LMFDB - Embedded newform 132.2.o.b.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.b.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39680 - 0.221232i) q^{2} +(0.0877853 + 1.72982i) q^{3} +(1.90211 - 0.618034i) q^{4} +(-0.951057 - 1.30902i) q^{5} +(0.505311 + 2.39680i) q^{6} +(0.224514 - 0.0729490i) q^{7} +(2.52015 - 1.28408i) q^{8} +(-2.98459 + 0.303706i) q^{9} +O(q^{10})$	\(q+(1.39680 - 0.221232i) q^{2} +(0.0877853 + 1.72982i) q^{3} +(1.90211 - 0.618034i) q^{4} +(-0.951057 - 1.30902i) q^{5} +(0.505311 + 2.39680i) q^{6} +(0.224514 - 0.0729490i) q^{7} +(2.52015 - 1.28408i) 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} +(0.297463 - 0.151565i) q^{14} +(2.18088 - 1.76007i) q^{15} +(3.23607 - 2.35114i) q^{16} +(-2.99193 - 4.11803i) q^{17} +(-4.10169 + 1.08450i) 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} +(2.44246 + 4.24669i) q^{24} +(0.736068 - 2.26538i) q^{25} +(1.26007 + 0.642040i) q^{26} +(-0.787361 - 5.13615i) q^{27} +(0.381966 - 0.277515i) q^{28} +(3.80423 - 1.23607i) q^{29} +(2.65688 - 2.94095i) 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} +(-6.78022 - 1.07388i) q^{38} +(-0.945746 + 1.45106i) q^{39} +(-4.07768 - 2.07768i) q^{40} +(9.00854 + 2.92705i) q^{41} +(0.288294 + 0.501254i) 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} +(4.35114 + 5.39144i) q^{48} +(-5.61803 + 4.08174i) q^{49} +(0.526966 - 3.32714i) q^{50} +(6.86083 - 5.53701i) q^{51} +(1.90211 + 0.618034i) q^{52} +(-6.96767 + 9.59017i) q^{53} +(-2.23607 - 7.00000i) q^{54} +(5.34307 + 0.500000i) q^{55} +(0.472136 - 0.472136i) q^{56} +(2.18947 - 8.11746i) q^{57} +(5.04029 - 2.56816i) q^{58} +(-0.263932 - 0.812299i) q^{59} +(3.06050 - 4.69572i) q^{60} +(4.92705 - 3.57971i) q^{61} +(-3.75856 + 7.37660i) q^{62} +(-0.647927 + 0.285909i) q^{63} +(4.70228 - 6.47214i) q^{64} -1.61803i q^{65} +(-7.07492 - 3.99318i) q^{66} +2.85410i q^{67} +(-8.23607 - 5.98385i) q^{68} +(0.154847 + 3.05129i) q^{69} +(-0.481305 - 0.245237i) q^{70} +(4.92705 - 3.57971i) q^{71} +(-7.13162 + 4.59783i) q^{72} +(-2.38197 - 7.33094i) q^{73} +(6.57196 + 12.8982i) q^{74} +(3.98333 + 1.07440i) q^{75} -9.70820 q^{76} +(-0.310271 + 0.718847i) q^{77} +(-1.00000 + 2.23607i) q^{78} +(10.0984 - 13.8992i) q^{79} +(-6.15537 - 2.00000i) q^{80} +(8.81553 - 1.81288i) q^{81} +(13.2307 + 2.09554i) q^{82} +(-3.66312 + 2.66141i) q^{83} +(0.513583 + 0.636373i) 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} +(5.32057 + 4.33776i) q^{90} +(0.224514 + 0.0729490i) q^{91} +(3.35520 - 1.09017i) q^{92} +(-8.49463 - 5.53649i) q^{93} +(1.46412 - 9.24408i) q^{94} +(2.42705 + 7.46969i) q^{95} +(7.27044 + 6.56816i) 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} - 2 q^{6} - 4 q^{8} - 10 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 4 * q^3 - 2 * q^6 - 4 * q^8 - 10 * q^9	$ 8 q + 2 q^{2} - 4 q^{3} - 2 q^{6} - 4 q^{8} - 10 q^{9} - 4 q^{10} - 22 q^{11} - 8 q^{12} + 2 q^{13} + 14 q^{14} + 2 q^{15} + 8 q^{16} - 14 q^{18} - 12 q^{20} + 28 q^{21} - 8 q^{22} + 32 q^{23} + 20 q^{24} - 12 q^{25} - 2 q^{26} + 2 q^{27} + 12 q^{28} + 32 q^{32} - 4 q^{33} + 4 q^{34} + 2 q^{35} + 8 q^{36} - 6 q^{37} - 18 q^{38} - 6 q^{39} - 8 q^{40} - 10 q^{42} + 8 q^{45} - 2 q^{46} - 6 q^{47} + 16 q^{48} - 36 q^{49} + 2 q^{50} + 28 q^{51} - 32 q^{56} - 6 q^{57} - 8 q^{58} - 20 q^{59} + 16 q^{60} + 26 q^{61} + 10 q^{62} - 28 q^{63} - 2 q^{66} - 48 q^{68} - 16 q^{69} + 8 q^{70} + 26 q^{71} - 28 q^{72} - 28 q^{73} + 6 q^{74} + 16 q^{75} - 24 q^{76} - 8 q^{78} - 2 q^{81} + 30 q^{82} + 2 q^{83} - 16 q^{84} + 2 q^{85} + 18 q^{86} - 16 q^{87} + 36 q^{88} + 22 q^{90} - 10 q^{93} + 16 q^{94} + 6 q^{95} + 8 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 4 * q^3 - 2 * q^6 - 4 * q^8 - 10 * q^9 - 4 * q^10 - 22 * q^11 - 8 * q^12 + 2 * q^13 + 14 * q^14 + 2 * q^15 + 8 * q^16 - 14 * q^18 - 12 * q^20 + 28 * q^21 - 8 * q^22 + 32 * q^23 + 20 * q^24 - 12 * q^25 - 2 * q^26 + 2 * q^27 + 12 * q^28 + 32 * q^32 - 4 * q^33 + 4 * q^34 + 2 * q^35 + 8 * q^36 - 6 * q^37 - 18 * q^38 - 6 * q^39 - 8 * q^40 - 10 * q^42 + 8 * q^45 - 2 * q^46 - 6 * q^47 + 16 * q^48 - 36 * q^49 + 2 * q^50 + 28 * q^51 - 32 * q^56 - 6 * q^57 - 8 * q^58 - 20 * q^59 + 16 * q^60 + 26 * q^61 + 10 * q^62 - 28 * q^63 - 2 * q^66 - 48 * q^68 - 16 * q^69 + 8 * q^70 + 26 * q^71 - 28 * q^72 - 28 * q^73 + 6 * q^74 + 16 * q^75 - 24 * q^76 - 8 * q^78 - 2 * q^81 + 30 * q^82 + 2 * q^83 - 16 * q^84 + 2 * q^85 + 18 * q^86 - 16 * q^87 + 36 * q^88 + 22 * q^90 - 10 * q^93 + 16 * q^94 + 6 * q^95 + 8 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.39680	−	0.221232i	0.987688	−	0.156434i
$2$	1.39680	−	0.221232i	0.987688	−	0.156434i
$3$	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	$0.917839\pi$
$6$	0.505311	+	2.39680i	0.206292	+	0.978490i
$7$	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
$9$	−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	$0.655716\pi$
$14$	0.297463	−	0.151565i	0.0795003	−	0.0405074i
$15$	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	$-0.411763\pi$
$18$	−4.10169	+	1.08450i	−0.966777	+	0.255620i
$19$	−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	$-0.441127\pi$
$23$	1.76393			0.367805			0.183903	+	0.982944i	$0.441127\pi$
$24$	2.44246	+	4.24669i	0.498566	+	0.866852i
$25$	0.736068	−	2.26538i	0.147214	−	0.453077i
$26$	1.26007	+	0.642040i	0.247121	+	0.125914i
$27$	−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	$0.278881\pi$
$30$	2.65688	−	2.94095i	0.485077	−	0.536942i
$31$	−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
$33$	−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	$0.581732\pi$
$38$	−6.78022	−	1.07388i	−1.09990	−	0.174207i
$39$	−0.945746	+	1.45106i	−0.151441	+	0.232355i
$40$	−4.07768	−	2.07768i	−0.644738	−	0.328511i
$41$	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	$0.334991\pi$
$42$	0.288294	+	0.501254i	0.0444847	+	0.0773451i
$43$			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	$-0.739667\pi$
$47$	2.04508	−	6.29412i	0.298306	−	0.918092i	0.982091	−	0.188408i	$-0.0603328\pi$
