LMFDB - Embedded newform 132.2.o.a.59.2

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			59.2
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	132.59
Dual form			132.2.o.a.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.221232 - 1.39680i) q^{2} +(-0.0877853 - 1.72982i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-0.951057 - 1.30902i) q^{5} +(-2.39680 + 0.505311i) q^{6} +(-0.224514 + 0.0729490i) q^{7} +(1.28408 + 2.52015i) q^{8} +(-2.98459 + 0.303706i) q^{9} +O(q^{10})$	\(q+(-0.221232 - 1.39680i) q^{2} +(-0.0877853 - 1.72982i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-0.951057 - 1.30902i) q^{5} +(-2.39680 + 0.505311i) q^{6} +(-0.224514 + 0.0729490i) q^{7} +(1.28408 + 2.52015i) q^{8} +(-2.98459 + 0.303706i) 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} +(-2.18088 + 1.76007i) q^{15} +(3.23607 - 2.35114i) q^{16} +(-2.99193 - 4.11803i) q^{17} +(1.08450 + 4.10169i) 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} +(4.24669 - 2.44246i) q^{24} +(0.736068 - 2.26538i) q^{25} +(0.642040 - 1.26007i) q^{26} +(0.787361 + 5.13615i) q^{27} +(0.381966 - 0.277515i) q^{28} +(3.80423 - 1.23607i) q^{29} +(2.94095 + 2.65688i) q^{30} +(3.44095 - 4.73607i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-4.49942 - 3.57144i) q^{33} +(-5.09017 + 5.09017i) q^{34} +(0.309017 + 0.224514i) q^{35} +(5.48932 - 2.42226i) q^{36} +(3.16312 + 9.73508i) q^{37} +(1.07388 - 6.78022i) q^{38} +(0.945746 - 1.45106i) q^{39} +(2.07768 - 4.07768i) q^{40} +(9.00854 + 2.92705i) q^{41} +(0.501254 - 0.288294i) 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} +(-4.35114 - 5.39144i) q^{48} +(-5.61803 + 4.08174i) q^{49} +(-3.32714 - 0.526966i) q^{50} +(-6.86083 + 5.53701i) 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} +(2.18947 - 8.11746i) q^{57} +(-2.56816 - 5.04029i) q^{58} +(0.263932 + 0.812299i) q^{59} +(3.06050 - 4.69572i) q^{60} +(4.92705 - 3.57971i) q^{61} +(-7.37660 - 3.75856i) q^{62} +(0.647927 - 0.285909i) q^{63} +(-4.70228 + 6.47214i) q^{64} -1.61803i q^{65} +(-3.99318 + 7.07492i) q^{66} -2.85410i q^{67} +(8.23607 + 5.98385i) q^{68} +(0.154847 + 3.05129i) q^{69} +(0.245237 - 0.481305i) q^{70} +(-4.92705 + 3.57971i) q^{71} +(-4.59783 - 7.13162i) q^{72} +(-2.38197 - 7.33094i) q^{73} +(12.8982 - 6.57196i) q^{74} +(-3.98333 - 1.07440i) 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} +(8.81553 - 1.81288i) q^{81} +(2.09554 - 13.2307i) q^{82} +(3.66312 - 2.66141i) q^{83} +(-0.513583 - 0.636373i) 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} +(4.33776 - 5.32057i) q^{90} +(-0.224514 - 0.0729490i) q^{91} +(3.35520 - 1.09017i) q^{92} +(-8.49463 - 5.53649i) q^{93} +(9.24408 + 1.46412i) q^{94} +(-2.42705 - 7.46969i) q^{95} +(-6.56816 + 7.27044i) q^{96} +(-2.69098 - 1.95511i) q^{97} +(6.94427 + 6.94427i) q^{98} +(-5.78298 + 8.09673i) 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 $

$2$	−0.221232	−	1.39680i	−0.156434	−	0.987688i
$2$	−0.221232	−	1.39680i	−0.156434	−	0.987688i
$3$	−0.0877853	−	1.72982i	−0.0506828	−	0.998715i
$3$	−0.0877853	−	1.72982i	−0.0506828	−	0.998715i
$4$	−1.90211	+	0.618034i	−0.951057	+	0.309017i
$5$	−0.951057	−	1.30902i	−0.425325	−	0.585410i	0.541547	−	0.840670i	$-0.317839\pi$
$5$	−0.951057	−	1.30902i	−0.425325	−	0.585410i	−0.966872	+	0.255260i	$0.917839\pi$
$6$	−2.39680	+	0.505311i	−0.978490	+	0.206292i
$7$	−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
$9$	−2.98459	+	0.303706i	−0.994862	+	0.101235i
$10$	−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
$15$	−2.18088	+	1.76007i	−0.563101	+	0.454449i
$16$	3.23607	−	2.35114i	0.809017	−	0.587785i
$17$	−2.99193	−	4.11803i	−0.725649	−	0.998770i	−0.999317	−	0.0369459i	$-0.988237\pi$
$17$	−2.99193	−	4.11803i	−0.725649	−	0.998770i	0.273668	−	0.961824i	$-0.411763\pi$
$18$	1.08450	+	4.10169i	0.255620	+	0.966777i
$19$	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	$-0.558873\pi$
$23$	−1.76393			−0.367805			−0.183903	+	0.982944i	$0.558873\pi$
$24$	4.24669	−	2.44246i	0.866852	−	0.498566i
$25$	0.736068	−	2.26538i	0.147214	−	0.453077i
$26$	0.642040	−	1.26007i	0.125914	−	0.247121i
$27$	0.787361	+	5.13615i	0.151528	+	0.988453i
$28$	0.381966	−	0.277515i	0.0721848	−	0.0524453i
$29$	3.80423	−	1.23607i	0.706427	−	0.229532i	0.0662984	−	0.997800i	$-0.478881\pi$
$29$	3.80423	−	1.23607i	0.706427	−	0.229532i	0.640129	+	0.768268i	$0.278881\pi$
$30$	2.94095	+	2.65688i	0.536942	+	0.485077i
$31$	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
$33$	−4.49942	−	3.57144i	−0.783249	−	0.621708i
$34$	−5.09017	+	5.09017i	−0.872957	+	0.872957i
$35$	0.309017	+	0.224514i	0.0522334	+	0.0379498i
$36$	5.48932	−	2.42226i	0.914887	−	0.403710i
$37$	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
$39$	0.945746	−	1.45106i	0.151441	−	0.232355i
$40$	2.07768	−	4.07768i	0.328511	−	0.644738i
$41$	9.00854	+	2.92705i	1.40690	+	0.457129i	0.911415	−	0.411489i	$-0.134991\pi$
$41$	9.00854	+	2.92705i	1.40690	+	0.457129i	0.495482	+	0.868618i	$0.334991\pi$
$42$	0.501254	−	0.288294i	0.0773451	−	0.0444847i
$43$		−	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	$0.260333\pi$
$47$	−2.04508	+	6.29412i	−0.298306	+	0.918092i	−0.982091	+	0.188408i	$0.939667\pi$
$48$	−4.35114	−	5.39144i	−0.628033	−	0.778187i
$49$	−5.61803	+	4.08174i	−0.802576	+	0.583106i
$50$	−3.32714	−	0.526966i	−0.470528	−	0.0745243i
$51$	−6.86083	+	5.53701i	−0.960708	+	0.775337i
$52$	−1.90211	−	0.618034i	−0.263776	−	0.0857059i
$53$	−6.96767	+	9.59017i	−0.957083	+	1.31731i	−0.00877397	+	0.999962i	$0.502793\pi$
$53$	−6.96767	+	9.59017i	−0.957083	+	1.31731i	−0.948309	+	0.317350i	$0.897207\pi$
$54$	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
$57$	2.18947	−	8.11746i	0.290003	−	1.07518i
$58$	−2.56816	−	5.04029i	−0.337216	−	0.661823i
$59$	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	$0.882294\pi$
$60$	3.06050	−	4.69572i	0.395109	−	0.606215i
$61$	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
$63$	0.647927	−	0.285909i	0.0816311	−	0.0360212i
$64$	−4.70228	+	6.47214i	−0.587785	+	0.809017i
$65$		−	1.61803i		−	0.200692i
$66$	−3.99318	+	7.07492i	−0.491527	+	0.870863i
