i	$-0.222994\pi$
$192$	−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	$0.495813\pi$
$194$	4.19130	+	2.13558i	0.300918	+	0.153325i
$195$	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	$0.924243\pi$
$198$	13.2095	+	4.84873i	0.938755	+	0.344585i
$199$			2.05573i			0.145727i	0.997342	+	0.0728634i	$0.0232137\pi$
$199$			2.05573i			0.145727i	−0.997342	+	0.0728634i	$0.976786\pi$
$200$	1.05393	+	6.65427i	0.0745243	+	0.470528i
$201$	3.84693	+	3.10465i	0.271341	+	0.218985i
$202$	3.21020	−	6.30037i	0.225869	−	0.443292i
$203$	−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
$206$	21.9460	−	11.1820i	1.52905	−	0.779088i
$207$	1.11736	+	5.17249i	0.0776616	+	0.359513i
$208$	4.00000			0.277350
$209$	−13.8496	+	8.20820i	−0.957995	+	0.567773i
$210$	−0.854102	+	0.381966i	−0.0589386	+	0.0263582i
$211$	6.69015	−	9.20820i	0.460569	−	0.633919i	−0.514058	−	0.857756i	$-0.671858\pi$
$211$	6.69015	−	9.20820i	0.460569	−	0.633919i	0.974627	+	0.223837i	$0.0718582\pi$
$212$	7.32624	−	22.5478i	0.503168	−	1.54859i
$213$	−0.534627	+	10.5349i	−0.0366320	+	0.721841i
$214$	0.0522257	−	0.329740i	0.00357008	−	0.0225406i
$215$	−8.16312	+	5.93085i	−0.556720	+	0.404481i
$216$	14.6968	−	0.0729839i	0.999988	−	0.00496592i
$217$	−0.427051	+	1.31433i	−0.0289901	+	0.0892224i
$218$	−17.8287	+	2.82379i	−1.20751	+	0.191251i
$219$	−12.4721	−	4.76393i	−0.842789	−	0.321917i
$220$	10.4721	−	2.35114i	0.706031	−	0.158514i
$221$			5.09017i			0.342402i
$222$	−24.5338	−	5.17240i	−1.64660	−	0.347148i
$223$	19.6947	+	6.39919i	1.31885	+	0.428521i	0.882101	−	0.471061i	$-0.156129\pi$
$223$	19.6947	+	6.39919i	1.31885	+	0.428521i	0.436752	+	0.899582i	$0.356129\pi$
$224$	−0.606260	+	1.18985i	−0.0405074	+	0.0795003i
$225$	−7.10919	−	0.723418i	−0.473946	−	0.0482279i
$226$	−1.39680	−	0.221232i	−0.0929139	−	0.0147161i
$227$	3.21885	+	9.90659i	0.213642	+	0.657524i	0.999247	+	0.0387950i	$0.0123519\pi$
$227$	3.21885	+	9.90659i	0.213642	+	0.657524i	−0.785605	+	0.618729i	$0.787648\pi$
$228$	−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	$-0.00803939\pi$
$234$	−1.08450	+	4.10169i	−0.0708962	+	0.268136i
$235$	−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
$238$	−1.51414	−	0.771491i	−0.0981469	−	0.0500084i
$239$	−5.95492	+	18.3273i	−0.385191	+	1.18550i	0.551150	+	0.834406i	$0.314189\pi$
$239$	−5.95492	+	18.3273i	−0.385191	+	1.18550i	−0.936341	+	0.351091i	$0.885811\pi$
$240$	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	$0.444185\pi$
$242$	4.36817	+	14.9305i	0.280797	+	0.959767i
$243$	−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
$246$	17.2166	−	15.5536i	1.09769	−	0.991663i
$247$	−2.85317	−	3.92705i	−0.181543	−	0.249872i
$248$	2.59023	−	16.3540i	0.164480	−	1.03848i
$249$	0.397480	−	7.83241i	0.0251893	−	0.496359i
$250$	−15.0507	+	7.66869i	−0.951887	+	0.485011i
$251$	18.0623	+	13.1230i	1.14008	+	0.828319i	0.987131	−	0.159915i	$-0.0511221\pi$
$251$	18.0623	+	13.1230i	1.14008	+	0.828319i	0.152952	+	0.988234i	$0.451122\pi$
$252$	−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	$0.249930\pi$
$258$	−13.2413	−	7.61568i	−0.824369	−	0.474132i
$259$	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
$262$	−23.2121	+	3.67644i	−1.43405	+	0.227131i
$263$	−4.85410			−0.299317			−0.149658	−	0.988738i	$-0.547817\pi$
$263$	−4.85410			−0.299317			−0.149658	+	0.988738i	$0.547817\pi$
$264$	9.72133	+	13.0191i	0.598307	+	0.801267i
$265$	19.1803			1.17824
$266$	1.60059	−	0.253509i	0.0981387	−	0.0155436i
$267$	−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	$-0.410928\pi$
$270$	3.73034	+	11.2897i	0.227022	+	0.687072i
$271$	−12.9515	+	4.20820i	−0.786749	+	0.255630i	−0.674719	−	0.738075i	$-0.735735\pi$
$271$	−12.9515	+	4.20820i	−0.786749	+	0.255630i	−0.112030	+	0.993705i	$0.535735\pi$
$272$	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	$0.866388\pi$
$278$	−8.93414	+	4.55217i	−0.535834	+	0.273021i
$279$	16.0675	+	7.09008i	0.961938	+	0.424472i
$280$	−1.06706	−	0.169006i	−0.0637691	−	0.0101000i
$281$	−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	$0.859016\pi$
$282$	−10.8671	−	12.0290i	−0.647125	−	0.716317i
$283$	−21.0948	−	6.85410i	−1.25395	−	0.407434i	−0.394617	−	0.918846i	$-0.629123\pi$
$283$	−21.0948	−	6.85410i	−1.25395	−	0.407434i	−0.859336	+	0.511412i	$0.829123\pi$
$284$	−7.15942	+	9.85410i	−0.424834	+	0.584733i
$285$	−12.7082	−	4.85410i	−0.752769	−	0.287532i
$286$	−4.35941	+	1.73076i	−0.257777	+	0.102342i
$287$	−2.23607			−0.131991
$288$	14.2632	+	9.19566i	0.840469	+	0.541860i
$289$	−2.75329	+	8.47375i	−0.161958	+	0.498456i
$290$	8.15537	+	4.15537i	0.478900	+	0.244012i
$291$	−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	$0.441178\pi$
$294$	−1.80602	−	16.9138i	−0.105329	−	0.986431i
