LMFDB - Embedded newform 363.2.e.d.202.1

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			202.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	363.202
Dual form			363.2.e.d.124.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61803 - 1.17557i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.618034 + 1.90211i) q^{4} +(-3.23607 + 2.35114i) q^{5} +(1.61803 - 1.17557i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.61803 - 1.17557i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.618034 + 1.90211i) q^{4} +(-3.23607 + 2.35114i) q^{5} +(1.61803 - 1.17557i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.809017 - 0.587785i) q^{9} +8.00000 q^{10} -2.00000 q^{12} +(-1.61803 - 1.17557i) q^{13} +(-0.618034 + 1.90211i) q^{14} +(-1.23607 - 3.80423i) q^{15} +(3.23607 - 2.35114i) q^{16} +(3.23607 - 2.35114i) q^{17} +(0.618034 + 1.90211i) q^{18} +(0.927051 - 2.85317i) q^{19} +(-6.47214 - 4.70228i) q^{20} +1.00000 q^{21} +2.00000 q^{23} +(3.39919 - 10.4616i) q^{25} +(1.23607 + 3.80423i) q^{26} +(0.809017 - 0.587785i) q^{27} +(1.61803 - 1.17557i) q^{28} +(-1.85410 - 5.70634i) q^{29} +(-2.47214 + 7.60845i) q^{30} +(4.04508 + 2.93893i) q^{31} -8.00000 q^{32} -8.00000 q^{34} +(3.23607 + 2.35114i) q^{35} +(0.618034 - 1.90211i) q^{36} +(0.927051 + 2.85317i) q^{37} +(-4.85410 + 3.52671i) q^{38} +(1.61803 - 1.17557i) q^{39} +(0.618034 - 1.90211i) q^{41} +(-1.61803 - 1.17557i) q^{42} -12.0000 q^{43} +4.00000 q^{45} +(-3.23607 - 2.35114i) q^{46} +(0.618034 - 1.90211i) q^{47} +(1.23607 + 3.80423i) q^{48} +(4.85410 - 3.52671i) q^{49} +(-17.7984 + 12.9313i) q^{50} +(1.23607 + 3.80423i) q^{51} +(1.23607 - 3.80423i) q^{52} +(-4.85410 - 3.52671i) q^{53} -2.00000 q^{54} +(2.42705 + 1.76336i) q^{57} +(-3.70820 + 11.4127i) q^{58} +(-3.09017 - 9.51057i) q^{59} +(6.47214 - 4.70228i) q^{60} +(2.42705 - 1.76336i) q^{61} +(-3.09017 - 9.51057i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(6.47214 + 4.70228i) q^{64} +8.00000 q^{65} -1.00000 q^{67} +(6.47214 + 4.70228i) q^{68} +(-0.618034 + 1.90211i) q^{69} +(-2.47214 - 7.60845i) q^{70} +(3.39919 + 10.4616i) q^{73} +(1.85410 - 5.70634i) q^{74} +(8.89919 + 6.46564i) q^{75} +6.00000 q^{76} -4.00000 q^{78} +(8.89919 + 6.46564i) q^{79} +(-4.94427 + 15.2169i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-3.23607 + 2.35114i) q^{82} +(4.85410 - 3.52671i) q^{83} +(0.618034 + 1.90211i) q^{84} +(-4.94427 + 15.2169i) q^{85} +(19.4164 + 14.1068i) q^{86} +6.00000 q^{87} +12.0000 q^{89} +(-6.47214 - 4.70228i) q^{90} +(-0.618034 + 1.90211i) q^{91} +(1.23607 + 3.80423i) q^{92} +(-4.04508 + 2.93893i) q^{93} +(-3.23607 + 2.35114i) q^{94} +(3.70820 + 11.4127i) q^{95} +(2.47214 - 7.60845i) q^{96} +(-4.04508 - 2.93893i) 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 $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.61803	−	1.17557i	−1.14412	−	0.831254i	−0.156434	−	0.987688i	$-0.550000\pi$
$2$	−1.61803	−	1.17557i	−1.14412	−	0.831254i	−0.987688	+	0.156434i	$0.950000\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	0.618034	+	1.90211i	0.309017	+	0.951057i
$5$	−3.23607	+	2.35114i	−1.44721	+	1.05146i	−0.460741	+	0.887535i	$0.652416\pi$
$5$	−3.23607	+	2.35114i	−1.44721	+	1.05146i	−0.986472	+	0.163928i	$0.947584\pi$
$6$	1.61803	−	1.17557i	0.660560	−	0.479925i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i	0.875520	−	0.483181i	$-0.160519\pi$
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i	−0.992318	+	0.123716i	$0.960519\pi$
$8$		0			0
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	8.00000			2.52982
$11$		0			0
$11$		0			0
$12$	−2.00000			−0.577350
$13$	−1.61803	−	1.17557i	−0.448762	−	0.326045i	0.340345	−	0.940301i	$-0.389456\pi$
$13$	−1.61803	−	1.17557i	−0.448762	−	0.326045i	−0.789107	+	0.614256i	$0.789456\pi$
$14$	−0.618034	+	1.90211i	−0.165177	+	0.508361i
$15$	−1.23607	−	3.80423i	−0.319151	−	0.982247i
$16$	3.23607	−	2.35114i	0.809017	−	0.587785i
$17$	3.23607	−	2.35114i	0.784862	−	0.570235i	−0.121572	−	0.992583i	$-0.538794\pi$
$17$	3.23607	−	2.35114i	0.784862	−	0.570235i	0.906434	+	0.422347i	$0.138794\pi$
$18$	0.618034	+	1.90211i	0.145672	+	0.448332i
$19$	0.927051	−	2.85317i	0.212680	−	0.654562i	−0.786630	−	0.617425i	$-0.788176\pi$
$19$	0.927051	−	2.85317i	0.212680	−	0.654562i	0.999310	−	0.0371374i	$-0.0118239\pi$
$20$	−6.47214	−	4.70228i	−1.44721	−	1.05146i
$21$	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
$25$	3.39919	−	10.4616i	0.679837	−	2.09232i
$26$	1.23607	+	3.80423i	0.242413	+	0.746070i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	1.61803	−	1.17557i	0.305780	−	0.222162i
$29$	−1.85410	−	5.70634i	−0.344298	−	1.05964i	−0.961958	−	0.273196i	$-0.911919\pi$
$29$	−1.85410	−	5.70634i	−0.344298	−	1.05964i	0.617660	−	0.786445i	$-0.288081\pi$
$30$	−2.47214	+	7.60845i	−0.451348	+	1.38911i
$31$	4.04508	+	2.93893i	0.726519	+	0.527847i	0.888460	−	0.458954i	$-0.151776\pi$
$31$	4.04508	+	2.93893i	0.726519	+	0.527847i	−0.161942	+	0.986800i	$0.551776\pi$
$32$	−8.00000			−1.41421
$33$		0			0
$34$	−8.00000			−1.37199
$35$	3.23607	+	2.35114i	0.546995	+	0.397415i
$36$	0.618034	−	1.90211i	0.103006	−	0.317019i
$37$	0.927051	+	2.85317i	0.152406	+	0.469058i	0.997889	−	0.0649448i	$-0.0206871\pi$
$37$	0.927051	+	2.85317i	0.152406	+	0.469058i	−0.845483	+	0.534003i	$0.820687\pi$
$38$	−4.85410	+	3.52671i	−0.787439	+	0.572108i
$39$	1.61803	−	1.17557i	0.259093	−	0.188242i
$40$		0			0
$41$	0.618034	−	1.90211i	0.0965207	−	0.297060i	−0.891126	−	0.453755i	$-0.850084\pi$
$41$	0.618034	−	1.90211i	0.0965207	−	0.297060i	0.987647	+	0.156695i	$0.0500840\pi$
$42$	−1.61803	−	1.17557i	−0.249668	−	0.181394i
$43$	−12.0000			−1.82998			−0.914991	−	0.403473i	$-0.867803\pi$
$43$	−12.0000			−1.82998			−0.914991	+	0.403473i	$0.867803\pi$
$44$		0			0
$45$	4.00000			0.596285
$46$	−3.23607	−	2.35114i	−0.477132	−	0.346657i
$47$	0.618034	−	1.90211i	0.0901495	−	0.277452i	−0.895810	−	0.444438i	$-0.853403\pi$
$47$	0.618034	−	1.90211i	0.0901495	−	0.277452i	0.985959	+	0.166986i	$0.0534035\pi$
$48$	1.23607	+	3.80423i	0.178411	+	0.549093i
$49$	4.85410	−	3.52671i	0.693443	−	0.503816i
$50$	−17.7984	+	12.9313i	−2.51707	+	1.82876i
$51$	1.23607	+	3.80423i	0.173084	+	0.532698i