$48$	4.35114	+	5.39144i	0.628033	+	0.778187i
$49$	−5.61803	+	4.08174i	−0.802576	+	0.583106i
$50$	0.526966	−	3.32714i	0.0745243	−	0.470528i
$51$	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	$0.897207\pi$
$54$	−2.23607	−	7.00000i	−0.304290	−	0.952579i
$55$	5.34307	+	0.500000i	0.720459	+	0.0674200i
$56$	0.472136	−	0.472136i	0.0630918	−	0.0630918i
$57$	2.18947	−	8.11746i	0.290003	−	1.07518i
$58$	5.04029	−	2.56816i	0.661823	−	0.337216i
$59$	−0.263932	−	0.812299i	−0.0343610	−	0.105752i	0.932405	−	0.361415i	$-0.117706\pi$
$59$	−0.263932	−	0.812299i	−0.0343610	−	0.105752i	−0.966766	+	0.255663i	$0.917706\pi$
$60$	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	$0.172515\pi$
$62$	−3.75856	+	7.37660i	−0.477338	+	0.936829i
$63$	−0.647927	+	0.285909i	−0.0816311	+	0.0360212i
$64$	4.70228	−	6.47214i	0.587785	−	0.809017i
$65$		−	1.61803i		−	0.200692i
$66$	−7.07492	−	3.99318i	−0.870863	−	0.491527i
$67$			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
$69$	0.154847	+	3.05129i	0.0186414	+	0.367333i
$70$	−0.481305	−	0.245237i	−0.0575270	−	0.0293115i
$71$	4.92705	−	3.57971i	0.584733	−	0.424834i	−0.255694	−	0.966758i	$-0.582304\pi$
$71$	4.92705	−	3.57971i	0.584733	−	0.424834i	0.840427	+	0.541924i	$0.182304\pi$
$72$	−7.13162	+	4.59783i	−0.840469	+	0.541860i
$73$	−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
$75$	3.98333	+	1.07440i	0.459956	+	0.124061i
$76$	−9.70820			−1.11361
$77$	−0.310271	+	0.718847i	−0.0353586	+	0.0819202i
$78$	−1.00000	+	2.23607i	−0.113228	+	0.253185i
$79$	10.0984	−	13.8992i	1.13615	−	1.56378i	0.360336	−	0.932822i	$-0.382662\pi$
$79$	10.0984	−	13.8992i	1.13615	−	1.56378i	0.775817	−	0.630958i	$-0.217338\pi$
$80$	−6.15537	−	2.00000i	−0.688191	−	0.223607i
$81$	8.81553	−	1.81288i	0.979503	−	0.201431i
$82$	13.2307	+	2.09554i	1.46109	+	0.231413i
$83$	−3.66312	+	2.66141i	−0.402080	+	0.292128i	−0.770387	−	0.637576i	$-0.779937\pi$
$83$	−3.66312	+	2.66141i	−0.402080	+	0.292128i	0.368308	+	0.929704i	$0.379937\pi$
$84$	0.513583	+	0.636373i	0.0560364	+	0.0694339i
$85$	−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	$0.124268\pi$
$89$			7.18034i			0.761115i	−0.924757	+	0.380557i	$0.875732\pi$
$90$	5.32057	+	4.33776i	0.560837	+	0.457240i
$91$	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
$94$	1.46412	−	9.24408i	0.151012	−	0.953455i
$95$	2.42705	+	7.46969i	0.249010	+	0.766375i
$96$	7.27044	+	6.56816i	0.742036	+	0.670360i
$97$	−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	$0.119977\pi$
$102$	8.35826	−	9.25194i	0.827591	−	0.916079i
$103$	−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
$105$	0.361243	−	0.554254i	0.0352537	−	0.0540897i
$106$	−7.61080	+	14.9370i	−0.739226	+	1.45081i
$107$	0.0729490	−	0.224514i	0.00705225	−	0.0217046i	−0.947468	−	0.319849i	$-0.896368\pi$
$107$	0.0729490	−	0.224514i	0.00705225	−	0.0217046i	0.954521	+	0.298145i	$0.0963678\pi$
$108$	−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	$0.290654\pi$
$110$	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	0.263941	−	0.964539i	$-0.414978\pi$
$113$	−0.951057	−	0.309017i	−0.0894679	−	0.0290699i	−0.353409	+	0.935469i	$0.614978\pi$
$114$	1.26242	−	11.8229i	0.118237	−	1.10731i
$115$	−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
$118$	−0.548367	−	1.07623i	−0.0504813	−	0.0990751i
$119$	−0.972136	−	0.706298i	−0.0891156	−	0.0647462i
$120$	3.23607	−	7.23607i	0.295411	−	0.660560i
$121$	−1.39919	−	10.9106i	−0.127199	−	0.991877i
$122$	6.09017	−	6.09017i	0.551378	−	0.551378i
$123$	−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
$126$	−0.841773	+	0.542700i	−0.0749911	+	0.0483476i
$127$	−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
$129$	−10.7873	+	0.547435i	−0.949769	+	0.0481989i
$130$	−0.357960	−	2.26007i	−0.0313952	−	0.198222i
$131$	−16.6180			−1.45192			−0.725962	−	0.687735i	$-0.758605\pi$
$131$	−16.6180			−1.45192			−0.725962	+	0.687735i	$0.758605\pi$
$132$	−10.7657	−	4.01249i	−0.937033	−	0.349242i
$133$	−1.14590			−0.0993620
$134$	0.631418	+	3.98662i	0.0545462	+	0.344391i
$135$	−5.97449	+	5.91544i	−0.514202	+	0.509120i
$136$	−12.8280	−	6.53618i	−1.09999	−	0.560473i
$137$	−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	$0.936952\pi$
$138$	0.891334	+	4.22780i	0.0758754	+	0.359894i
$139$	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
$141$	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
$146$	−4.94897	−	9.71290i	−0.409580	−	0.803846i
$147$	−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	$0.835384\pi$
$150$	5.80162	+	0.619486i	0.473700	+	0.0505808i
$151$	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
$156$	−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	$0.0685479\pi$
$158$	11.0305	−	21.6485i	0.877536	−	1.72226i
$159$	−17.2010	−	11.2110i	−1.36413	−	0.889087i
$160$	−9.04029	−	1.43184i	−0.714698	−	0.113197i
$161$	0.396027	−	0.128677i	0.0312113	−	0.0101412i
$162$	11.9125	−	4.48250i	0.935933	−	0.352179i
$163$	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
$165$	−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	0.749586	−	0.661907i	$-0.230253\pi$
$167$	4.54508	+	3.30220i	0.351709	+	0.255532i	−0.397876	+	0.917439i	$0.630253\pi$
$168$	0.858159	+	0.775266i	0.0662084	+	0.0598131i
$169$	−3.70820	−	11.4127i	−0.285246	−	0.877898i
$170$	−1.82208	+	11.5042i	−0.139747	+	0.882329i
$171$	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	$0.553877\pi$
$174$	4.88493	+	8.49338i	0.370325	+	0.643881i
$175$		−	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	$0.201849\pi$
$179$	−2.60081	+	8.00448i	−0.194394	+	0.598283i	−0.999983	+	0.00580843i	$0.998151\pi$
$180$	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	$0.454159\pi$
$182$	0.329740	+	0.0522257i	0.0244420	+	0.00387123i
$183$	6.62480	+	8.20869i	0.489719	+	0.606804i
$184$	4.44537	−	2.26503i	0.327717	−	0.166980i
$185$	9.73508	−	13.3992i	0.715737	−	0.985128i
$186$	−13.0902	−	5.85410i	−0.959818	−	0.429244i
$187$	16.8087	+	1.57295i	1.22918	+	0.115025i
$188$		−	13.2361i		−	0.965339i