$67$		−	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
$69$	0.154847	+	3.05129i	0.0186414	+	0.367333i
$70$	0.245237	−	0.481305i	0.0293115	−	0.0575270i
$71$	−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	$0.417696\pi$
$72$	−4.59783	−	7.13162i	−0.541860	−	0.840469i
$73$	−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
$75$	−3.98333	−	1.07440i	−0.459956	−	0.124061i
$76$	−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	$0.617338\pi$
$79$	−10.0984	+	13.8992i	−1.13615	+	1.56378i	−0.775817	+	0.630958i	$0.782662\pi$
$80$	−6.15537	−	2.00000i	−0.688191	−	0.223607i
$81$	8.81553	−	1.81288i	0.979503	−	0.201431i
$82$	2.09554	−	13.2307i	0.231413	−	1.46109i
$83$	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	$0.220063\pi$
$84$	−0.513583	−	0.636373i	−0.0560364	−	0.0694339i
$85$	−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	$0.124268\pi$
$89$			7.18034i			0.761115i	−0.924757	+	0.380557i	$0.875732\pi$
$90$	4.33776	−	5.32057i	0.457240	−	0.560837i
$91$	−0.224514	−	0.0729490i	−0.0235355	−	0.00764713i
$92$	3.35520	−	1.09017i	0.349804	−	0.113658i
$93$	−8.49463	−	5.53649i	−0.880852	−	0.574107i
$94$	9.24408	+	1.46412i	0.953455	+	0.151012i
$95$	−2.42705	−	7.46969i	−0.249010	−	0.766375i
$96$	−6.56816	+	7.27044i	−0.670360	+	0.742036i
$97$	−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
$99$	−5.78298	+	8.09673i	−0.581212	+	0.813752i
$100$			4.76393i			0.476393i
$101$	2.93893	−	4.04508i	0.292434	−	0.402501i	−0.637369	−	0.770559i	$-0.719977\pi$
$101$	2.93893	−	4.04508i	0.292434	−	0.402501i	0.929803	+	0.368058i	$0.119977\pi$
$102$	9.25194	+	8.35826i	0.916079	+	0.827591i
$103$	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
$105$	0.361243	−	0.554254i	0.0352537	−	0.0540897i
$106$	14.9370	+	7.61080i	1.45081	+	0.739226i
$107$	−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	$0.103632\pi$
$108$	−4.67197	−	9.28293i	−0.449560	−	0.893250i
$109$	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	0.263941	−	0.964539i	$-0.414978\pi$
$113$	−0.951057	−	0.309017i	−0.0894679	−	0.0290699i	−0.353409	+	0.935469i	$0.614978\pi$
$114$	−11.8229	−	1.26242i	−1.10731	−	0.118237i
$115$	1.67760	+	2.30902i	0.156437	+	0.215317i
$116$	−6.47214	+	4.70228i	−0.600923	+	0.436596i
$117$	−2.59310	−	1.50859i	−0.239732	−	0.139469i
$118$	1.07623	−	0.548367i	0.0990751	−	0.0504813i
$119$	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
$123$	4.27247	−	15.8401i	0.385236	−	1.42826i
$124$	−3.61803	+	11.1352i	−0.324909	+	0.999967i
$125$	−11.3597	+	3.69098i	−1.01604	+	0.330132i
$126$	−0.542700	−	0.841773i	−0.0483476	−	0.0749911i
$127$	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
$129$	−10.7873	+	0.547435i	−0.949769	+	0.0481989i
$130$	−2.26007	+	0.357960i	−0.198222	+	0.0313952i
$131$	16.6180			1.45192			0.725962	−	0.687735i	$-0.241395\pi$
$131$	16.6180			1.45192			0.725962	+	0.687735i	$0.241395\pi$
$132$	10.7657	+	4.01249i	0.937033	+	0.349242i
$133$	−1.14590			−0.0993620
$134$	−3.98662	+	0.631418i	−0.344391	+	0.0545462i
$135$	5.97449	−	5.91544i	0.514202	−	0.509120i
$136$	6.53618	−	12.8280i	0.560473	−	1.09999i
$137$	−5.73910	−	7.89919i	−0.490324	−	0.674873i	0.490124	−	0.871653i	$-0.336952\pi$
$137$	−5.73910	−	7.89919i	−0.490324	−	0.674873i	−0.980448	+	0.196780i	$0.936952\pi$
$138$	4.22780	−	0.891334i	0.359894	−	0.0758754i
$139$	−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
$141$	11.0673	+	2.98511i	0.932031	+	0.251391i
$142$	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
$147$	7.55388	+	9.35990i	0.623033	+	0.771991i
$148$	−12.0332	−	16.5623i	−0.989125	−	1.36141i
$149$	−1.59184	−	2.19098i	−0.130409	−	0.179492i	0.738819	−	0.673904i	$-0.235384\pi$
$149$	−1.59184	−	2.19098i	−0.130409	−	0.179492i	−0.869228	+	0.494411i	$0.835384\pi$
$150$	−0.619486	+	5.80162i	−0.0505808	+	0.473700i
$151$	−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
$156$	−0.902113	+	3.34458i	−0.0722268	+	0.267780i
$157$	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
$159$	17.2010	+	11.2110i	1.36413	+	0.889087i
$160$	−1.43184	+	9.04029i	−0.113197	+	0.714698i
$161$	0.396027	−	0.128677i	0.0312113	−	0.0101412i
$162$	−4.48250	−	11.9125i	−0.352179	−	0.935933i
$163$	−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
$165$	−0.395870	+	9.28646i	−0.0308184	+	0.722950i
$166$	−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	$0.769747\pi$
$168$	−0.775266	+	0.858159i	−0.0598131	+	0.0662084i
$169$	−3.70820	−	11.4127i	−0.285246	−	0.877898i
$170$	11.5042	+	1.82208i	0.882329	+	0.139747i
$171$	−14.2340	−	3.07481i	−1.08850	−	0.235137i
$172$	3.85410	+	11.8617i	0.293873	+	0.904447i
$173$	3.61247	+	1.17376i	0.274651	+	0.0892395i	0.443104	−	0.896470i	$-0.353877\pi$
$173$	3.61247	+	1.17376i	0.274651	+	0.0892395i	−0.168453	+	0.985710i	$0.553877\pi$
$174$	−8.49338	+	4.88493i	−0.643881	+	0.370325i
$175$			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	$-0.798151\pi$
$179$	2.60081	−	8.00448i	0.194394	−	0.598283i	0.999983	−	0.00580843i	$-0.00184889\pi$
$180$	−8.39144	−	4.88191i	−0.625461	−	0.363876i
$181$	−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
$183$	−6.62480	−	8.20869i	−0.489719	−	0.606804i
$184$	−2.26503	−	4.44537i	−0.166980	−	0.327717i
$185$	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
$189$	−0.551451	−	1.09570i	−0.0401122	−	0.0797005i
$190$	−9.89675	+	5.04264i	−0.717985	+	0.365832i
$191$	−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	$-0.222994\pi$
$192$	11.6085	+	7.56597i	0.837768	+	0.546027i
$193$	−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
$195$	−2.79892	+	0.142040i	−0.200434	+	0.0101717i
$196$	8.16348	−	11.2361i	0.583106	−	0.802576i
$197$		−	6.61803i		−	0.471515i	−0.971812	−	0.235758i	$-0.924243\pi$
$197$		−	6.61803i		−	0.471515i	0.971812	−	0.235758i	$-0.0757572\pi$
$198$	12.5889	+	6.28643i	0.894655	+	0.446757i
$199$		−	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
$201$	−4.93710	+	0.250548i	−0.348236	+	0.0176723i
$202$	−6.30037	−	3.21020i	−0.443292	−	0.225869i
$203$	−0.763932	+	0.555029i	−0.0536175	+	0.0389554i
$204$	9.62801	−	14.7722i	0.674096	−	1.03426i
$205$	−4.73607	−	14.5761i	−0.330781	−	1.01804i
