LMFDB - Embedded newform 363.2.e.i.130.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(124,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("363.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.e (of order $5$, degree $4$, not 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:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			130.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	363.130
Dual form			363.2.e.i.148.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.618034 + 1.90211i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-1.61803 - 1.17557i) q^{4} +(1.23607 + 3.80423i) q^{5} +(0.618034 + 1.90211i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.618034 + 1.90211i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-1.61803 - 1.17557i) q^{4} +(1.23607 + 3.80423i) q^{5} +(0.618034 + 1.90211i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(0.309017 - 0.951057i) q^{9} -8.00000 q^{10} -2.00000 q^{12} +(-0.618034 + 1.90211i) q^{13} +(1.61803 - 1.17557i) q^{14} +(3.23607 + 2.35114i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(1.23607 + 3.80423i) q^{17} +(1.61803 + 1.17557i) q^{18} +(2.42705 - 1.76336i) q^{19} +(2.47214 - 7.60845i) q^{20} -1.00000 q^{21} +2.00000 q^{23} +(-8.89919 + 6.46564i) q^{25} +(-3.23607 - 2.35114i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.618034 + 1.90211i) q^{28} +(-4.85410 - 3.52671i) q^{29} +(-6.47214 + 4.70228i) q^{30} +(-1.54508 + 4.75528i) q^{31} +8.00000 q^{32} -8.00000 q^{34} +(1.23607 - 3.80423i) q^{35} +(-1.61803 + 1.17557i) q^{36} +(-2.42705 - 1.76336i) q^{37} +(1.85410 + 5.70634i) q^{38} +(0.618034 + 1.90211i) q^{39} +(1.61803 - 1.17557i) q^{41} +(0.618034 - 1.90211i) q^{42} +12.0000 q^{43} +4.00000 q^{45} +(-1.23607 + 3.80423i) q^{46} +(-1.61803 + 1.17557i) q^{47} +(-3.23607 - 2.35114i) q^{48} +(-1.85410 - 5.70634i) q^{49} +(-6.79837 - 20.9232i) q^{50} +(3.23607 + 2.35114i) q^{51} +(3.23607 - 2.35114i) q^{52} +(1.85410 - 5.70634i) q^{53} +2.00000 q^{54} +(0.927051 - 2.85317i) q^{57} +(9.70820 - 7.05342i) q^{58} +(8.09017 + 5.87785i) q^{59} +(-2.47214 - 7.60845i) q^{60} +(0.927051 + 2.85317i) q^{61} +(-8.09017 - 5.87785i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(-2.47214 + 7.60845i) q^{64} -8.00000 q^{65} -1.00000 q^{67} +(2.47214 - 7.60845i) q^{68} +(1.61803 - 1.17557i) q^{69} +(6.47214 + 4.70228i) q^{70} +(8.89919 + 6.46564i) q^{73} +(4.85410 - 3.52671i) q^{74} +(-3.39919 + 10.4616i) q^{75} -6.00000 q^{76} -4.00000 q^{78} +(3.39919 - 10.4616i) q^{79} +(12.9443 - 9.40456i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(1.23607 + 3.80423i) q^{82} +(1.85410 + 5.70634i) q^{83} +(1.61803 + 1.17557i) q^{84} +(-12.9443 + 9.40456i) q^{85} +(-7.41641 + 22.8254i) q^{86} -6.00000 q^{87} +12.0000 q^{89} +(-2.47214 + 7.60845i) q^{90} +(1.61803 - 1.17557i) q^{91} +(-3.23607 - 2.35114i) q^{92} +(1.54508 + 4.75528i) q^{93} +(-1.23607 - 3.80423i) q^{94} +(9.70820 + 7.05342i) q^{95} +(6.47214 - 4.70228i) q^{96} +(1.54508 - 4.75528i) q^{97} +12.0000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} - q^{7} - q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 - q^7 - q^9	$ 4 q + 2 q^{2} + q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} - q^{7} - q^{9} - 32 q^{10} - 8 q^{12} + 2 q^{13} + 2 q^{14} + 4 q^{15} + 4 q^{16} - 4 q^{17} + 2 q^{18} + 3 q^{19} - 8 q^{20} - 4 q^{21} + 8 q^{23} - 11 q^{25} - 4 q^{26} + q^{27} - 2 q^{28} - 6 q^{29} - 8 q^{30} + 5 q^{31} + 32 q^{32} - 32 q^{34} - 4 q^{35} - 2 q^{36} - 3 q^{37} - 6 q^{38} - 2 q^{39} + 2 q^{41} - 2 q^{42} + 48 q^{43} + 16 q^{45} + 4 q^{46} - 2 q^{47} - 4 q^{48} + 6 q^{49} + 22 q^{50} + 4 q^{51} + 4 q^{52} - 6 q^{53} + 8 q^{54} - 3 q^{57} + 12 q^{58} + 10 q^{59} + 8 q^{60} - 3 q^{61} - 10 q^{62} - q^{63} + 8 q^{64} - 32 q^{65} - 4 q^{67} - 8 q^{68} + 2 q^{69} + 8 q^{70} + 11 q^{73} + 6 q^{74} + 11 q^{75} - 24 q^{76} - 16 q^{78} - 11 q^{79} + 16 q^{80} - q^{81} - 4 q^{82} - 6 q^{83} + 2 q^{84} - 16 q^{85} + 24 q^{86} - 24 q^{87} + 48 q^{89} + 8 q^{90} + 2 q^{91} - 4 q^{92} - 5 q^{93} + 4 q^{94} + 12 q^{95} + 8 q^{96} - 5 q^{97} + 48 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 - q^7 - q^9 - 32 * q^10 - 8 * q^12 + 2 * q^13 + 2 * q^14 + 4 * q^15 + 4 * q^16 - 4 * q^17 + 2 * q^18 + 3 * q^19 - 8 * q^20 - 4 * q^21 + 8 * q^23 - 11 * q^25 - 4 * q^26 + q^27 - 2 * q^28 - 6 * q^29 - 8 * q^30 + 5 * q^31 + 32 * q^32 - 32 * q^34 - 4 * q^35 - 2 * q^36 - 3 * q^37 - 6 * q^38 - 2 * q^39 + 2 * q^41 - 2 * q^42 + 48 * q^43 + 16 * q^45 + 4 * q^46 - 2 * q^47 - 4 * q^48 + 6 * q^49 + 22 * q^50 + 4 * q^51 + 4 * q^52 - 6 * q^53 + 8 * q^54 - 3 * q^57 + 12 * q^58 + 10 * q^59 + 8 * q^60 - 3 * q^61 - 10 * q^62 - q^63 + 8 * q^64 - 32 * q^65 - 4 * q^67 - 8 * q^68 + 2 * q^69 + 8 * q^70 + 11 * q^73 + 6 * q^74 + 11 * q^75 - 24 * q^76 - 16 * q^78 - 11 * q^79 + 16 * q^80 - q^81 - 4 * q^82 - 6 * q^83 + 2 * q^84 - 16 * q^85 + 24 * q^86 - 24 * q^87 + 48 * q^89 + 8 * q^90 + 2 * q^91 - 4 * q^92 - 5 * q^93 + 4 * q^94 + 12 * q^95 + 8 * q^96 - 5 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.618034	+	1.90211i	−0.437016	+	1.34500i	0.453990	+	0.891007i	$0.350000\pi$
$2$	−0.618034	+	1.90211i	−0.437016	+	1.34500i	−0.891007	+	0.453990i	$0.850000\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	−1.61803	−	1.17557i	−0.809017	−	0.587785i
$5$	1.23607	+	3.80423i	0.552786	+	1.70130i	0.701719	+	0.712454i	$0.252416\pi$
$5$	1.23607	+	3.80423i	0.552786	+	1.70130i	−0.148932	+	0.988847i	$0.547584\pi$
$6$	0.618034	+	1.90211i	0.252311	+	0.776534i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i	0.424304	−	0.905520i	$-0.360519\pi$
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i	−0.730084	+	0.683358i	$0.760519\pi$
$8$		0			0
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−8.00000			−2.52982
$11$		0			0
$11$		0			0
$12$	−2.00000			−0.577350
$13$	−0.618034	+	1.90211i	−0.171412	+	0.527551i	−0.999451	−	0.0331183i	$-0.989456\pi$
$13$	−0.618034	+	1.90211i	−0.171412	+	0.527551i	0.828040	+	0.560670i	$0.189456\pi$
$14$	1.61803	−	1.17557i	0.432438	−	0.314184i
$15$	3.23607	+	2.35114i	0.835549	+	0.607062i
$16$	−1.23607	−	3.80423i	−0.309017	−	0.951057i
$17$	1.23607	+	3.80423i	0.299791	+	0.922660i	0.981570	+	0.191103i	$0.0612063\pi$
$17$	1.23607	+	3.80423i	0.299791	+	0.922660i	−0.681780	+	0.731558i	$0.738794\pi$
$18$	1.61803	+	1.17557i	0.381374	+	0.277085i
$19$	2.42705	−	1.76336i	0.556804	−	0.404542i	−0.273484	−	0.961877i	$-0.588176\pi$
$19$	2.42705	−	1.76336i	0.556804	−	0.404542i	0.830288	+	0.557335i	$0.188176\pi$
$20$	2.47214	−	7.60845i	0.552786	−	1.70130i
$21$	−1.00000			−0.218218
$22$		0			0
$23$	2.00000			0.417029			0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000			0.417029			0.208514	+	0.978019i	$0.433137\pi$
$24$		0			0
$25$	−8.89919	+	6.46564i	−1.77984	+	1.29313i