$189$	−0.551451	−	1.09570i	−0.0401122	−	0.0797005i
$190$	5.04264	+	9.89675i	0.365832	+	0.717985i
$191$	3.21885	+	9.90659i	0.232908	+	0.716816i	0.997392	+	0.0721737i	$0.0229936\pi$
$191$	3.21885	+	9.90659i	0.232908	+	0.716816i	−0.764484	+	0.644642i	$0.777006\pi$
$192$	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	$0.495813\pi$
$194$	−4.19130	−	2.13558i	−0.300918	−	0.153325i
$195$	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	$-0.0757572\pi$
$198$	6.28643	−	12.5889i	0.446757	−	0.894655i
$199$			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
$201$	−4.93710	+	0.250548i	−0.348236	+	0.0176723i
$202$	3.21020	−	6.30037i	0.225869	−	0.443292i
$203$	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
$206$	−21.9460	+	11.1820i	−1.52905	+	0.779088i
$207$	−5.26461	+	0.535717i	−0.365916	+	0.0372349i
$208$	4.00000			0.277350
$209$	13.8496	−	8.20820i	0.957995	−	0.567773i
$210$	0.381966	−	0.854102i	0.0263582	−	0.0589386i
$211$	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
$213$	6.62480	+	8.20869i	0.453924	+	0.562450i
$214$	0.0522257	−	0.329740i	0.00357008	−	0.0225406i
$215$	8.16312	−	5.93085i	0.556720	−	0.404481i
$216$	−8.57949	−	11.9328i	−0.583760	−	0.811926i
$217$	−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
$222$	−21.7347	+	12.5006i	−1.45874	+	0.838986i
$223$	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
$225$	−1.50885	+	6.98479i	−0.100590	+	0.465652i
$226$	−1.39680	−	0.221232i	−0.0929139	−	0.0147161i
$227$	−3.21885	−	9.90659i	−0.213642	−	0.657524i	−0.999247	−	0.0387950i	$-0.987648\pi$
$227$	−3.21885	−	9.90659i	−0.213642	−	0.657524i	0.785605	−	0.618729i	$-0.212352\pi$
$228$	−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	$0.991961\pi$
$234$	−3.95579	−	1.53353i	−0.258598	−	0.100250i
$235$	−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
$238$	−1.51414	−	0.771491i	−0.0981469	−	0.0500084i
$239$	5.95492	−	18.3273i	0.385191	−	1.18550i	−0.551150	−	0.834406i	$-0.685811\pi$
$239$	5.95492	−	18.3273i	0.385191	−	1.18550i	0.936341	−	0.351091i	$-0.114189\pi$
$240$	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	$0.444185\pi$
$242$	−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
$246$	−2.46345	+	23.0708i	−0.157064	+	1.47094i
$247$	−2.85317	−	3.92705i	−0.181543	−	0.249872i
$248$	−2.59023	+	16.3540i	−0.164480	+	1.03848i
$249$	−4.92534	−	6.10292i	−0.312131	−	0.386757i
$250$	−15.0507	+	7.66869i	−0.951887	+	0.485011i
$251$	−18.0623	−	13.1230i	−1.14008	−	0.828319i	−0.152952	−	0.988234i	$-0.548878\pi$
$251$	−18.0623	−	13.1230i	−1.14008	−	0.828319i	−0.987131	+	0.159915i	$0.948878\pi$
$252$	−1.05573	+	0.944272i	−0.0665046	+	0.0594835i
$253$	−3.86475	+	4.39201i	−0.242974	+	0.276123i
$254$	−8.18034	−	8.18034i	−0.513280	−	0.513280i
$255$	−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	$0.550070\pi$
$258$	−14.9466	+	3.15115i	−0.930536	+	0.196182i
$259$	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
$262$	−23.2121	+	3.67644i	−1.43405	+	0.227131i
$263$	4.85410			0.299317			0.149658	−	0.988738i	$-0.452183\pi$
$263$	4.85410			0.299317			0.149658	+	0.988738i	$0.452183\pi$
$264$	−15.9252	−	3.22294i	−0.980130	−	0.198358i
$265$	19.1803			1.17824
$266$	−1.60059	+	0.253509i	−0.0981387	+	0.0155436i
$267$	−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	$0.589072\pi$
$270$	−7.03649	+	9.58445i	−0.428227	+	0.583291i
$271$	−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
$273$	−0.106480	+	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	$0.866388\pi$
$278$	8.93414	−	4.55217i	0.535834	−	0.273021i
$279$	8.83146	−	15.1802i	0.528726	−	0.908818i
$280$	−1.06706	−	0.169006i	−0.0637691	−	0.0101000i
$281$	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	$0.740984\pi$
$282$	16.1192	+	1.72118i	0.959883	+	0.102494i
$283$	−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
$288$	−10.7235	+	13.1532i	−0.631890	+	0.775058i
$289$	−2.75329	+	8.47375i	−0.161958	+	0.498456i
$290$	−8.15537	−	4.15537i	−0.478900	−	0.244012i
$291$	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	$0.358822\pi$
$294$	−12.6220	−	11.4028i	−0.736129	−	0.665023i
$295$	−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
$302$	7.72133	+	1.22294i	0.444313	+	0.0703722i
$303$	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
$306$	16.7380	+	13.6461i	0.956846	+	0.780098i
$307$			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	$-0.613169\pi$
$311$	8.54508	−	26.2991i	0.484547	−	1.49128i	0.832635	−	0.553821i	$-0.186831\pi$
$312$	−0.520147	+	4.87129i	−0.0294475	+	0.275782i
$313$	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
$315$	0.990475	+	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	$0.0793094\pi$
$318$	−26.5066	−	11.8541i	−1.48642	−	0.664745i
$319$	−5.25731	+	12.1803i	−0.294353	+	0.681968i
$320$	−12.9443			−0.723607
$321$	0.394774	+	0.106480i	0.0220341	+	0.00594313i
$322$	0.524705	−	0.267350i	0.0292406	−	0.0148989i
$323$	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
$326$	3.45543	−	6.78167i	0.191379	−	0.375602i
$327$	1.12048	+	22.0794i	0.0619630	+	1.22099i
$328$	26.4614	−	4.19107i	1.46109	−	0.231413i
$329$		−	1.56231i		−	0.0861327i
$330$	1.50151	+	13.0589i	0.0826553	+	0.718871i
$331$		−	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
$333$	−12.3972	−	28.0945i	−0.679363	−	1.53957i
$334$	7.07914	+	3.60700i	0.387353	+	0.197366i
$335$	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	$0.561876\pi$
$338$	−7.70447	−	15.1209i	−0.419068	−	0.822468i
$339$	0.451057	−	1.67229i	0.0244980	−	0.0908262i
$340$			16.4721i			0.893327i
$341$	−4.25325	−	18.9443i	−0.230327	−	1.02589i
$342$	20.5623	+	1.14590i	1.11188	+	0.0619631i
$343$	−1.93487	+	2.66312i	−0.104473	+	0.143795i
$344$	8.00760	+	15.7158i	0.431741	+	0.847340i
$345$	3.84693	−	3.10465i	0.207112	−	0.167149i
$346$	5.30558	+	0.840321i	0.285230	+	0.0451759i
$347$	−26.7984	+	19.4702i	−1.43861	+	1.04521i	−0.450282	+	0.892886i	$0.648676\pi$
$347$	−26.7984	+	19.4702i	−1.43861	+	1.04521i	−0.988330	+	0.152326i	$0.951324\pi$
$348$	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	$-0.133324\pi$