$295$	−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
$302$	−7.72133	−	1.22294i	−0.444313	−	0.0703722i
$303$	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
$306$	−11.7019	+	18.1506i	−0.668951	+	1.03760i
$307$			0.618034i			0.0352731i	0.999844	+	0.0176365i	$0.00561417\pi$
$307$			0.618034i			0.0352731i	−0.999844	+	0.0176365i	$0.994386\pi$
$308$	0.145898	−	1.55909i	0.00831331	−	0.0888372i
$309$	−10.7639	+	28.1803i	−0.612339	+	1.60312i
$310$	13.2307	−	2.09554i	0.751453	−	0.119019i
$311$	−8.54508	+	26.2991i	−0.484547	+	1.49128i	0.348088	+	0.937462i	$0.386831\pi$
$311$	−8.54508	+	26.2991i	−0.484547	+	1.49128i	−0.832635	+	0.553821i	$0.813169\pi$
$312$	−3.63522	+	3.28408i	−0.205804	+	0.185924i
$313$	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	$0.209320\pi$
$314$	−0.546915	+	3.45309i	−0.0308642	+	0.194869i
$315$	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	$0.320691\pi$
$318$	11.8541	+	26.5066i	0.664745	+	1.48642i
$319$	−5.25731	+	12.1803i	−0.294353	+	0.681968i
$320$	12.9443			0.723607
$321$	0.223260	+	0.342548i	0.0124612	+	0.0191192i
$322$	0.524705	−	0.267350i	0.0292406	−	0.0148989i
$323$	−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
$326$	−3.45543	+	6.78167i	−0.191379	+	0.375602i
$327$	13.8844	−	17.2040i	0.767810	−	0.951382i
$328$	26.4614	−	4.19107i	1.46109	−	0.231413i
$329$			1.56231i			0.0861327i
$330$	−7.58680	+	10.7346i	−0.417639	+	0.590918i
$331$		−	13.2918i		−	0.730583i	−0.930893	−	0.365292i	$-0.880969\pi$
$331$		−	13.2918i		−	0.730583i	0.930893	−	0.365292i	$-0.119031\pi$
$332$	5.32282	−	7.32624i	0.292128	−	0.402080i
$333$	26.5431	−	15.4421i	1.45455	−	0.846220i
$334$	7.07914	+	3.60700i	0.387353	+	0.197366i
$335$	−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	$0.561876\pi$
$338$	7.70447	+	15.1209i	0.419068	+	0.822468i
$339$	1.45106	−	0.945746i	0.0788106	−	0.0513659i
$340$			16.4721i			0.893327i
$341$	4.25325	+	18.9443i	0.230327	+	1.02589i
$342$	−1.14590	−	20.5623i	−0.0619631	−	1.11188i
$343$	−1.93487	+	2.66312i	−0.104473	+	0.143795i
$344$	−8.00760	−	15.7158i	−0.431741	−	0.847340i
$345$	−4.93710	−	0.250548i	−0.265804	−	0.0134891i
$346$	5.30558	+	0.840321i	0.285230	+	0.0451759i
$347$	26.7984	−	19.4702i	1.43861	−	1.04521i	0.450282	−	0.892886i	$-0.351324\pi$
$347$	26.7984	−	19.4702i	1.43861	−	1.04521i	0.988330	−	0.152326i	$-0.0486765\pi$
$348$	−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	$-0.133324\pi$
$350$	0.124400	+	0.785430i	0.00664946	+	0.0419830i
$351$	−2.38197	−	4.61803i	−0.127140	−	0.246492i
$352$	1.19566	+	18.7235i	0.0637290	+	0.997967i
$353$		−	15.7082i		−	0.836063i	−0.908432	−	0.418032i	$-0.862720\pi$
$353$		−	15.7082i		−	0.836063i	0.908432	−	0.418032i	$-0.137280\pi$
$354$	−2.04711	−	0.431587i	−0.108803	−	0.0229386i
$355$	−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
$358$	−1.86198	+	11.7561i	−0.0984085	+	0.621327i
$359$	−5.52786	−	17.0130i	−0.291750	−	0.897913i	−0.984294	−	0.176537i	$-0.943510\pi$
$359$	−5.52786	−	17.0130i	−0.291750	−	0.897913i	0.692544	−	0.721375i	$-0.256490\pi$
$360$	−3.50953	+	13.2733i	−0.184968	+	0.699567i
$361$	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
$366$	1.58389	+	14.8335i	0.0827914	+	0.775359i
$367$	12.6740	−	4.11803i	0.661578	−	0.214960i	0.0410655	−	0.999156i	$-0.486925\pi$
$367$	12.6740	−	4.11803i	0.661578	−	0.214960i	0.620512	+	0.784197i	$0.286925\pi$
$368$	−5.70820	+	4.14725i	−0.297561	+	0.216191i
$369$	−2.87675	+	28.2704i	−0.149757	+	1.47170i
$370$	10.6337	−	20.8697i	0.552817	−	1.08497i
$371$	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	$0.729210\pi$
$374$	−23.8265	+	1.52153i	−1.23204	+	0.0786764i
$375$	7.38197	−	19.3262i	0.381203	−	0.998003i
$376$	−2.92824	−	18.4882i	−0.151012	−	0.953455i
$377$	−3.80423	−	1.23607i	−0.195928	−	0.0636607i
$378$	1.73472	−	0.00861458i	0.0892242	−	0.000443086i
$379$	13.7966	+	18.9894i	0.708682	+	0.975418i	0.999824	+	0.0187379i	$0.00596480\pi$
$379$	13.7966	+	18.9894i	0.708682	+	0.975418i	−0.291142	+	0.956680i	$0.594035\pi$
$380$	−9.23305	−	12.7082i	−0.473646	−	0.651917i
$381$	−14.1506	−	0.718113i	−0.724955	−	0.0367901i
$382$	6.68775	+	13.1254i	0.342175	+	0.671556i
$383$	−20.6074	−	14.9721i	−1.05299	−	0.765041i	−0.0802100	−	0.996778i	$-0.525559\pi$
$383$	−20.6074	−	14.9721i	−1.05299	−	0.765041i	−0.972778	+	0.231737i	$0.925559\pi$
$384$	8.00000	+	17.8885i	0.408248	+	0.912871i
$385$	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	$0.123120\pi$
$390$	−3.43564	−	1.97599i	−0.173971	−	0.100058i
$391$	−5.27756	−	7.26393i	−0.266897	−	0.367353i
$392$	8.91699	−	17.5006i	0.450376	−	0.883913i
$393$	18.0769	−	22.3988i	0.911857	−	1.12987i
$394$	−1.46412	−	9.24408i	−0.0737613	−	0.465710i
$395$	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	$0.511762\pi$