$52$	1.23607	−	3.80423i	0.171412	−	0.527551i
$53$	−4.85410	−	3.52671i	−0.666762	−	0.484431i	0.202178	−	0.979349i	$-0.435198\pi$
$53$	−4.85410	−	3.52671i	−0.666762	−	0.484431i	−0.868940	+	0.494918i	$0.835198\pi$
$54$	−2.00000			−0.272166
$55$		0			0
$56$		0			0
$57$	2.42705	+	1.76336i	0.321471	+	0.233562i
$58$	−3.70820	+	11.4127i	−0.486911	+	1.49856i
$59$	−3.09017	−	9.51057i	−0.402306	−	1.23817i	−0.923124	−	0.384502i	$-0.874373\pi$
$59$	−3.09017	−	9.51057i	−0.402306	−	1.23817i	0.520818	−	0.853668i	$-0.325627\pi$
$60$	6.47214	−	4.70228i	0.835549	−	0.607062i
$61$	2.42705	−	1.76336i	0.310752	−	0.225775i	−0.421467	−	0.906844i	$-0.638485\pi$
$61$	2.42705	−	1.76336i	0.310752	−	0.225775i	0.732219	+	0.681069i	$0.238485\pi$
$62$	−3.09017	−	9.51057i	−0.392452	−	1.20784i
$63$	−0.309017	+	0.951057i	−0.0389325	+	0.119822i
$64$	6.47214	+	4.70228i	0.809017	+	0.587785i
$65$	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	$0.519456\pi$
$68$	6.47214	+	4.70228i	0.784862	+	0.570235i
$69$	−0.618034	+	1.90211i	−0.0744025	+	0.228988i
$70$	−2.47214	−	7.60845i	−0.295477	−	0.909384i
$71$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$71$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$72$		0			0
$73$	3.39919	+	10.4616i	0.397845	+	1.22444i	0.926724	+	0.375743i	$0.122612\pi$
$73$	3.39919	+	10.4616i	0.397845	+	1.22444i	−0.528879	+	0.848697i	$0.677388\pi$
$74$	1.85410	−	5.70634i	0.215535	−	0.663348i
$75$	8.89919	+	6.46564i	1.02759	+	0.746588i
$76$	6.00000			0.688247
$77$		0			0
$78$	−4.00000			−0.452911
$79$	8.89919	+	6.46564i	1.00124	+	0.727441i	0.962353	−	0.271803i	$-0.0876198\pi$
$79$	8.89919	+	6.46564i	1.00124	+	0.727441i	0.0388837	+	0.999244i	$0.487620\pi$
$80$	−4.94427	+	15.2169i	−0.552786	+	1.70130i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−3.23607	+	2.35114i	−0.357364	+	0.259640i
$83$	4.85410	−	3.52671i	0.532807	−	0.387107i	−0.288600	−	0.957450i	$-0.593190\pi$
$83$	4.85410	−	3.52671i	0.532807	−	0.387107i	0.821407	+	0.570343i	$0.193190\pi$
$84$	0.618034	+	1.90211i	0.0674330	+	0.207538i
$85$	−4.94427	+	15.2169i	−0.536282	+	1.65051i
$86$	19.4164	+	14.1068i	2.09373	+	1.52118i
$87$	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	$0.280588\pi$
$90$	−6.47214	−	4.70228i	−0.682223	−	0.495664i
$91$	−0.618034	+	1.90211i	−0.0647876	+	0.199396i
$92$	1.23607	+	3.80423i	0.128869	+	0.396618i
$93$	−4.04508	+	2.93893i	−0.419456	+	0.304752i
$94$	−3.23607	+	2.35114i	−0.333775	+	0.242502i
$95$	3.70820	+	11.4127i	0.380454	+	1.17092i
$96$	2.47214	−	7.60845i	0.252311	−	0.776534i
$97$	−4.04508	−	2.93893i	−0.410716	−	0.298403i	0.363176	−	0.931721i	$-0.381693\pi$
$97$	−4.04508	−	2.93893i	−0.410716	−	0.298403i	−0.773892	+	0.633318i	$0.781693\pi$
$98$	−12.0000			−1.21218
$99$		0			0
$100$	22.0000			2.20000
$101$	−8.09017	−	5.87785i	−0.805002	−	0.584868i	0.107375	−	0.994219i	$-0.465755\pi$
$101$	−8.09017	−	5.87785i	−0.805002	−	0.584868i	−0.912377	+	0.409350i	$0.865755\pi$
$102$	2.47214	−	7.60845i	0.244778	−	0.753349i
$103$	−2.16312	−	6.65740i	−0.213138	−	0.655973i	−0.999281	−	0.0379269i	$-0.987925\pi$
$103$	−2.16312	−	6.65740i	−0.213138	−	0.655973i	0.786142	−	0.618046i	$-0.212075\pi$
$104$		0			0
$105$	−3.23607	+	2.35114i	−0.315808	+	0.229448i
$106$	3.70820	+	11.4127i	0.360173	+	1.10850i
$107$	5.56231	−	17.1190i	0.537728	−	1.65496i	−0.199950	−	0.979806i	$-0.564078\pi$
$107$	5.56231	−	17.1190i	0.537728	−	1.65496i	0.737679	−	0.675152i	$-0.235922\pi$
$108$	1.61803	+	1.17557i	0.155695	+	0.113119i
$109$	−1.00000			−0.0957826			−0.0478913	−	0.998853i	$-0.515250\pi$
$109$	−1.00000			−0.0957826			−0.0478913	+	0.998853i	$0.515250\pi$
$110$		0			0
$111$	−3.00000			−0.284747
$112$	−3.23607	−	2.35114i	−0.305780	−	0.222162i
$113$	1.85410	−	5.70634i	0.174419	−	0.536807i	−0.825187	−	0.564859i	$-0.808930\pi$
$113$	1.85410	−	5.70634i	0.174419	−	0.536807i	0.999606	+	0.0280521i	$0.00893043\pi$
$114$	−1.85410	−	5.70634i	−0.173653	−	0.534448i
$115$	−6.47214	+	4.70228i	−0.603530	+	0.438490i
$116$	9.70820	−	7.05342i	0.901384	−	0.654894i
$117$	0.618034	+	1.90211i	0.0571373	+	0.175850i
$118$	−6.18034	+	19.0211i	−0.568946	+	1.75104i
$119$	−3.23607	−	2.35114i	−0.296650	−	0.215529i
$120$		0			0
$121$		0			0
$122$	−6.00000			−0.543214
$123$	1.61803	+	1.17557i	0.145893	+	0.105998i
$124$	−3.09017	+	9.51057i	−0.277505	+	0.854074i
$125$	7.41641	+	22.8254i	0.663344	+	2.04156i
$126$	1.61803	−	1.17557i	0.144146	−	0.104728i
$127$	−10.5172	+	7.64121i	−0.933252	+	0.678048i	−0.946787	−	0.321861i	$-0.895692\pi$
$127$	−10.5172	+	7.64121i	−0.933252	+	0.678048i	0.0135346	+	0.999908i	$0.495692\pi$
$128$		0			0
$129$	3.70820	−	11.4127i	0.326489	−	1.00483i
$130$	−12.9443	−	9.40456i	−1.13529	−	0.824835i
$131$	6.00000			0.524222			0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000			0.524222			0.262111	+	0.965038i	$0.415581\pi$
$132$		0			0
$133$	−3.00000			−0.260133
$134$	1.61803	+	1.17557i	0.139777	+	0.101554i
$135$	−1.23607	+	3.80423i	−0.106384	+	0.327416i
$136$		0			0
$137$	−6.47214	+	4.70228i	−0.552952	+	0.401743i	−0.828873	−	0.559437i	$-0.811017\pi$
$137$	−6.47214	+	4.70228i	−0.552952	+	0.401743i	0.275921	+	0.961180i	$0.411017\pi$
$138$	3.23607	−	2.35114i	0.275472	−	0.200142i
$139$	−4.94427	−	15.2169i	−0.419368	−	1.29068i	−0.908285	−	0.418351i	$-0.862608\pi$
$139$	−4.94427	−	15.2169i	−0.419368	−	1.29068i	0.488918	−	0.872330i	$-0.337392\pi$
$140$	−2.47214	+	7.60845i	−0.208934	+	0.643032i
$141$	1.61803	+	1.17557i	0.136263	+	0.0990009i
$142$		0			0
$143$		0			0
$144$	−4.00000			−0.333333
$145$	19.4164	+	14.1068i	1.61244	+	1.17151i
$146$	6.79837	−	20.9232i	0.562637	−	1.73162i
$147$	1.85410	+	5.70634i	0.152924	+	0.470651i
$148$	−4.85410	+	3.52671i	−0.399005	+	0.289894i
$149$	−12.9443	+	9.40456i	−1.06044	+	0.770452i	−0.974169	−	0.225820i	$-0.927494\pi$
$149$	−12.9443	+	9.40456i	−1.06044	+	0.770452i	−0.0862671	+	0.996272i	$0.527494\pi$
$150$	−6.79837	−	20.9232i	−0.555085	−	1.70838i
$151$	4.94427	−	15.2169i	0.402359	−	1.23833i	−0.520721	−	0.853727i	$-0.674337\pi$
$151$	4.94427	−	15.2169i	0.402359	−	1.23833i	0.923080	−	0.384607i	$-0.125663\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$		0			0
$155$	−20.0000			−1.60644
$156$	3.23607	+	2.35114i	0.259093	+	0.188242i