$206$	−11.1820	−	21.9460i	−0.779088	−	1.52905i
$207$	5.26461	−	0.535717i	0.365916	−	0.0372349i
$208$	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	−0.974627	−	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
$213$	6.62480	+	8.20869i	0.453924	+	0.562450i
$214$	0.329740	+	0.0522257i	0.0225406	+	0.00357008i
$215$	−8.16312	+	5.93085i	−0.556720	+	0.404481i
$216$	−11.9328	+	8.57949i	−0.811926	+	0.583760i
$217$	−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
$222$	−12.5006	−	21.7347i	−0.838986	−	1.45874i
$223$	−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
$225$	−1.50885	+	6.98479i	−0.100590	+	0.465652i
$226$	−0.221232	+	1.39680i	−0.0147161	+	0.0929139i
$227$	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	$0.787648\pi$
$228$	0.852237	+	16.7935i	0.0564408	+	1.11218i
$229$	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
$231$	1.27072	+	0.473610i	0.0836070	+	0.0311612i
$232$	8.00000	+	8.00000i	0.525226	+	0.525226i
$233$	−10.9106	+	15.0172i	−0.714780	+	0.983811i	0.284901	+	0.958557i	$0.408039\pi$
$233$	−10.9106	+	15.0172i	−0.714780	+	0.983811i	−0.999681	+	0.0252538i	$0.991961\pi$
$234$	−1.53353	+	3.95579i	−0.100250	+	0.258598i
$235$	10.1841	−	3.30902i	0.664338	−	0.215856i
$236$	−1.00406	−	1.38197i	−0.0653585	−	0.0899583i
$237$	24.9296	+	16.2482i	1.61935	+	1.05544i
$238$	0.771491	−	1.51414i	0.0500084	−	0.0981469i
$239$	−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	$0.885811\pi$
$240$	−2.91930	+	10.8233i	−0.188440	+	0.698640i
$241$	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
$246$	−23.0708	−	2.46345i	−1.47094	−	0.157064i
$247$	2.85317	+	3.92705i	0.181543	+	0.249872i
$248$	16.3540	+	2.59023i	1.03848	+	0.164480i
$249$	−4.92534	−	6.10292i	−0.312131	−	0.386757i
$250$	7.66869	+	15.0507i	0.485011	+	0.951887i
$251$	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
$255$	13.7731	+	3.71493i	0.862504	+	0.232638i
$256$	4.94427	−	15.2169i	0.309017	−	0.951057i
$257$	−13.8496	+	4.50000i	−0.863913	+	0.280702i	−0.707262	−	0.706952i	$-0.750070\pi$
$257$	−13.8496	+	4.50000i	−0.863913	+	0.280702i	−0.156651	+	0.987654i	$0.550070\pi$
$258$	3.15115	+	14.9466i	0.196182	+	0.930536i
$259$	−1.42033	−	1.95492i	−0.0882549	−	0.121473i
$260$	1.00000	+	3.07768i	0.0620174	+	0.190870i
$261$	−10.9786	+	4.84452i	−0.679561	+	0.299868i
$262$	−3.67644	−	23.2121i	−0.227131	−	1.43405i
$263$	−4.85410			−0.299317			−0.149658	−	0.988738i	$-0.547817\pi$
$263$	−4.85410			−0.299317			−0.149658	+	0.988738i	$0.547817\pi$
$264$	3.22294	−	15.9252i	0.198358	−	0.980130i
$265$	19.1803			1.17824
$266$	0.253509	+	1.60059i	0.0155436	+	0.0981387i
$267$	12.4207	−	0.630328i	0.760136	−	0.0385754i
$268$	1.76393	+	5.42882i	0.107749	+	0.331618i
$269$	11.8617	+	16.3262i	0.723221	+	0.995428i	0.999411	+	0.0343252i	$0.0109282\pi$
$269$	11.8617	+	16.3262i	0.723221	+	0.995428i	−0.276190	+	0.961103i	$0.589072\pi$
$270$	−9.58445	−	7.03649i	−0.583291	−	0.428227i
$271$	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
$273$	−0.106480	+	0.394774i	−0.00644446	+	0.0238928i
$274$	−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
$279$	−8.83146	+	15.1802i	−0.528726	+	0.908818i
$280$	−0.169006	+	1.06706i	−0.0101000	+	0.0637691i
$281$	3.63271	+	5.00000i	0.216709	+	0.298275i	0.903507	−	0.428574i	$-0.140984\pi$
$281$	3.63271	+	5.00000i	0.216709	+	0.298275i	−0.686797	+	0.726849i	$0.740984\pi$
$282$	1.72118	−	16.1192i	0.102494	−	0.959883i
$283$	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
$288$	13.1532	+	10.7235i	0.775058	+	0.631890i
$289$	−2.75329	+	8.47375i	−0.161958	+	0.498456i
$290$	−4.15537	+	8.15537i	−0.244012	+	0.478900i
$291$	−3.14578	+	4.82656i	−0.184409	+	0.282938i
$292$	9.06154	+	12.4721i	0.530286	+	0.729877i
$293$	4.20025	−	1.36475i	0.245381	−	0.0797293i	−0.183744	−	0.982974i	$-0.558822\pi$
$293$	4.20025	−	1.36475i	0.245381	−	0.0797293i	0.429126	+	0.903245i	$0.358822\pi$
$294$	11.4028	−	12.6220i	0.665023	−	0.736129i
$295$	0.812299	−	1.11803i	0.0472939	−	0.0650945i
$296$	−20.4721	+	20.4721i	−1.18992	+	1.18992i
$297$	14.5136	+	9.29277i	0.842164	+	0.539221i
$298$	−2.70820	+	2.70820i	−0.156882	+	0.156882i
$299$	−1.42705	−	1.03681i	−0.0825285	−	0.0599605i
$300$	8.24077	−	0.418203i	0.475781	−	0.0241450i
$301$	0.454915	+	1.40008i	0.0262209	+	0.0806995i
$302$	−1.22294	+	7.72133i	−0.0703722	+	0.444313i
$303$	−7.25528	−	4.72873i	−0.416805	−	0.271658i
$304$	18.4661	−	6.00000i	1.05910	−	0.344124i
$305$	−9.37181	−	3.04508i	−0.536628	−	0.174361i
$306$	13.6461	−	16.7380i	0.780098	−	0.956846i
$307$		−	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	$0.386831\pi$
$311$	−8.54508	+	26.2991i	−0.484547	+	1.49128i	−0.832635	+	0.553821i	$0.813169\pi$
$312$	4.87129	+	0.520147i	0.275782	+	0.0294475i
$313$	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
$315$	−0.990475	−	0.576231i	−0.0558069	−	0.0324670i
$316$	10.6180	−	32.6789i	0.597311	−	1.83833i
$317$	7.74721	−	10.6631i	0.435127	−	0.598900i	−0.533994	−	0.845488i	$-0.679309\pi$
$317$	7.74721	−	10.6631i	0.435127	−	0.598900i	0.969120	+	0.246588i	$0.0793094\pi$
$318$	11.8541	−	26.5066i	0.664745	−	1.48642i
$319$	5.25731	−	12.1803i	0.294353	−	0.681968i
$320$	12.9443			0.723607
$321$	0.394774	+	0.106480i	0.0220341	+	0.00594313i
$322$	−0.267350	−	0.524705i	−0.0148989	−	0.0292406i
$323$	−7.63525	−	23.4989i	−0.424837	−	1.30751i
$324$	−15.6477	+	8.89659i	−0.869317	+	0.494255i
$325$	1.92705	−	1.40008i	0.106894	−	0.0776627i
$326$	6.78167	+	3.45543i	0.375602	+	0.191379i
$327$	−1.12048	−	22.0794i	−0.0619630	−	1.22099i
$328$	4.19107	+	26.4614i	0.231413	+	1.46109i
$329$		−	1.56231i		−	0.0861327i
$330$	13.0589	−	1.50151i	0.718871	−	0.0826553i
$331$			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
$333$	−12.3972	−	28.0945i	−0.679363	−	1.53957i
$334$	−3.60700	+	7.07914i	−0.197366	+	0.387353i
$335$	−3.73607	+	2.71441i	−0.204123	+	0.148304i
$336$	1.37019	+	0.893041i	0.0747501	+	0.0487194i
$337$	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
$339$	−0.451057	+	1.67229i	−0.0244980	+	0.0908262i
$340$		−	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
$344$	15.7158	−	8.00760i	0.847340	−	0.431741i
$345$	3.84693	−	3.10465i	0.207112	−	0.167149i