$398$	−0.454792	−	2.87145i	−0.0227967	−	0.143933i
$399$	−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	$0.897149\pi$
$402$	−6.06024	−	3.48552i	−0.302257	−	0.173842i
$403$	−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
$408$	−22.7639	+	10.1803i	−1.12698	+	0.504002i
$409$	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	$0.413210\pi$
$410$	9.84005	+	19.3122i	0.485965	+	0.953761i
$411$	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
$414$	−2.70504	−	6.97775i	−0.132946	−	0.342938i
$415$	6.96767	+	2.26393i	0.342029	+	0.111132i
$416$	−5.58721	+	0.884927i	−0.273935	+	0.0433871i
$417$	4.38197	−	11.4721i	0.214586	−	0.561793i
$418$	17.5292	−	14.5292i	0.857381	−	0.710647i
$419$	−7.03444			−0.343655			−0.171827	−	0.985127i	$-0.554967\pi$
$419$	−7.03444			−0.343655			−0.171827	+	0.985127i	$0.554967\pi$
$420$	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	$0.125829\pi$
$422$	−7.30767	+	14.3421i	−0.355732	+	0.698163i
$423$	19.7521	+	2.00994i	0.960380	+	0.0977265i
$424$	−5.24501	+	33.1157i	−0.254720	+	1.60824i
$425$	11.5312	−	3.74671i	0.559345	−	0.181742i
$426$	−1.58389	−	14.8335i	−0.0767398	−	0.718685i
$427$	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	0.268091	−	0.963394i	$-0.413607\pi$
$431$	−11.7361	−	8.52675i	−0.565307	−	0.410719i	−0.833397	+	0.552674i	$0.813607\pi$
$432$	−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	$0.804563\pi$
$434$	0.305735	−	1.93033i	0.0146757	−	0.0926590i
$435$	−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
$438$	18.4750	+	3.89504i	0.882772	+	0.186112i
$439$			23.3607i			1.11494i	0.830196	+	0.557472i	$0.188229\pi$
$439$			23.3607i			1.11494i	−0.830196	+	0.557472i	$0.811771\pi$
$440$	−14.1074	+	5.60085i	−0.672542	+	0.267010i
$441$	15.5279	+	13.8885i	0.739422	+	0.661359i
$442$	−1.12611	−	7.10996i	−0.0535635	−	0.338186i
$443$	4.61803	−	14.2128i	0.219409	−	0.675273i	−0.779402	−	0.626525i	$-0.784477\pi$
$443$	4.61803	−	14.2128i	0.219409	−	0.675273i	0.998811	−	0.0487482i	$-0.0155232\pi$
$444$	35.4132	+	1.79715i	1.68064	+	0.0852890i
$445$	9.39919	−	6.82891i	0.445564	−	0.323721i
$446$	−28.9253	−	4.58131i	−1.36965	−	0.216931i
$447$	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	$0.152044\pi$
$450$	10.0902	−	0.562306i	0.475655	−	0.0265074i
$451$	−27.0256	+	16.0172i	−1.27259	+	0.754221i
$452$	2.00000			0.0940721
$453$	8.02124	−	5.22795i	0.376871	−	0.245631i
$454$	−6.68775	−	13.1254i	−0.313871	−	0.616007i
$455$	0.118034	+	0.363271i	0.00553352	+	0.0170304i
$456$	11.8560	−	20.6139i	0.555207	−	0.965333i
$457$	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	$0.241193\pi$
$458$	−16.9057	−	8.61386i	−0.789950	−	0.402499i
$459$	−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	$0.852899\pi$
$462$	1.14745	+	1.53669i	0.0533841	+	0.0714933i
$463$		−	3.56231i		−	0.165554i	−0.996568	−	0.0827772i	$-0.973621\pi$
$463$		−	3.56231i		−	0.165554i	0.996568	−	0.0827772i	$-0.0263790\pi$
$464$	−9.40456	+	12.9443i	−0.436596	+	0.600923i
$465$	−10.3036	+	12.7671i	−0.477820	+	0.592060i
$466$	−11.9177	+	23.3899i	−0.552078	+	1.08351i
$467$	−2.04508	+	1.48584i	−0.0946352	+	0.0687565i	−0.634097	−	0.773254i	$-0.718628\pi$
$467$	−2.04508	+	1.48584i	−0.0946352	+	0.0687565i	0.539461	+	0.842010i	$0.318628\pi$
$468$	0.607412	−	5.96917i	0.0280776	−	0.275925i
$469$	0.208204	+	0.640786i	0.00961396	+	0.0295887i
$470$	13.4931	−	6.87509i	0.622391	−	0.317124i
$471$	−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
$474$	17.1803	+	38.4164i	0.789119	+	1.76452i
$475$	−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
$478$	4.26325	−	26.9171i	0.194996	−	1.23116i
$479$	−1.97214	+	1.43284i	−0.0901092	+	0.0654682i	−0.631928	−	0.775027i	$-0.717736\pi$
$479$	−1.97214	+	1.43284i	−0.0901092	+	0.0654682i	0.541818	+	0.840496i	$0.317736\pi$
$480$	−11.7638	+	10.6275i	−0.536942	+	0.485077i
$481$	−3.16312	+	9.73508i	−0.144226	+	0.443881i
$482$	−7.56565	+	1.19828i	−0.344606	+	0.0545802i
$483$	−0.257354	+	0.673762i	−0.0117100	+	0.0306572i
$484$	−9.40456	−	19.8885i	−0.427480	−	0.904025i
$485$		−	5.38197i		−	0.244382i
$486$	2.12283	−	21.9430i	0.0962937	−	0.995353i
$487$	−12.9843	−	4.21885i	−0.588374	−	0.191174i	−0.000325311	−	1.00000i	$-0.500104\pi$
$487$	−12.9843	−	4.21885i	−0.588374	−	0.191174i	−0.588048	+	0.808826i	$0.700104\pi$
$488$	−7.82026	+	15.3481i	−0.354007	+	0.694777i
$489$	−2.42757	−	9.00020i	−0.109779	−	0.407003i
$490$	15.6946	+	2.48577i	0.709008	+	0.112296i
$491$	12.0451	+	37.0710i	0.543587	+	1.67299i	0.724326	+	0.689458i	$0.242151\pi$
$491$	12.0451	+	37.0710i	0.543587	+	1.67299i	−0.180739	+	0.983531i	$0.557849\pi$
$492$	−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
$498$	1.17758	+	11.0283i	0.0527685	+	0.494188i