$157$	−0.309017	+	0.951057i	−0.0246622	+	0.0759026i	−0.962630	−	0.270820i	$-0.912705\pi$
$157$	−0.309017	+	0.951057i	−0.0246622	+	0.0759026i	0.937968	+	0.346722i	$0.112705\pi$
$158$	−6.79837	−	20.9232i	−0.540850	−	1.66456i
$159$	4.85410	−	3.52671i	0.384955	−	0.279686i
$160$	25.8885	−	18.8091i	2.04667	−	1.48699i
$161$	−0.618034	−	1.90211i	−0.0487079	−	0.149908i
$162$	0.618034	−	1.90211i	0.0485573	−	0.149444i
$163$	−20.2254	−	14.6946i	−1.58418	−	1.15097i	−0.911701	−	0.410854i	$-0.865231\pi$
$163$	−20.2254	−	14.6946i	−1.58418	−	1.15097i	−0.672476	−	0.740119i	$-0.734769\pi$
$164$	4.00000			0.312348
$165$		0			0
$166$	−12.0000			−0.931381
$167$	−14.5623	−	10.5801i	−1.12687	−	0.818715i	−0.141630	−	0.989920i	$-0.545234\pi$
$167$	−14.5623	−	10.5801i	−1.12687	−	0.818715i	−0.985236	+	0.171204i	$0.945234\pi$
$168$		0			0
$169$	−2.78115	−	8.55951i	−0.213935	−	0.658424i
$170$	25.8885	−	18.8091i	1.98556	−	1.44259i
$171$	−2.42705	+	1.76336i	−0.185601	+	0.134847i
$172$	−7.41641	−	22.8254i	−0.565496	−	1.74042i
$173$	−7.41641	+	22.8254i	−0.563859	+	1.73538i	0.107458	+	0.994210i	$0.465729\pi$
$173$	−7.41641	+	22.8254i	−0.563859	+	1.73538i	−0.671317	+	0.741170i	$0.734271\pi$
$174$	−9.70820	−	7.05342i	−0.735977	−	0.534719i
$175$	−11.0000			−0.831522
$176$		0			0
$177$	10.0000			0.751646
$178$	−19.4164	−	14.1068i	−1.45532	−	1.05735i
$179$	1.85410	−	5.70634i	0.138582	−	0.426512i	−0.857548	−	0.514404i	$-0.828013\pi$
$179$	1.85410	−	5.70634i	0.138582	−	0.426512i	0.996130	+	0.0878923i	$0.0280131\pi$
$180$	2.47214	+	7.60845i	0.184262	+	0.567101i
$181$	18.6074	−	13.5191i	1.38308	−	1.00486i	0.386491	−	0.922293i	$-0.373687\pi$
$181$	18.6074	−	13.5191i	1.38308	−	1.00486i	0.996585	−	0.0825708i	$-0.0263131\pi$
$182$	3.23607	−	2.35114i	0.239873	−	0.174278i
$183$	0.927051	+	2.85317i	0.0685296	+	0.210912i
$184$		0			0
$185$	−9.70820	−	7.05342i	−0.713761	−	0.518578i
$186$	10.0000			0.733236
$187$		0			0
$188$	4.00000			0.291730
$189$	−0.809017	−	0.587785i	−0.0588473	−	0.0427551i
$190$	7.41641	−	22.8254i	0.538043	−	1.65593i
$191$	2.47214	+	7.60845i	0.178877	+	0.550528i	0.999789	−	0.0205267i	$-0.00653431\pi$
$191$	2.47214	+	7.60845i	0.178877	+	0.550528i	−0.820912	+	0.571055i	$0.806534\pi$
$192$	−6.47214	+	4.70228i	−0.467086	+	0.339358i
$193$	−4.04508	+	2.93893i	−0.291172	+	0.211549i	−0.723775	−	0.690036i	$-0.757595\pi$
$193$	−4.04508	+	2.93893i	−0.291172	+	0.211549i	0.432604	+	0.901584i	$0.357595\pi$
$194$	3.09017	+	9.51057i	0.221861	+	0.682819i
$195$	−2.47214	+	7.60845i	−0.177033	+	0.544853i
$196$	9.70820	+	7.05342i	0.693443	+	0.503816i
$197$	8.00000			0.569976			0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000			0.569976			0.284988	+	0.958531i	$0.408010\pi$
$198$		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
$201$	0.309017	−	0.951057i	0.0217964	−	0.0670824i
$202$	6.18034	+	19.0211i	0.434847	+	1.33832i
$203$	−4.85410	+	3.52671i	−0.340691	+	0.247527i
$204$	−6.47214	+	4.70228i	−0.453140	+	0.329226i
$205$	2.47214	+	7.60845i	0.172661	+	0.531397i
$206$	−4.32624	+	13.3148i	−0.301423	+	0.927685i
$207$	−1.61803	−	1.17557i	−0.112461	−	0.0817078i
$208$	−8.00000			−0.554700
$209$		0			0
$210$	8.00000			0.552052
$211$	−16.9894	−	12.3435i	−1.16960	−	0.849761i	−0.178635	−	0.983915i	$-0.557168\pi$
$211$	−16.9894	−	12.3435i	−1.16960	−	0.849761i	−0.990960	+	0.134154i	$0.957168\pi$
$212$	3.70820	−	11.4127i	0.254680	−	0.783826i
$213$		0			0
$214$	−29.1246	+	21.1603i	−1.99092	+	1.44649i
$215$	38.8328	−	28.2137i	2.64838	−	1.92416i
$216$		0			0
$217$	1.54508	−	4.75528i	0.104887	−	0.322810i
$218$	1.61803	+	1.17557i	0.109587	+	0.0796197i
$219$	−11.0000			−0.743311
$220$		0			0
$221$	−8.00000			−0.538138
$222$	4.85410	+	3.52671i	0.325786	+	0.236697i
$223$	−5.25329	+	16.1680i	−0.351786	+	1.08269i	0.606063	+	0.795416i	$0.292748\pi$
$223$	−5.25329	+	16.1680i	−0.351786	+	1.08269i	−0.957850	+	0.287270i	$0.907252\pi$
$224$	2.47214	+	7.60845i	0.165177	+	0.508361i
$225$	−8.89919	+	6.46564i	−0.593279	+	0.431043i
$226$	−9.70820	+	7.05342i	−0.645780	+	0.469187i
$227$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$227$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$228$	−1.85410	+	5.70634i	−0.122791	+	0.377912i
$229$	14.5623	+	10.5801i	0.962304	+	0.699155i	0.953685	−	0.300808i	$-0.0972563\pi$
$229$	14.5623	+	10.5801i	0.962304	+	0.699155i	0.00861950	+	0.999963i	$0.497256\pi$
$230$	16.0000			1.05501
$231$		0			0
$232$		0			0
$233$	14.5623	+	10.5801i	0.954008	+	0.693128i	0.951752	−	0.306870i	$-0.0992816\pi$
$233$	14.5623	+	10.5801i	0.954008	+	0.693128i	0.00225687	+	0.999997i	$0.499282\pi$
$234$	1.23607	−	3.80423i	0.0808043	−	0.248690i
$235$	2.47214	+	7.60845i	0.161264	+	0.496321i
$236$	16.1803	−	11.7557i	1.05325	−	0.765231i
$237$	−8.89919	+	6.46564i	−0.578064	+	0.419988i
$238$	2.47214	+	7.60845i	0.160245	+	0.493183i
$239$	−1.85410	+	5.70634i	−0.119932	+	0.369112i	−0.992944	−	0.118587i	$-0.962164\pi$
$239$	−1.85410	+	5.70634i	−0.119932	+	0.369112i	0.873012	+	0.487699i	$0.162164\pi$
$240$	−12.9443	−	9.40456i	−0.835549	−	0.607062i
$241$	14.0000			0.901819			0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000			0.901819			0.450910	+	0.892570i	$0.351100\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$	4.85410	+	3.52671i	0.310752	+	0.225775i
$245$	−7.41641	+	22.8254i	−0.473817	+	1.45826i
$246$	−1.23607	−	3.80423i	−0.0788088	−	0.242549i
$247$	−4.85410	+	3.52671i	−0.308859	+	0.224399i
$248$		0			0
$249$	1.85410	+	5.70634i	0.117499	+	0.361625i
$250$	14.8328	−	45.6507i	0.938110	−	2.88720i
$251$	1.61803	+	1.17557i	0.102129	+	0.0742014i	0.637678	−	0.770303i	$-0.279895\pi$
$251$	1.61803	+	1.17557i	0.102129	+	0.0742014i	−0.535548	+	0.844504i	$0.679895\pi$
$252$	−2.00000			−0.125988
$253$		0			0
$254$	26.0000			1.63139
$255$	−12.9443	−	9.40456i	−0.810602	−	0.588937i
$256$	4.94427	−	15.2169i	0.309017	−	0.951057i
$257$	−4.32624	−	13.3148i	−0.269863	−	0.830554i	−0.990533	−	0.137275i	$-0.956166\pi$
$257$	−4.32624	−	13.3148i	−0.269863	−	0.830554i	0.720670	−	0.693279i	$-0.243834\pi$
$258$	−19.4164	+	14.1068i	−1.20881	+	0.878254i
$259$	2.42705	−	1.76336i	0.150810	−	0.109570i
$260$	4.94427	+	15.2169i	0.306631	+	0.943712i
$261$	−1.85410	+	5.70634i	−0.114766	+	0.353214i