$26$	−3.23607	−	2.35114i	−0.634645	−	0.461097i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	0.618034	+	1.90211i	0.116797	+	0.359466i
$29$	−4.85410	−	3.52671i	−0.901384	−	0.654894i	0.0374370	−	0.999299i	$-0.488081\pi$
$29$	−4.85410	−	3.52671i	−0.901384	−	0.654894i	−0.938821	+	0.344405i	$0.888081\pi$
$30$	−6.47214	+	4.70228i	−1.18164	+	0.858515i
$31$	−1.54508	+	4.75528i	−0.277505	+	0.854074i	0.711040	+	0.703151i	$0.248224\pi$
$31$	−1.54508	+	4.75528i	−0.277505	+	0.854074i	−0.988546	+	0.150923i	$0.951776\pi$
$32$	8.00000			1.41421
$33$		0			0
$34$	−8.00000			−1.37199
$35$	1.23607	−	3.80423i	0.208934	−	0.643032i
$36$	−1.61803	+	1.17557i	−0.269672	+	0.195928i
$37$	−2.42705	−	1.76336i	−0.399005	−	0.289894i	0.370131	−	0.928980i	$-0.379313\pi$
$37$	−2.42705	−	1.76336i	−0.399005	−	0.289894i	−0.769135	+	0.639086i	$0.779313\pi$
$38$	1.85410	+	5.70634i	0.300775	+	0.925690i
$39$	0.618034	+	1.90211i	0.0989646	+	0.304582i
$40$		0			0
$41$	1.61803	−	1.17557i	0.252694	−	0.183593i	−0.454226	−	0.890887i	$-0.650084\pi$
$41$	1.61803	−	1.17557i	0.252694	−	0.183593i	0.706920	+	0.707293i	$0.250084\pi$
$42$	0.618034	−	1.90211i	0.0953647	−	0.293502i
$43$	12.0000			1.82998			0.914991	−	0.403473i	$-0.132197\pi$
$43$	12.0000			1.82998			0.914991	+	0.403473i	$0.132197\pi$
$44$		0			0
$45$	4.00000			0.596285
$46$	−1.23607	+	3.80423i	−0.182248	+	0.560903i
$47$	−1.61803	+	1.17557i	−0.236015	+	0.171475i	−0.699506	−	0.714627i	$-0.746597\pi$
$47$	−1.61803	+	1.17557i	−0.236015	+	0.171475i	0.463491	+	0.886101i	$0.346597\pi$
$48$	−3.23607	−	2.35114i	−0.467086	−	0.339358i
$49$	−1.85410	−	5.70634i	−0.264872	−	0.815191i
$50$	−6.79837	−	20.9232i	−0.961435	−	2.95899i
$51$	3.23607	+	2.35114i	0.453140	+	0.329226i
$52$	3.23607	−	2.35114i	0.448762	−	0.326045i
$53$	1.85410	−	5.70634i	0.254680	−	0.783826i	−0.739212	−	0.673473i	$-0.764802\pi$
$53$	1.85410	−	5.70634i	0.254680	−	0.783826i	0.993892	−	0.110353i	$-0.0351982\pi$
$54$	2.00000			0.272166
$55$		0			0
$56$		0			0
$57$	0.927051	−	2.85317i	0.122791	−	0.377912i
$58$	9.70820	−	7.05342i	1.27475	−	0.926160i
$59$	8.09017	+	5.87785i	1.05325	+	0.765231i	0.972828	−	0.231530i	$-0.0743730\pi$
$59$	8.09017	+	5.87785i	1.05325	+	0.765231i	0.0804226	+	0.996761i	$0.474373\pi$
$60$	−2.47214	−	7.60845i	−0.319151	−	0.982247i
$61$	0.927051	+	2.85317i	0.118697	+	0.365311i	0.992700	−	0.120609i	$-0.0384847\pi$
$61$	0.927051	+	2.85317i	0.118697	+	0.365311i	−0.874003	+	0.485920i	$0.838485\pi$
$62$	−8.09017	−	5.87785i	−1.02745	−	0.746488i
$63$	−0.809017	+	0.587785i	−0.101927	+	0.0740540i
$64$	−2.47214	+	7.60845i	−0.309017	+	0.951057i
$65$	−8.00000			−0.992278
$66$		0			0
$67$	−1.00000			−0.122169			−0.0610847	−	0.998133i	$-0.519456\pi$
$67$	−1.00000			−0.122169			−0.0610847	+	0.998133i	$0.519456\pi$
$68$	2.47214	−	7.60845i	0.299791	−	0.922660i
$69$	1.61803	−	1.17557i	0.194788	−	0.141522i
$70$	6.47214	+	4.70228i	0.773568	+	0.562030i
$71$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$71$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$72$		0			0
$73$	8.89919	+	6.46564i	1.04157	+	0.756746i	0.970592	−	0.240732i	$-0.0773875\pi$
$73$	8.89919	+	6.46564i	1.04157	+	0.756746i	0.0709795	+	0.997478i	$0.477388\pi$
$74$	4.85410	−	3.52671i	0.564278	−	0.409972i
$75$	−3.39919	+	10.4616i	−0.392504	+	1.20800i
$76$	−6.00000			−0.688247
$77$		0			0
$78$	−4.00000			−0.452911
$79$	3.39919	−	10.4616i	0.382438	−	1.17702i	−0.555883	−	0.831260i	$-0.687620\pi$
$79$	3.39919	−	10.4616i	0.382438	−	1.17702i	0.938322	−	0.345764i	$-0.112380\pi$
$80$	12.9443	−	9.40456i	1.44721	−	1.05146i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	1.23607	+	3.80423i	0.136501	+	0.420106i
$83$	1.85410	+	5.70634i	0.203514	+	0.626352i	0.999771	+	0.0213936i	$0.00681031\pi$
$83$	1.85410	+	5.70634i	0.203514	+	0.626352i	−0.796257	+	0.604959i	$0.793190\pi$
$84$	1.61803	+	1.17557i	0.176542	+	0.128265i
$85$	−12.9443	+	9.40456i	−1.40400	+	1.02007i
$86$	−7.41641	+	22.8254i	−0.799732	+	2.46132i
$87$	−6.00000			−0.643268
$88$		0			0
$89$	12.0000			1.27200			0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000			1.27200			0.635999	+	0.771690i	$0.280588\pi$
$90$	−2.47214	+	7.60845i	−0.260586	+	0.802001i
$91$	1.61803	−	1.17557i	0.169616	−	0.123233i
$92$	−3.23607	−	2.35114i	−0.337383	−	0.245123i
$93$	1.54508	+	4.75528i	0.160218	+	0.493100i
$94$	−1.23607	−	3.80423i	−0.127491	−	0.392376i
$95$	9.70820	+	7.05342i	0.996041	+	0.723666i
$96$	6.47214	−	4.70228i	0.660560	−	0.479925i
$97$	1.54508	−	4.75528i	0.156880	−	0.482826i	−0.841467	−	0.540309i	$-0.818307\pi$
$97$	1.54508	−	4.75528i	0.156880	−	0.482826i	0.998346	+	0.0574829i	$0.0183075\pi$
$98$	12.0000			1.21218
$99$		0			0
$100$	22.0000			2.20000
$101$	−3.09017	+	9.51057i	−0.307483	+	0.946337i	0.671255	+	0.741226i	$0.265755\pi$
$101$	−3.09017	+	9.51057i	−0.307483	+	0.946337i	−0.978739	+	0.205110i	$0.934245\pi$
$102$	−6.47214	+	4.70228i	−0.640837	+	0.465595i
$103$	5.66312	+	4.11450i	0.558004	+	0.405413i	0.830728	−	0.556679i	$-0.187925\pi$
$103$	5.66312	+	4.11450i	0.558004	+	0.405413i	−0.272724	+	0.962092i	$0.587925\pi$
$104$		0			0
$105$	−1.23607	−	3.80423i	−0.120628	−	0.371254i
$106$	9.70820	+	7.05342i	0.942944	+	0.685089i
$107$	14.5623	−	10.5801i	1.40779	−	1.02282i	0.414152	−	0.910208i	$-0.364078\pi$
$107$	14.5623	−	10.5801i	1.40779	−	1.02282i	0.993639	−	0.112613i	$-0.0359219\pi$
$108$	−0.618034	+	1.90211i	−0.0594703	+	0.183031i
$109$	1.00000			0.0957826			0.0478913	−	0.998853i	$-0.484750\pi$
$109$	1.00000			0.0957826			0.0478913	+	0.998853i	$0.484750\pi$
$110$		0			0
$111$	−3.00000			−0.284747
$112$	−1.23607	+	3.80423i	−0.116797	+	0.359466i
$113$	−4.85410	+	3.52671i	−0.456636	+	0.331765i	−0.792210	−	0.610249i	$-0.791070\pi$
$113$	−4.85410	+	3.52671i	−0.456636	+	0.331765i	0.335575	+	0.942014i	$0.391070\pi$
$114$	4.85410	+	3.52671i	0.454628	+	0.330307i
$115$	2.47214	+	7.60845i	0.230528	+	0.709492i
$116$	3.70820	+	11.4127i	0.344298	+	1.05964i
$117$	1.61803	+	1.17557i	0.149587	+	0.108682i
$118$	−16.1803	+	11.7557i	−1.48952	+	1.08220i
$119$	1.23607	−	3.80423i	0.113310	−	0.348733i
$120$		0			0
$121$		0			0
$122$	−6.00000			−0.543214
$123$	0.618034	−	1.90211i	0.0557262	−	0.171508i
$124$	8.09017	−	5.87785i	0.726519	−	0.527847i
$125$	−19.4164	−	14.1068i	−1.73666	−	1.26175i
$126$	−0.618034	−	1.90211i	−0.0550588	−	0.169454i
$127$	−4.01722	−	12.3637i	−0.356471	−	1.09710i	−0.955152	−	0.296117i	$-0.904308\pi$
$127$	−4.01722	−	12.3637i	−0.356471	−	1.09710i	0.598681	−	0.800987i	$-0.295692\pi$
$128$		0			0
$129$	9.70820	−	7.05342i	0.854760	−	0.621019i
$130$	4.94427	−	15.2169i	0.433641	−	1.33461i
$131$	−6.00000			−0.524222			−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000			−0.524222			−0.262111	+	0.965038i	$0.584419\pi$
$132$		0			0
$133$	−3.00000			−0.260133
$134$	0.618034	−	1.90211i	0.0533900	−	0.164318i
$135$	3.23607	−	2.35114i	0.278516	−	0.202354i
$136$		0			0