$499$	2.99193	−	0.972136i	0.133937	−	0.0435188i	−0.241281	−	0.970455i	$-0.577568\pi$
$499$	2.99193	−	0.972136i	0.133937	−	0.0435188i	0.375218	+	0.926936i	$0.377568\pi$
$500$	19.3262	−	14.0413i	0.864296	−	0.627948i
$501$	−9.39497	+	2.53405i	−0.419736	+	0.113213i
$502$	−28.1327	−	14.3343i	−1.25562	−	0.639772i
$503$	−9.20163	+	28.3197i	−0.410280	+	1.26271i	0.506125	+	0.862460i	$0.331078\pi$
$503$	−9.20163	+	28.3197i	−0.410280	+	1.26271i	−0.916405	+	0.400252i	$0.868922\pi$
$504$	1.68355	+	1.08540i	0.0749911	+	0.0483476i
$505$	−8.09017			−0.360008
$506$	4.42663	−	6.98978i	0.196788	−	0.310733i
$507$	−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	$0.878355\pi$
$510$	−13.5239	−	14.9700i	−0.598851	−	0.662881i
$511$	−1.06957	−	1.47214i	−0.0473150	−	0.0651235i
$512$	−3.53971	+	22.3488i	−0.156434	+	0.987688i
$513$	17.9235	+	17.7463i	0.791340	+	0.783519i
$514$	−18.3496	+	9.34958i	−0.809365	+	0.412392i
$515$	−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
$520$	−2.07768	−	4.07768i	−0.0911125	−	0.178818i
$521$	−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	$0.672424\pi$
$522$	−10.7235	−	13.1532i	−0.469356	−	0.575699i
$523$	−9.66183	−	13.2984i	−0.422483	−	0.581497i	0.543725	−	0.839264i	$-0.317014\pi$
$523$	−9.66183	−	13.2984i	−0.422483	−	0.581497i	−0.966207	+	0.257766i	$0.917014\pi$
$524$	31.6094	−	10.2705i	1.38086	−	0.448669i
$525$	−0.757909	−	0.611668i	−0.0330779	−	0.0266954i
$526$	6.78022	−	1.07388i	0.295632	−	0.0468235i
$527$	−29.7984			−1.29804
$528$	−16.4590	−	16.0344i	−0.716286	−	0.697806i
$529$	−19.8885			−0.864719
$530$	−26.7911	+	4.24330i	−1.16373	+	0.184317i
$531$	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
$534$	15.2463	+	8.76886i	0.659774	+	0.379466i
$535$	−0.363271	+	0.118034i	−0.0157056	+	0.00510305i
$536$	−3.66489	−	7.19276i	−0.158299	−	0.310680i
$537$	−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	$0.745824\pi$
$542$	17.1597	−	8.74332i	0.737073	−	0.375558i
$543$	−1.09976	+	21.6710i	−0.0471953	+	0.929992i
$544$	−28.4398	−	4.50443i	−1.21935	−	0.193126i
$545$	12.1392	+	16.7082i	0.519987	+	0.715701i
$546$	−0.429080	+	0.387633i	−0.0183629	+	0.0165892i
$547$	24.8662	+	8.07953i	1.06320	+	0.345456i	0.787837	−	0.615884i	$-0.211201\pi$
$547$	24.8662	+	8.07953i	1.06320	+	0.345456i	0.275366	+	0.961339i	$0.411201\pi$
$548$	15.7984	+	11.4782i	0.674873	+	0.490324i
$549$	−13.6180	−	12.1803i	−0.581204	−	0.519844i
$550$	7.12965	+	8.60179i	0.304009	+	0.366782i
$551$	19.4164			0.827167
$552$	1.78267	−	8.45559i	0.0758754	−	0.359894i
$553$	1.25329	−	3.85723i	0.0532953	−	0.164026i
$554$	20.9399	+	10.6694i	0.889653	+	0.453301i
$555$	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	$0.460064\pi$
$558$	−24.0117	−	6.34879i	−1.01650	−	0.268766i
$559$	−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	0.458607	−	0.888639i	$-0.348348\pi$
$563$	−5.80902	−	4.22050i	−0.244821	−	0.177873i	−0.703428	+	0.710766i	$0.748348\pi$
$564$	17.8404	+	14.3980i	0.751214	+	0.606265i
$565$	0.500000	+	1.53884i	0.0210352	+	0.0647396i
$566$	30.9815	+	4.90700i	1.30225	+	0.206256i
$567$	−1.56945	+	1.43207i	−0.0659106	+	0.0601411i
$568$	7.82026	−	15.3481i	0.328131	−	0.643993i
$569$	−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	$0.725750\pi$
$570$	18.8247	+	3.96876i	0.788481	+	0.166233i
$571$		−	32.5623i		−	1.36269i	−0.731962	−	0.681345i	$-0.761395\pi$
$571$		−	32.5623i		−	1.36269i	0.731962	−	0.681345i	$-0.238605\pi$
$572$	5.70634	−	3.38197i	0.238594	−	0.141407i
$573$	−16.8541	−	6.43769i	−0.704090	−	0.268939i
$574$	3.12334	−	0.494689i	0.130366	−	0.0206479i
$575$	−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	$0.231277\pi$
$578$	1.97114	−	12.4453i	0.0819885	−	0.517655i
$579$	−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
$582$	7.43769	−	3.32624i	0.308302	−	0.137877i
$583$	−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
$586$	5.56500	−	2.83551i	0.229888	−	0.117134i
$587$	−1.12868	−	3.47371i	−0.0465855	−	0.143375i	0.925058	−	0.379826i	$-0.124016\pi$
$587$	−1.12868	−	3.47371i	−0.0465855	−	0.143375i	−0.971644	+	0.236450i	$0.924016\pi$
$588$	6.26452	+	23.2256i	0.258344	+	0.957810i
$589$	22.9894	−	16.7027i	0.947260	−	0.688225i
$590$	0.887277	−	1.74138i	0.0365286	−	0.0716914i
$591$	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	$0.936723\pi$
$594$	20.9045	−	12.5301i	0.857721	−	0.514116i
$595$			1.94427i			0.0797074i
$596$	4.38197	+	3.18368i	0.179492	+	0.130409i
$597$	2.77083	+	2.23619i	0.113403	+	0.0915212i
$598$	2.22268	+	1.13251i	0.0908923	+	0.0463119i
$599$	17.0344	−	12.3762i	0.696008	−	0.505680i	−0.182621	−	0.983183i	$-0.558458\pi$
$599$	17.0344	−	12.3762i	0.696008	−	0.505680i	0.878630	+	0.477504i	$0.158458\pi$
$600$	10.1155	+	5.81787i	0.412962	+	0.237513i