$346$	0.840321	−	5.30558i	0.0451759	−	0.285230i
$347$	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	$-0.0486765\pi$
$348$	8.70228	+	10.7829i	0.466491	+	0.578023i
$349$	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	$0.137280\pi$
$353$			15.7082i			0.836063i	−0.908432	+	0.418032i	$0.862720\pi$
$354$	−1.04306	−	1.81355i	−0.0554378	−	0.0963893i
$355$	9.37181	+	3.04508i	0.497404	+	0.161616i
$356$	−4.43769	−	13.6578i	−0.235197	−	0.723863i
$357$	1.13643	−	1.74363i	0.0601464	−	0.0922825i
$358$	−11.7561	−	1.86198i	−0.621327	−	0.0984085i
$359$	−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	$-0.256490\pi$
$360$	−4.96261	+	12.8012i	−0.261553	+	0.674683i
$361$	3.69098	+	2.68166i	0.194262	+	0.141140i
$362$	12.5279	+	12.5279i	0.658450	+	0.658450i
$363$	−18.7507	+	3.37814i	−0.984156	+	0.177306i
$364$	0.472136			0.0247466
$365$	−7.33094	+	10.0902i	−0.383719	+	0.528144i
$366$	−10.0003	+	11.0696i	−0.522724	+	0.578615i
$367$	−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
$369$	−27.7757	−	6.00009i	−1.44595	−	0.312352i
$370$	−20.8697	−	10.6337i	−1.08497	−	0.552817i
$371$	0.864745	−	2.66141i	0.0448953	−	0.138174i
$372$	19.5795	+	5.28106i	1.01515	+	0.273810i
$373$	−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
$378$	−1.40848	+	1.01267i	−0.0724443	+	0.0520862i
$379$	−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
$381$	11.0259	−	8.89845i	0.564876	−	0.455882i
$382$	−13.1254	+	6.68775i	−0.671556	+	0.342175i
$383$	−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
$387$	1.89393	+	18.6121i	0.0962740	+	0.946106i
$388$	6.32688	+	2.05573i	0.321199	+	0.104364i
$389$	−28.6705	+	9.31559i	−1.45365	+	0.472319i	−0.926124	−	0.377220i	$-0.876880\pi$
$389$	−28.6705	+	9.31559i	−1.45365	+	0.472319i	−0.527526	+	0.849539i	$0.676880\pi$
$390$	0.817610	+	3.87811i	0.0414013	+	0.196376i
$391$	5.27756	+	7.26393i	0.266897	+	0.367353i
$392$	−17.5006	−	8.91699i	−0.883913	−	0.450376i
$393$	−1.45882	−	28.7463i	−0.0735876	−	1.45006i
$394$	−9.24408	+	1.46412i	−0.465710	+	0.0737613i
$395$	27.7984			1.39869
$396$	5.99583	−	18.9750i	0.301302	−	0.953529i
$397$	−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
$399$	0.100593	+	1.98220i	0.00503595	+	0.0992343i
$400$	−2.94427	−	9.06154i	−0.147214	−	0.453077i
$401$	7.07367	+	9.73607i	0.353242	+	0.486196i	0.948250	−	0.317524i	$-0.102851\pi$
$401$	7.07367	+	9.73607i	0.353242	+	0.486196i	−0.595008	+	0.803720i	$0.702851\pi$
$402$	1.44221	+	6.84072i	0.0719308	+	0.341184i
$403$	5.56758	−	1.80902i	0.277341	−	0.0901136i
$404$	−3.09017	+	9.51057i	−0.153742	+	0.473168i
$405$	−10.7571	−	9.81553i	−0.534527	−	0.487737i
$406$	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	$0.413210\pi$
$410$	−19.3122	+	9.84005i	−0.953761	+	0.485965i
$411$	−13.1604	+	10.6211i	−0.649155	+	0.523898i
$412$	−28.1803	+	20.4742i	−1.38835	+	1.00869i
$413$	−0.118513	−	0.163119i	−0.00583164	−	0.00802656i
$414$	−1.91299	−	7.23510i	−0.0940183	−	0.355586i
$415$	−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	$-0.554967\pi$
$419$	−7.03444			−0.343655			−0.171827	+	0.985127i	$0.554967\pi$
$420$	−0.344577	+	1.27751i	−0.0168136	+	0.0623363i
$421$	−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
$423$	4.19217	−	19.4065i	0.203830	−	0.943575i
$424$	−33.1157	−	5.24501i	−1.60824	−	0.254720i
$425$	−11.5312	+	3.74671i	−0.559345	+	0.181742i
$426$	10.0003	−	11.0696i	0.484516	−	0.536322i
$427$	−0.845055	+	1.16312i	−0.0408951	+	0.0562873i
$428$		−	0.472136i		−	0.0228216i
$429$	−1.54087	−	5.53405i	−0.0743939	−	0.267186i
$430$	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	$0.813607\pi$
$432$	14.6238	+	14.7697i	0.703587	+	0.710610i
$433$	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
$435$	−6.12099	+	9.39144i	−0.293479	+	0.450285i
$436$	−24.2784	+	7.88854i	−1.16273	+	0.377793i
$437$	−8.14324	−	2.64590i	−0.389544	−	0.126570i
$438$	9.41350	+	16.3672i	0.449795	+	0.782054i
$439$		−	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	$-0.784477\pi$
$443$	4.61803	−	14.2128i	0.219409	−	0.675273i	0.998811	−	0.0487482i	$-0.0155232\pi$
$444$	−27.5935	+	22.2693i	−1.30953	+	1.05685i
$445$	9.39919	−	6.82891i	0.445564	−	0.323721i
$446$	−4.58131	+	28.9253i	−0.216931	+	1.36965i
$447$	−3.65028	+	2.94594i	−0.172652	+	0.139338i
$448$	0.583592	−	1.79611i	0.0275721	−	0.0848583i
$449$	−3.73871	+	5.14590i	−0.176441	+	0.242850i	−0.888073	−	0.459702i	$-0.847956\pi$
$449$	−3.73871	+	5.14590i	−0.176441	+	0.242850i	0.711632	+	0.702552i	$0.247956\pi$
$450$	10.0902	+	0.562306i	0.475655	+	0.0265074i
$451$	27.0256	−	16.0172i	1.27259	−	0.754221i
$452$	2.00000			0.0940721
$453$	−2.49338	+	9.24418i	−0.117149	+	0.434330i
$454$	13.1254	−	6.68775i	0.616007	−	0.313871i
$455$	0.118034	+	0.363271i	0.00553352	+	0.0170304i
$456$	23.2686	−	4.90566i	1.08965	−	0.229729i
$457$	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
$459$	18.7951	−	18.6094i	0.877281	−	0.868611i
$460$	−4.61803	−	3.35520i	−0.215317	−	0.156437i
$461$		−	19.1459i		−	0.891713i	−0.895104	−	0.445857i	$-0.852899\pi$
$461$		−	19.1459i		−	0.891713i	0.895104	−	0.445857i	$-0.147101\pi$
$462$	0.380416	−	1.87972i	0.0176986	−	0.0874524i
$463$			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
$465$	0.831514	+	16.3851i	0.0385605	+	0.759842i
$466$	23.3899	+	11.9177i	1.08351	+	0.552078i
$467$	−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	$0.318628\pi$
$468$	5.86472	+	1.26689i	0.271097	+	0.0585621i
$469$	0.208204	+	0.640786i	0.00961396	+	0.0295887i
$470$	−6.87509	−	13.4931i	−0.317124	−	0.622391i
$471$	−4.13412	−	1.11507i	−0.190490	−	0.0513799i
$472$	−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
$477$	17.8830	−	30.7388i	0.818807	−	1.40743i
$478$	26.9171	+	4.26325i	1.23116	+	0.194996i
$479$	−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	$0.317736\pi$
$480$	15.7638	+	1.68323i	0.719517	+	0.0768286i
$481$	−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
$486$	−20.2130	+	8.79968i	−0.916881	+	0.399162i
$487$	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
$489$	7.80954	+	5.08997i	0.353159	+	0.230176i
$490$	2.48577	−	15.6946i	0.112296	−	0.709008i