$262$	−9.70820	−	7.05342i	−0.599775	−	0.435762i
$263$	10.0000			0.616626			0.308313	−	0.951285i	$-0.400236\pi$
$263$	10.0000			0.616626			0.308313	+	0.951285i	$0.400236\pi$
$264$		0			0
$265$	24.0000			1.47431
$266$	4.85410	+	3.52671i	0.297624	+	0.216237i
$267$	−3.70820	+	11.4127i	−0.226938	+	0.698445i
$268$	−0.618034	−	1.90211i	−0.0377524	−	0.116190i
$269$	11.3262	−	8.22899i	0.690573	−	0.501731i	−0.186275	−	0.982498i	$-0.559642\pi$
$269$	11.3262	−	8.22899i	0.690573	−	0.501731i	0.876848	+	0.480767i	$0.159642\pi$
$270$	6.47214	−	4.70228i	0.393882	−	0.286172i
$271$	−2.47214	−	7.60845i	−0.150172	−	0.462181i	0.847468	−	0.530846i	$-0.178126\pi$
$271$	−2.47214	−	7.60845i	−0.150172	−	0.462181i	−0.997640	+	0.0686657i	$0.978126\pi$
$272$	4.94427	−	15.2169i	0.299791	−	0.922660i
$273$	−1.61803	−	1.17557i	−0.0979279	−	0.0711488i
$274$	16.0000			0.966595
$275$		0			0
$276$	−4.00000			−0.240772
$277$	−8.89919	−	6.46564i	−0.534700	−	0.388483i	0.287413	−	0.957807i	$-0.407205\pi$
$277$	−8.89919	−	6.46564i	−0.534700	−	0.388483i	−0.822113	+	0.569324i	$0.807205\pi$
$278$	−9.88854	+	30.4338i	−0.593075	+	1.82530i
$279$	−1.54508	−	4.75528i	−0.0925018	−	0.284691i
$280$		0			0
$281$	−9.70820	+	7.05342i	−0.579143	+	0.420772i	−0.838415	−	0.545032i	$-0.816517\pi$
$281$	−9.70820	+	7.05342i	−0.579143	+	0.420772i	0.259272	+	0.965804i	$0.416517\pi$
$282$	−1.23607	−	3.80423i	−0.0736068	−	0.226538i
$283$	3.39919	−	10.4616i	0.202061	−	0.621879i	−0.797761	−	0.602974i	$-0.793982\pi$
$283$	3.39919	−	10.4616i	0.202061	−	0.621879i	0.999821	−	0.0189045i	$-0.00601786\pi$
$284$		0			0
$285$	−12.0000			−0.710819
$286$		0			0
$287$	−2.00000			−0.118056
$288$	6.47214	+	4.70228i	0.381374	+	0.277085i
$289$	−0.309017	+	0.951057i	−0.0181775	+	0.0559445i
$290$	−14.8328	−	45.6507i	−0.871013	−	2.68070i
$291$	4.04508	−	2.93893i	0.237127	−	0.172283i
$292$	−17.7984	+	12.9313i	−1.04157	+	0.756746i
$293$	−3.70820	−	11.4127i	−0.216636	−	0.666736i	−0.999033	−	0.0439568i	$-0.986004\pi$
$293$	−3.70820	−	11.4127i	−0.216636	−	0.666736i	0.782398	−	0.622779i	$-0.213996\pi$
$294$	3.70820	−	11.4127i	0.216267	−	0.665601i
$295$	32.3607	+	23.5114i	1.88411	+	1.36889i
$296$		0			0
$297$		0			0
$298$	32.0000			1.85371
$299$	−3.23607	−	2.35114i	−0.187147	−	0.135970i
$300$	−6.79837	+	20.9232i	−0.392504	+	1.20800i
$301$	3.70820	+	11.4127i	0.213737	+	0.657816i
$302$	−25.8885	+	18.8091i	−1.48972	+	1.08234i
$303$	8.09017	−	5.87785i	0.464768	−	0.337674i
$304$	−3.70820	−	11.4127i	−0.212680	−	0.654562i
$305$	−3.70820	+	11.4127i	−0.212331	+	0.653488i
$306$	6.47214	+	4.70228i	0.369987	+	0.268812i
$307$	19.0000			1.08439			0.542194	−	0.840254i	$-0.317594\pi$
$307$	19.0000			1.08439			0.542194	+	0.840254i	$0.317594\pi$
$308$		0			0
$309$	7.00000			0.398216
$310$	32.3607	+	23.5114i	1.83796	+	1.33536i
$311$	7.41641	−	22.8254i	0.420546	−	1.29431i	−0.486649	−	0.873597i	$-0.661781\pi$
$311$	7.41641	−	22.8254i	0.420546	−	1.29431i	0.907195	−	0.420710i	$-0.138219\pi$
$312$		0			0
$313$	8.09017	−	5.87785i	0.457283	−	0.332236i	−0.335181	−	0.942154i	$-0.608798\pi$
$313$	8.09017	−	5.87785i	0.457283	−	0.332236i	0.792465	+	0.609918i	$0.208798\pi$
$314$	1.61803	−	1.17557i	0.0913109	−	0.0663413i
$315$	−1.23607	−	3.80423i	−0.0696445	−	0.214344i
$316$	−6.79837	+	20.9232i	−0.382438	+	1.17702i
$317$	16.1803	+	11.7557i	0.908778	+	0.660266i	0.940706	−	0.339224i	$-0.110164\pi$
$317$	16.1803	+	11.7557i	0.908778	+	0.660266i	−0.0319272	+	0.999490i	$0.510164\pi$
$318$	−12.0000			−0.672927
$319$		0			0
$320$	−32.0000			−1.78885
$321$	14.5623	+	10.5801i	0.812789	+	0.590526i
$322$	−1.23607	+	3.80423i	−0.0688834	+	0.212001i
$323$	−3.70820	−	11.4127i	−0.206330	−	0.635018i
$324$	−1.61803	+	1.17557i	−0.0898908	+	0.0653095i
$325$	−17.7984	+	12.9313i	−0.987276	+	0.717298i
$326$	15.4508	+	47.5528i	0.855743	+	2.63371i
$327$	0.309017	−	0.951057i	0.0170887	−	0.0525935i
$328$		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	$0.597757\pi$
$332$	9.70820	+	7.05342i	0.532807	+	0.387107i
$333$	0.927051	−	2.85317i	0.0508021	−	0.156353i
$334$	11.1246	+	34.2380i	0.608712	+	1.87342i
$335$	3.23607	−	2.35114i	0.176805	−	0.128457i
$336$	3.23607	−	2.35114i	0.176542	−	0.128265i
$337$	−1.54508	−	4.75528i	−0.0841661	−	0.259037i	0.900113	−	0.435656i	$-0.143484\pi$
$337$	−1.54508	−	4.75528i	−0.0841661	−	0.259037i	−0.984279	+	0.176620i	$0.943484\pi$
$338$	−5.56231	+	17.1190i	−0.302550	+	0.931152i
$339$	4.85410	+	3.52671i	0.263639	+	0.191545i
$340$	−32.0000			−1.73544
$341$		0			0
$342$	6.00000			0.324443
$343$	−10.5172	−	7.64121i	−0.567877	−	0.412586i
$344$		0			0
$345$	−2.47214	−	7.60845i	−0.133095	−	0.409625i
$346$	38.8328	−	28.2137i	2.08767	−	1.51678i
$347$	−1.61803	+	1.17557i	−0.0868606	+	0.0631079i	−0.630368	−	0.776296i	$-0.717096\pi$
$347$	−1.61803	+	1.17557i	−0.0868606	+	0.0631079i	0.543507	+	0.839404i	$0.317096\pi$
$348$	3.70820	+	11.4127i	0.198781	+	0.611784i
$349$	−4.63525	+	14.2658i	−0.248120	+	0.763633i	0.746988	+	0.664837i	$0.231499\pi$
$349$	−4.63525	+	14.2658i	−0.248120	+	0.763633i	−0.995108	+	0.0987960i	$0.968501\pi$
$350$	17.7984	+	12.9313i	0.951363	+	0.691206i
$351$	−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	$0.603464\pi$
$354$	−16.1803	−	11.7557i	−0.859975	−	0.624809i
$355$		0			0
$356$	7.41641	+	22.8254i	0.393069	+	1.20974i
$357$	3.23607	−	2.35114i	0.171271	−	0.124436i
$358$	−9.70820	+	7.05342i	−0.513095	+	0.372785i
$359$	−1.23607	−	3.80423i	−0.0652372	−	0.200779i	0.913125	−	0.407680i	$-0.133662\pi$
$359$	−1.23607	−	3.80423i	−0.0652372	−	0.200779i	−0.978362	+	0.206901i	$0.933662\pi$
$360$		0			0
$361$	8.09017	+	5.87785i	0.425798	+	0.309361i
$362$	−46.0000			−2.41771
$363$		0			0
$364$	−4.00000			−0.209657
$365$	−35.5967	−	25.8626i	−1.86322	−	1.35371i
$366$	1.85410	−	5.70634i	0.0969155	−	0.298275i
$367$	−2.47214	−	7.60845i	−0.129044	−	0.397158i	0.865572	−	0.500785i	$-0.166955\pi$
$367$	−2.47214	−	7.60845i	−0.129044	−	0.397158i	−0.994616	+	0.103627i	$0.966955\pi$
$368$	6.47214	−	4.70228i	0.337383	−	0.245123i
$369$	−1.61803	+	1.17557i	−0.0842315	+	0.0611978i
$370$	7.41641	+	22.8254i	0.385561	+	1.18663i
$371$	−1.85410	+	5.70634i	−0.0962602	+	0.296258i
$372$	−8.09017	−	5.87785i	−0.419456	−	0.304752i