$601$	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	$0.806228\pi$
$602$	−0.945169	−	1.85500i	−0.0385222	−	0.0756041i
$603$	8.36926	−	1.80792i	0.340823	−	0.0736242i
$604$	11.0557			0.449851
$605$	12.9515	−	12.2082i	0.526554	−	0.496334i
$606$	−5.00000	−	11.1803i	−0.203111	−	0.454170i
$607$	−18.2743	+	25.1525i	−0.741733	+	1.02091i	0.256784	+	0.966469i	$0.417337\pi$
$607$	−18.2743	+	25.1525i	−0.741733	+	1.02091i	−0.998517	+	0.0544388i	$0.982663\pi$
$608$	24.4661	−	12.4661i	0.992231	−	0.505567i
$609$	−0.0828931	+	1.63342i	−0.00335900	+	0.0661897i
$610$	−13.7642	−	2.18004i	−0.557297	−	0.0882672i
$611$	−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	$0.0700487\pi$
$614$	−0.136729	−	0.863271i	−0.00551792	−	0.0348388i
$615$	−24.7984	−	9.47214i	−0.999967	−	0.381953i
$616$	0.141129	+	2.21001i	0.00568624	+	0.0890439i
$617$		−	24.2361i		−	0.975707i	−0.872925	−	0.487854i	$-0.837780\pi$
$617$		−	24.2361i		−	0.975707i	0.872925	−	0.487854i	$-0.162220\pi$
$618$	8.80070	−	41.7437i	0.354016	−	1.67918i
$619$	25.4665	+	8.27458i	1.02359	+	0.332583i	0.772251	−	0.635317i	$-0.219131\pi$
$619$	25.4665	+	8.27458i	1.02359	+	0.332583i	0.251335	+	0.967900i	$0.419131\pi$
$620$	−18.0171	+	5.85410i	−0.723583	+	0.235106i
$621$	8.18723	+	4.12052i	0.328542	+	0.165351i
$622$	6.11761	−	38.6250i	0.245294	−	1.54872i
$623$	−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
$630$	−0.414243	+	1.56671i	−0.0165038	+	0.0624191i
$631$	35.7239	−	11.6074i	1.42215	−	0.462083i	0.505862	−	0.862614i	$-0.331174\pi$
$631$	35.7239	−	11.6074i	1.42215	−	0.462083i	0.916283	+	0.400531i	$0.131174\pi$
$632$	−7.60167	+	47.9951i	−0.302378	+	1.90914i
$633$	−5.13391	−	19.0339i	−0.204055	−	0.756531i
$634$	8.46230	−	16.6082i	0.336081	−	0.659596i
$635$	4.09017	−	12.5882i	0.162313	−	0.499549i
$636$	−22.4219	−	34.4019i	−0.889087	−	1.36413i
$637$	−6.94427			−0.275142
$638$	4.64875	−	18.1766i	0.184046	−	0.719619i
$639$	13.6180	+	12.1803i	0.538721	+	0.481847i
$640$	−18.0806	+	2.86368i	−0.714698	+	0.113197i
$641$	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	$0.455823\pi$
$642$	−0.387633	−	0.429080i	−0.0152987	−	0.0169344i
$643$	15.4742	+	21.2984i	0.610242	+	0.839926i	0.996597	−	0.0824241i	$-0.0262662\pi$
$643$	15.4742	+	21.2984i	0.610242	+	0.839926i	−0.386355	+	0.922350i	$0.626266\pi$
$644$	−0.673762	+	0.489517i	−0.0265499	+	0.0192897i
$645$	−0.885768	+	17.4542i	−0.0348771	+	0.687259i
$646$	15.8636	+	31.1342i	0.624147	+	1.22496i
$647$	5.02786	+	3.65296i	0.197666	+	0.143613i	0.682216	−	0.731151i	$-0.261017\pi$
$647$	5.02786	+	3.65296i	0.197666	+	0.143613i	−0.484550	+	0.874764i	$0.661017\pi$
$648$	15.8885	−	19.8885i	0.624161	−	0.781296i
$649$	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	$0.411550\pi$
$654$	−15.5877	+	27.1022i	−0.609528	+	1.05978i
$655$	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
$658$	−0.345632	−	2.18223i	−0.0134741	−	0.0850723i
$659$	13.4164			0.522629			0.261315	−	0.965254i	$-0.415844\pi$
$659$	13.4164			0.522629			0.261315	+	0.965254i	$0.415844\pi$
$660$	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	$0.855541\pi$
$662$	2.94057	+	18.5660i	0.114288	+	0.721588i
$663$	6.86083	+	5.53701i	0.266453	+	0.215040i
$664$	−5.81414	+	11.4109i	−0.225632	+	0.442828i
$665$	−1.08981	−	1.50000i	−0.0422612	−	0.0581675i
$666$	−33.6592	+	27.4417i	−1.30427	+	1.06334i
$667$	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
$672$	0.944272	+	2.11146i	0.0364261	+	0.0814512i
$673$	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	$0.653308\pi$
$674$	−20.5895	−	40.4092i	−0.793078	−	1.55650i
$675$	−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	$0.777298\pi$
$678$	−1.81761	+	1.64204i	−0.0698049	+	0.0630621i
$679$	−0.746787	−	0.242646i	−0.0286591	−	0.00931189i
$680$	−3.64416	−	23.0083i	−0.139747	−	0.882329i
$681$	16.8541	+	6.43769i	0.645851	+	0.246693i
$682$	−10.1320	−	25.5204i	−0.387975	−	0.977228i
$683$	−22.4164			−0.857740			−0.428870	−	0.903366i	$-0.641088\pi$
$683$	−22.4164			−0.857740			−0.428870	+	0.903366i	$0.641088\pi$
$684$	6.14963	+	28.4680i	0.235137	+	1.08850i
$685$	−4.88197	+	15.0251i	−0.186530	+	0.574081i
$686$	2.11346	−	4.14791i	0.0806924	−	0.158368i
$687$	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
$690$	6.95158	−	0.742276i	0.264642	−	0.0282580i
$691$	1.00406	−	1.38197i	0.0381961	−	0.0525725i	−0.789492	−	0.613761i	$-0.789656\pi$
$691$	1.00406	−	1.38197i	0.0381961	−	0.0525725i	0.827688	+	0.561189i	$0.189656\pi$
$692$	−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
$696$	−2.08059	−	19.4852i	−0.0788645	−	0.738583i
$697$	−14.8992	−	45.8550i	−0.564347	−	1.73688i
$698$	−5.53079	+	34.9201i	−0.209344	+	1.32174i
$699$	−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	$0.744456\pi$