$350$	−0.124400	−	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	$0.137280\pi$
$353$			15.7082i			0.836063i	−0.908432	+	0.418032i	$0.862720\pi$
$354$	1.81355	−	1.04306i	0.0963893	−	0.0554378i
$355$	−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
$358$	−1.86198	+	11.7561i	−0.0984085	+	0.621327i
$359$	5.52786	+	17.0130i	0.291750	+	0.897913i	0.984294	+	0.176537i	$0.0564897\pi$
$359$	5.52786	+	17.0130i	0.291750	+	0.897913i	−0.692544	+	0.721375i	$0.743510\pi$
$360$	12.8012	+	4.96261i	0.674683	+	0.261553i
$361$	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
$366$	11.0696	+	10.0003i	0.578615	+	0.522724i
$367$	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
$369$	−27.7757	−	6.00009i	−1.44595	−	0.312352i
$370$	10.6337	−	20.8697i	0.552817	−	1.08497i
$371$	−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	$0.729210\pi$
$374$	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
$378$	−1.01267	−	1.40848i	−0.0520862	−	0.0724443i
$379$	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
$381$	11.0259	−	8.89845i	0.564876	−	0.455882i
$382$	6.68775	+	13.1254i	0.342175	+	0.671556i
$383$	20.6074	+	14.9721i	1.05299	+	0.765041i	0.972778	−	0.231737i	$-0.0744409\pi$
$383$	20.6074	+	14.9721i	1.05299	+	0.765041i	0.0802100	+	0.996778i	$0.474441\pi$
$384$	17.8885	+	8.00000i	0.912871	+	0.408248i
$385$	1.23607	−	0.277515i	0.0629959	−	0.0141435i
$386$	−16.0344	+	16.0344i	−0.816132	+	0.816132i
$387$	−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	$0.676880\pi$
$390$	3.87811	−	0.817610i	0.196376	−	0.0414013i
$391$	−5.27756	−	7.26393i	−0.266897	−	0.367353i
$392$	−8.91699	+	17.5006i	−0.450376	+	0.883913i
$393$	−1.45882	−	28.7463i	−0.0735876	−	1.45006i
$394$	−1.46412	−	9.24408i	−0.0737613	−	0.465710i
$395$	−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	$0.511762\pi$
$398$	0.454792	+	2.87145i	0.0227967	+	0.143933i
$399$	−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	$0.702851\pi$
$402$	−6.84072	+	1.44221i	−0.341184	+	0.0719308i
$403$	−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
$408$	10.1803	−	22.7639i	0.504002	−	1.12698i
$409$	25.6525	+	18.6376i	1.26843	+	0.921571i	0.999139	−	0.0414872i	$-0.0132096\pi$
$409$	25.6525	+	18.6376i	1.26843	+	0.921571i	0.269294	+	0.963058i	$0.413210\pi$
$410$	−9.84005	−	19.3122i	−0.485965	−	0.953761i
$411$	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
$414$	−7.23510	+	1.91299i	−0.355586	+	0.0940183i
$415$	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	$-0.445033\pi$
$419$	7.03444			0.343655			0.171827	+	0.985127i	$0.445033\pi$
$420$	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	$0.125829\pi$
$422$	7.30767	−	14.3421i	0.355732	−	0.698163i
$423$	−4.19217	+	19.4065i	−0.203830	+	0.943575i
$424$	−5.24501	+	33.1157i	−0.254720	+	1.60824i
$425$	−11.5312	+	3.74671i	−0.559345	+	0.181742i
$426$	11.0696	+	10.0003i	0.536322	+	0.484516i
$427$	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	0.833397	−	0.552674i	$-0.186393\pi$
$431$	11.7361	+	8.52675i	0.565307	+	0.410719i	−0.268091	+	0.963394i	$0.586393\pi$
$432$	−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	$0.804563\pi$
$434$	−0.305735	+	1.93033i	−0.0146757	+	0.0926590i
$435$	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
$438$	16.3672	−	9.41350i	0.782054	−	0.449795i
$439$			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	$0.215523\pi$
$443$	−4.61803	+	14.2128i	−0.219409	+	0.675273i	−0.998811	+	0.0487482i	$0.984477\pi$
$444$	−27.5935	+	22.2693i	−1.30953	+	1.05685i
$445$	9.39919	−	6.82891i	0.445564	−	0.323721i
$446$	28.9253	+	4.58131i	1.36965	+	0.216931i
$447$	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	$0.247956\pi$
$450$	−0.562306	+	10.0902i	−0.0265074	+	0.475655i
$451$	−27.0256	+	16.0172i	−1.27259	+	0.754221i
$452$	−2.00000			−0.0940721
$453$	−2.49338	+	9.24418i	−0.117149	+	0.434330i
$454$	−6.68775	−	13.1254i	−0.313871	−	0.616007i
$455$	−0.118034	−	0.363271i	−0.00553352	−	0.0170304i
$456$	−4.90566	−	23.2686i	−0.229729	−	1.08965i
$457$	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
$459$	−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	$-0.147101\pi$
$462$	−1.87972	−	0.380416i	−0.0874524	−	0.0176986i
$463$		−	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
$465$	0.831514	+	16.3851i	0.0385605	+	0.759842i
$466$	−11.9177	+	23.3899i	−0.552078	+	1.08351i
$467$	2.04508	−	1.48584i	0.0946352	−	0.0687565i	−0.539461	−	0.842010i	$-0.681372\pi$
$467$	2.04508	−	1.48584i	0.0946352	−	0.0687565i	0.634097	+	0.773254i	$0.281372\pi$
$468$	−5.86472	−	1.26689i	−0.271097	−	0.0585621i
$469$	0.208204	+	0.640786i	0.00961396	+	0.0295887i
$470$	−13.4931	+	6.87509i	−0.622391	+	0.317124i
$471$	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
$474$	38.4164	+	17.1803i	1.76452	+	0.789119i
$475$	−6.79615	+	9.35410i	−0.311829	+	0.429196i
$476$	−2.28563	−	0.742646i	−0.104762	−	0.0340391i
$477$	17.8830	−	30.7388i	0.818807	−	1.40743i
$478$	4.26325	−	26.9171i	0.194996	−	1.23116i
$479$	1.97214	−	1.43284i	0.0901092	−	0.0654682i	−0.541818	−	0.840496i	$-0.682264\pi$
$479$	1.97214	−	1.43284i	0.0901092	−	0.0654682i	0.631928	+	0.775027i	$0.282264\pi$
$480$	1.68323	−	15.7638i	0.0768286	−	0.719517i
$481$	−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
$486$	8.79968	+	20.2130i	0.399162	+	0.916881i
$487$	−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
$489$	7.80954	+	5.08997i	0.353159	+	0.230176i
$490$	15.6946	+	2.48577i	0.709008	+	0.112296i
$491$	−12.0451	−	37.0710i	−0.543587	−	1.67299i	−0.724326	−	0.689458i	$-0.757849\pi$
$491$	−12.0451	−	37.0710i	−0.543587	−	1.67299i	0.180739	−	0.983531i	$-0.442151\pi$
$492$	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
$498$	−8.22989	−	7.43493i	−0.368790	−	0.333167i
$499$	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
$501$	−5.31323	+	8.15208i	−0.237378	+	0.364208i
$502$	−28.1327	−	14.3343i	−1.25562	−	0.639772i
$503$	9.20163	−	28.3197i	0.410280	−	1.26271i	−0.506125	−	0.862460i	$-0.668922\pi$