$491$	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	$0.557849\pi$
$492$	1.66303	+	32.7703i	0.0749751	+	1.47740i
$493$	−16.4721	−	11.9677i	−0.741868	−	0.538998i
$494$	4.85410	−	4.85410i	0.218396	−	0.218396i
$495$	16.0987	−	0.130429i	0.723583	−	0.00586235i
$496$		−	23.4164i		−	1.05143i
$497$	0.845055	−	1.16312i	0.0379059	−	0.0521730i
$498$	−7.43493	+	8.22989i	−0.333167	+	0.368790i
$499$	−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
$501$	−5.31323	+	8.15208i	−0.237378	+	0.364208i
$502$	14.3343	−	28.1327i	0.639772	−	1.25562i
$503$	−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	$0.868922\pi$
$504$	1.55252	+	1.26574i	0.0691548	+	0.0563806i
$505$	−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	0.927862	−	0.372925i	$-0.121645\pi$
$509$	32.9237	+	10.6976i	1.45932	+	0.474161i	0.531456	+	0.847086i	$0.321645\pi$
$510$	2.14198	−	20.0601i	0.0948486	−	0.888277i
$511$	1.06957	+	1.47214i	0.0473150	+	0.0651235i
$512$	−22.3488	−	3.53971i	−0.987688	−	0.156434i
$513$	−4.06936	+	24.8922i	−0.179666	+	1.09902i
$514$	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
$519$	1.71328	−	6.35198i	0.0752047	−	0.278821i
$520$	4.07768	−	2.07768i	0.178818	−	0.0911125i
$521$	32.7849	−	10.6525i	1.43633	−	0.466693i	0.515582	−	0.856840i	$-0.327576\pi$
$521$	32.7849	−	10.6525i	1.43633	−	0.466693i	0.920753	+	0.390147i	$0.127576\pi$
$522$	9.19566	+	14.2632i	0.402483	+	0.624285i
$523$	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
$525$	0.972691	−	0.0493622i	0.0424517	−	0.00215434i
$526$	1.07388	+	6.78022i	0.0468235	+	0.295632i
$527$	−29.7984			−1.29804
$528$	−22.9574	−	0.978644i	−0.999093	−	0.0425900i
$529$	−19.8885			−0.864719
$530$	−4.24330	−	26.7911i	−0.184317	−	1.16373i
$531$	−1.03443	−	2.34422i	−0.0448904	−	0.101730i
$532$	2.17963	−	0.708204i	0.0944988	−	0.0307045i
$533$	5.56758	+	7.66312i	0.241159	+	0.331927i
$534$	−3.62830	−	17.2099i	−0.157012	−	0.744743i
$535$	0.363271	−	0.118034i	0.0157056	−	0.00510305i
$536$	7.19276	−	3.66489i	0.310680	−	0.158299i
$537$	−14.0747	−	3.79628i	−0.607366	−	0.163821i
$538$	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
$543$	13.6276	+	16.8858i	0.584817	+	0.724639i
$544$	−4.50443	+	28.4398i	−0.193126	+	1.21935i
$545$	−12.1392	−	16.7082i	−0.519987	−	0.715701i
$546$	0.574978	+	0.0613950i	0.0246068	+	0.00262746i
$547$	−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
$552$	−7.49087	+	4.30834i	−0.318833	+	0.183375i
$553$	1.25329	−	3.85723i	0.0532953	−	0.164026i
$554$	−10.6694	+	20.9399i	−0.453301	+	0.889653i
$555$	−24.0328	−	15.6637i	−1.02014	−	0.664888i
$556$	11.4721	−	8.33499i	0.486527	−	0.353483i
$557$	8.42075	−	2.73607i	0.356799	−	0.115931i	−0.125132	−	0.992140i	$-0.539936\pi$
$557$	8.42075	−	2.73607i	0.356799	−	0.115931i	0.481931	+	0.876209i	$0.339936\pi$
$558$	23.1576	+	8.97745i	0.980340	+	0.380046i
$559$	3.66547	−	5.04508i	0.155033	−	0.213384i
$560$	1.52786			0.0645640
$561$	−1.24537	+	29.2143i	−0.0525794	+	1.23343i
$562$	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	$0.748348\pi$
$564$	−22.8961	+	1.16193i	−0.964099	+	0.0489261i
$565$	0.500000	+	1.53884i	0.0210352	+	0.0647396i
$566$	4.90700	−	30.9815i	0.206256	−	1.30225i
$567$	−1.84696	+	1.05010i	−0.0775651	+	0.0441000i
$568$	−15.3481	−	7.82026i	−0.643993	−	0.328131i
$569$	17.4620	+	5.67376i	0.732047	+	0.237856i	0.651238	−	0.758873i	$-0.274250\pi$
$569$	17.4620	+	5.67376i	0.732047	+	0.237856i	0.0808085	+	0.996730i	$0.474250\pi$
$570$	9.59168	+	16.6770i	0.401751	+	0.698521i
$571$			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
$576$	12.0687	−	20.7448i	0.502864	−	0.864365i
$577$	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
$579$	17.4420	+	21.6122i	0.724866	+	0.898171i
$580$	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
$585$	0.491407	+	4.82916i	0.0203172	+	0.199661i
$586$	−2.83551	−	5.56500i	−0.117134	−	0.229888i
$587$	−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	$0.924016\pi$
$588$	−20.1531	−	13.1350i	−0.831098	−	0.541680i
$589$	22.9894	−	16.7027i	0.947260	−	0.688225i
$590$	−1.74138	−	0.887277i	−0.0716914	−	0.0365286i
$591$	−11.4480	+	0.580966i	−0.470909	+	0.0238977i
$592$	33.1246	+	24.0664i	1.36141	+	0.989125i
$593$		−	9.61803i		−	0.394965i	−0.980306	−	0.197483i	$-0.936723\pi$
$593$		−	9.61803i		−	0.394965i	0.980306	−	0.197483i	$-0.0632766\pi$
$594$	9.76930	−	22.3285i	0.400839	−	0.916148i
$595$		−	1.94427i		−	0.0797074i
$596$	4.38197	+	3.18368i	0.179492	+	0.130409i
$597$	−3.55605	+	0.180463i	−0.145539	+	0.00738584i
$598$	−1.13251	+	2.22268i	−0.0463119	+	0.0908923i
$599$	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	$0.158458\pi$
$600$	−2.40727	−	11.4182i	−0.0982762	−	0.466146i
$601$	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
$603$	0.866808	+	8.51832i	0.0352992	+	0.346893i
$604$	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	$-0.582663\pi$
$607$	18.2743	−	25.1525i	0.741733	−	1.02091i	0.998517	−	0.0544388i	$-0.0173370\pi$
$608$	−12.4661	−	24.4661i	−0.505567	−	0.992231i
$609$	1.02717	+	1.27275i	0.0416228	+	0.0515742i
$610$	−2.18004	+	13.7642i	−0.0882672	+	0.557297i
$611$	−5.35410	+	3.88998i	−0.216604	+	0.157372i
$612$	−26.3986	−	15.3580i	−1.06710	−	0.620810i
$613$	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	$0.162220\pi$
$617$			24.2361i			0.975707i	−0.872925	+	0.487854i	$0.837780\pi$
$618$	−36.9810	+	21.2695i	−1.48760	+	0.855584i
$619$	−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
$621$	−1.38885	−	9.05982i	−0.0557327	−	0.363558i
$622$	38.6250	+	6.11761i	1.54872	+	0.245294i
$623$	−0.523799	−	1.61209i	−0.0209856	−	0.0645869i
$624$	−0.351141	−	6.91930i	−0.0140569	−	0.276994i
$625$	6.00000	+	4.35926i	0.240000	+	0.174370i
$626$	−9.94427	−	9.94427i	−0.397453	−	0.397453i
$627$	−15.4145	−	23.2368i	−0.615598	−	0.927988i
$628$			4.94427i			0.197298i
$629$	30.6256	−	42.1525i	1.22112	−	1.68073i
$630$	−0.585757	+	1.51098i	−0.0233371	+	0.0601988i
$631$	−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
$633$	16.5159	+	10.7644i	0.656447	+	0.427848i
$634$	−16.6082	−	8.46230i	−0.659596	−	0.336081i
$635$	4.09017	−	12.5882i	0.162313	−	0.499549i
$636$	−39.6470	−	10.6937i	−1.57210	−	0.424034i