$702$	4.34879	+	5.92351i	0.164135	+	0.223569i
$703$		−	49.6869i		−	1.87398i
$704$	−5.81234	−	25.8885i	−0.219061	−	0.975711i
$705$	−6.61803	+	17.3262i	−0.249250	+	0.652544i
$706$	3.47515	+	21.9413i	0.130789	+	0.825770i
$707$	−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	$0.0360451\pi$
$710$	13.7642	+	2.18004i	0.516562	+	0.0818154i
$711$	−47.1542	−	20.8076i	−1.76842	−	0.780347i
$712$	9.22012	+	18.0955i	0.345539	+	0.678158i
$713$	6.06961	−	8.35410i	0.227309	−	0.312864i
$714$	−2.68692	+	1.20163i	−0.100555	+	0.0449697i
$715$	4.02874	+	3.54508i	0.150666	+	0.132579i
$716$		−	16.8328i		−	0.629072i
$717$	18.2250	+	27.9626i	0.680625	+	1.04428i
$718$	11.4852	+	22.5409i	0.428622	+	0.841218i
$719$	−9.10739	−	28.0297i	−0.339648	−	1.04533i	−0.964387	−	0.264496i	$-0.914794\pi$
$719$	−9.10739	−	28.0297i	−0.339648	−	1.04533i	0.624738	−	0.780834i	$-0.285206\pi$
$720$	1.96563	−	19.3167i	0.0732546	−	0.719889i
$721$	−3.32624	+	2.41665i	−0.123876	+	0.0900009i
$722$	−5.74884	−	2.92918i	−0.213950	−	0.109013i
$723$	5.89189	−	7.30055i	0.219122	−	0.271510i
$724$	−14.7274	+	20.2705i	−0.547339	+	0.753348i
$725$			9.52786i			0.353856i
$726$	24.8758	+	10.3535i	0.923228	+	0.384254i
$727$		−	26.2148i		−	0.972252i	−0.873889	−	0.486126i	$-0.838410\pi$
$727$		−	26.2148i		−	0.972252i	0.873889	−	0.486126i	$-0.161590\pi$
$728$	−0.659481	+	0.104451i	−0.0244420	+	0.00387123i
$729$	16.0864	+	21.6848i	0.595791	+	0.803139i
$730$	−8.00760	+	15.7158i	−0.296375	+	0.581668i
$731$	−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	$0.961951\pi$
$734$	−16.7920	+	8.55597i	−0.619805	+	0.315807i
$735$	−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
$738$	−2.23607	−	40.1246i	−0.0823108	−	1.47701i
$739$	−9.30630	+	12.8090i	−0.342338	+	0.471187i	−0.945122	−	0.326717i	$-0.894058\pi$
$739$	−9.30630	+	12.8090i	−0.342338	+	0.471187i	0.602785	+	0.797904i	$0.294058\pi$
$740$	−10.2361	+	31.5034i	−0.376285	+	1.15809i
$741$	−8.39675	−	0.426119i	−0.308462	−	0.0156539i
$742$	−0.619089	+	3.90877i	−0.0227275	+	0.143496i
$743$	15.8992	−	11.5514i	0.583285	−	0.423781i	−0.256622	−	0.966512i	$-0.582610\pi$
$743$	15.8992	−	11.5514i	0.583285	−	0.423781i	0.839907	+	0.542731i	$0.182610\pi$
$744$	−19.2253	−	21.2809i	−0.704835	−	0.780197i
$745$	−1.35410	+	4.16750i	−0.0496105	+	0.152685i
$746$	35.5795	−	5.63525i	1.30266	−	0.206321i
$747$	−10.1246	−	9.05573i	−0.370440	−	0.331332i
$748$	32.9443	−	7.39645i	1.20456	−	0.270441i
$749$			0.0557281i			0.00203626i
$750$	−6.03557	+	28.6281i	−0.220388	+	1.04535i
$751$	−19.4499	−	6.31966i	−0.709737	−	0.230608i	−0.0681694	−	0.997674i	$-0.521716\pi$
$751$	−19.4499	−	6.31966i	−0.709737	−	0.230608i	−0.641568	+	0.767066i	$0.721716\pi$
$752$	8.18034	+	25.1765i	0.298306	+	0.918092i
$753$	37.3359	−	10.0704i	1.36060	−	0.366986i
$754$	5.58721	+	0.884927i	0.203474	+	0.0322271i
$755$	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	$0.0161468\pi$
$762$	19.9244	−	2.12749i	0.721785	−	0.0770708i
$763$	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
$766$	32.0968	+	16.3541i	1.15970	+	0.590898i
$767$	−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	$0.648353\pi$
$770$	−1.66515	+	0.661090i	−0.0600078	+	0.0238240i
$771$	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	$0.514128\pi$
$774$	−24.6686	+	9.56320i	−0.886694	+	0.343742i
$775$	8.19624	+	11.2812i	0.294418	+	0.405231i
$776$	9.29219	+	1.47174i	0.333570	+	0.0528323i
$777$	4.17996	+	0.212125i	0.149955	+	0.00760994i
$778$	−37.9860	+	19.3549i	−1.36187	+	0.693905i
$779$	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
$786$	−20.2945	+	35.2858i	−0.723880	+	1.25860i
$787$	−1.79611	−	2.47214i	−0.0640245	−	0.0881221i	0.775804	−	0.630974i	$-0.217345\pi$
$787$	−1.79611	−	2.47214i	−0.0640245	−	0.0881221i	−0.839829	+	0.542852i	$0.817345\pi$
$788$	4.09017	+	12.5882i	0.145706	+	0.448438i
$789$	−5.28022	+	6.54264i	−0.187981	+	0.232924i
$790$	−38.8288	+	6.14988i	−1.38147	+	0.218803i
$791$	0.236068			0.00839361
$792$	28.1226	+	1.05895i	0.999292	+	0.0376281i
$793$	6.09017			0.216268
$794$	2.05628	−	0.325683i	0.0729747	−	0.0115581i
$795$	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	$0.492263\pi$
$798$	1.39941	−	2.43314i	0.0495385	−	0.0861321i
$799$	−32.0382	+	10.4098i	−1.13343	+	0.368273i
$800$	6.11727	+	12.0058i	0.216278	+	0.424469i
$801$	−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
$806$	7.37660	−	3.75856i	0.259830	−	0.132390i
$807$	−34.9085	−	1.77154i	−1.22884	−	0.0623610i
$808$	2.21232	−	13.9680i	0.0778291	−	0.491393i
$809$	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	$0.671280\pi$
$810$	19.2748	+	7.25284i	0.677247	+	0.254839i
$811$	4.56352	+	1.48278i	0.160247	+	0.0520674i	0.388042	−	0.921642i	$-0.373152\pi$