$503$	9.20163	−	28.3197i	0.410280	−	1.26271i	0.916405	−	0.400252i	$-0.131078\pi$
$504$	−1.26574	+	1.55252i	−0.0563806	+	0.0691548i
$505$	−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	0.927862	−	0.372925i	$-0.121645\pi$
$509$	32.9237	+	10.6976i	1.45932	+	0.474161i	0.531456	+	0.847086i	$0.321645\pi$
$510$	−20.0601	−	2.14198i	−0.888277	−	0.0948486i
$511$	−1.06957	−	1.47214i	−0.0473150	−	0.0651235i
$512$	3.53971	−	22.3488i	0.156434	−	0.987688i
$513$	−4.06936	+	24.8922i	−0.179666	+	1.09902i
$514$	−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
$519$	−1.71328	+	6.35198i	−0.0752047	+	0.278821i
$520$	−2.07768	−	4.07768i	−0.0911125	−	0.178818i
$521$	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	$0.127576\pi$
$522$	−14.2632	+	9.19566i	−0.624285	+	0.402483i
$523$	−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
$525$	0.972691	−	0.0493622i	0.0424517	−	0.00215434i
$526$	6.78022	−	1.07388i	0.295632	−	0.0468235i
$527$	29.7984			1.29804
$528$	−22.9574	−	0.978644i	−0.999093	−	0.0425900i
$529$	−19.8885			−0.864719
$530$	26.7911	−	4.24330i	1.16373	−	0.184317i
$531$	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
$534$	−17.2099	+	3.62830i	−0.744743	+	0.157012i
$535$	−0.363271	+	0.118034i	−0.0157056	+	0.00510305i
$536$	3.66489	+	7.19276i	0.158299	+	0.310680i
$537$	−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	$0.745824\pi$
$542$	−17.1597	+	8.74332i	−0.737073	+	0.375558i
$543$	−13.6276	−	16.8858i	−0.584817	−	0.724639i
$544$	−28.4398	−	4.50443i	−1.21935	−	0.193126i
$545$	−12.1392	−	16.7082i	−0.519987	−	0.715701i
$546$	−0.0613950	+	0.574978i	−0.00262746	+	0.0246068i
$547$	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
$552$	4.30834	+	7.49087i	0.183375	+	0.318833i
$553$	1.25329	−	3.85723i	0.0532953	−	0.164026i
$554$	−20.9399	−	10.6694i	−0.889653	−	0.453301i
$555$	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	$0.339936\pi$
$558$	8.97745	−	23.1576i	0.380046	−	0.980340i
$559$	−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	0.703428	−	0.710766i	$-0.251652\pi$
$563$	5.80902	+	4.22050i	0.244821	+	0.177873i	−0.458607	+	0.888639i	$0.651652\pi$
$564$	22.8961	−	1.16193i	0.964099	−	0.0489261i
$565$	0.500000	+	1.53884i	0.0210352	+	0.0647396i
$566$	−30.9815	−	4.90700i	−1.30225	−	0.206256i
$567$	1.84696	−	1.05010i	0.0775651	−	0.0441000i
$568$	7.82026	−	15.3481i	0.328131	−	0.643993i
$569$	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	$0.474250\pi$
$570$	−16.6770	+	9.59168i	−0.698521	+	0.401751i
$571$		−	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
$576$	−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	$0.231277\pi$
$578$	−1.97114	+	12.4453i	−0.0819885	+	0.517655i
$579$	−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
$582$	3.32624	−	7.43769i	0.137877	−	0.308302i
$583$	−8.61251	−	38.3607i	−0.356694	−	1.58874i
$584$	−15.4164	−	15.4164i	−0.637935	−	0.637935i
$585$	0.491407	+	4.82916i	0.0203172	+	0.199661i
$586$	5.56500	−	2.83551i	0.229888	−	0.117134i
$587$	1.12868	+	3.47371i	0.0465855	+	0.143375i	0.971644	−	0.236450i	$-0.0759840\pi$
$587$	1.12868	+	3.47371i	0.0465855	+	0.143375i	−0.925058	+	0.379826i	$0.875984\pi$
$588$	−20.1531	−	13.1350i	−0.831098	−	0.541680i
$589$	22.9894	−	16.7027i	0.947260	−	0.688225i
$590$	−0.887277	+	1.74138i	−0.0365286	+	0.0716914i
$591$	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	$-0.0632766\pi$
$594$	22.3285	+	9.76930i	0.916148	+	0.400839i
$595$			1.94427i			0.0797074i
$596$	−4.38197	−	3.18368i	−0.179492	−	0.130409i
$597$	−3.55605	+	0.180463i	−0.145539	+	0.00738584i
$598$	2.22268	+	1.13251i	0.0908923	+	0.0463119i
$599$	−17.0344	+	12.3762i	−0.696008	+	0.505680i	−0.878630	−	0.477504i	$-0.841542\pi$
$599$	−17.0344	+	12.3762i	−0.696008	+	0.505680i	0.182621	+	0.983183i	$0.441542\pi$
$600$	11.4182	−	2.40727i	0.466146	−	0.0982762i
$601$	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
$603$	−0.866808	−	8.51832i	−0.0352992	−	0.346893i
$604$	11.0557			0.449851
$605$	−12.9515	+	12.2082i	−0.526554	+	0.496334i
$606$	11.1803	+	5.00000i	0.454170	+	0.203111i
$607$	−18.2743	+	25.1525i	−0.741733	+	1.02091i	0.256784	+	0.966469i	$0.417337\pi$
$607$	−18.2743	+	25.1525i	−0.741733	+	1.02091i	−0.998517	+	0.0544388i	$0.982663\pi$
$608$	−24.4661	+	12.4661i	−0.992231	+	0.505567i
$609$	1.02717	+	1.27275i	0.0416228	+	0.0515742i
$610$	−13.7642	−	2.18004i	−0.557297	−	0.0882672i
$611$	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	$0.0700487\pi$
$614$	0.136729	+	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	$0.162220\pi$
$617$			24.2361i			0.975707i	−0.872925	+	0.487854i	$0.837780\pi$
$618$	−21.2695	−	36.9810i	−0.855584	−	1.48760i
$619$	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
$621$	−1.38885	−	9.05982i	−0.0557327	−	0.363558i
$622$	6.11761	−	38.6250i	0.245294	−	1.54872i
$623$	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
$630$	1.51098	+	0.585757i	0.0601988	+	0.0233371i
$631$	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
$633$	16.5159	+	10.7644i	0.656447	+	0.427848i
$634$	8.46230	−	16.6082i	0.336081	−	0.659596i
$635$	−4.09017	+	12.5882i	−0.162313	+	0.499549i
$636$	−39.6470	−	10.6937i	−1.57210	−	0.424034i
$637$	−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	−0.138340	−	0.990385i	$-0.544177\pi$
$641$	−21.0745	−	6.84752i	−0.832393	−	0.270461i	−0.694053	+	0.719924i	$0.744177\pi$
$642$	0.574978	+	0.0613950i	0.0226926	+	0.00242307i
$643$	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
$645$	10.9759	+	13.6001i	0.432177	+	0.535504i
$646$	15.8636	+	31.1342i	0.624147	+	1.22496i
$647$	−5.02786	−	3.65296i	−0.197666	−	0.143613i	0.484550	−	0.874764i	$-0.338983\pi$
$647$	−5.02786	−	3.65296i	−0.197666	−	0.143613i	−0.682216	+	0.731151i	$0.738983\pi$
$648$	19.8885	−	15.8885i	0.781296	−	0.624161i
$649$	2.60081	+	1.12257i	0.102091	+	0.0440647i
$650$	2.38197	−	2.38197i	0.0934284	−	0.0934284i
$651$	−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	$0.388450\pi$
$654$	6.44975	+	30.5926i	0.252205	+	1.19627i
$655$	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