$637$	−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	−0.138340	−	0.990385i	$-0.544177\pi$
$641$	−21.0745	−	6.84752i	−0.832393	−	0.270461i	−0.694053	+	0.719924i	$0.744177\pi$
$642$	0.0613950	−	0.574978i	0.00242307	−	0.0226926i
$643$	−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
$645$	10.9759	+	13.6001i	0.432177	+	0.535504i
$646$	−31.1342	+	15.8636i	−1.22496	+	0.624147i
$647$	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
$651$	2.31105	+	0.623345i	0.0905770	+	0.0244308i
$652$	3.32624	−	10.2371i	0.130266	−	0.400916i
$653$	1.76336	−	0.572949i	0.0690054	−	0.0224212i	−0.274311	−	0.961641i	$-0.588450\pi$
$653$	1.76336	−	0.572949i	0.0690054	−	0.0224212i	0.343316	+	0.939220i	$0.388450\pi$
$654$	−30.5926	+	6.44975i	−1.19627	+	0.252205i
$655$	−15.8047	−	21.7533i	−0.617540	−	0.849971i
$656$	36.0341	−	11.7082i	1.40690	−	0.457129i
$657$	9.33564	+	21.1564i	0.364218	+	0.825390i
$658$	−2.18223	+	0.345632i	−0.0850723	+	0.0134741i
$659$	13.4164			0.522629			0.261315	−	0.965254i	$-0.415844\pi$
$659$	13.4164			0.522629			0.261315	+	0.965254i	$0.415844\pi$
$660$	−4.98636	−	17.9086i	−0.194094	−	0.697090i
$661$	−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
$663$	−8.80510	+	0.446842i	−0.341962	+	0.0173539i
$664$	11.4109	+	5.81414i	0.442828	+	0.225632i
$665$	1.08981	+	1.50000i	0.0422612	+	0.0581675i
$666$	−36.4999	+	23.5319i	−1.41434	+	0.911841i
$667$	−6.71040	+	2.18034i	−0.259828	+	0.0844231i
$668$	10.6861	+	3.47214i	0.413459	+	0.134341i
$669$	−9.34057	+	34.6301i	−0.361127	+	1.33888i
$670$	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	$0.653308\pi$
$674$	40.4092	−	20.5895i	1.55650	−	0.793078i
$675$	12.2149	+	1.99688i	0.470152	+	0.0768600i
$676$	14.1068	+	19.4164i	0.542571	+	0.746785i
$677$	−2.17963	−	3.00000i	−0.0837699	−	0.115299i	0.765075	−	0.643941i	$-0.222702\pi$
$677$	−2.17963	−	3.00000i	−0.0837699	−	0.115299i	−0.848845	+	0.528641i	$0.822702\pi$
$678$	2.43564	+	0.260074i	0.0935403	+	0.00998806i
$679$	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	$-0.641088\pi$
$683$	−22.4164			−0.857740			−0.428870	+	0.903366i	$0.641088\pi$
$684$	28.9750	−	2.94844i	1.10789	−	0.112736i
$685$	−4.88197	+	15.0251i	−0.186530	+	0.574081i
$686$	−4.14791	−	2.11346i	−0.158368	−	0.0806924i
$687$	12.6885	−	19.4680i	0.484097	−	0.742749i
$688$	−14.6619	−	20.1803i	−0.558979	−	0.769368i
$689$	−11.2739	+	3.66312i	−0.429502	+	0.139554i
$690$	−5.18764	−	4.68655i	−0.197490	−	0.178414i
$691$	−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
$693$	0.707712	−	2.23969i	0.0268837	−	0.0850789i
$694$	−33.1246	−	33.1246i	−1.25739	−	1.25739i
$695$	9.28115	+	6.74315i	0.352054	+	0.255782i
$696$	13.1363	−	14.5409i	0.497931	−	0.551171i
$697$	−14.8992	−	45.8550i	−0.564347	−	1.73688i
$698$	−34.9201	−	5.53079i	−1.32174	−	0.209344i
$699$	26.9350	+	17.5552i	1.01877	+	0.663999i
$700$	−0.347524	−	1.06957i	−0.0131352	−	0.0404259i
$701$	22.0786	+	7.17376i	0.833896	+	0.270949i	0.694686	−	0.719314i	$-0.255544\pi$
$701$	22.0786	+	7.17376i	0.833896	+	0.270949i	0.139211	+	0.990263i	$0.455544\pi$
$702$	6.97745	+	2.30548i	0.263347	+	0.0870147i
$703$			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
$708$	−2.30242	+	1.85816i	−0.0865302	+	0.0698339i
$709$	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
$711$	25.9181	−	44.5503i	0.972006	−	1.67077i
$712$	−18.0955	+	9.22012i	−0.678158	+	0.345539i
$713$	−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
$717$	32.2258	+	8.69209i	1.20350	+	0.324612i
$718$	−22.5409	+	11.4852i	−0.841218	+	0.428622i
$719$	−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	$-0.285206\pi$
$720$	18.9786	+	4.09975i	0.707292	+	0.152789i
$721$	−3.32624	+	2.41665i	−0.123876	+	0.0900009i
$722$	2.92918	−	5.74884i	0.109013	−	0.213950i
$723$	−0.475481	−	9.36944i	−0.0176833	−	0.348453i
$724$	14.7274	−	20.2705i	0.547339	−	0.753348i
$725$		−	9.52786i		−	0.353856i
$726$	8.86684	+	25.4436i	0.329079	+	0.944302i
$727$			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
$729$	−25.7601	+	8.08802i	−0.954079	+	0.299556i
$730$	15.7158	+	8.00760i	0.581668	+	0.296375i
$731$	−25.6803	+	18.6579i	−0.949822	+	0.690086i
$732$	17.6744	+	11.5195i	0.653263	+	0.425773i
$733$	−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
$735$	5.06810	−	18.7899i	0.186940	−	0.693078i
$736$	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	−0.602785	−	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
$741$	6.54264	−	5.28022i	0.240350	−	0.193974i
$742$	−3.90877	−	0.619089i	−0.143496	−	0.0227275i
$743$	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	$0.182610\pi$
$744$	3.04499	−	28.5170i	0.111635	−	1.04548i
$745$	−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
$750$	25.3618	−	14.5867i	0.926082	−	0.532632i
$751$	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
$753$	21.1149	−	32.3966i	0.769471	−	1.18060i
$754$	0.884927	−	5.58721i	0.0322271	−	0.203474i
$755$	2.76393	+	8.50651i	0.100590	+	0.309584i
$756$	1.72610	+	1.74333i	0.0627777	+	0.0634044i
$757$	−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
$759$	7.93668	+	6.29978i	0.288083	+	0.228667i
$760$	15.7082	−	15.7082i	0.569796	−	0.569796i
$761$	−17.7068	+	24.3713i	−0.641871	+	0.883460i	−0.998714	−	0.0507048i	$-0.983853\pi$
$761$	−17.7068	+	24.3713i	−0.641871	+	0.883460i	0.356843	+	0.934165i	$0.383853\pi$
$762$	−14.8687	−	13.4324i	−0.538635	−	0.486606i
$763$	−2.86568	+	0.931116i	−0.103745	+	0.0337087i
$764$	12.2452	+	16.8541i	0.443017	+	0.609760i
$765$	5.21711	−	24.1511i	0.188625	−	0.873186i
$766$	−16.3541	+	32.0968i	−0.590898	+	1.15970i
$767$	−0.263932	+	0.812299i	−0.00953003	+	0.0293304i
$768$	−26.7566	−	7.21690i	−0.965496	−	0.260418i
$769$	−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	0.0443713	−	0.999015i	$-0.485872\pi$
$773$	−14.0943	−	4.57953i	−0.506938	−	0.164714i	−0.551309	+	0.834301i	$0.685872\pi$
$774$	25.5784	−	6.76303i	0.919397	−	0.243092i
$775$	−8.19624	−	11.2812i	−0.294418	−	0.405231i
$776$	1.47174	−	9.29219i	0.0528323	−	0.333570i
$777$	−3.25698	+	2.62853i	−0.116843	+	0.0942981i
$778$	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
$783$	9.34393	+	18.5659i	0.333925	+	0.663489i