$373$	−7.00000			−0.362446			−0.181223	−	0.983442i	$-0.558006\pi$
$373$	−7.00000			−0.362446			−0.181223	+	0.983442i	$0.558006\pi$
$374$		0			0
$375$	−24.0000			−1.23935
$376$		0			0
$377$	−3.70820	+	11.4127i	−0.190982	+	0.587783i
$378$	0.618034	+	1.90211i	0.0317882	+	0.0978341i
$379$	−12.9443	+	9.40456i	−0.664903	+	0.483080i	−0.868315	−	0.496013i	$-0.834797\pi$
$379$	−12.9443	+	9.40456i	−0.664903	+	0.483080i	0.203412	+	0.979093i	$0.434797\pi$
$380$	−19.4164	+	14.1068i	−0.996041	+	0.723666i
$381$	−4.01722	−	12.3637i	−0.205808	−	0.633413i
$382$	4.94427	−	15.2169i	0.252971	−	0.778565i
$383$	−21.0344	−	15.2824i	−1.07481	−	0.780895i	−0.0980391	−	0.995183i	$-0.531257\pi$
$383$	−21.0344	−	15.2824i	−1.07481	−	0.780895i	−0.976771	+	0.214288i	$0.931257\pi$
$384$		0			0
$385$		0			0
$386$	10.0000			0.508987
$387$	9.70820	+	7.05342i	0.493496	+	0.358546i
$388$	3.09017	−	9.51057i	0.156880	−	0.482826i
$389$	5.56231	+	17.1190i	0.282020	+	0.867969i	0.987276	+	0.159016i	$0.0508321\pi$
$389$	5.56231	+	17.1190i	0.282020	+	0.867969i	−0.705256	+	0.708953i	$0.749168\pi$
$390$	12.9443	−	9.40456i	0.655459	−	0.476219i
$391$	6.47214	−	4.70228i	0.327310	−	0.237805i
$392$		0			0
$393$	−1.85410	+	5.70634i	−0.0935271	+	0.287847i
$394$	−12.9443	−	9.40456i	−0.652123	−	0.473795i
$395$	−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	$0.216273\pi$
$398$	33.9787	+	24.6870i	1.70320	+	1.23745i
$399$	0.927051	−	2.85317i	0.0464106	−	0.142837i
$400$	−13.5967	−	41.8465i	−0.679837	−	2.09232i
$401$	22.6525	−	16.4580i	1.13121	−	0.821873i	0.145340	−	0.989382i	$-0.453572\pi$
$401$	22.6525	−	16.4580i	1.13121	−	0.821873i	0.985871	+	0.167509i	$0.0535724\pi$
$402$	−1.61803	+	1.17557i	−0.0807002	+	0.0586321i
$403$	−3.09017	−	9.51057i	−0.153932	−	0.473755i
$404$	6.18034	−	19.0211i	0.307483	−	0.946337i
$405$	−3.23607	−	2.35114i	−0.160802	−	0.116829i
$406$	12.0000			0.595550
$407$		0			0
$408$		0			0
$409$	16.9894	+	12.3435i	0.840070	+	0.610346i	0.922390	−	0.386260i	$-0.126233\pi$
$409$	16.9894	+	12.3435i	0.840070	+	0.610346i	−0.0823205	+	0.996606i	$0.526233\pi$
$410$	4.94427	−	15.2169i	0.244180	−	0.751509i
$411$	−2.47214	−	7.60845i	−0.121941	−	0.375297i
$412$	11.3262	−	8.22899i	0.558004	−	0.405413i
$413$	−8.09017	+	5.87785i	−0.398091	+	0.289230i
$414$	1.23607	+	3.80423i	0.0607494	+	0.186968i
$415$	−7.41641	+	22.8254i	−0.364057	+	1.12045i
$416$	12.9443	+	9.40456i	0.634645	+	0.461097i
$417$	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	$0.280962\pi$
$420$	−6.47214	−	4.70228i	−0.315808	−	0.229448i
$421$	−0.618034	+	1.90211i	−0.0301211	+	0.0927033i	−0.964987	−	0.262298i	$-0.915520\pi$
$421$	−0.618034	+	1.90211i	−0.0301211	+	0.0927033i	0.934866	+	0.355001i	$0.115520\pi$
$422$	12.9787	+	39.9444i	0.631794	+	1.94446i
$423$	−1.61803	+	1.17557i	−0.0786715	+	0.0571582i
$424$		0			0
$425$	−13.5967	−	41.8465i	−0.659539	−	2.02985i
$426$		0			0
$427$	−2.42705	−	1.76336i	−0.117453	−	0.0853348i
$428$	36.0000			1.74013
$429$		0			0
$430$	−96.0000			−4.62953
$431$	14.5623	+	10.5801i	0.701442	+	0.509627i	0.880401	−	0.474229i	$-0.157273\pi$
$431$	14.5623	+	10.5801i	0.701442	+	0.509627i	−0.178960	+	0.983856i	$0.557273\pi$
$432$	1.23607	−	3.80423i	0.0594703	−	0.183031i
$433$	−5.25329	−	16.1680i	−0.252457	−	0.776983i	−0.994320	−	0.106431i	$-0.966058\pi$
$433$	−5.25329	−	16.1680i	−0.252457	−	0.776983i	0.741863	−	0.670551i	$-0.233942\pi$
$434$	−8.09017	+	5.87785i	−0.388341	+	0.282146i
$435$	−19.4164	+	14.1068i	−0.930946	+	0.676371i
$436$	−0.618034	−	1.90211i	−0.0295985	−	0.0910947i
$437$	1.85410	−	5.70634i	0.0886937	−	0.272971i
$438$	17.7984	+	12.9313i	0.850439	+	0.617880i
$439$	−37.0000			−1.76591			−0.882957	−	0.469454i	$-0.844451\pi$
$439$	−37.0000			−1.76591			−0.882957	+	0.469454i	$0.844451\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$	12.9443	+	9.40456i	0.615696	+	0.447329i
$443$	1.23607	−	3.80423i	0.0587274	−	0.180744i	−0.917389	−	0.397991i	$-0.869708\pi$
$443$	1.23607	−	3.80423i	0.0587274	−	0.180744i	0.976117	+	0.217247i	$0.0697076\pi$
$444$	−1.85410	−	5.70634i	−0.0879918	−	0.270811i
$445$	−38.8328	+	28.2137i	−1.84085	+	1.33746i
$446$	27.5066	−	19.9847i	1.30247	−	0.946303i
$447$	−4.94427	−	15.2169i	−0.233856	−	0.719735i
$448$	2.47214	−	7.60845i	0.116797	−	0.359466i
$449$	−16.1803	−	11.7557i	−0.763597	−	0.554786i	0.136414	−	0.990652i	$-0.456442\pi$
$449$	−16.1803	−	11.7557i	−0.763597	−	0.554786i	−0.900012	+	0.435866i	$0.856442\pi$
$450$	22.0000			1.03709
$451$		0			0
$452$	12.0000			0.564433
$453$	12.9443	+	9.40456i	0.608175	+	0.441865i
$454$		0			0
$455$	−2.47214	−	7.60845i	−0.115896	−	0.356690i
$456$		0			0
$457$	14.5623	−	10.5801i	0.681196	−	0.494918i	−0.192558	−	0.981286i	$-0.561678\pi$
$457$	14.5623	−	10.5801i	0.681196	−	0.494918i	0.873754	+	0.486368i	$0.161678\pi$
$458$	−11.1246	−	34.2380i	−0.519819	−	1.59984i
$459$	1.23607	−	3.80423i	0.0576947	−	0.177566i
$460$	−12.9443	−	9.40456i	−0.603530	−	0.438490i
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	−19.4164	−	14.1068i	−0.901384	−	0.654894i
$465$	6.18034	−	19.0211i	0.286606	−	0.882084i
$466$	−11.1246	−	34.2380i	−0.515338	−	1.58605i
$467$	−19.4164	+	14.1068i	−0.898484	+	0.652787i	−0.938076	−	0.346429i	$-0.887394\pi$
$467$	−19.4164	+	14.1068i	−0.898484	+	0.652787i	0.0395920	+	0.999216i	$0.487394\pi$
$468$	−3.23607	+	2.35114i	−0.149587	+	0.108682i
$469$	0.309017	+	0.951057i	0.0142691	+	0.0439157i
$470$	4.94427	−	15.2169i	0.228062	−	0.701903i
$471$	−0.809017	−	0.587785i	−0.0372775	−	0.0270837i
$472$		0			0
$473$		0			0
$474$	22.0000			1.01049
$475$	−26.6976	−	19.3969i	−1.22497	−	0.889991i
$476$	2.47214	−	7.60845i	0.113310	−	0.348733i
$477$	1.85410	+	5.70634i	0.0848935	+	0.261275i
$478$	9.70820	−	7.05342i	0.444043	−	0.322616i
$479$	−17.7984	+	12.9313i	−0.813228	+	0.590845i	−0.914765	−	0.403987i	$-0.867624\pi$
$479$	−17.7984	+	12.9313i	−0.813228	+	0.590845i	0.101536	+	0.994832i	$0.467624\pi$
$480$	9.88854	+	30.4338i	0.451348	+	1.38911i
$481$	1.85410	−	5.70634i	0.0845398	−	0.260187i
$482$	−22.6525	−	16.4580i	−1.03179	−	0.749641i
$483$	2.00000			0.0910032
$484$		0			0
$485$	20.0000			0.908153
$486$	1.61803	+	1.17557i	0.0733955	+	0.0533250i
$487$	−12.3607	+	38.0423i	−0.560116	+	1.72386i	0.121919	+	0.992540i	$0.461095\pi$