$658$	−0.345632	−	2.18223i	−0.0134741	−	0.0850723i
$659$	−13.4164			−0.522629			−0.261315	−	0.965254i	$-0.584156\pi$
$659$	−13.4164			−0.522629			−0.261315	+	0.965254i	$0.584156\pi$
$660$	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	$0.855541\pi$
$662$	−2.94057	−	18.5660i	−0.114288	−	0.721588i
$663$	8.80510	−	0.446842i	0.341962	−	0.0173539i
$664$	−5.81414	+	11.4109i	−0.225632	+	0.442828i
$665$	1.08981	+	1.50000i	0.0422612	+	0.0581675i
$666$	−23.5319	−	36.4999i	−0.911841	−	1.41434i
$667$	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
$672$	2.11146	+	0.944272i	0.0814512	+	0.0364261i
$673$	6.13525	+	4.45752i	0.236497	+	0.171825i	0.699721	−	0.714416i	$-0.253308\pi$
$673$	6.13525	+	4.45752i	0.236497	+	0.171825i	−0.463224	+	0.886241i	$0.653308\pi$
$674$	20.5895	+	40.4092i	0.793078	+	1.55650i
$675$	−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	$0.822702\pi$
$678$	0.260074	−	2.43564i	0.00998806	−	0.0935403i
$679$	−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	$-0.358912\pi$
$683$	22.4164			0.857740			0.428870	+	0.903366i	$0.358912\pi$
$684$	28.9750	−	2.94844i	1.10789	−	0.112736i
$685$	−4.88197	+	15.0251i	−0.186530	+	0.574081i
$686$	−2.11346	+	4.14791i	−0.0806924	+	0.158368i
$687$	−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
$690$	4.68655	−	5.18764i	0.178414	−	0.197490i
$691$	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
$693$	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
$696$	14.5409	+	13.1363i	0.551171	+	0.497931i
$697$	−14.8992	−	45.8550i	−0.564347	−	1.73688i
$698$	5.53079	−	34.9201i	0.209344	−	1.32174i
$699$	−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	$0.455544\pi$
$702$	2.30548	−	6.97745i	0.0870147	−	0.263347i
$703$		−	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
$708$	2.30242	−	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	$0.0360451\pi$
$710$	−13.7642	−	2.18004i	−0.516562	−	0.0818154i
$711$	−25.9181	+	44.5503i	−0.972006	+	1.67077i
$712$	9.22012	+	18.0955i	0.345539	+	0.678158i
$713$	−6.06961	+	8.35410i	−0.227309	+	0.312864i
$714$	1.20163	−	2.68692i	0.0449697	−	0.100555i
$715$	4.02874	+	3.54508i	0.150666	+	0.132579i
$716$			16.8328i			0.629072i
$717$	32.2258	+	8.69209i	1.20350	+	0.324612i
$718$	11.4852	+	22.5409i	0.428622	+	0.841218i
$719$	9.10739	+	28.0297i	0.339648	+	1.04533i	0.964387	+	0.264496i	$0.0852056\pi$
$719$	9.10739	+	28.0297i	0.339648	+	1.04533i	−0.624738	+	0.780834i	$0.714794\pi$
$720$	18.9786	+	4.09975i	0.707292	+	0.152789i
$721$	−3.32624	+	2.41665i	−0.123876	+	0.0900009i
$722$	5.74884	+	2.92918i	0.213950	+	0.109013i
$723$	0.475481	+	9.36944i	0.0176833	+	0.348453i
$724$	−14.7274	+	20.2705i	−0.547339	+	0.753348i
$725$		−	9.52786i		−	0.353856i
$726$	25.4436	−	8.86684i	0.944302	−	0.329079i
$727$		−	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
$729$	−25.7601	+	8.08802i	−0.954079	+	0.299556i
$730$	−8.00760	+	15.7158i	−0.296375	+	0.581668i
$731$	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	$0.961951\pi$
$734$	16.7920	−	8.55597i	0.619805	−	0.315807i
$735$	−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
$738$	−40.1246	−	2.23607i	−1.47701	−	0.0823108i
$739$	−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
$741$	6.54264	−	5.28022i	0.240350	−	0.193974i
$742$	−0.619089	+	3.90877i	−0.0227275	+	0.143496i
$743$	−15.8992	+	11.5514i	−0.583285	+	0.423781i	−0.839907	−	0.542731i	$-0.817390\pi$
$743$	−15.8992	+	11.5514i	−0.583285	+	0.423781i	0.256622	+	0.966512i	$0.417390\pi$
$744$	−28.5170	−	3.04499i	−1.04548	−	0.111635i
$745$	−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
$750$	−14.5867	−	25.3618i	−0.532632	−	0.926082i
$751$	−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
$753$	21.1149	−	32.3966i	0.769471	−	1.18060i
$754$	5.58721	+	0.884927i	0.203474	+	0.0322271i
$755$	−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	$0.383853\pi$
$762$	13.4324	−	14.8687i	0.486606	−	0.538635i
$763$	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
$766$	32.0968	+	16.3541i	1.15970	+	0.590898i
$767$	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	$0.648353\pi$
$770$	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	0.0443713	−	0.999015i	$-0.485872\pi$
$773$	−14.0943	−	4.57953i	−0.506938	−	0.164714i	−0.551309	+	0.834301i	$0.685872\pi$
$774$	−6.76303	−	25.5784i	−0.243092	−	0.919397i
$775$	8.19624	+	11.2812i	0.294418	+	0.405231i
$776$	−9.29219	−	1.47174i	−0.333570	−	0.0528323i
$777$	−3.25698	+	2.62853i	−0.116843	+	0.0942981i
$778$	−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
$783$	−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
$786$	−8.39727	−	39.8301i	−0.299521	−	1.42069i
$787$	−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
$789$	0.426119	+	8.39675i	0.0151702	+	0.298932i
$790$	−38.8288	+	6.14988i	−1.38147	+	0.218803i
$791$	−0.236068			−0.00839361
$792$	4.17712	−	27.8308i	0.148428	−	0.988923i
$793$	6.09017			0.216268
$794$	−2.05628	+	0.325683i	−0.0729747	+	0.0115581i
$795$	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	$-0.507737\pi$
$798$	−0.579035	−	2.74649i	−0.0204976	−	0.0972247i
$799$	−32.0382	+	10.4098i	−1.13343	+	0.368273i
$800$	−6.11727	−	12.0058i	−0.216278	−	0.424469i
$801$	−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
$806$	−7.37660	+	3.75856i	−0.259830	+	0.132390i
$807$	−27.2002	+	21.9519i	−0.957494	+	0.772743i
$808$	2.21232	−	13.9680i	0.0778291	−	0.491393i
$809$	−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	$0.928720\pi$
$810$	−17.1971	−	11.3305i	−0.604245	−	0.398114i
$811$	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
$816$	9.18382	−	34.0489i	0.321498	−	1.19195i
$817$	9.35410	−	28.7890i	0.327259	−	1.00720i
$818$	39.9547	+	20.3579i	1.39698	+	0.711798i
$819$	−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	$0.660474\pi$
$822$	16.0328	−	17.7470i	0.559207	−	0.618998i
$823$	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
$825$	−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	0.305068	−	0.952331i	$-0.401321\pi$