$137$	2.47214	+	7.60845i	0.211209	+	0.650034i	0.999401	+	0.0346048i	$0.0110173\pi$
$137$	2.47214	+	7.60845i	0.211209	+	0.650034i	−0.788192	+	0.615429i	$0.788983\pi$
$138$	1.23607	+	3.80423i	0.105221	+	0.323837i
$139$	−12.9443	−	9.40456i	−1.09792	−	0.797685i	−0.117200	−	0.993108i	$-0.537392\pi$
$139$	−12.9443	−	9.40456i	−1.09792	−	0.797685i	−0.980719	+	0.195424i	$0.937392\pi$
$140$	−6.47214	+	4.70228i	−0.546995	+	0.397415i
$141$	−0.618034	+	1.90211i	−0.0520479	+	0.160187i
$142$		0			0
$143$		0			0
$144$	−4.00000			−0.333333
$145$	7.41641	−	22.8254i	0.615899	−	1.89554i
$146$	−17.7984	+	12.9313i	−1.47300	+	1.07020i
$147$	−4.85410	−	3.52671i	−0.400360	−	0.290878i
$148$	1.85410	+	5.70634i	0.152406	+	0.469058i
$149$	−4.94427	−	15.2169i	−0.405051	−	1.24662i	−0.920853	−	0.389910i	$-0.872506\pi$
$149$	−4.94427	−	15.2169i	−0.405051	−	1.24662i	0.515802	−	0.856708i	$-0.327494\pi$
$150$	−17.7984	−	12.9313i	−1.45323	−	1.05583i
$151$	12.9443	−	9.40456i	1.05339	−	0.765333i	0.0805358	−	0.996752i	$-0.474337\pi$
$151$	12.9443	−	9.40456i	1.05339	−	0.765333i	0.972854	+	0.231419i	$0.0743369\pi$
$152$		0			0
$153$	4.00000			0.323381
$154$		0			0
$155$	−20.0000			−1.60644
$156$	1.23607	−	3.80423i	0.0989646	−	0.304582i
$157$	0.809017	−	0.587785i	0.0645666	−	0.0469104i	−0.555034	−	0.831828i	$-0.687295\pi$
$157$	0.809017	−	0.587785i	0.0645666	−	0.0469104i	0.619600	+	0.784917i	$0.287295\pi$
$158$	17.7984	+	12.9313i	1.41596	+	1.02876i
$159$	−1.85410	−	5.70634i	−0.147040	−	0.452542i
$160$	9.88854	+	30.4338i	0.781758	+	2.40600i
$161$	−1.61803	−	1.17557i	−0.127519	−	0.0926479i
$162$	1.61803	−	1.17557i	0.127125	−	0.0923615i
$163$	7.72542	−	23.7764i	0.605102	−	1.86231i	0.109014	−	0.994040i	$-0.465231\pi$
$163$	7.72542	−	23.7764i	0.605102	−	1.86231i	0.496088	−	0.868272i	$-0.334769\pi$
$164$	−4.00000			−0.312348
$165$		0			0
$166$	−12.0000			−0.931381
$167$	−5.56231	+	17.1190i	−0.430424	+	1.32471i	0.467280	+	0.884110i	$0.345234\pi$
$167$	−5.56231	+	17.1190i	−0.430424	+	1.32471i	−0.897704	+	0.440600i	$0.854766\pi$
$168$		0			0
$169$	7.28115	+	5.29007i	0.560089	+	0.406928i
$170$	−9.88854	−	30.4338i	−0.758417	−	2.33417i
$171$	−0.927051	−	2.85317i	−0.0708934	−	0.218187i
$172$	−19.4164	−	14.1068i	−1.48049	−	1.07564i
$173$	−19.4164	+	14.1068i	−1.47620	+	1.07252i	−0.497446	+	0.867495i	$0.665729\pi$
$173$	−19.4164	+	14.1068i	−1.47620	+	1.07252i	−0.978756	+	0.205029i	$0.934271\pi$
$174$	3.70820	−	11.4127i	0.281118	−	0.865193i
$175$	11.0000			0.831522
$176$		0			0
$177$	10.0000			0.751646
$178$	−7.41641	+	22.8254i	−0.555883	+	1.71083i
$179$	−4.85410	+	3.52671i	−0.362813	+	0.263599i	−0.754224	−	0.656617i	$-0.771987\pi$
$179$	−4.85410	+	3.52671i	−0.362813	+	0.263599i	0.391412	+	0.920216i	$0.371987\pi$
$180$	−6.47214	−	4.70228i	−0.482405	−	0.350487i
$181$	−7.10739	−	21.8743i	−0.528288	−	1.62590i	−0.757720	−	0.652579i	$-0.773687\pi$
$181$	−7.10739	−	21.8743i	−0.528288	−	1.62590i	0.229432	−	0.973325i	$-0.426313\pi$
$182$	1.23607	+	3.80423i	0.0916235	+	0.281988i
$183$	2.42705	+	1.76336i	0.179413	+	0.130351i
$184$		0			0
$185$	3.70820	−	11.4127i	0.272633	−	0.839077i
$186$	−10.0000			−0.733236
$187$		0			0
$188$	4.00000			0.291730
$189$	−0.309017	+	0.951057i	−0.0224777	+	0.0691792i
$190$	−19.4164	+	14.1068i	−1.40861	+	1.02342i
$191$	−6.47214	−	4.70228i	−0.468307	−	0.340245i	0.328474	−	0.944513i	$-0.393466\pi$
$191$	−6.47214	−	4.70228i	−0.468307	−	0.340245i	−0.796781	+	0.604268i	$0.793466\pi$
$192$	2.47214	+	7.60845i	0.178411	+	0.549093i
$193$	−1.54508	−	4.75528i	−0.111218	−	0.342293i	0.879922	−	0.475119i	$-0.157595\pi$
$193$	−1.54508	−	4.75528i	−0.111218	−	0.342293i	−0.991139	+	0.132826i	$0.957595\pi$
$194$	8.09017	+	5.87785i	0.580840	+	0.422005i
$195$	−6.47214	+	4.70228i	−0.463479	+	0.336737i
$196$	−3.70820	+	11.4127i	−0.264872	+	0.815191i
$197$	−8.00000			−0.569976			−0.284988	−	0.958531i	$-0.591990\pi$
$197$	−8.00000			−0.569976			−0.284988	+	0.958531i	$0.591990\pi$
$198$		0			0
$199$	−21.0000			−1.48865			−0.744325	−	0.667817i	$-0.767229\pi$
$199$	−21.0000			−1.48865			−0.744325	+	0.667817i	$0.767229\pi$
$200$		0			0
$201$	−0.809017	+	0.587785i	−0.0570637	+	0.0414592i
$202$	−16.1803	−	11.7557i	−1.13844	−	0.827129i
$203$	1.85410	+	5.70634i	0.130132	+	0.400506i
$204$	−2.47214	−	7.60845i	−0.173084	−	0.532698i
$205$	6.47214	+	4.70228i	0.452034	+	0.328422i
$206$	−11.3262	+	8.22899i	−0.789136	+	0.573341i
$207$	0.618034	−	1.90211i	0.0429563	−	0.132206i
$208$	8.00000			0.554700
$209$		0			0
$210$	8.00000			0.552052
$211$	−6.48936	+	19.9722i	−0.446746	+	1.37494i	0.433812	+	0.901003i	$0.357168\pi$
$211$	−6.48936	+	19.9722i	−0.446746	+	1.37494i	−0.880558	+	0.473939i	$0.842832\pi$
$212$	−9.70820	+	7.05342i	−0.666762	+	0.484431i
$213$		0			0
$214$	11.1246	+	34.2380i	0.760463	+	2.34046i
$215$	14.8328	+	45.6507i	1.01159	+	3.11335i
$216$		0			0
$217$	4.04508	−	2.93893i	0.274598	−	0.199507i
$218$	−0.618034	+	1.90211i	−0.0418585	+	0.128827i
$219$	11.0000			0.743311
$220$		0			0
$221$	−8.00000			−0.538138
$222$	1.85410	−	5.70634i	0.124439	−	0.382984i
$223$	13.7533	−	9.99235i	0.920988	−	0.669137i	−0.0227815	−	0.999740i	$-0.507252\pi$
$223$	13.7533	−	9.99235i	0.920988	−	0.669137i	0.943770	+	0.330603i	$0.107252\pi$
$224$	−6.47214	−	4.70228i	−0.432438	−	0.314184i
$225$	3.39919	+	10.4616i	0.226612	+	0.697441i
$226$	−3.70820	−	11.4127i	−0.246666	−	0.759160i
$227$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$227$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$228$	−4.85410	+	3.52671i	−0.321471	+	0.233562i
$229$	−5.56231	+	17.1190i	−0.367568	+	1.13126i	0.580790	+	0.814053i	$0.302744\pi$
$229$	−5.56231	+	17.1190i	−0.367568	+	1.13126i	−0.948358	+	0.317203i	$0.897256\pi$
$230$	−16.0000			−1.05501
$231$		0			0
$232$		0			0
$233$	5.56231	−	17.1190i	0.364399	−	1.12150i	−0.585958	−	0.810341i	$-0.699282\pi$
$233$	5.56231	−	17.1190i	0.364399	−	1.12150i	0.950357	−	0.311163i	$-0.100718\pi$
$234$	−3.23607	+	2.35114i	−0.211548	+	0.153699i
$235$	−6.47214	−	4.70228i	−0.422196	−	0.306743i
$236$	−6.18034	−	19.0211i	−0.402306	−	1.23817i
$237$	−3.39919	−	10.4616i	−0.220801	−	0.679555i
$238$	6.47214	+	4.70228i	0.419526	+	0.304804i
$239$	−4.85410	+	3.52671i	−0.313986	+	0.228124i	−0.733605	−	0.679576i	$-0.762164\pi$
$239$	−4.85410	+	3.52671i	−0.313986	+	0.228124i	0.419619	+	0.907700i	$0.362164\pi$
$240$	4.94427	−	15.2169i	0.319151	−	0.982247i
$241$	−14.0000			−0.901819			−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000			−0.901819			−0.450910	+	0.892570i	$0.648900\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$	1.85410	−	5.70634i	0.118697	−	0.365311i
$245$	19.4164	−	14.1068i	1.24047	−	0.901253i
$246$	3.23607	+	2.35114i	0.206324	+	0.149903i
$247$	1.85410	+	5.70634i	0.117974	+	0.363086i
$248$		0			0
$249$	4.85410	+	3.52671i	0.307616	+	0.223496i
$250$	38.8328	−	28.2137i	2.45600	−	1.78439i
$251$	−0.618034	+	1.90211i	−0.0390100	+	0.120060i	−0.968665	−	0.248371i	$-0.920105\pi$