$487$	−12.3607	+	38.0423i	−0.560116	+	1.72386i	−0.682035	+	0.731319i	$0.738905\pi$
$488$		0			0
$489$	20.2254	−	14.6946i	0.914625	−	0.664514i
$490$	38.8328	−	28.2137i	1.75429	−	1.27456i
$491$	4.32624	+	13.3148i	0.195240	+	0.600888i	0.999974	+	0.00725163i	$0.00230829\pi$
$491$	4.32624	+	13.3148i	0.195240	+	0.600888i	−0.804733	+	0.593636i	$0.797692\pi$
$492$	−1.23607	+	3.80423i	−0.0557262	+	0.171508i
$493$	−19.4164	−	14.1068i	−0.874471	−	0.635340i
$494$	12.0000			0.539906
$495$		0			0
$496$	20.0000			0.898027
$497$		0			0
$498$	3.70820	−	11.4127i	0.166169	−	0.511414i
$499$	7.10739	+	21.8743i	0.318171	+	0.979228i	0.974430	+	0.224693i	$0.0721378\pi$
$499$	7.10739	+	21.8743i	0.318171	+	0.979228i	−0.656259	+	0.754536i	$0.727862\pi$
$500$	−38.8328	+	28.2137i	−1.73666	+	1.26175i
$501$	14.5623	−	10.5801i	0.650596	−	0.472686i
$502$	−1.23607	−	3.80423i	−0.0551684	−	0.169791i
$503$	9.88854	−	30.4338i	0.440908	−	1.35698i	−0.446001	−	0.895033i	$-0.647152\pi$
$503$	9.88854	−	30.4338i	0.440908	−	1.35698i	0.886909	−	0.461944i	$-0.152848\pi$
$504$		0			0
$505$	40.0000			1.77998
$506$		0			0
$507$	9.00000			0.399704
$508$	−21.0344	−	15.2824i	−0.933252	−	0.678048i
$509$	1.85410	−	5.70634i	0.0821816	−	0.252929i	−0.901520	−	0.432737i	$-0.857548\pi$
$509$	1.85410	−	5.70634i	0.0821816	−	0.252929i	0.983702	+	0.179808i	$0.0575477\pi$
$510$	9.88854	+	30.4338i	0.437872	+	1.34763i
$511$	8.89919	−	6.46564i	0.393677	−	0.286023i
$512$	−25.8885	+	18.8091i	−1.14412	+	0.831254i
$513$	−0.927051	−	2.85317i	−0.0409303	−	0.125971i
$514$	−8.65248	+	26.6296i	−0.381644	+	1.17458i
$515$	22.6525	+	16.4580i	0.998187	+	0.725226i
$516$	24.0000			1.05654
$517$		0			0
$518$	−6.00000			−0.263625
$519$	−19.4164	−	14.1068i	−0.852286	−	0.619222i
$520$		0			0
$521$	−1.85410	−	5.70634i	−0.0812297	−	0.249999i	0.902191	−	0.431336i	$-0.141958\pi$
$521$	−1.85410	−	5.70634i	−0.0812297	−	0.249999i	−0.983421	+	0.181337i	$0.941958\pi$
$522$	9.70820	−	7.05342i	0.424917	−	0.308720i
$523$	23.4615	−	17.0458i	1.02590	−	0.745360i	0.0584156	−	0.998292i	$-0.481395\pi$
$523$	23.4615	−	17.0458i	1.02590	−	0.745360i	0.967484	+	0.252933i	$0.0813951\pi$
$524$	3.70820	+	11.4127i	0.161994	+	0.498565i
$525$	3.39919	−	10.4616i	0.148353	−	0.456583i
$526$	−16.1803	−	11.7557i	−0.705496	−	0.512573i
$527$	20.0000			0.871214
$528$		0			0
$529$	−19.0000			−0.826087
$530$	−38.8328	−	28.2137i	−1.68679	−	1.22552i
$531$	−3.09017	+	9.51057i	−0.134102	+	0.412723i
$532$	−1.85410	−	5.70634i	−0.0803855	−	0.247401i
$533$	−3.23607	+	2.35114i	−0.140170	+	0.101839i
$534$	19.4164	−	14.1068i	0.840230	−	0.610463i
$535$	22.2492	+	68.4761i	0.961918	+	2.96048i
$536$		0			0
$537$	4.85410	+	3.52671i	0.209470	+	0.152189i
$538$	−28.0000			−1.20717
$539$		0			0
$540$	−8.00000			−0.344265
$541$	−1.61803	−	1.17557i	−0.0695647	−	0.0505417i	0.552459	−	0.833540i	$-0.313689\pi$
$541$	−1.61803	−	1.17557i	−0.0695647	−	0.0505417i	−0.622024	+	0.782998i	$0.713689\pi$
$542$	−4.94427	+	15.2169i	−0.212375	+	0.653622i
$543$	7.10739	+	21.8743i	0.305007	+	0.938716i
$544$	−25.8885	+	18.8091i	−1.10996	+	0.806435i
$545$	3.23607	−	2.35114i	0.138618	−	0.100712i
$546$	1.23607	+	3.80423i	0.0528988	+	0.162806i
$547$	−6.18034	+	19.0211i	−0.264252	+	0.813285i	0.727612	+	0.685988i	$0.240630\pi$
$547$	−6.18034	+	19.0211i	−0.264252	+	0.813285i	−0.991865	+	0.127296i	$0.959370\pi$
$548$	−12.9443	−	9.40456i	−0.552952	−	0.401743i
$549$	−3.00000			−0.128037
$550$		0			0
$551$	−18.0000			−0.766826
$552$		0			0
$553$	3.39919	−	10.4616i	0.144548	−	0.444873i
$554$	6.79837	+	20.9232i	0.288835	+	0.888943i
$555$	9.70820	−	7.05342i	0.412090	−	0.299401i
$556$	25.8885	−	18.8091i	1.09792	−	0.797685i
$557$	2.47214	+	7.60845i	0.104748	+	0.322380i	0.989671	−	0.143356i	$-0.0457894\pi$
$557$	2.47214	+	7.60845i	0.104748	+	0.322380i	−0.884923	+	0.465737i	$0.845789\pi$
$558$	−3.09017	+	9.51057i	−0.130817	+	0.402614i
$559$	19.4164	+	14.1068i	0.821227	+	0.596656i
$560$	16.0000			0.676123
$561$		0			0
$562$	24.0000			1.01238
$563$	22.6525	+	16.4580i	0.954688	+	0.693621i	0.951911	−	0.306375i	$-0.0991160\pi$
$563$	22.6525	+	16.4580i	0.954688	+	0.693621i	0.00277703	+	0.999996i	$0.499116\pi$
$564$	−1.23607	+	3.80423i	−0.0520479	+	0.160187i
$565$	7.41641	+	22.8254i	0.312011	+	0.960270i
$566$	−17.7984	+	12.9313i	−0.748121	+	0.543542i
$567$	0.809017	−	0.587785i	0.0339755	−	0.0246847i
$568$		0			0
$569$	−3.70820	+	11.4127i	−0.155456	+	0.478444i	−0.998207	−	0.0598595i	$-0.980935\pi$
$569$	−3.70820	+	11.4127i	−0.155456	+	0.478444i	0.842751	+	0.538304i	$0.180935\pi$
$570$	19.4164	+	14.1068i	0.813264	+	0.590871i
$571$	25.0000			1.04622			0.523109	−	0.852266i	$-0.324772\pi$
$571$	25.0000			1.04622			0.523109	+	0.852266i	$0.324772\pi$
$572$		0			0
$573$	−8.00000			−0.334205
$574$	3.23607	+	2.35114i	0.135071	+	0.0981347i
$575$	6.79837	−	20.9232i	0.283512	−	0.872560i
$576$	−2.47214	−	7.60845i	−0.103006	−	0.317019i
$577$	−12.1353	+	8.81678i	−0.505197	+	0.367047i	−0.810999	−	0.585048i	$-0.801076\pi$
$577$	−12.1353	+	8.81678i	−0.505197	+	0.367047i	0.305801	+	0.952095i	$0.401076\pi$
$578$	1.61803	−	1.17557i	0.0673013	−	0.0488973i
$579$	−1.54508	−	4.75528i	−0.0642115	−	0.197623i
$580$	−14.8328	+	45.6507i	−0.615899	+	1.89554i
$581$	−4.85410	−	3.52671i	−0.201382	−	0.146313i
$582$	−10.0000			−0.414513
$583$		0			0
$584$		0			0
$585$	−6.47214	−	4.70228i	−0.267590	−	0.194415i
$586$	−7.41641	+	22.8254i	−0.306369	+	0.942907i
$587$	1.23607	+	3.80423i	0.0510180	+	0.157017i	0.973320	−	0.229454i	$-0.0736940\pi$
$587$	1.23607	+	3.80423i	0.0510180	+	0.157017i	−0.922302	+	0.386471i	$0.873694\pi$
$588$	−9.70820	+	7.05342i	−0.400360	+	0.290878i
$589$	12.1353	−	8.81678i	0.500024	−	0.363289i
$590$	−24.7214	−	76.0845i	−1.01776	−	3.13235i
$591$	−2.47214	+	7.60845i	−0.101690	+	0.312970i
$592$	9.70820	+	7.05342i	0.399005	+	0.289894i
$593$	46.0000			1.88899			0.944497	−	0.328521i	$-0.106550\pi$
$593$	46.0000			1.88899			0.944497	+	0.328521i	$0.106550\pi$
$594$		0			0
$595$	16.0000			0.655936
$596$	−25.8885	−	18.8091i	−1.06044	−	0.770452i
$597$	6.48936	−	19.9722i	0.265592	−	0.817407i
$598$	2.47214	+	7.60845i	0.101093	+	0.311133i
$599$	6.47214	−	4.70228i	0.264444	−	0.192130i	−0.447660	−	0.894204i	$-0.647742\pi$