$784$	−8.58359	+	26.4176i	−0.306557	+	0.943485i
$785$	−3.80423	+	1.23607i	−0.135779	+	0.0441172i
$786$	−39.8301	+	8.39727i	−1.42069	+	0.299521i
$787$	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
$789$	0.426119	+	8.39675i	0.0151702	+	0.298932i
$790$	−6.14988	−	38.8288i	−0.218803	−	1.38147i
$791$	0.236068			0.00839361
$792$	−27.8308	−	4.17712i	−0.988923	−	0.148428i
$793$	6.09017			0.216268
$794$	0.325683	+	2.05628i	0.0115581	+	0.0729747i
$795$	−1.68375	−	33.1786i	−0.0597165	−	1.17672i
$796$	1.27051	+	3.91023i	0.0450320	+	0.138594i
$797$	−27.3156	−	37.5967i	−0.967569	−	1.33175i	−0.943265	−	0.332041i	$-0.892263\pi$
$797$	−27.3156	−	37.5967i	−0.967569	−	1.33175i	−0.0243044	−	0.999705i	$-0.507737\pi$
$798$	2.74649	−	0.579035i	0.0972247	−	0.0204976i
$799$	32.0382	−	10.4098i	1.13343	−	0.368273i
$800$	−12.0058	+	6.11727i	−0.424469	+	0.216278i
$801$	−2.18071	−	21.4304i	−0.0770517	−	0.757204i
$802$	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
$807$	27.2002	−	21.9519i	0.957494	−	0.772743i
$808$	13.9680	+	2.21232i	0.491393	+	0.0778291i
$809$	−13.1558	−	18.1074i	−0.462533	−	0.636622i	0.512499	−	0.858688i	$-0.328720\pi$
$809$	−13.1558	−	18.1074i	−0.462533	−	0.636622i	−0.975032	+	0.222066i	$0.928720\pi$
$810$	−11.3305	+	17.1971i	−0.398114	+	0.604245i
$811$	−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
$816$	−9.18382	+	34.0489i	−0.321498	+	1.19195i
$817$	9.35410	−	28.7890i	0.327259	−	1.00720i
$818$	20.3579	−	39.9547i	0.711798	−	1.39698i
$819$	0.692237	+	0.149536i	0.0241887	+	0.00522523i
$820$	18.0171	+	24.7984i	0.629183	+	0.865997i
$821$	−39.7854	+	12.9271i	−1.38852	+	0.451157i	−0.905460	−	0.424431i	$-0.860474\pi$
$821$	−39.7854	+	12.9271i	−1.38852	+	0.451157i	−0.483059	+	0.875588i	$0.660474\pi$
$822$	17.7470	+	16.0328i	0.618998	+	0.559207i
$823$	−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
$825$	−11.4026	+	7.56410i	−0.396986	+	0.263348i
$826$	−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	$0.598679\pi$
$828$	−9.68279	+	4.27270i	−0.336500	+	0.148487i
$829$	−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
$831$	−15.7164	+	24.1137i	−0.545197	+	0.836495i
$832$	−7.60845	+	2.47214i	−0.263776	+	0.0857059i
$833$	33.6175	+	10.9230i	1.16478	+	0.378459i
$834$	15.0549	−	8.65874i	0.521308	−	0.299828i
$835$			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	−0.998234	−	0.0594111i	$-0.981078\pi$
$839$	−4.51064	+	13.8823i	−0.155725	+	0.479271i	0.842509	+	0.538682i	$0.181078\pi$
$840$	1.86067	+	0.198678i	0.0641991	+	0.00685506i
$841$	−10.5172	+	7.64121i	−0.362663	+	0.263490i
$842$	4.64610	+	0.735869i	0.160115	+	0.0253597i
$843$	8.33023	−	6.72288i	0.286908	−	0.231548i
$844$	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
$849$	10.0046	−	37.0919i	0.343357	−	1.27299i
$850$	7.78448	+	15.2779i	0.267005	+	0.524028i
$851$	−5.57953	−	17.1720i	−0.191264	−	0.588649i
$852$	−17.6744	−	11.5195i	−0.605514	−	0.394652i
$853$	−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
$855$	9.51234	+	21.5568i	0.325315	+	0.737229i
$856$	−0.659481	+	0.104451i	−0.0225406	+	0.00357008i
$857$		−	5.11146i		−	0.174604i	−0.996182	−	0.0873020i	$-0.972175\pi$
$857$		−	5.11146i		−	0.174604i	0.996182	−	0.0873020i	$-0.0278245\pi$
$858$	−7.38909	+	3.37660i	−0.252259	+	0.115275i
$859$		−	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
$861$	0.196294	+	3.86801i	0.00668967	+	0.131821i
$862$	−9.31380	+	18.2794i	−0.317229	+	0.622597i
$863$	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	$0.0680440\pi$
$864$	17.3952	−	23.6941i	0.591796	−	0.806088i
$865$	−1.89919	−	5.84510i	−0.0645743	−	0.198739i
$866$	15.4886	−	7.89182i	0.526323	−	0.268175i
$867$	14.8998	+	4.01884i	0.506024	+	0.136487i
$868$		−	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
$872$	16.3899	+	32.1670i	0.555032	+	1.08931i
$873$	8.62525	+	5.01794i	0.291921	+	0.169832i
$874$	−1.89425	+	11.9598i	−0.0640741	+	0.404548i
$875$	2.28115	−	1.65735i	0.0771170	−	0.0560288i
$876$	20.7791	−	16.7697i	0.702062	−	0.566597i
$877$	−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	$-0.913945\pi$
$881$		−	15.8541i		−	0.534138i	0.963677	−	0.267069i	$-0.0860552\pi$
$882$	−22.8348	−	18.6168i	−0.768888	−	0.626859i
$883$	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
$885$	−2.00531	−	1.30699i	−0.0674078	−	0.0439339i
$886$	−20.8742	−	3.30615i	−0.701282	−	0.111072i
$887$	−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	$-0.246259\pi$
$888$	37.2104	+	33.6161i	1.24870	+	1.12808i
$889$	−1.56231	−	1.13508i	−0.0523981	−	0.0380694i
$890$	−11.6180	−	11.6180i	−0.389437	−	0.389437i
$891$	14.8008	−	25.9217i	0.495845	−	0.868411i
$892$	41.4164			1.38672
$893$	−18.8824	+	25.9894i	−0.631875	+	0.869701i
$894$	4.92246	+	4.44698i	0.164632	+	0.148729i
$895$	−12.9515	+	4.20820i	−0.432922	+	0.140665i
$896$	−2.63792	−	0.417806i	−0.0881268	−	0.0139579i
$897$	−1.66823	+	2.55957i	−0.0557006	+	0.0854614i
$898$	8.01492	+	4.08381i	0.267461	+	0.136278i
$899$	7.23607	−	22.2703i	0.241336	−	0.742757i
$900$	−1.44684	−	14.2184i	−0.0482279	−	0.473946i
$901$	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
$906$	13.4639	+	1.43765i	0.447308	+	0.0477628i
$907$	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
$909$	−7.54297	+	12.9655i	−0.250184	+	0.430038i
$910$	0.481305	−	0.245237i	0.0159551	−	0.00812954i
$911$	−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
$915$	−4.44476	+	16.4789i	−0.146939	+	0.544776i
$916$	−25.5195	−	8.29180i	−0.843189	−	0.273969i
$917$	−3.73098	+	1.21227i	−0.123208	+	0.0400327i
$918$	−30.1517	−	22.1361i	−0.995154	−	0.730600i
$919$	−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
$921$	−1.06909	+	0.0542543i	−0.0352277	+	0.00178774i
$922$	−26.7430	+	4.23568i	−0.880735	+	0.139495i
$923$	−6.09017			−0.200460
$924$	−2.70975	−	0.115513i	−0.0891443	−	0.00380011i
$925$	24.3820			0.801674
$926$	4.97584	−	0.788095i	0.163516	−	0.0258984i
$927$	−47.8021	+	21.0935i	−1.57003	+	0.692803i
$928$	−20.1612	−	10.2726i	−0.661823	−	0.337216i
$929$	2.66141	+	3.66312i	0.0873181	+	0.120183i	0.850441	−	0.526070i	$-0.176335\pi$
$929$	2.66141	+	3.66312i	0.0873181	+	0.120183i	−0.763123	+	0.646253i	$0.776335\pi$