$251$	−0.618034	+	1.90211i	−0.0390100	+	0.120060i	0.929655	+	0.368431i	$0.120105\pi$
$252$	2.00000			0.125988
$253$		0			0
$254$	26.0000			1.63139
$255$	−4.94427	+	15.2169i	−0.309622	+	0.952920i
$256$	−12.9443	+	9.40456i	−0.809017	+	0.587785i
$257$	11.3262	+	8.22899i	0.706511	+	0.513311i	0.882046	−	0.471163i	$-0.156166\pi$
$257$	11.3262	+	8.22899i	0.706511	+	0.513311i	−0.175535	+	0.984473i	$0.556166\pi$
$258$	7.41641	+	22.8254i	0.461725	+	1.42104i
$259$	0.927051	+	2.85317i	0.0576041	+	0.177287i
$260$	12.9443	+	9.40456i	0.802770	+	0.583246i
$261$	−4.85410	+	3.52671i	−0.300461	+	0.218298i
$262$	3.70820	−	11.4127i	0.229094	−	0.705078i
$263$	−10.0000			−0.616626			−0.308313	−	0.951285i	$-0.599764\pi$
$263$	−10.0000			−0.616626			−0.308313	+	0.951285i	$0.599764\pi$
$264$		0			0
$265$	24.0000			1.47431
$266$	1.85410	−	5.70634i	0.113682	−	0.349878i
$267$	9.70820	−	7.05342i	0.594132	−	0.431662i
$268$	1.61803	+	1.17557i	0.0988372	+	0.0718094i
$269$	−4.32624	−	13.3148i	−0.263775	−	0.811817i	−0.991973	−	0.126450i	$-0.959642\pi$
$269$	−4.32624	−	13.3148i	−0.263775	−	0.811817i	0.728198	−	0.685367i	$-0.240358\pi$
$270$	2.47214	+	7.60845i	0.150449	+	0.463036i
$271$	−6.47214	−	4.70228i	−0.393154	−	0.285643i	0.373593	−	0.927593i	$-0.378126\pi$
$271$	−6.47214	−	4.70228i	−0.393154	−	0.285643i	−0.766747	+	0.641950i	$0.778126\pi$
$272$	12.9443	−	9.40456i	0.784862	−	0.570235i
$273$	0.618034	−	1.90211i	0.0374051	−	0.115121i
$274$	−16.0000			−0.966595
$275$		0			0
$276$	−4.00000			−0.240772
$277$	−3.39919	+	10.4616i	−0.204237	+	0.628578i	0.795506	+	0.605945i	$0.207205\pi$
$277$	−3.39919	+	10.4616i	−0.204237	+	0.628578i	−0.999744	+	0.0226329i	$0.992795\pi$
$278$	25.8885	−	18.8091i	1.55269	−	1.12810i
$279$	4.04508	+	2.93893i	0.242173	+	0.175949i
$280$		0			0
$281$	−3.70820	−	11.4127i	−0.221213	−	0.680823i	−0.998654	−	0.0518675i	$-0.983483\pi$
$281$	−3.70820	−	11.4127i	−0.221213	−	0.680823i	0.777441	−	0.628956i	$-0.216517\pi$
$282$	−3.23607	−	2.35114i	−0.192705	−	0.140008i
$283$	8.89919	−	6.46564i	0.529002	−	0.384342i	−0.290982	−	0.956728i	$-0.593982\pi$
$283$	8.89919	−	6.46564i	0.529002	−	0.384342i	0.819984	+	0.572386i	$0.193982\pi$
$284$		0			0
$285$	12.0000			0.710819
$286$		0			0
$287$	−2.00000			−0.118056
$288$	2.47214	−	7.60845i	0.145672	−	0.448332i
$289$	0.809017	−	0.587785i	0.0475892	−	0.0345756i
$290$	38.8328	+	28.2137i	2.28034	+	1.65677i
$291$	−1.54508	−	4.75528i	−0.0905745	−	0.278760i
$292$	−6.79837	−	20.9232i	−0.397845	−	1.22444i
$293$	−9.70820	−	7.05342i	−0.567159	−	0.412065i	0.266913	−	0.963721i	$-0.413996\pi$
$293$	−9.70820	−	7.05342i	−0.567159	−	0.412065i	−0.834072	+	0.551655i	$0.813996\pi$
$294$	9.70820	−	7.05342i	0.566194	−	0.411364i
$295$	−12.3607	+	38.0423i	−0.719667	+	2.21491i
$296$		0			0
$297$		0			0
$298$	32.0000			1.85371
$299$	−1.23607	+	3.80423i	−0.0714837	+	0.220004i
$300$	17.7984	−	12.9313i	1.02759	−	0.746588i
$301$	−9.70820	−	7.05342i	−0.559572	−	0.406553i
$302$	9.88854	+	30.4338i	0.569022	+	1.75127i
$303$	3.09017	+	9.51057i	0.177526	+	0.546368i
$304$	−9.70820	−	7.05342i	−0.556804	−	0.404542i
$305$	−9.70820	+	7.05342i	−0.555890	+	0.403878i
$306$	−2.47214	+	7.60845i	−0.141323	+	0.434946i
$307$	−19.0000			−1.08439			−0.542194	−	0.840254i	$-0.682406\pi$
$307$	−19.0000			−1.08439			−0.542194	+	0.840254i	$0.682406\pi$
$308$		0			0
$309$	7.00000			0.398216
$310$	12.3607	−	38.0423i	0.702039	−	2.16066i
$311$	−19.4164	+	14.1068i	−1.10100	+	0.799926i	−0.981223	−	0.192875i	$-0.938219\pi$
$311$	−19.4164	+	14.1068i	−1.10100	+	0.799926i	−0.119780	+	0.992800i	$0.538219\pi$
$312$		0			0
$313$	−3.09017	−	9.51057i	−0.174667	−	0.537569i	0.824951	−	0.565204i	$-0.191202\pi$
$313$	−3.09017	−	9.51057i	−0.174667	−	0.537569i	−0.999618	+	0.0276348i	$0.991202\pi$
$314$	0.618034	+	1.90211i	0.0348777	+	0.107342i
$315$	−3.23607	−	2.35114i	−0.182332	−	0.132472i
$316$	−17.7984	+	12.9313i	−1.00124	+	0.727441i
$317$	−6.18034	+	19.0211i	−0.347122	+	1.06833i	0.613315	+	0.789838i	$0.289836\pi$
$317$	−6.18034	+	19.0211i	−0.347122	+	1.06833i	−0.960438	+	0.278495i	$0.910164\pi$
$318$	12.0000			0.672927
$319$		0			0
$320$	−32.0000			−1.78885
$321$	5.56231	−	17.1190i	0.310458	−	0.955490i
$322$	3.23607	−	2.35114i	0.180339	−	0.131024i
$323$	9.70820	+	7.05342i	0.540179	+	0.392463i
$324$	0.618034	+	1.90211i	0.0343352	+	0.105673i
$325$	−6.79837	−	20.9232i	−0.377106	−	1.16061i
$326$	40.4508	+	29.3893i	2.24037	+	1.62772i
$327$	0.809017	−	0.587785i	0.0447387	−	0.0325046i
$328$		0			0
$329$	2.00000			0.110264
$330$		0			0
$331$	−11.0000			−0.604615			−0.302307	−	0.953211i	$-0.597757\pi$
$331$	−11.0000			−0.604615			−0.302307	+	0.953211i	$0.597757\pi$
$332$	3.70820	−	11.4127i	0.203514	−	0.626352i
$333$	−2.42705	+	1.76336i	−0.133002	+	0.0966313i
$334$	−29.1246	−	21.1603i	−1.59363	−	1.15784i
$335$	−1.23607	−	3.80423i	−0.0675336	−	0.207847i
$336$	1.23607	+	3.80423i	0.0674330	+	0.207538i
$337$	−4.04508	−	2.93893i	−0.220350	−	0.160094i	0.472134	−	0.881527i	$-0.343484\pi$
$337$	−4.04508	−	2.93893i	−0.220350	−	0.160094i	−0.692484	+	0.721433i	$0.743484\pi$
$338$	−14.5623	+	10.5801i	−0.792085	+	0.575483i
$339$	−1.85410	+	5.70634i	−0.100701	+	0.309926i
$340$	32.0000			1.73544
$341$		0			0
$342$	6.00000			0.324443
$343$	−4.01722	+	12.3637i	−0.216910	+	0.667579i
$344$		0			0
$345$	6.47214	+	4.70228i	0.348448	+	0.253162i
$346$	−14.8328	−	45.6507i	−0.797417	−	2.45420i
$347$	−0.618034	−	1.90211i	−0.0331778	−	0.102111i	0.933096	−	0.359627i	$-0.117096\pi$
$347$	−0.618034	−	1.90211i	−0.0331778	−	0.102111i	−0.966274	+	0.257516i	$0.917096\pi$
$348$	9.70820	+	7.05342i	0.520414	+	0.378103i
$349$	−12.1353	+	8.81678i	−0.649585	+	0.471951i	−0.863130	−	0.504982i	$-0.831499\pi$
$349$	−12.1353	+	8.81678i	−0.649585	+	0.471951i	0.213545	+	0.976933i	$0.431499\pi$
$350$	−6.79837	+	20.9232i	−0.363388	+	1.11839i
$351$	2.00000			0.106752
$352$		0			0
$353$	−12.0000			−0.638696			−0.319348	−	0.947638i	$-0.603464\pi$
$353$	−12.0000			−0.638696			−0.319348	+	0.947638i	$0.603464\pi$
$354$	−6.18034	+	19.0211i	−0.328481	+	1.01096i
$355$		0			0
$356$	−19.4164	−	14.1068i	−1.02907	−	0.747661i
$357$	−1.23607	−	3.80423i	−0.0654197	−	0.201341i
$358$	−3.70820	−	11.4127i	−0.195985	−	0.603179i
$359$	−3.23607	−	2.35114i	−0.170793	−	0.124088i	0.499105	−	0.866542i	$-0.333662\pi$
$359$	−3.23607	−	2.35114i	−0.170793	−	0.124088i	−0.669898	+	0.742453i	$0.733662\pi$
$360$		0			0
$361$	−3.09017	+	9.51057i	−0.162641	+	0.500556i
$362$	46.0000			2.41771
$363$		0			0
$364$	−4.00000			−0.209657
$365$	−13.5967	+	41.8465i	−0.711686	+	2.19035i
$366$	−4.85410	+	3.52671i	−0.253728	+	0.184344i
$367$	6.47214	+	4.70228i	0.337843	+	0.245457i	0.743751	−	0.668457i	$-0.233045\pi$
$367$	6.47214	+	4.70228i	0.337843	+	0.245457i	−0.405908	+	0.913914i	$0.633045\pi$
$368$	−2.47214	−	7.60845i	−0.128869	−	0.396618i