$599$	6.47214	−	4.70228i	0.264444	−	0.192130i	0.712104	+	0.702074i	$0.247742\pi$
$600$		0			0
$601$	0.309017	+	0.951057i	0.0126051	+	0.0387944i	0.957161	−	0.289556i	$-0.0935075\pi$
$601$	0.309017	+	0.951057i	0.0126051	+	0.0387944i	−0.944556	+	0.328350i	$0.893507\pi$
$602$	7.41641	−	22.8254i	0.302270	−	0.930292i
$603$	0.809017	+	0.587785i	0.0329457	+	0.0239365i
$604$	32.0000			1.30206
$605$		0			0
$606$	−20.0000			−0.812444
$607$	6.47214	+	4.70228i	0.262696	+	0.190860i	0.711335	−	0.702853i	$-0.248091\pi$
$607$	6.47214	+	4.70228i	0.262696	+	0.190860i	−0.448639	+	0.893713i	$0.648091\pi$
$608$	−7.41641	+	22.8254i	−0.300775	+	0.925690i
$609$	−1.85410	−	5.70634i	−0.0751320	−	0.231233i
$610$	19.4164	−	14.1068i	0.786147	−	0.571170i
$611$	−3.23607	+	2.35114i	−0.130917	+	0.0951170i
$612$	−2.47214	−	7.60845i	−0.0999302	−	0.307553i
$613$	4.01722	−	12.3637i	0.162254	−	0.499367i	−0.836569	−	0.547861i	$-0.815442\pi$
$613$	4.01722	−	12.3637i	0.162254	−	0.499367i	0.998823	+	0.0484944i	$0.0154423\pi$
$614$	−30.7426	−	22.3358i	−1.24067	−	0.901401i
$615$	−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	$0.660490\pi$
$618$	−11.3262	−	8.22899i	−0.455608	−	0.331019i
$619$	−1.23607	+	3.80423i	−0.0496818	+	0.152905i	−0.972820	−	0.231565i	$-0.925616\pi$
$619$	−1.23607	+	3.80423i	−0.0496818	+	0.152905i	0.923138	+	0.384469i	$0.125616\pi$
$620$	−12.3607	−	38.0423i	−0.496417	−	1.52781i
$621$	1.61803	−	1.17557i	0.0649295	−	0.0471740i
$622$	−38.8328	+	28.2137i	−1.55705	+	1.13127i
$623$	−3.70820	−	11.4127i	−0.148566	−	0.457239i
$624$	2.47214	−	7.60845i	0.0989646	−	0.304582i
$625$	−33.1697	−	24.0992i	−1.32679	−	0.963968i
$626$	−20.0000			−0.799361
$627$		0			0
$628$	−2.00000			−0.0798087
$629$	9.70820	+	7.05342i	0.387091	+	0.281238i
$630$	−2.47214	+	7.60845i	−0.0984923	+	0.303128i
$631$	−9.88854	−	30.4338i	−0.393657	−	1.21155i	−0.930003	−	0.367553i	$-0.880196\pi$
$631$	−9.88854	−	30.4338i	−0.393657	−	1.21155i	0.536346	−	0.843998i	$-0.319804\pi$
$632$		0			0
$633$	16.9894	−	12.3435i	0.675266	−	0.490610i
$634$	−12.3607	−	38.0423i	−0.490905	−	1.51085i
$635$	16.0689	−	49.4549i	0.637674	−	1.96256i
$636$	9.70820	+	7.05342i	0.384955	+	0.279686i
$637$	−12.0000			−0.475457
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−7.41641	+	22.8254i	−0.292930	+	0.901547i	0.690978	+	0.722876i	$0.257180\pi$
$641$	−7.41641	+	22.8254i	−0.292930	+	0.901547i	−0.983909	+	0.178672i	$0.942820\pi$
$642$	−11.1246	−	34.2380i	−0.439053	−	1.35127i
$643$	29.9336	−	21.7481i	1.18047	−	0.857660i	0.188243	−	0.982123i	$-0.439721\pi$
$643$	29.9336	−	21.7481i	1.18047	−	0.857660i	0.992224	+	0.124463i	$0.0397208\pi$
$644$	3.23607	−	2.35114i	0.127519	−	0.0926479i
$645$	14.8328	+	45.6507i	0.584042	+	1.79750i
$646$	−7.41641	+	22.8254i	−0.291795	+	0.898052i
$647$	3.23607	+	2.35114i	0.127223	+	0.0924329i	0.649577	−	0.760296i	$-0.274946\pi$
$647$	3.23607	+	2.35114i	0.127223	+	0.0924329i	−0.522354	+	0.852729i	$0.674946\pi$
$648$		0			0
$649$		0			0
$650$	44.0000			1.72582
$651$	4.04508	+	2.93893i	0.158539	+	0.115186i
$652$	15.4508	−	47.5528i	0.605102	−	1.86231i
$653$	3.09017	+	9.51057i	0.120928	+	0.372177i	0.993137	−	0.116955i	$-0.0373134\pi$
$653$	3.09017	+	9.51057i	0.120928	+	0.372177i	−0.872209	+	0.489133i	$0.837313\pi$
$654$	−1.61803	+	1.17557i	−0.0632701	+	0.0459684i
$655$	−19.4164	+	14.1068i	−0.758662	+	0.551200i
$656$	−2.47214	−	7.60845i	−0.0965207	−	0.297060i
$657$	3.39919	−	10.4616i	0.132615	−	0.408147i
$658$	3.23607	+	2.35114i	0.126155	+	0.0916570i
$659$	−46.0000			−1.79191			−0.895953	−	0.444149i	$-0.853506\pi$
$659$	−46.0000			−1.79191			−0.895953	+	0.444149i	$0.853506\pi$
$660$		0			0
$661$	−5.00000			−0.194477			−0.0972387	−	0.995261i	$-0.531001\pi$
$661$	−5.00000			−0.194477			−0.0972387	+	0.995261i	$0.531001\pi$
$662$	17.7984	+	12.9313i	0.691753	+	0.502588i
$663$	2.47214	−	7.60845i	0.0960098	−	0.295488i
$664$		0			0
$665$	9.70820	−	7.05342i	0.376468	−	0.273520i
$666$	−4.85410	+	3.52671i	−0.188093	+	0.136657i
$667$	−3.70820	−	11.4127i	−0.143582	−	0.441901i
$668$	11.1246	−	34.2380i	0.430424	−	1.32471i
$669$	−13.7533	−	9.99235i	−0.531733	−	0.386327i
$670$	−8.00000			−0.309067
$671$		0			0
$672$	−8.00000			−0.308607
$673$	−10.5172	−	7.64121i	−0.405409	−	0.294547i	0.366332	−	0.930484i	$-0.380614\pi$
$673$	−10.5172	−	7.64121i	−0.405409	−	0.294547i	−0.771741	+	0.635937i	$0.780614\pi$
$674$	−3.09017	+	9.51057i	−0.119029	+	0.366333i
$675$	−3.39919	−	10.4616i	−0.130835	−	0.402668i
$676$	14.5623	−	10.5801i	0.560089	−	0.406928i
$677$	9.70820	−	7.05342i	0.373117	−	0.271085i	−0.385386	−	0.922756i	$-0.625932\pi$
$677$	9.70820	−	7.05342i	0.373117	−	0.271085i	0.758502	+	0.651671i	$0.225932\pi$
$678$	−3.70820	−	11.4127i	−0.142413	−	0.438301i
$679$	−1.54508	+	4.75528i	−0.0592949	+	0.182491i
$680$		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	$0.725435\pi$
$684$	−4.85410	−	3.52671i	−0.185601	−	0.134847i
$685$	9.88854	−	30.4338i	0.377822	−	1.16282i
$686$	8.03444	+	24.7275i	0.306756	+	0.944099i
$687$	−14.5623	+	10.5801i	−0.555587	+	0.403657i
$688$	−38.8328	+	28.2137i	−1.48049	+	1.07564i
$689$	3.70820	+	11.4127i	0.141271	+	0.434788i
$690$	−4.94427	+	15.2169i	−0.188225	+	0.579298i
$691$	−8.89919	−	6.46564i	−0.338541	−	0.245964i	0.405505	−	0.914093i	$-0.367096\pi$
$691$	−8.89919	−	6.46564i	−0.338541	−	0.245964i	−0.744046	+	0.668128i	$0.767096\pi$
$692$	−48.0000			−1.82469
$693$		0			0
$694$	4.00000			0.151838
$695$	51.7771	+	37.6183i	1.96402	+	1.42694i
$696$		0			0
$697$	−2.47214	−	7.60845i	−0.0936388	−	0.288191i
$698$	24.2705	−	17.6336i	0.918652	−	0.667440i
$699$	−14.5623	+	10.5801i	−0.550797	+	0.400177i
$700$	−6.79837	−	20.9232i	−0.256954	−	0.790824i
$701$	−15.4508	+	47.5528i	−0.583571	+	1.79605i	0.0213660	+	0.999772i	$0.493198\pi$
$701$	−15.4508	+	47.5528i	−0.583571	+	1.79605i	−0.604936	+	0.796274i	$0.706802\pi$
$702$	3.23607	+	2.35114i	0.122138	+	0.0887381i
$703$	9.00000			0.339441
$704$		0			0
$705$	−8.00000			−0.301297
$706$	19.4164	+	14.1068i	0.730746	+	0.530918i
$707$	−3.09017	+	9.51057i	−0.116218	+	0.357682i
$708$	6.18034	+	19.0211i	0.232271	+	0.714858i
$709$	−21.0344	+	15.2824i	−0.789965	+	0.573943i	−0.907953	−	0.419072i	$-0.862356\pi$
$709$	−21.0344	+	15.2824i	−0.789965	+	0.573943i	0.117988	+	0.993015i	$0.462356\pi$