$811$	4.56352	+	1.48278i	0.160247	+	0.0520674i	−0.227795	+	0.973709i	$0.573152\pi$
$812$	−1.11006	+	1.52786i	−0.0389554	+	0.0536175i
$813$	−8.41641	+	22.0344i	−0.295176	+	0.772782i
$814$	−46.5143	−	11.8962i	−1.63032	−	0.416962i
$815$	8.70820			0.305035
$816$	29.5445	−	19.2560i	1.03426	−	0.674096i
$817$	9.35410	−	28.7890i	0.327259	−	1.00720i
$818$	−39.9547	−	20.3579i	−1.39698	−	0.711798i
$819$	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	$0.139526\pi$
$822$	−23.7815	+	2.53934i	−0.829474	+	0.0885697i
$823$	21.4455	−	29.5172i	0.747544	−	1.02891i	−0.250605	−	0.968089i	$-0.580630\pi$
$823$	21.4455	−	29.5172i	0.747544	−	1.02891i	0.998149	−	0.0608163i	$-0.0193704\pi$
$824$	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	0.811449	−	0.584423i	$-0.198679\pi$
$827$	14.5623	+	10.5801i	0.506381	+	0.367907i	−0.305068	+	0.952331i	$0.598679\pi$
$828$	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	$0.959658\pi$
$830$	−10.2333	−	1.62080i	−0.355203	−	0.0562587i
$831$	−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
$834$	−3.58274	+	16.9937i	−0.124060	+	0.588445i
$835$		−	9.09017i		−	0.314578i
$836$	−21.2705	+	24.1724i	−0.735656	+	0.836021i
$837$	27.0344	−	13.9443i	0.934447	−	0.481985i
$838$	9.82572	−	1.55624i	0.339424	−	0.0537595i
$839$	−4.51064	+	13.8823i	−0.155725	+	0.479271i	−0.998234	−	0.0594111i	$-0.981078\pi$
$839$	−4.51064	+	13.8823i	−0.155725	+	0.479271i	0.842509	+	0.538682i	$0.181078\pi$
$840$	−1.38853	+	1.25441i	−0.0479089	+	0.0432811i
$841$	−10.5172	+	7.64121i	−0.362663	+	0.263490i
$842$	0.735869	−	4.64610i	0.0253597	−	0.160115i
$843$	−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
$846$	−28.0344	+	1.56231i	−0.963844	+	0.0537132i
$847$	−1.11006	−	2.34752i	−0.0381421	−	0.0806619i
$848$		−	47.4164i		−	1.62829i
$849$	−32.1849	+	20.9770i	−1.10458	+	0.719927i
$850$	−15.2779	+	7.78448i	−0.524028	+	0.267005i
$851$	−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	$0.532707\pi$
$854$	−0.923056	+	1.81160i	−0.0315863	+	0.0619917i
$855$	−20.3664	+	11.8486i	−0.696518	+	0.405215i
$856$	−0.104451	−	0.659481i	−0.00357008	−	0.0225406i
$857$			5.11146i			0.174604i	0.996182	+	0.0873020i	$0.0278245\pi$
$857$			5.11146i			0.174604i	−0.996182	+	0.0873020i	$0.972175\pi$
$858$	−2.40929	+	7.75856i	−0.0822518	+	0.264873i
$859$			51.6525i			1.76236i	0.472781	+	0.881180i	$0.343250\pi$
$859$			51.6525i			1.76236i	−0.472781	+	0.881180i	$0.656750\pi$
$860$	−11.8617	+	16.3262i	−0.404481	+	0.556720i
$861$	−2.43236	+	3.01390i	−0.0828947	+	0.102714i
$862$	18.2794	+	9.31380i	0.622597	+	0.317229i
$863$	31.6525	−	22.9969i	1.07746	−	0.782823i	0.100224	−	0.994965i	$-0.468044\pi$
$863$	31.6525	−	22.9969i	1.07746	−	0.782823i	0.977239	+	0.212142i	$0.0680440\pi$
$864$	27.9098	−	9.22192i	0.949510	−	0.313736i
$865$	−1.89919	−	5.84510i	−0.0645743	−	0.198739i
$866$	−7.89182	−	15.4886i	−0.268175	−	0.526323i
$867$	8.42643	+	12.9287i	0.286177	+	0.439081i
$868$			2.76393i			0.0938140i
$869$	−12.4822	−	55.5967i	−0.423431	−	1.88599i
$870$	14.4721	−	6.47214i	0.490651	−	0.219426i
$871$	−1.67760	+	2.30902i	−0.0568433	+	0.0782381i
$872$	−32.1670	+	16.3899i	−1.08931	+	0.555032i
$873$	−4.02851	+	9.12940i	−0.136344	+	0.308983i
$874$	−11.9598	−	1.89425i	−0.404548	−	0.0640741i
$875$	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	$0.141242\pi$
$878$	−5.16812	−	32.6302i	−0.174416	−	1.10122i
$879$	−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	$0.913945\pi$
$882$	−24.7619	−	15.9643i	−0.833778	−	0.537546i
$883$	−29.6013	−	9.61803i	−0.996162	−	0.323673i	−0.234831	−	0.972036i	$-0.575454\pi$
$883$	−29.6013	−	9.61803i	−0.996162	−	0.323673i	−0.761331	+	0.648364i	$0.775454\pi$
$884$	3.14590	+	9.68208i	0.105808	+	0.325644i
$885$	0.623345	+	2.31105i	0.0209535	+	0.0776849i
$886$	−3.30615	+	20.8742i	−0.111072	+	0.701282i
$887$	−8.16312	−	25.1235i	−0.274091	−	0.843564i	−0.989459	−	0.144816i	$-0.953741\pi$
$887$	−8.16312	−	25.1235i	−0.274091	−	0.843564i	0.715368	−	0.698748i	$-0.246259\pi$
$888$	−49.8628	+	5.32426i	−1.67329	+	0.178670i
$889$	−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
$894$	−6.59622	+	0.704332i	−0.220611	+	0.0235564i
$895$	12.9515	−	4.20820i	0.432922	−	0.140665i
$896$	−0.417806	+	2.63792i	−0.0139579	+	0.0881268i
$897$	−2.94980	+	0.795633i	−0.0984910	+	0.0265654i
$898$	−4.08381	+	8.01492i	−0.136278	+	0.267461i
$899$	7.23607	−	22.2703i	0.241336	−	0.742757i
$900$	−13.9696	+	3.01770i	−0.465652	+	0.100590i
$901$	60.3394			2.01020
$902$	34.2059	−	28.3518i	1.13893	−	0.944012i
$903$	2.38197	+	0.909830i	0.0792669	+	0.0302772i
$904$	−2.79360	+	0.442463i	−0.0929139	+	0.0147161i
$905$	−19.2784	−	6.26393i	−0.640836	−	0.208220i
$906$	−10.0475	+	9.07697i	−0.333806	+	0.301562i