$369$	−0.618034	−	1.90211i	−0.0321736	−	0.0990200i
$370$	19.4164	+	14.1068i	1.00941	+	0.733380i
$371$	−4.85410	+	3.52671i	−0.252012	+	0.183098i
$372$	3.09017	−	9.51057i	0.160218	−	0.493100i
$373$	7.00000			0.362446			0.181223	−	0.983442i	$-0.441994\pi$
$373$	7.00000			0.362446			0.181223	+	0.983442i	$0.441994\pi$
$374$		0			0
$375$	−24.0000			−1.23935
$376$		0			0
$377$	9.70820	−	7.05342i	0.499998	−	0.363270i
$378$	−1.61803	−	1.17557i	−0.0832227	−	0.0604648i
$379$	4.94427	+	15.2169i	0.253970	+	0.781640i	0.994031	+	0.109100i	$0.0347968\pi$
$379$	4.94427	+	15.2169i	0.253970	+	0.781640i	−0.740061	+	0.672540i	$0.765203\pi$
$380$	−7.41641	−	22.8254i	−0.380454	−	1.17092i
$381$	−10.5172	−	7.64121i	−0.538814	−	0.391471i
$382$	12.9443	−	9.40456i	0.662287	−	0.481179i
$383$	8.03444	−	24.7275i	0.410541	−	1.26351i	−0.505638	−	0.862746i	$-0.668743\pi$
$383$	8.03444	−	24.7275i	0.410541	−	1.26351i	0.916179	−	0.400769i	$-0.131257\pi$
$384$		0			0
$385$		0			0
$386$	10.0000			0.508987
$387$	3.70820	−	11.4127i	0.188499	−	0.580139i
$388$	−8.09017	+	5.87785i	−0.410716	+	0.298403i
$389$	−14.5623	−	10.5801i	−0.738338	−	0.536434i	0.153852	−	0.988094i	$-0.450832\pi$
$389$	−14.5623	−	10.5801i	−0.738338	−	0.536434i	−0.892190	+	0.451660i	$0.850832\pi$
$390$	−4.94427	−	15.2169i	−0.250363	−	0.770538i
$391$	2.47214	+	7.60845i	0.125021	+	0.384776i
$392$		0			0
$393$	−4.85410	+	3.52671i	−0.244857	+	0.177899i
$394$	4.94427	−	15.2169i	0.249089	−	0.766617i
$395$	44.0000			2.21388
$396$		0			0
$397$	31.0000			1.55585			0.777923	−	0.628360i	$-0.216273\pi$
$397$	31.0000			1.55585			0.777923	+	0.628360i	$0.216273\pi$
$398$	12.9787	−	39.9444i	0.650564	−	2.00223i
$399$	−2.42705	+	1.76336i	−0.121505	+	0.0882782i
$400$	35.5967	+	25.8626i	1.77984	+	1.29313i
$401$	−8.65248	−	26.6296i	−0.432084	−	1.32982i	−0.896045	−	0.443962i	$-0.853572\pi$
$401$	−8.65248	−	26.6296i	−0.432084	−	1.32982i	0.463961	−	0.885855i	$-0.346428\pi$
$402$	−0.618034	−	1.90211i	−0.0308247	−	0.0948688i
$403$	−8.09017	−	5.87785i	−0.403000	−	0.292797i
$404$	16.1803	−	11.7557i	0.805002	−	0.584868i
$405$	1.23607	−	3.80423i	0.0614207	−	0.189034i
$406$	−12.0000			−0.595550
$407$		0			0
$408$		0			0
$409$	6.48936	−	19.9722i	0.320878	−	0.987561i	−0.652389	−	0.757884i	$-0.726233\pi$
$409$	6.48936	−	19.9722i	0.320878	−	0.987561i	0.973267	−	0.229677i	$-0.0737669\pi$
$410$	−12.9443	+	9.40456i	−0.639272	+	0.464458i
$411$	6.47214	+	4.70228i	0.319247	+	0.231946i
$412$	−4.32624	−	13.3148i	−0.213138	−	0.655973i
$413$	−3.09017	−	9.51057i	−0.152057	−	0.467984i
$414$	3.23607	+	2.35114i	0.159044	+	0.115552i
$415$	−19.4164	+	14.1068i	−0.953114	+	0.692478i
$416$	−4.94427	+	15.2169i	−0.242413	+	0.746070i
$417$	−16.0000			−0.783523
$418$		0			0
$419$	26.0000			1.27018			0.635092	−	0.772437i	$-0.280962\pi$
$419$	26.0000			1.27018			0.635092	+	0.772437i	$0.280962\pi$
$420$	−2.47214	+	7.60845i	−0.120628	+	0.371254i
$421$	1.61803	−	1.17557i	0.0788582	−	0.0572938i	−0.547658	−	0.836702i	$-0.684480\pi$
$421$	1.61803	−	1.17557i	0.0788582	−	0.0572938i	0.626516	+	0.779409i	$0.284480\pi$
$422$	−33.9787	−	24.6870i	−1.65406	−	1.20174i
$423$	0.618034	+	1.90211i	0.0300498	+	0.0924839i
$424$		0			0
$425$	−35.5967	−	25.8626i	−1.72670	−	1.25452i
$426$		0			0
$427$	0.927051	−	2.85317i	0.0448631	−	0.138075i
$428$	−36.0000			−1.74013
$429$		0			0
$430$	−96.0000			−4.62953
$431$	5.56231	−	17.1190i	0.267927	−	0.824594i	−0.723078	−	0.690767i	$-0.757273\pi$
$431$	5.56231	−	17.1190i	0.267927	−	0.824594i	0.991005	−	0.133827i	$-0.0427268\pi$
$432$	−3.23607	+	2.35114i	−0.155695	+	0.113119i
$433$	13.7533	+	9.99235i	0.660941	+	0.480202i	0.866981	−	0.498342i	$-0.166058\pi$
$433$	13.7533	+	9.99235i	0.660941	+	0.480202i	−0.206040	+	0.978544i	$0.566058\pi$
$434$	3.09017	+	9.51057i	0.148333	+	0.456522i
$435$	−7.41641	−	22.8254i	−0.355590	−	1.09439i
$436$	−1.61803	−	1.17557i	−0.0774898	−	0.0562996i
$437$	4.85410	−	3.52671i	0.232203	−	0.168705i
$438$	−6.79837	+	20.9232i	−0.324839	+	0.999751i
$439$	37.0000			1.76591			0.882957	−	0.469454i	$-0.155549\pi$
$439$	37.0000			1.76591			0.882957	+	0.469454i	$0.155549\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$	4.94427	−	15.2169i	0.235175	−	0.723794i
$443$	−3.23607	+	2.35114i	−0.153750	+	0.111706i	−0.662001	−	0.749503i	$-0.730292\pi$
$443$	−3.23607	+	2.35114i	−0.153750	+	0.111706i	0.508250	+	0.861209i	$0.330292\pi$
$444$	4.85410	+	3.52671i	0.230365	+	0.167370i
$445$	14.8328	+	45.6507i	0.703143	+	2.16405i
$446$	10.5066	+	32.3359i	0.497501	+	1.53115i
$447$	−12.9443	−	9.40456i	−0.612243	−	0.444821i
$448$	6.47214	−	4.70228i	0.305780	−	0.222162i
$449$	6.18034	−	19.0211i	0.291668	−	0.897663i	−0.692652	−	0.721272i	$-0.743558\pi$
$449$	6.18034	−	19.0211i	0.291668	−	0.897663i	0.984320	−	0.176391i	$-0.0564422\pi$
$450$	−22.0000			−1.03709
$451$		0			0
$452$	12.0000			0.564433
$453$	4.94427	−	15.2169i	0.232302	−	0.714953i
$454$		0			0
$455$	6.47214	+	4.70228i	0.303418	+	0.220446i
$456$		0			0
$457$	5.56231	+	17.1190i	0.260194	+	0.800794i	0.992762	+	0.120100i	$0.0383216\pi$
$457$	5.56231	+	17.1190i	0.260194	+	0.800794i	−0.732568	+	0.680694i	$0.761678\pi$
$458$	−29.1246	−	21.1603i	−1.36090	−	0.988754i
$459$	3.23607	−	2.35114i	0.151047	−	0.109742i
$460$	4.94427	−	15.2169i	0.230528	−	0.709492i
$461$	−6.00000			−0.279448			−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000			−0.279448			−0.139724	+	0.990190i	$0.544622\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	−7.41641	+	22.8254i	−0.344298	+	1.05964i
$465$	−16.1803	+	11.7557i	−0.750345	+	0.545158i
$466$	29.1246	+	21.1603i	1.34917	+	0.980231i
$467$	7.41641	+	22.8254i	0.343190	+	1.05623i	0.962545	+	0.271120i	$0.0873942\pi$
$467$	7.41641	+	22.8254i	0.343190	+	1.05623i	−0.619355	+	0.785111i	$0.712606\pi$
$468$	−1.23607	−	3.80423i	−0.0571373	−	0.175850i
$469$	0.809017	+	0.587785i	0.0373569	+	0.0271414i
$470$	12.9443	−	9.40456i	0.597075	−	0.433800i
$471$	0.309017	−	0.951057i	0.0142388	−	0.0438224i
$472$		0			0
$473$		0			0
$474$	22.0000			1.01049
$475$	−10.1976	+	31.3849i	−0.467896	+	1.44004i
$476$	−6.47214	+	4.70228i	−0.296650	+	0.215529i
$477$	−4.85410	−	3.52671i	−0.222254	−	0.161477i
$478$	−3.70820	−	11.4127i	−0.169609	−	0.522004i
$479$	−6.79837	−	20.9232i	−0.310626	−	0.956007i	−0.977518	−	0.210853i	$-0.932376\pi$
$479$	−6.79837	−	20.9232i	−0.310626	−	0.956007i	0.666892	−	0.745154i	$-0.267624\pi$
$480$	25.8885	+	18.8091i	1.18164	+	0.858515i
$481$	4.85410	−	3.52671i	0.221328	−	0.160804i
$482$	8.65248	−	26.6296i	0.394109	−	1.21294i
$483$	−2.00000			−0.0910032
$484$		0			0
$485$	20.0000			0.908153
$486$	0.618034	−	1.90211i	0.0280346	−	0.0862816i
$487$	32.3607	−	23.5114i	1.46640	−	1.06540i	0.484766	−	0.874644i	$-0.338905\pi$
$487$	32.3607	−	23.5114i	1.46640	−	1.06540i	0.981637	−	0.190760i	$-0.0610951\pi$
$488$		0			0
$489$	−7.72542	−	23.7764i	−0.349356	−	1.07521i
$490$	14.8328	+	45.6507i	0.670078	+	2.06229i