$827$	−14.5623	−	10.5801i	−0.506381	−	0.367907i	−0.811449	+	0.584423i	$0.801321\pi$
$828$	−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	$0.959658\pi$
$830$	10.2333	+	1.62080i	0.355203	+	0.0562587i
$831$	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
$834$	8.65874	+	15.0549i	0.299828	+	0.521308i
$835$		−	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	−0.842509	−	0.538682i	$-0.818922\pi$
$839$	4.51064	−	13.8823i	0.155725	−	0.479271i	0.998234	+	0.0594111i	$0.0189223\pi$
$840$	0.198678	−	1.86067i	0.00685506	−	0.0641991i
$841$	−10.5172	+	7.64121i	−0.362663	+	0.263490i
$842$	−0.735869	+	4.64610i	−0.0253597	+	0.160115i
$843$	−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
$846$	−1.56231	+	28.0344i	−0.0537132	+	0.963844i
$847$	−1.11006	−	2.34752i	−0.0381421	−	0.0806619i
$848$			47.4164i			1.62829i
$849$	10.0046	−	37.0919i	0.343357	−	1.27299i
$850$	−15.2779	+	7.78448i	−0.524028	+	0.267005i
$851$	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	$0.532707\pi$
$854$	0.923056	−	1.81160i	0.0315863	−	0.0619917i
$855$	−9.51234	−	21.5568i	−0.325315	−	0.737229i
$856$	−0.104451	−	0.659481i	−0.00357008	−	0.0225406i
$857$		−	5.11146i		−	0.174604i	−0.996182	−	0.0873020i	$-0.972175\pi$
$857$		−	5.11146i		−	0.174604i	0.996182	−	0.0873020i	$-0.0278245\pi$
$858$	−3.37660	−	7.38909i	−0.115275	−	0.252259i
$859$			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
$861$	0.196294	+	3.86801i	0.00668967	+	0.131821i
$862$	18.2794	+	9.31380i	0.622597	+	0.317229i
$863$	−31.6525	+	22.9969i	−1.07746	+	0.782823i	−0.977239	−	0.212142i	$-0.931956\pi$
$863$	−31.6525	+	22.9969i	−1.07746	+	0.782823i	−0.100224	+	0.994965i	$0.531956\pi$
$864$	−23.6941	−	17.3952i	−0.806088	−	0.591796i
$865$	−1.89919	−	5.84510i	−0.0645743	−	0.198739i
$866$	7.89182	+	15.4886i	0.268175	+	0.526323i
$867$	−14.8998	−	4.01884i	−0.506024	−	0.136487i
$868$			2.76393i			0.0938140i
$869$	12.4822	+	55.5967i	0.423431	+	1.88599i
$870$	6.47214	−	14.4721i	0.219426	−	0.490651i
$871$	−1.67760	+	2.30902i	−0.0568433	+	0.0782381i
$872$	32.1670	−	16.3899i	1.08931	−	0.555032i
$873$	8.62525	+	5.01794i	0.291921	+	0.169832i
$874$	−11.9598	−	1.89425i	−0.404548	−	0.0640741i
$875$	−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	$0.141242\pi$
$878$	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	$-0.913945\pi$
$881$		−	15.8541i		−	0.534138i	0.963677	−	0.267069i	$-0.0860552\pi$
$882$	18.6168	−	22.8348i	0.626859	−	0.768888i
$883$	−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
$885$	−2.00531	−	1.30699i	−0.0674078	−	0.0439339i
$886$	−3.30615	+	20.8742i	−0.111072	+	0.701282i
$887$	8.16312	+	25.1235i	0.274091	+	0.843564i	0.989459	+	0.144816i	$0.0462592\pi$
$887$	8.16312	+	25.1235i	0.274091	+	0.843564i	−0.715368	+	0.698748i	$0.753741\pi$
$888$	−33.6161	+	37.2104i	−1.12808	+	1.24870i
$889$	−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
$894$	4.44698	−	4.92246i	0.148729	−	0.164632i
$895$	12.9515	−	4.20820i	0.432922	−	0.140665i
$896$	0.417806	−	2.63792i	0.0139579	−	0.0881268i
$897$	−1.66823	+	2.55957i	−0.0557006	+	0.0854614i
$898$	−4.08381	+	8.01492i	−0.136278	+	0.267461i
$899$	−7.23607	+	22.2703i	−0.241336	+	0.742757i
$900$	1.44684	+	14.2184i	0.0482279	+	0.473946i
$901$	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
$906$	−1.43765	+	13.4639i	−0.0477628	+	0.447308i
$907$	−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
$909$	−7.54297	+	12.9655i	−0.250184	+	0.430038i
$910$	−0.245237	−	0.481305i	−0.00812954	−	0.0159551i
$911$	7.42705	+	5.39607i	0.246069	+	0.178780i	0.703983	−	0.710217i	$-0.251403\pi$
$911$	7.42705	+	5.39607i	0.246069	+	0.178780i	−0.457914	+	0.888997i	$0.651403\pi$
$912$	−12.0000	−	31.4164i	−0.397360	−	1.04030i
$913$	1.39919	−	14.9519i	0.0463063	−	0.494836i
$914$	7.85410	−	7.85410i	0.259791	−	0.259791i
$915$	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
$918$	−22.1361	+	30.1517i	−0.730600	+	0.995154i
$919$	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
$921$	−1.06909	+	0.0542543i	−0.0352277	+	0.00178774i
$922$	−4.23568	−	26.7430i	−0.139495	−	0.880735i
$923$	6.09017			0.200460
$924$	−2.70975	−	0.115513i	−0.0891443	−	0.00380011i
$925$	24.3820			0.801674
$926$	−0.788095	−	4.97584i	−0.0258984	−	0.163516i
$927$	47.8021	−	21.0935i	1.57003	−	0.692803i
$928$	10.2726	−	20.1612i	0.337216	−	0.661823i
$929$	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	$0.776335\pi$
$930$	4.78637	+	22.7028i	0.156951	+	0.744455i
$931$	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
$936$	−8.47214	−	0.472136i	−0.276920	−	0.0154322i
$937$	5.66312	+	4.11450i	0.185006	+	0.134415i	0.676433	−	0.736504i	$-0.263525\pi$
$937$	5.66312	+	4.11450i	0.185006	+	0.134415i	−0.491427	+	0.870919i	$0.663525\pi$
$938$	0.432582	+	0.848990i	0.0141243	+	0.0277205i
$939$	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	$0.760664\pi$
$942$	6.02124	+	0.642937i	0.196183	+	0.0209480i
$943$	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	$-0.190850\pi$
$947$	50.8115			1.65115			0.825576	+	0.564290i	$0.190850\pi$
$948$	57.4610	+	15.4986i	1.86625	+	0.503371i
$949$	2.38197	−	7.33094i	0.0773219	−	0.237972i
$950$	−7.42346	+	14.5694i	−0.240849	+	0.472692i
$951$	19.1254	+	12.4653i	0.620184	+	0.404213i
$952$	−3.35687	−	0.531676i	−0.108797	−	0.0172317i
$953$	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	$0.0731199\pi$
$954$	18.1786	−	46.8924i	0.588555	−	1.51820i
$955$	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
$962$	−2.26454	+	14.2978i	−0.0730118	+	0.460978i
$963$	−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
$966$	0.508531	+	0.884177i	0.0163617	+	0.0284479i
$967$			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	$0.248320\pi$
$971$	−8.65248	+	26.6296i	−0.277671	+	0.854584i	−0.988500	+	0.151219i	$0.951680\pi$
$972$	16.7632	+	26.2868i	0.537679	+	0.843150i
$973$	1.35410	−	0.983813i	0.0434105	−	0.0315396i
$974$	−19.0698	−	3.02036i	−0.611036	−	0.0967786i
$975$	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	$0.137870\pi$