$907$	−31.4504	−	43.2877i	−1.04429	−	1.43735i	−0.893654	−	0.448757i	$-0.851867\pi$
$907$	−31.4504	−	43.2877i	−1.04429	−	1.43735i	−0.150639	−	0.988589i	$-0.548133\pi$
$908$	12.2452	+	16.8541i	0.406372	+	0.559323i
$909$	13.7233	+	6.05565i	0.455173	+	0.200853i
$910$	−0.245237	−	0.481305i	−0.00812954	−	0.0159551i
$911$	−7.42705	−	5.39607i	−0.246069	−	0.178780i	0.457914	−	0.888997i	$-0.348597\pi$
$911$	−7.42705	−	5.39607i	−0.246069	−	0.178780i	−0.703983	+	0.710217i	$0.748597\pi$
$912$	−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
$918$	11.7353	+	35.5164i	0.387322	+	1.17222i
$919$	28.8015	+	39.6418i	0.950073	+	1.30766i	0.951495	+	0.307664i	$0.0995474\pi$
$919$	28.8015	+	39.6418i	0.950073	+	1.30766i	−0.00142186	+	0.999999i	$0.500453\pi$
$920$	7.19276	+	3.66489i	0.237138	+	0.120828i
$921$	0.833023	+	0.672288i	0.0274490	+	0.0221527i
$922$	−4.23568	−	26.7430i	−0.139495	−	0.880735i
$923$	−6.09017			−0.200460
$924$	−1.94272	−	1.89260i	−0.0639109	−	0.0622620i
$925$	24.3820			0.801674
$926$	0.788095	+	4.97584i	0.0258984	+	0.163516i
$927$	26.2743	+	45.1624i	0.862960	+	1.48333i
$928$	10.2726	−	20.1612i	0.337216	−	0.661823i
$929$	−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	$0.823665\pi$
$930$	11.5677	−	20.1126i	0.379319	−	0.659518i
$931$	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
$936$	0.472136	+	8.47214i	0.0154322	+	0.276920i
$937$	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	$0.663525\pi$
$938$	−0.432582	−	0.848990i	−0.0141243	−	0.0277205i
$939$	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	$0.839336\pi$
$942$	4.05934	+	4.49338i	0.132261	+	0.146402i
$943$	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
$946$	−24.7111	−	15.6496i	−0.803427	−	0.508811i
$947$	−50.8115			−1.65115			−0.825576	−	0.564290i	$-0.809150\pi$
$947$	−50.8115			−1.65115			−0.825576	+	0.564290i	$0.809150\pi$
$948$	−32.4965	−	49.8593i	−1.05544	−	1.61935i
$949$	2.38197	−	7.33094i	0.0773219	−	0.237972i
$950$	7.42346	−	14.5694i	0.240849	−	0.472692i
$951$	5.94508	+	22.0413i	0.192782	+	0.714739i
$952$	−3.35687	−	0.531676i	−0.108797	−	0.0172317i
$953$	−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	$0.726880\pi$
$954$	48.6218	+	12.8558i	1.57419	+	0.416222i
$955$	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
$962$	2.26454	−	14.2978i	0.0730118	−	0.460978i
$963$	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
$966$	0.210415	−	0.998047i	0.00677000	−	0.0321116i
$967$			39.6869i			1.27625i	0.769935	+	0.638123i	$0.220289\pi$
$967$			39.6869i			1.27625i	−0.769935	+	0.638123i	$0.779711\pi$
$968$	17.5363	+	25.6998i	0.563638	+	0.826022i
$969$	−39.9787	−	15.2705i	−1.28430	−	0.490559i
$970$	1.19066	+	7.51754i	0.0382298	+	0.241374i
$971$	8.65248	−	26.6296i	0.277671	−	0.854584i	−0.710829	−	0.703365i	$-0.751680\pi$
$971$	8.65248	−	26.6296i	0.277671	−	0.854584i	0.988500	−	0.151219i	$-0.0483199\pi$
$972$	1.88930	+	31.1196i	0.0605993	+	0.998162i
$973$	1.35410	−	0.983813i	0.0434105	−	0.0315396i
$974$	19.0698	+	3.02036i	0.611036	+	0.0967786i
$975$	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	$0.262130\pi$
$978$	5.38197	+	12.0344i	0.172096	+	0.384819i
$979$	−17.8783	−	15.7320i	−0.571393	−	0.502797i
$980$	−22.4721			−0.717846
$981$	−8.08527	−	37.4285i	−0.258143	−	1.19500i
$982$	−25.0259	−	49.1160i	−0.798608	−	1.56736i
$983$	14.7426	+	45.3732i	0.470217	+	1.44718i	0.852301	+	0.523052i	$0.175207\pi$
$983$	14.7426	+	45.3732i	0.470217	+	1.44718i	−0.382083	+	0.924128i	$0.624793\pi$
$984$	23.1353	−	40.2252i	0.737528	−	1.28233i
$985$	−8.66312	+	6.29412i	−0.276030	+	0.200547i
$986$	25.6560	+	13.0724i	0.817052	+	0.416309i
$987$	2.10577	+	1.69945i	0.0670273	+	0.0540942i
$988$	−7.85410	−	5.70634i	−0.249872	−	0.181543i
$989$		−	11.0000i		−	0.349780i
$990$	6.21586	+	21.9028i	0.197553	+	0.696117i
$991$		−	25.3262i		−	0.804514i	−0.915527	−	0.402257i	$-0.868226\pi$
$991$		−	25.3262i		−	0.804514i	0.915527	−	0.402257i	$-0.131774\pi$
$992$	−5.18045	−	32.7081i	−0.164480	−	1.03848i
$993$	−17.9155	−	14.4586i	−0.568530	−	0.458830i
$994$	0.923056	−	1.81160i	0.0292776	−	0.0574605i
$995$	−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	$0.723045\pi$
$998$	−3.96406	+	2.01979i	−0.125480	+	0.0639354i
$999$	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.a.59.1	yes	8
3.2	odd	2		132.2.o.b.59.2	yes	8
4.3	odd	2		132.2.o.b.59.1	yes	8
11.3	even	5	inner	132.2.o.a.47.2	yes	8
12.11	even	2	inner	132.2.o.a.59.2	yes	8
33.14	odd	10		132.2.o.b.47.1	yes	8
44.3	odd	10		132.2.o.b.47.2	yes	8
132.47	even	10	inner	132.2.o.a.47.1	✓	8

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

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)

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

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