$491$	11.3262	+	8.22899i	0.511146	+	0.371369i	0.813258	−	0.581903i	$-0.197692\pi$
$491$	11.3262	+	8.22899i	0.511146	+	0.371369i	−0.302112	+	0.953272i	$0.597692\pi$
$492$	−3.23607	+	2.35114i	−0.145893	+	0.105998i
$493$	7.41641	−	22.8254i	0.334018	−	1.02800i
$494$	−12.0000			−0.539906
$495$		0			0
$496$	20.0000			0.898027
$497$		0			0
$498$	−9.70820	+	7.05342i	−0.435035	+	0.316071i
$499$	−18.6074	−	13.5191i	−0.832981	−	0.605196i	0.0874200	−	0.996172i	$-0.472138\pi$
$499$	−18.6074	−	13.5191i	−0.832981	−	0.605196i	−0.920401	+	0.390975i	$0.872138\pi$
$500$	14.8328	+	45.6507i	0.663344	+	2.04156i
$501$	5.56231	+	17.1190i	0.248506	+	0.764821i
$502$	−3.23607	−	2.35114i	−0.144433	−	0.104937i
$503$	25.8885	−	18.8091i	1.15431	−	0.838658i	0.165265	−	0.986249i	$-0.447152\pi$
$503$	25.8885	−	18.8091i	1.15431	−	0.838658i	0.989048	+	0.147592i	$0.0471521\pi$
$504$		0			0
$505$	−40.0000			−1.77998
$506$		0			0
$507$	9.00000			0.399704
$508$	−8.03444	+	24.7275i	−0.356471	+	1.09710i
$509$	−4.85410	+	3.52671i	−0.215154	+	0.156319i	−0.690143	−	0.723673i	$-0.742452\pi$
$509$	−4.85410	+	3.52671i	−0.215154	+	0.156319i	0.474988	+	0.879992i	$0.342452\pi$
$510$	−25.8885	−	18.8091i	−1.14636	−	0.832882i
$511$	−3.39919	−	10.4616i	−0.150371	−	0.462795i
$512$	−9.88854	−	30.4338i	−0.437016	−	1.34500i
$513$	−2.42705	−	1.76336i	−0.107157	−	0.0778541i
$514$	−22.6525	+	16.4580i	−0.999158	+	0.725931i
$515$	−8.65248	+	26.6296i	−0.381274	+	1.17344i
$516$	−24.0000			−1.05654
$517$		0			0
$518$	−6.00000			−0.263625
$519$	−7.41641	+	22.8254i	−0.325544	+	1.00192i
$520$		0			0
$521$	4.85410	+	3.52671i	0.212662	+	0.154508i	0.689017	−	0.724745i	$-0.258042\pi$
$521$	4.85410	+	3.52671i	0.212662	+	0.154508i	−0.476355	+	0.879253i	$0.658042\pi$
$522$	−3.70820	−	11.4127i	−0.162304	−	0.499519i
$523$	8.96149	+	27.5806i	0.391859	+	1.20602i	0.931381	+	0.364046i	$0.118605\pi$
$523$	8.96149	+	27.5806i	0.391859	+	1.20602i	−0.539522	+	0.841971i	$0.681395\pi$
$524$	9.70820	+	7.05342i	0.424105	+	0.308130i
$525$	8.89919	−	6.46564i	0.388392	−	0.282184i
$526$	6.18034	−	19.0211i	0.269476	−	0.829361i
$527$	−20.0000			−0.871214
$528$		0			0
$529$	−19.0000			−0.826087
$530$	−14.8328	+	45.6507i	−0.644296	+	1.98294i
$531$	8.09017	−	5.87785i	0.351083	−	0.255077i
$532$	4.85410	+	3.52671i	0.210452	+	0.152902i
$533$	1.23607	+	3.80423i	0.0535400	+	0.164779i
$534$	7.41641	+	22.8254i	0.320939	+	0.987750i
$535$	58.2492	+	42.3205i	2.51833	+	1.82968i
$536$		0			0
$537$	−1.85410	+	5.70634i	−0.0800104	+	0.246247i
$538$	28.0000			1.20717
$539$		0			0
$540$	−8.00000			−0.344265
$541$	−0.618034	+	1.90211i	−0.0265714	+	0.0817782i	−0.963463	−	0.267842i	$-0.913689\pi$
$541$	−0.618034	+	1.90211i	−0.0265714	+	0.0817782i	0.936891	+	0.349620i	$0.113689\pi$
$542$	12.9443	−	9.40456i	0.556004	−	0.403961i
$543$	−18.6074	−	13.5191i	−0.798520	−	0.580158i
$544$	9.88854	+	30.4338i	0.423968	+	1.30484i
$545$	1.23607	+	3.80423i	0.0529473	+	0.162955i
$546$	3.23607	+	2.35114i	0.138491	+	0.100620i
$547$	−16.1803	+	11.7557i	−0.691821	+	0.502638i	−0.877258	−	0.480019i	$-0.840630\pi$
$547$	−16.1803	+	11.7557i	−0.691821	+	0.502638i	0.185437	+	0.982656i	$0.440630\pi$
$548$	4.94427	−	15.2169i	0.211209	−	0.650034i
$549$	3.00000			0.128037
$550$		0			0
$551$	−18.0000			−0.766826
$552$		0			0
$553$	−8.89919	+	6.46564i	−0.378432	+	0.274947i
$554$	−17.7984	−	12.9313i	−0.756180	−	0.549397i
$555$	−3.70820	−	11.4127i	−0.157404	−	0.484441i
$556$	9.88854	+	30.4338i	0.419368	+	1.29068i
$557$	6.47214	+	4.70228i	0.274233	+	0.199242i	0.716398	−	0.697692i	$-0.245789\pi$
$557$	6.47214	+	4.70228i	0.274233	+	0.199242i	−0.442165	+	0.896934i	$0.645789\pi$
$558$	−8.09017	+	5.87785i	−0.342484	+	0.248829i
$559$	−7.41641	+	22.8254i	−0.313681	+	0.965410i
$560$	−16.0000			−0.676123
$561$		0			0
$562$	24.0000			1.01238
$563$	8.65248	−	26.6296i	0.364658	−	1.12230i	−0.585536	−	0.810646i	$-0.699116\pi$
$563$	8.65248	−	26.6296i	0.364658	−	1.12230i	0.950195	−	0.311657i	$-0.100884\pi$
$564$	3.23607	−	2.35114i	0.136263	−	0.0990009i
$565$	−19.4164	−	14.1068i	−0.816854	−	0.593479i
$566$	6.79837	+	20.9232i	0.285757	+	0.879470i
$567$	0.309017	+	0.951057i	0.0129775	+	0.0399406i
$568$		0			0
$569$	−9.70820	+	7.05342i	−0.406989	+	0.295695i	−0.772382	−	0.635159i	$-0.780935\pi$
$569$	−9.70820	+	7.05342i	−0.406989	+	0.295695i	0.365393	+	0.930853i	$0.380935\pi$
$570$	−7.41641	+	22.8254i	−0.310639	+	0.956049i
$571$	−25.0000			−1.04622			−0.523109	−	0.852266i	$-0.675228\pi$
$571$	−25.0000			−1.04622			−0.523109	+	0.852266i	$0.675228\pi$
$572$		0			0
$573$	−8.00000			−0.334205
$574$	1.23607	−	3.80423i	0.0515925	−	0.158785i
$575$	−17.7984	+	12.9313i	−0.742243	+	0.539271i
$576$	6.47214	+	4.70228i	0.269672	+	0.195928i
$577$	4.63525	+	14.2658i	0.192968	+	0.593895i	0.999994	+	0.00337925i	$0.00107565\pi$
$577$	4.63525	+	14.2658i	0.192968	+	0.593895i	−0.807026	+	0.590516i	$0.798924\pi$
$578$	0.618034	+	1.90211i	0.0257068	+	0.0791175i
$579$	−4.04508	−	2.93893i	−0.168108	−	0.122138i
$580$	−38.8328	+	28.2137i	−1.61244	+	1.17151i
$581$	1.85410	−	5.70634i	0.0769211	−	0.236739i
$582$	10.0000			0.414513
$583$		0			0
$584$		0			0
$585$	−2.47214	+	7.60845i	−0.102210	+	0.314571i
$586$	19.4164	−	14.1068i	0.802084	−	0.582748i
$587$	−3.23607	−	2.35114i	−0.133567	−	0.0970420i	0.518996	−	0.854777i	$-0.326306\pi$
$587$	−3.23607	−	2.35114i	−0.133567	−	0.0970420i	−0.652563	+	0.757735i	$0.726306\pi$
$588$	3.70820	+	11.4127i	0.152924	+	0.470651i
$589$	4.63525	+	14.2658i	0.190992	+	0.587814i
$590$	−64.7214	−	47.0228i	−2.66454	−	1.93590i
$591$	−6.47214	+	4.70228i	−0.266228	+	0.193426i
$592$	−3.70820	+	11.4127i	−0.152406	+	0.469058i
$593$	−46.0000			−1.88899			−0.944497	−	0.328521i	$-0.893450\pi$
$593$	−46.0000			−1.88899			−0.944497	+	0.328521i	$0.893450\pi$
$594$		0			0
$595$	16.0000			0.655936
$596$	−9.88854	+	30.4338i	−0.405051	+	1.24662i
$597$	−16.9894	+	12.3435i	−0.695328	+	0.505185i
$598$	−6.47214	−	4.70228i	−0.264665	−	0.192291i
$599$	−2.47214	−	7.60845i	−0.101009	−	0.310873i	0.887764	−	0.460298i	$-0.152258\pi$
$599$	−2.47214	−	7.60845i	−0.101009	−	0.310873i	−0.988773	+	0.149425i	$0.952258\pi$
$600$		0			0
$601$	0.809017	+	0.587785i	0.0330005	+	0.0239763i	0.604163	−	0.796861i	$-0.293507\pi$
$601$	0.809017	+	0.587785i	0.0330005	+	0.0239763i	−0.571163	+	0.820837i	$0.693507\pi$
$602$	19.4164	−	14.1068i	0.791354	−	0.574952i
$603$	−0.309017	+	0.951057i	−0.0125841	+	0.0387300i
$604$	−32.0000			−1.30206
$605$		0			0
$606$	−20.0000			−0.812444
$607$	2.47214	−	7.60845i	0.100341	−	0.308818i	−0.888268	−	0.459326i	$-0.848091\pi$
$607$	2.47214	−	7.60845i	0.100341	−	0.308818i	0.988609	+	0.150508i	$0.0480910\pi$
$608$	19.4164	−	14.1068i	0.787439	−	0.572108i
$609$	4.85410	+	3.52671i	0.196698	+	0.142910i
$610$	−7.41641	−	22.8254i	−0.300282	−	0.924172i
$611$	−1.23607	−	3.80423i	−0.0500060	−	0.153903i
$612$	−6.47214	−	4.70228i	−0.261621	−	0.190078i