$710$		0			0
$711$	−3.39919	−	10.4616i	−0.127479	−	0.392341i
$712$		0			0
$713$	8.09017	+	5.87785i	0.302979	+	0.220127i
$714$	−8.00000			−0.299392
$715$		0			0
$716$	12.0000			0.448461
$717$	−4.85410	−	3.52671i	−0.181280	−	0.131707i
$718$	−2.47214	+	7.60845i	−0.0922593	+	0.283945i
$719$	−1.85410	−	5.70634i	−0.0691463	−	0.212811i	0.910512	−	0.413482i	$-0.135688\pi$
$719$	−1.85410	−	5.70634i	−0.0691463	−	0.212811i	−0.979659	+	0.200672i	$0.935688\pi$
$720$	12.9443	−	9.40456i	0.482405	−	0.350487i
$721$	−5.66312	+	4.11450i	−0.210906	+	0.153232i
$722$	−6.18034	−	19.0211i	−0.230008	−	0.707893i
$723$	−4.32624	+	13.3148i	−0.160895	+	0.495182i
$724$	37.2148	+	27.0381i	1.38308	+	1.00486i
$725$	−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
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	27.1935	+	83.6930i	1.00648	+	3.09762i
$731$	−38.8328	+	28.2137i	−1.43628	+	1.04352i
$732$	−4.85410	+	3.52671i	−0.179413	+	0.130351i
$733$	9.27051	+	28.5317i	0.342414	+	1.05384i	0.962954	+	0.269667i	$0.0869136\pi$
$733$	9.27051	+	28.5317i	0.342414	+	1.05384i	−0.620540	+	0.784175i	$0.713086\pi$
$734$	−4.94427	+	15.2169i	−0.182496	+	0.561666i
$735$	−19.4164	−	14.1068i	−0.716185	−	0.520339i
$736$	−16.0000			−0.589768
$737$		0			0
$738$	4.00000			0.147242
$739$	33.1697	+	24.0992i	1.22017	+	0.886503i	0.996114	−	0.0880737i	$-0.0280711\pi$
$739$	33.1697	+	24.0992i	1.22017	+	0.886503i	0.224053	+	0.974577i	$0.428071\pi$
$740$	7.41641	−	22.8254i	0.272633	−	0.839077i
$741$	−1.85410	−	5.70634i	−0.0681121	−	0.209628i
$742$	9.70820	−	7.05342i	0.356399	−	0.258939i
$743$	−16.1803	+	11.7557i	−0.593599	+	0.431275i	−0.843601	−	0.536970i	$-0.819569\pi$
$743$	−16.1803	+	11.7557i	−0.593599	+	0.431275i	0.250002	+	0.968245i	$0.419569\pi$
$744$		0			0
$745$	19.7771	−	60.8676i	0.724576	−	2.23002i
$746$	11.3262	+	8.22899i	0.414683	+	0.301285i
$747$	−6.00000			−0.219529
$748$		0			0
$749$	−18.0000			−0.657706
$750$	38.8328	+	28.2137i	1.41797	+	1.03022i
$751$	5.87132	−	18.0701i	0.214248	−	0.659386i	−0.784959	−	0.619548i	$-0.787316\pi$
$751$	5.87132	−	18.0701i	0.214248	−	0.659386i	0.999206	−	0.0398381i	$-0.0126842\pi$
$752$	−2.47214	−	7.60845i	−0.0901495	−	0.277452i
$753$	−1.61803	+	1.17557i	−0.0589644	+	0.0428402i
$754$	19.4164	−	14.1068i	0.707104	−	0.513741i
$755$	19.7771	+	60.8676i	0.719762	+	2.21520i
$756$	0.618034	−	1.90211i	0.0224777	−	0.0691792i
$757$	−4.04508	−	2.93893i	−0.147021	−	0.106817i	0.511843	−	0.859079i	$-0.328963\pi$
$757$	−4.04508	−	2.93893i	−0.147021	−	0.106817i	−0.658864	+	0.752262i	$0.728963\pi$
$758$	32.0000			1.16229
$759$		0			0
$760$		0			0
$761$	−19.4164	−	14.1068i	−0.703844	−	0.511373i	0.177338	−	0.984150i	$-0.443252\pi$
$761$	−19.4164	−	14.1068i	−0.703844	−	0.511373i	−0.881182	+	0.472777i	$0.843252\pi$
$762$	−8.03444	+	24.7275i	−0.291057	+	0.895782i
$763$	0.309017	+	0.951057i	0.0111872	+	0.0344306i
$764$	−12.9443	+	9.40456i	−0.468307	+	0.340245i
$765$	12.9443	−	9.40456i	0.468001	−	0.340023i
$766$	16.0689	+	49.4549i	0.580592	+	1.78688i
$767$	−6.18034	+	19.0211i	−0.223159	+	0.686813i
$768$	12.9443	+	9.40456i	0.467086	+	0.339358i
$769$	−11.0000			−0.396670			−0.198335	−	0.980134i	$-0.563553\pi$
$769$	−11.0000			−0.396670			−0.198335	+	0.980134i	$0.563553\pi$
$770$		0			0
$771$	14.0000			0.504198
$772$	−8.09017	−	5.87785i	−0.291172	−	0.211549i
$773$	11.1246	−	34.2380i	0.400124	−	1.23146i	−0.524774	−	0.851242i	$-0.675850\pi$
$773$	11.1246	−	34.2380i	0.400124	−	1.23146i	0.924898	−	0.380215i	$-0.124150\pi$
$774$

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)

\(f(q)\)	\(=\)	\(q+(-1.61803 - 1.17557i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.618034 + 1.90211i) q^{4} +(-3.23607 + 2.35114i) q^{5} +(1.61803 - 1.17557i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.61803 - 1.17557i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.618034 + 1.90211i) q^{4} +(-3.23607 + 2.35114i) q^{5} +(1.61803 - 1.17557i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.809017 - 0.587785i) q^{9} +8.00000 q^{10} -2.00000 q^{12} +(-1.61803 - 1.17557i) q^{13} +(-0.618034 + 1.90211i) q^{14} +(-1.23607 - 3.80423i) q^{15} +(3.23607 - 2.35114i) q^{16} +(3.23607 - 2.35114i) q^{17} +(0.618034 + 1.90211i) q^{18} +(0.927051 - 2.85317i) q^{19} +(-6.47214 - 4.70228i) q^{20} +1.00000 q^{21} +2.00000 q^{23} +(3.39919 - 10.4616i) q^{25} +(1.23607 + 3.80423i) q^{26} +(0.809017 - 0.587785i) q^{27} +(1.61803 - 1.17557i) q^{28} +(-1.85410 - 5.70634i) q^{29} +(-2.47214 + 7.60845i) q^{30} +(4.04508 + 2.93893i) q^{31} -8.00000 q^{32} -8.00000 q^{34} +(3.23607 + 2.35114i) q^{35} +(0.618034 - 1.90211i) q^{36} +(0.927051 + 2.85317i) q^{37} +(-4.85410 + 3.52671i) q^{38} +(1.61803 - 1.17557i) q^{39} +(0.618034 - 1.90211i) q^{41} +(-1.61803 - 1.17557i) q^{42} -12.0000 q^{43} +4.00000 q^{45} +(-3.23607 - 2.35114i) q^{46} +(0.618034 - 1.90211i) q^{47} +(1.23607 + 3.80423i) q^{48} +(4.85410 - 3.52671i) q^{49} +(-17.7984 + 12.9313i) q^{50} +(1.23607 + 3.80423i) q^{51} +(1.23607 - 3.80423i) q^{52} +(-4.85410 - 3.52671i) q^{53} -2.00000 q^{54} +(2.42705 + 1.76336i) q^{57} +(-3.70820 + 11.4127i) q^{58} +(-3.09017 - 9.51057i) q^{59} +(6.47214 - 4.70228i) q^{60} +(2.42705 - 1.76336i) q^{61} +(-3.09017 - 9.51057i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(6.47214 + 4.70228i) q^{64} +8.00000 q^{65} -1.00000 q^{67} +(6.47214 + 4.70228i) q^{68} +(-0.618034 + 1.90211i) q^{69} +(-2.47214 - 7.60845i) q^{70} +(3.39919 + 10.4616i) q^{73} +(1.85410 - 5.70634i) q^{74} +(8.89919 + 6.46564i) q^{75} +6.00000 q^{76} -4.00000 q^{78} +(8.89919 + 6.46564i) q^{79} +(-4.94427 + 15.2169i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-3.23607 + 2.35114i) q^{82} +(4.85410 - 3.52671i) q^{83} +(0.618034 + 1.90211i) q^{84} +(-4.94427 + 15.2169i) q^{85} +(19.4164 + 14.1068i) q^{86} +6.00000 q^{87} +12.0000 q^{89} +(-6.47214 - 4.70228i) q^{90} +(-0.618034 + 1.90211i) q^{91} +(1.23607 + 3.80423i) q^{92} +(-4.04508 + 2.93893i) q^{93} +(-3.23607 + 2.35114i) q^{94} +(3.70820 + 11.4127i) q^{95} +(2.47214 - 7.60845i) q^{96} +(-4.04508 - 2.93893i) 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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