$930$	22.7028	−	4.78637i	0.744455	−	0.156951i
$931$	−32.0584	+	10.4164i	−1.05067	+	0.341384i
$932$	11.4721	−	35.3076i	0.375782	−	1.15654i
$933$	46.2429	+	12.4728i	1.51392	+	0.408342i
$934$	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	$0.663525\pi$
$938$	0.848990	−	0.432582i	0.0277205	−	0.0141243i
$939$	−10.8172	−	13.4035i	−0.353007	−	0.437406i
$940$	−17.3262	+	12.5882i	−0.565120	+	0.410583i
$941$	4.44501	+	6.11803i	0.144903	+	0.199442i	0.875299	−	0.483582i	$-0.160664\pi$
$941$	4.44501	+	6.11803i	0.144903	+	0.199442i	−0.730396	+	0.683024i	$0.760664\pi$
$942$	−0.642937	+	6.02124i	−0.0209480	+	0.196183i
$943$	−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	$-0.809150\pi$
$947$	−50.8115			−1.65115			−0.825576	+	0.564290i	$0.809150\pi$
$948$	−57.4610	−	15.4986i	−1.86625	−	0.503371i
$949$	2.38197	−	7.33094i	0.0773219	−	0.237972i
$950$	−14.5694	−	7.42346i	−0.472692	−	0.240849i
$951$	−19.1254	−	12.4653i	−0.620184	−	0.404213i
$952$	−0.531676	+	3.35687i	−0.0172317	+	0.108797i
$953$	50.2470	−	16.3262i	1.62766	−	0.528859i	0.653928	−	0.756557i	$-0.273120\pi$
$953$	50.2470	−	16.3262i	1.62766	−	0.528859i	0.973732	+	0.227698i	$0.0731199\pi$
$954$	−46.8924	−	18.1786i	−1.51820	−	0.588555i
$955$	−9.90659	+	13.6353i	−0.320570	+	0.441226i
$956$		−	38.5410i		−	1.24651i
$957$	−21.5314	−	8.02497i	−0.696010	−	0.259411i
$958$	2.43769	+	2.43769i	0.0787583	+	0.0787583i
$959$	1.86475	+	1.35482i	0.0602158	+	0.0437493i
$960$	−1.13632	−	22.3913i	−0.0366744	−	0.722677i
$961$	−1.01064	−	3.11044i	−0.0326014	−	0.100337i
$962$	14.2978	+	2.26454i	0.460978	+	0.0730118i
$963$	0.149536	−	0.692237i	0.00481874	−	0.0223070i
$964$	−10.3026	+	3.34752i	−0.331825	+	0.107816i
$965$	24.6745	+	8.01722i	0.794299	+	0.258083i
$966$	−0.884177	+	0.508531i	−0.0284479	+	0.0163617i
$967$		−	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	$-0.751680\pi$
$971$	8.65248	−	26.6296i	0.277671	−	0.854584i	0.988500	−	0.151219i	$-0.0483199\pi$
$972$	16.7632	+	26.2868i	0.537679	+	0.843150i
$973$	1.35410	−	0.983813i	0.0434105	−	0.0315396i
$974$	3.02036	−	19.0698i	0.0967786	−	0.611036i
$975$	−2.59107	−	3.21055i	−0.0829806	−	0.102820i
$976$	7.52786	−	23.1684i	0.240961	−	0.741602i
$977$	7.12667	−	9.80902i	0.228002	−	0.313818i	−0.679654	−	0.733533i	$-0.737870\pi$
$977$	7.12667	−	9.80902i	0.228002	−	0.313818i	0.907656	+	0.419715i	$0.137870\pi$
$978$	5.38197	−	12.0344i	0.172096	−	0.384819i
$979$	17.8783	+	15.7320i	0.571393	+	0.502797i
$980$	−22.4721			−0.717846
$981$	−38.0951	+	3.87649i	−1.21628	+	0.123767i
$982$	49.1160	−	25.0259i	1.56736	−	0.798608i
$983$	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	$0.624793\pi$
$984$	45.4057	−	9.57274i	1.44748	−	0.305168i
$985$	−8.66312	+	6.29412i	−0.276030	+	0.200547i
$986$	−13.0724	+	25.6560i	−0.416309	+	0.817052i
$987$	−2.70252	+	0.137147i	−0.0860220	+	0.00436545i
$988$	−7.85410	−	5.70634i	−0.249872	−	0.181543i
$989$			11.0000i			0.349780i
$990$	−3.74373	−	22.4579i	−0.118984	−	0.713757i
$991$			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
$993$	22.9925	−	1.16682i	0.729644	−	0.0370280i
$994$	−1.81160	−	0.923056i	−0.0574605	−	0.0292776i
$995$	−2.69098	+	1.95511i	−0.0853099	+	0.0619813i
$996$	13.1404	+	8.56442i	0.416369	+	0.271374i
$997$	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
$999$	−47.5103	+	23.9113i	−1.50316	+	0.756520i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.221232 - 1.39680i) q^{2} +(-0.0877853 - 1.72982i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-0.951057 - 1.30902i) q^{5} +(-2.39680 + 0.505311i) q^{6} +(-0.224514 + 0.0729490i) q^{7} +(1.28408 + 2.52015i) q^{8} +(-2.98459 + 0.303706i) q^{9} +O(q^{10})\)	\(q+(-0.221232 - 1.39680i) q^{2} +(-0.0877853 - 1.72982i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-0.951057 - 1.30902i) q^{5} +(-2.39680 + 0.505311i) q^{6} +(-0.224514 + 0.0729490i) q^{7} +(1.28408 + 2.52015i) q^{8} +(-2.98459 + 0.303706i) 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} +(-2.18088 + 1.76007i) q^{15} +(3.23607 - 2.35114i) q^{16} +(-2.99193 - 4.11803i) q^{17} +(1.08450 + 4.10169i) 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} +(4.24669 - 2.44246i) q^{24} +(0.736068 - 2.26538i) q^{25} +(0.642040 - 1.26007i) q^{26} +(0.787361 + 5.13615i) q^{27} +(0.381966 - 0.277515i) q^{28} +(3.80423 - 1.23607i) q^{29} +(2.94095 + 2.65688i) q^{30} +(3.44095 - 4.73607i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-4.49942 - 3.57144i) q^{33} +(-5.09017 + 5.09017i) q^{34} +(0.309017 + 0.224514i) q^{35} +(5.48932 - 2.42226i) q^{36} +(3.16312 + 9.73508i) q^{37} +(1.07388 - 6.78022i) q^{38} +(0.945746 - 1.45106i) q^{39} +(2.07768 - 4.07768i) q^{40} +(9.00854 + 2.92705i) q^{41} +(0.501254 - 0.288294i) 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} +(-4.35114 - 5.39144i) q^{48} +(-5.61803 + 4.08174i) q^{49} +(-3.32714 - 0.526966i) q^{50} +(-6.86083 + 5.53701i) 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} +(2.18947 - 8.11746i) q^{57} +(-2.56816 - 5.04029i) q^{58} +(0.263932 + 0.812299i) q^{59} +(3.06050 - 4.69572i) q^{60} +(4.92705 - 3.57971i) q^{61} +(-7.37660 - 3.75856i) q^{62} +(0.647927 - 0.285909i) q^{63} +(-4.70228 + 6.47214i) q^{64} -1.61803i q^{65} +(-3.99318 + 7.07492i) q^{66} -2.85410i q^{67} +(8.23607 + 5.98385i) q^{68} +(0.154847 + 3.05129i) q^{69} +(0.245237 - 0.481305i) q^{70} +(-4.92705 + 3.57971i) q^{71} +(-4.59783 - 7.13162i) q^{72} +(-2.38197 - 7.33094i) q^{73} +(12.8982 - 6.57196i) q^{74} +(-3.98333 - 1.07440i) 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} +(8.81553 - 1.81288i) q^{81} +(2.09554 - 13.2307i) q^{82} +(3.66312 - 2.66141i) q^{83} +(-0.513583 - 0.636373i) 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} +(4.33776 - 5.32057i) q^{90} +(-0.224514 - 0.0729490i) q^{91} +(3.35520 - 1.09017i) q^{92} +(-8.49463 - 5.53649i) q^{93} +(9.24408 + 1.46412i) q^{94} +(-2.42705 - 7.46969i) q^{95} +(-6.56816 + 7.27044i) q^{96} +(-2.69098 - 1.95511i) q^{97} +(6.94427 + 6.94427i) q^{98} +(-5.78298 + 8.09673i) 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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