$613$	10.5172	−	7.64121i	0.424787	−	0.308625i	−0.354774	−	0.934952i	$-0.615442\pi$
$613$	10.5172	−	7.64121i	0.424787	−	0.308625i	0.779561	+	0.626326i	$0.215442\pi$
$614$	11.7426	−	36.1401i	0.473895	−	1.45850i
$615$	8.00000			0.322591
$616$		0			0
$617$	−24.0000			−0.966204			−0.483102	−	0.875564i	$-0.660490\pi$
$617$	−24.0000			−0.966204			−0.483102	+	0.875564i	$0.660490\pi$
$618$	−4.32624	+	13.3148i	−0.174027	+	0.535599i
$619$	3.23607	−	2.35114i	0.130069	−	0.0945003i	−0.520849	−	0.853649i	$-0.674384\pi$
$619$	3.23607	−	2.35114i	0.130069	−	0.0945003i	0.650917	+	0.759149i	$0.274384\pi$
$620$	32.3607	+	23.5114i	1.29964	+	0.944241i
$621$	−0.618034	−	1.90211i	−0.0248008	−	0.0763292i
$622$	−14.8328	−	45.6507i	−0.594742	−	1.83043i
$623$	−9.70820	−	7.05342i	−0.388951	−	0.282589i
$624$	6.47214	−	4.70228i	0.259093	−	0.188242i
$625$	12.6697	−	38.9933i	0.506788	−	1.55973i
$626$	20.0000			0.799361
$627$		0			0
$628$	−2.00000			−0.0798087
$629$	3.70820	−	11.4127i	0.147856	−	0.455053i
$630$	6.47214	−	4.70228i	0.257856	−	0.187343i
$631$	25.8885	+	18.8091i	1.03061	+	0.748780i	0.968430	−	0.249286i	$-0.0801958\pi$
$631$	25.8885	+	18.8091i	1.03061	+	0.748780i	0.0621766	+	0.998065i	$0.480196\pi$
$632$		0			0
$633$	6.48936	+	19.9722i	0.257929	+	0.793823i
$634$	−32.3607	−	23.5114i	−1.28521	−	0.933757i
$635$	42.0689	−	30.5648i	1.66945	−	1.21293i
$636$	−3.70820	+	11.4127i	−0.147040	+	0.452542i
$637$	12.0000			0.475457
$638$		0			0
$639$		0			0
$640$		0			0
$641$	19.4164	−	14.1068i	0.766902	−	0.557187i	−0.134118	−	0.990965i	$-0.542820\pi$
$641$	19.4164	−	14.1068i	0.766902	−	0.557187i	0.901020	+	0.433779i	$0.142820\pi$
$642$	29.1246	+	21.1603i	1.14946	+	0.835129i
$643$	−11.4336	−	35.1891i	−0.450898	−	1.38772i	−0.875884	−	0.482522i	$-0.839721\pi$
$643$	−11.4336	−	35.1891i	−0.450898	−	1.38772i	0.424985	−	0.905200i	$-0.360279\pi$
$644$	1.23607	+	3.80423i	0.0487079	+	0.149908i
$645$	38.8328	+	28.2137i	1.52904	+	1.11091i
$646$	−19.4164	+	14.1068i	−0.763928	+	0.555026i
$647$	−1.23607	+	3.80423i	−0.0485948	+	0.149560i	−0.972409	−	0.233281i	$-0.925054\pi$
$647$	−1.23607	+	3.80423i	−0.0485948	+	0.149560i	0.923815	+	0.382840i	$0.125054\pi$
$648$		0			0
$649$		0			0
$650$	44.0000			1.72582
$651$	1.54508	−	4.75528i	0.0605567	−	0.186374i
$652$	−40.4508	+	29.3893i	−1.58418	+	1.15097i
$653$	−8.09017	−	5.87785i	−0.316593	−	0.230018i	0.418127	−	0.908388i	$-0.362687\pi$
$653$	−8.09017	−	5.87785i	−0.316593	−	0.230018i	−0.734720	+	0.678370i	$0.762687\pi$
$654$	0.618034	+	1.90211i	0.0241670	+	0.0743785i
$655$	−7.41641	−	22.8254i	−0.289783	−	0.891860i
$656$	−6.47214	−	4.70228i	−0.252694	−	0.183593i
$657$	8.89919	−	6.46564i	0.347190	−	0.252249i
$658$	−1.23607	+	3.80423i	−0.0481869	+	0.148304i
$659$	46.0000			1.79191			0.895953	−	0.444149i	$-0.146494\pi$
$659$	46.0000			1.79191			0.895953	+	0.444149i	$0.146494\pi$
$660$		0			0
$661$	−5.00000			−0.194477			−0.0972387	−	0.995261i	$-0.531001\pi$
$661$	−5.00000			−0.194477			−0.0972387	+	0.995261i	$0.531001\pi$
$662$	6.79837	−	20.9232i	0.264226	−	0.813205i
$663$	−6.47214	+	4.70228i	−0.251357	+	0.182622i
$664$		0			0
$665$	−3.70820	−	11.4127i	−0.143798	−	0.442565i
$666$	−1.85410	−	5.70634i	−0.0718450	−	0.221116i
$667$	−9.70820	−	7.05342i	−0.375903	−	0.273110i
$668$	29.1246	−	21.1603i	1.12687	−	0.818715i
$669$	5.25329	−	16.1680i	0.203104	−	0.625089i
$670$	8.00000			0.309067
$671$		0			0
$672$	−8.00000			−0.308607
$673$	−4.01722	+	12.3637i	−0.154852	+	0.476587i	−0.998146	−	0.0608665i	$-0.980614\pi$
$673$	−4.01722	+	12.3637i	−0.154852	+	0.476587i	0.843293	+	0.537453i	$0.180614\pi$
$674$	8.09017	−	5.87785i	0.311622	−	0.226406i
$675$	8.89919	+	6.46564i	0.342530	+	0.248863i
$676$	−5.56231	−	17.1190i	−0.213935	−	0.658424i
$677$	3.70820	+	11.4127i	0.142518	+	0.438625i	0.996683	−	0.0813762i	$-0.0259315\pi$
$677$	3.70820	+	11.4127i	0.142518	+	0.438625i	−0.854166	+	0.520001i	$0.825932\pi$
$678$	−9.70820	−	7.05342i	−0.372841	−	0.270885i
$679$	−4.04508	+	2.93893i	−0.155236	+	0.112786i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−34.0000			−1.30097			−0.650487	−	0.759517i	$-0.725435\pi$
$683$	−34.0000			−1.30097			−0.650487	+	0.759517i	$0.725435\pi$
$684$	−1.85410	+	5.70634i	−0.0708934	+	0.218187i
$685$	−25.8885	+	18.8091i	−0.989150	+	0.718660i
$686$	−21.0344	−	15.2824i	−0.803099	−	0.583485i
$687$	5.56231	+	17.1190i	0.212215	+	0.653131i
$688$	−14.8328	−	45.6507i	−0.565496	−	1.74042i
$689$	9.70820	+	7.05342i	0.369853	+	0.268714i
$690$	−12.9443	+	9.40456i	−0.492780	+	0.358026i
$691$	3.39919	−	10.4616i	0.129311	−	0.397979i	−0.865351	−	0.501167i	$-0.832904\pi$
$691$	3.39919	−	10.4616i	0.129311	−	0.397979i	0.994662	+	0.103188i	$0.0329043\pi$
$692$	48.0000			1.82469
$693$		0			0
$694$	4.00000			0.151838
$695$	19.7771	−	60.8676i	0.750188	−	2.30884i
$696$		0			0
$697$	6.47214	+	4.70228i	0.245150	+	0.178112i
$698$	−9.27051	−	28.5317i	−0.350894	−	1.07994i
$699$	−5.56231	−	17.1190i	−0.210386	−	0.647501i
$700$	−17.7984	−	12.9313i	−0.672715	−	0.488756i
$701$	−40.4508	+	29.3893i	−1.52781	+	1.11002i	−0.570366	+	0.821391i	$0.693198\pi$
$701$	−40.4508	+	29.3893i	−1.52781	+	1.11002i	−0.957442	+	0.288626i	$0.906802\pi$
$702$	−1.23607	+	3.80423i	−0.0466524	+	0.143581i
$703$	−9.00000			−0.339441
$704$		0			0
$705$	−8.00000			−0.301297
$706$	7.41641	−	22.8254i	0.279120	−	0.859044i
$707$	8.09017	−	5.87785i	0.304262	−	0.221059i
$708$	−16.1803	−	11.7557i	−0.608094	−	0.441806i
$709$	8.03444	+	24.7275i	0.301740	+	0.928660i	0.980874	+	0.194645i	$0.0623555\pi$
$709$	8.03444	+	24.7275i	0.301740	+	0.928660i	−0.679134	+	0.734014i	$0.737644\pi$
$710$		0			0
$711$	−8.89919	−	6.46564i	−0.333746	−	0.242480i
$712$		0			0
$713$	−3.09017	+	9.51057i	−0.115728	+	0.356173i
$714$	8.00000			0.299392
$715$		0			0
$716$	12.0000			0.448461
$717$	−1.85410	+	5.70634i	−0.0692427	+	0.213107i
$718$	6.47214	−	4.70228i	0.241538	−	0.175488i
$719$	4.85410	+	3.52671i	0.181027	+	0.131524i	0.674609	−	0.738176i	$-0.264312\pi$
$719$	4.85410	+	3.52671i	0.181027	+	0.131524i	−0.493581	+	0.869700i	$0.664312\pi$
$720$	−4.94427	−	15.2169i	−0.184262	−	0.567101i
$721$	−2.16312	−	6.65740i	−0.0805588	−	0.247934i
$722$	−16.1803	−	11.7557i	−0.602170	−	0.437502i
$723$	−11.3262	+	8.22899i	−0.421227	+	0.306040i
$724$	−14.2148	+	43.7486i	−0.528288	+	1.62590i
$725$	66.0000			2.45118
$726$		0			0
$727$	−12.0000			−0.445055			−0.222528	−	0.974926i	$-0.571431\pi$
$727$	−12.0000			−0.445055			−0.222528	+	0.974926i	$0.571431\pi$
$728$		0			0
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−71.1935	−	51.7251i	−2.63499	−	1.91443i
$731$	14.8328	+	45.6507i	0.548612	+	1.68845i
$732$	−1.85410	−	5.70634i	−0.0685296	−	0.210912i
$733$	24.2705	+	17.6336i	0.896452	+	0.651310i	0.937552	−	0.347845i	$-0.113086\pi$
$733$	24.2705	+	17.6336i	0.896452	+	0.651310i	−0.0411004	+	0.999155i	$0.513086\pi$