$978$	12.0344	+	5.38197i	0.384819	+	0.172096i
$979$	−17.8783	−	15.7320i	−0.571393	−	0.502797i
$980$	22.4721			0.717846
$981$	−38.0951	+	3.87649i	−1.21628	+	0.123767i
$982$	−25.0259	−	49.1160i	−0.798608	−	1.56736i
$983$	−14.7426	−	45.3732i	−0.470217	−	1.44718i	−0.852301	−	0.523052i	$-0.824793\pi$
$983$	−14.7426	−	45.3732i	−0.470217	−	1.44718i	0.382083	−	0.924128i	$-0.375207\pi$
$984$	9.57274	+	45.4057i	0.305168	+	1.44748i
$985$	−8.66312	+	6.29412i	−0.276030	+	0.200547i
$986$	−25.6560	−	13.0724i	−0.817052	−	0.416309i
$987$	2.70252	−	0.137147i	0.0860220	−	0.00436545i
$988$	−7.85410	−	5.70634i	−0.249872	−	0.181543i
$989$			11.0000i			0.349780i
$990$	−22.4579	+	3.74373i	−0.713757	+	0.118984i
$991$		−	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
$993$	22.9925	−	1.16682i	0.729644	−	0.0370280i
$994$	0.923056	−	1.81160i	0.0292776	−	0.0574605i
$995$	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	$0.723045\pi$
$998$	3.96406	−	2.01979i	0.125480	−	0.0639354i
$999$	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.b.59.2	yes	8
3.2	odd	2		132.2.o.a.59.1	yes	8
4.3	odd	2		132.2.o.a.59.2	yes	8
11.3	even	5	inner	132.2.o.b.47.1	yes	8
12.11	even	2	inner	132.2.o.b.59.1	yes	8
33.14	odd	10		132.2.o.a.47.2	yes	8
44.3	odd	10		132.2.o.a.47.1	✓	8
132.47	even	10	inner	132.2.o.b.47.2	yes	8

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

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)

\(f(q)\)	\(=\)	\(q+(1.39680 - 0.221232i) q^{2} +(0.0877853 + 1.72982i) q^{3} +(1.90211 - 0.618034i) q^{4} +(-0.951057 - 1.30902i) q^{5} +(0.505311 + 2.39680i) q^{6} +(0.224514 - 0.0729490i) q^{7} +(2.52015 - 1.28408i) q^{8} +(-2.98459 + 0.303706i) q^{9} +O(q^{10})\)	\(q+(1.39680 - 0.221232i) q^{2} +(0.0877853 + 1.72982i) q^{3} +(1.90211 - 0.618034i) q^{4} +(-0.951057 - 1.30902i) q^{5} +(0.505311 + 2.39680i) q^{6} +(0.224514 - 0.0729490i) q^{7} +(2.52015 - 1.28408i) 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} +(0.297463 - 0.151565i) q^{14} +(2.18088 - 1.76007i) q^{15} +(3.23607 - 2.35114i) q^{16} +(-2.99193 - 4.11803i) q^{17} +(-4.10169 + 1.08450i) 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} +(2.44246 + 4.24669i) q^{24} +(0.736068 - 2.26538i) q^{25} +(1.26007 + 0.642040i) q^{26} +(-0.787361 - 5.13615i) q^{27} +(0.381966 - 0.277515i) q^{28} +(3.80423 - 1.23607i) q^{29} +(2.65688 - 2.94095i) 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} +(-6.78022 - 1.07388i) q^{38} +(-0.945746 + 1.45106i) q^{39} +(-4.07768 - 2.07768i) q^{40} +(9.00854 + 2.92705i) q^{41} +(0.288294 + 0.501254i) 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} +(4.35114 + 5.39144i) q^{48} +(-5.61803 + 4.08174i) q^{49} +(0.526966 - 3.32714i) q^{50} +(6.86083 - 5.53701i) q^{51} +(1.90211 + 0.618034i) q^{52} +(-6.96767 + 9.59017i) q^{53} +(-2.23607 - 7.00000i) q^{54} +(5.34307 + 0.500000i) q^{55} +(0.472136 - 0.472136i) q^{56} +(2.18947 - 8.11746i) q^{57} +(5.04029 - 2.56816i) q^{58} +(-0.263932 - 0.812299i) q^{59} +(3.06050 - 4.69572i) q^{60} +(4.92705 - 3.57971i) q^{61} +(-3.75856 + 7.37660i) q^{62} +(-0.647927 + 0.285909i) q^{63} +(4.70228 - 6.47214i) q^{64} -1.61803i q^{65} +(-7.07492 - 3.99318i) q^{66} +2.85410i q^{67} +(-8.23607 - 5.98385i) q^{68} +(0.154847 + 3.05129i) q^{69} +(-0.481305 - 0.245237i) q^{70} +(4.92705 - 3.57971i) q^{71} +(-7.13162 + 4.59783i) q^{72} +(-2.38197 - 7.33094i) q^{73} +(6.57196 + 12.8982i) q^{74} +(3.98333 + 1.07440i) q^{75} -9.70820 q^{76} +(-0.310271 + 0.718847i) q^{77} +(-1.00000 + 2.23607i) q^{78} +(10.0984 - 13.8992i) q^{79} +(-6.15537 - 2.00000i) q^{80} +(8.81553 - 1.81288i) q^{81} +(13.2307 + 2.09554i) q^{82} +(-3.66312 + 2.66141i) q^{83} +(0.513583 + 0.636373i) 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} +(5.32057 + 4.33776i) q^{90} +(0.224514 + 0.0729490i) q^{91} +(3.35520 - 1.09017i) q^{92} +(-8.49463 - 5.53649i) q^{93} +(1.46412 - 9.24408i) q^{94} +(2.42705 + 7.46969i) q^{95} +(7.27044 + 6.56816i) q^{96} +(-2.69098 - 1.95511i) q^{97} +(-6.94427 + 6.94427i) q^{98} +(5.78298 - 8.09673i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 4 q^{3} - 2 q^{6} - 4 q^{8} - 10 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 4 * q^3 - 2 * q^6 - 4 * q^8 - 10 * q^9	\( 8 q + 2 q^{2} - 4 q^{3} - 2 q^{6} - 4 q^{8} - 10 q^{9} - 4 q^{10} - 22 q^{11} - 8 q^{12} + 2 q^{13} + 14 q^{14} + 2 q^{15} + 8 q^{16} - 14 q^{18} - 12 q^{20} + 28 q^{21} - 8 q^{22} + 32 q^{23} + 20 q^{24} - 12 q^{25} - 2 q^{26} + 2 q^{27} + 12 q^{28} + 32 q^{32} - 4 q^{33} + 4 q^{34} + 2 q^{35} + 8 q^{36} - 6 q^{37} - 18 q^{38} - 6 q^{39} - 8 q^{40} - 10 q^{42} + 8 q^{45} - 2 q^{46} - 6 q^{47} + 16 q^{48} - 36 q^{49} + 2 q^{50} + 28 q^{51} - 32 q^{56} - 6 q^{57} - 8 q^{58} - 20 q^{59} + 16 q^{60} + 26 q^{61} + 10 q^{62} - 28 q^{63} - 2 q^{66} - 48 q^{68} - 16 q^{69} + 8 q^{70} + 26 q^{71} - 28 q^{72} - 28 q^{73} + 6 q^{74} + 16 q^{75} - 24 q^{76} - 8 q^{78} - 2 q^{81} + 30 q^{82} + 2 q^{83} - 16 q^{84} + 2 q^{85} + 18 q^{86} - 16 q^{87} + 36 q^{88} + 22 q^{90} - 10 q^{93} + 16 q^{94} + 6 q^{95} + 8 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 4 * q^3 - 2 * q^6 - 4 * q^8 - 10 * q^9 - 4 * q^10 - 22 * q^11 - 8 * q^12 + 2 * q^13 + 14 * q^14 + 2 * q^15 + 8 * q^16 - 14 * q^18 - 12 * q^20 + 28 * q^21 - 8 * q^22 + 32 * q^23 + 20 * q^24 - 12 * q^25 - 2 * q^26 + 2 * q^27 + 12 * q^28 + 32 * q^32 - 4 * q^33 + 4 * q^34 + 2 * q^35 + 8 * q^36 - 6 * q^37 - 18 * q^38 - 6 * q^39 - 8 * q^40 - 10 * q^42 + 8 * q^45 - 2 * q^46 - 6 * q^47 + 16 * q^48 - 36 * q^49 + 2 * q^50 + 28 * q^51 - 32 * q^56 - 6 * q^57 - 8 * q^58 - 20 * q^59 + 16 * q^60 + 26 * q^61 + 10 * q^62 - 28 * q^63 - 2 * q^66 - 48 * q^68 - 16 * q^69 + 8 * q^70 + 26 * q^71 - 28 * q^72 - 28 * q^73 + 6 * q^74 + 16 * q^75 - 24 * q^76 - 8 * q^78 - 2 * q^81 + 30 * q^82 + 2 * q^83 - 16 * q^84 + 2 * q^85 + 18 * q^86 - 16 * q^87 + 36 * q^88 + 22 * q^90 - 10 * q^93 + 16 * q^94 + 6 * q^95 + 8 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

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