$734$	−12.9443	+	9.40456i	−0.477782	+	0.347129i
$735$	7.41641	−	22.8254i	0.273558	−	0.841926i
$736$	16.0000			0.589768
$737$		0			0
$738$	4.00000			0.147242
$739$	12.6697	−	38.9933i	0.466062	−	1.43439i	−0.391579	−	0.920144i	$-0.628071\pi$
$739$	12.6697	−	38.9933i	0.466062	−	1.43439i	0.857642	−	0.514248i	$-0.171929\pi$
$740$	−19.4164	+	14.1068i	−0.713761	+	0.518578i
$741$	4.85410	+	3.52671i	0.178320	+	0.129557i
$742$	−3.70820	−	11.4127i	−0.136132	−	0.418973i
$743$	−6.18034	−	19.0211i	−0.226735	−	0.697818i	−0.998111	−	0.0614382i	$-0.980431\pi$
$743$	−6.18034	−	19.0211i	−0.226735	−	0.697818i	0.771376	−	0.636379i	$-0.219569\pi$
$744$		0			0
$745$	51.7771	−	37.6183i	1.89697	−	1.37823i
$746$	−4.32624	+	13.3148i	−0.158395	+	0.487489i
$747$	6.00000			0.219529
$748$		0			0
$749$	−18.0000			−0.657706
$750$	14.8328	−	45.6507i	0.541618	−	1.66693i
$751$	−15.3713	+	11.1679i	−0.560908	+	0.407523i	−0.831791	−	0.555089i	$-0.812684\pi$
$751$	−15.3713	+	11.1679i	−0.560908	+	0.407523i	0.270883	+	0.962612i	$0.412684\pi$
$752$	6.47214	+	4.70228i	0.236015	+	0.171475i
$753$	0.618034	+	1.90211i	0.0225224	+	0.0693169i
$754$	7.41641	+	22.8254i	0.270090	+	0.831250i
$755$	51.7771	+	37.6183i	1.88436	+	1.36907i
$756$	1.61803	−	1.17557i	0.0588473	−	0.0427551i
$757$	1.54508	−	4.75528i	0.0561571	−	0.172834i	−0.919044	−	0.394156i	$-0.871037\pi$
$757$	1.54508	−	4.75528i	0.0561571	−	0.172834i	0.975201	+	0.221322i	$0.0710371\pi$
$758$	−32.0000			−1.16229
$759$		0			0
$760$		0			0
$761$	−7.41641	+	22.8254i	−0.268845	+	0.827419i	0.721938	+	0.691958i	$0.243252\pi$
$761$	−7.41641	+	22.8254i	−0.268845	+	0.827419i	−0.990783	+	0.135461i	$0.956748\pi$
$762$	21.0344	−	15.2824i	0.761997	−	0.553624i
$763$	−0.809017	−	0.587785i	−0.0292884	−	0.0212793i
$764$	4.94427	+	15.2169i	0.178877	+	0.550528i
$765$	4.94427	+	15.2169i	0.178761	+	0.550168i
$766$	42.0689	+	30.5648i	1.52001	+	1.10435i
$767$	−16.1803	+	11.7557i	−0.584238	+	0.424474i
$768$	−4.94427	+	15.2169i	−0.178411	+	0.549093i
$769$	11.0000			0.396670			0.198335	−	0.980134i	$-0.436447\pi$
$769$	11.0000			0.396670			0.198335	+	0.980134i	$0.436447\pi$
$770$		0			0
$771$	14.0000			0.504198
$772$	−3.09017	+	9.51057i	−0.111218	+	0.342293i
$773$	−29.1246	+	21.1603i

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.618034 + 1.90211i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-1.61803 - 1.17557i) q^{4} +(1.23607 + 3.80423i) q^{5} +(0.618034 + 1.90211i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.618034 + 1.90211i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-1.61803 - 1.17557i) q^{4} +(1.23607 + 3.80423i) q^{5} +(0.618034 + 1.90211i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(0.309017 - 0.951057i) q^{9} -8.00000 q^{10} -2.00000 q^{12} +(-0.618034 + 1.90211i) q^{13} +(1.61803 - 1.17557i) q^{14} +(3.23607 + 2.35114i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(1.23607 + 3.80423i) q^{17} +(1.61803 + 1.17557i) q^{18} +(2.42705 - 1.76336i) q^{19} +(2.47214 - 7.60845i) q^{20} -1.00000 q^{21} +2.00000 q^{23} +(-8.89919 + 6.46564i) q^{25} +(-3.23607 - 2.35114i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.618034 + 1.90211i) q^{28} +(-4.85410 - 3.52671i) q^{29} +(-6.47214 + 4.70228i) q^{30} +(-1.54508 + 4.75528i) q^{31} +8.00000 q^{32} -8.00000 q^{34} +(1.23607 - 3.80423i) q^{35} +(-1.61803 + 1.17557i) q^{36} +(-2.42705 - 1.76336i) q^{37} +(1.85410 + 5.70634i) q^{38} +(0.618034 + 1.90211i) q^{39} +(1.61803 - 1.17557i) q^{41} +(0.618034 - 1.90211i) q^{42} +12.0000 q^{43} +4.00000 q^{45} +(-1.23607 + 3.80423i) q^{46} +(-1.61803 + 1.17557i) q^{47} +(-3.23607 - 2.35114i) q^{48} +(-1.85410 - 5.70634i) q^{49} +(-6.79837 - 20.9232i) q^{50} +(3.23607 + 2.35114i) q^{51} +(3.23607 - 2.35114i) q^{52} +(1.85410 - 5.70634i) q^{53} +2.00000 q^{54} +(0.927051 - 2.85317i) q^{57} +(9.70820 - 7.05342i) q^{58} +(8.09017 + 5.87785i) q^{59} +(-2.47214 - 7.60845i) q^{60} +(0.927051 + 2.85317i) q^{61} +(-8.09017 - 5.87785i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(-2.47214 + 7.60845i) q^{64} -8.00000 q^{65} -1.00000 q^{67} +(2.47214 - 7.60845i) q^{68} +(1.61803 - 1.17557i) q^{69} +(6.47214 + 4.70228i) q^{70} +(8.89919 + 6.46564i) q^{73} +(4.85410 - 3.52671i) q^{74} +(-3.39919 + 10.4616i) q^{75} -6.00000 q^{76} -4.00000 q^{78} +(3.39919 - 10.4616i) q^{79} +(12.9443 - 9.40456i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(1.23607 + 3.80423i) q^{82} +(1.85410 + 5.70634i) q^{83} +(1.61803 + 1.17557i) q^{84} +(-12.9443 + 9.40456i) q^{85} +(-7.41641 + 22.8254i) q^{86} -6.00000 q^{87} +12.0000 q^{89} +(-2.47214 + 7.60845i) q^{90} +(1.61803 - 1.17557i) q^{91} +(-3.23607 - 2.35114i) q^{92} +(1.54508 + 4.75528i) q^{93} +(-1.23607 - 3.80423i) q^{94} +(9.70820 + 7.05342i) q^{95} +(6.47214 - 4.70228i) q^{96} +(1.54508 - 4.75528i) q^{97} +12.0000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} - q^{7} - q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 - q^7 - q^9	\( 4 q + 2 q^{2} + q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} - q^{7} - q^{9} - 32 q^{10} - 8 q^{12} + 2 q^{13} + 2 q^{14} + 4 q^{15} + 4 q^{16} - 4 q^{17} + 2 q^{18} + 3 q^{19} - 8 q^{20} - 4 q^{21} + 8 q^{23} - 11 q^{25} - 4 q^{26} + q^{27} - 2 q^{28} - 6 q^{29} - 8 q^{30} + 5 q^{31} + 32 q^{32} - 32 q^{34} - 4 q^{35} - 2 q^{36} - 3 q^{37} - 6 q^{38} - 2 q^{39} + 2 q^{41} - 2 q^{42} + 48 q^{43} + 16 q^{45} + 4 q^{46} - 2 q^{47} - 4 q^{48} + 6 q^{49} + 22 q^{50} + 4 q^{51} + 4 q^{52} - 6 q^{53} + 8 q^{54} - 3 q^{57} + 12 q^{58} + 10 q^{59} + 8 q^{60} - 3 q^{61} - 10 q^{62} - q^{63} + 8 q^{64} - 32 q^{65} - 4 q^{67} - 8 q^{68} + 2 q^{69} + 8 q^{70} + 11 q^{73} + 6 q^{74} + 11 q^{75} - 24 q^{76} - 16 q^{78} - 11 q^{79} + 16 q^{80} - q^{81} - 4 q^{82} - 6 q^{83} + 2 q^{84} - 16 q^{85} + 24 q^{86} - 24 q^{87} + 48 q^{89} + 8 q^{90} + 2 q^{91} - 4 q^{92} - 5 q^{93} + 4 q^{94} + 12 q^{95} + 8 q^{96} - 5 q^{97} + 48 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 - q^7 - q^9 - 32 * q^10 - 8 * q^12 + 2 * q^13 + 2 * q^14 + 4 * q^15 + 4 * q^16 - 4 * q^17 + 2 * q^18 + 3 * q^19 - 8 * q^20 - 4 * q^21 + 8 * q^23 - 11 * q^25 - 4 * q^26 + q^27 - 2 * q^28 - 6 * q^29 - 8 * q^30 + 5 * q^31 + 32 * q^32 - 32 * q^34 - 4 * q^35 - 2 * q^36 - 3 * q^37 - 6 * q^38 - 2 * q^39 + 2 * q^41 - 2 * q^42 + 48 * q^43 + 16 * q^45 + 4 * q^46 - 2 * q^47 - 4 * q^48 + 6 * q^49 + 22 * q^50 + 4 * q^51 + 4 * q^52 - 6 * q^53 + 8 * q^54 - 3 * q^57 + 12 * q^58 + 10 * q^59 + 8 * q^60 - 3 * q^61 - 10 * q^62 - q^63 + 8 * q^64 - 32 * q^65 - 4 * q^67 - 8 * q^68 + 2 * q^69 + 8 * q^70 + 11 * q^73 + 6 * q^74 + 11 * q^75 - 24 * q^76 - 16 * q^78 - 11 * q^79 + 16 * q^80 - q^81 - 4 * q^82 - 6 * q^83 + 2 * q^84 - 16 * q^85 + 24 * q^86 - 24 * q^87 + 48 * q^89 + 8 * q^90 + 2 * q^91 - 4 * q^92 - 5 * q^93 + 4 * q^94 + 12 * q^95 + 8 * q^96 - 5 * q^97 + 48 * q^98

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