LMFDB - Embedded newform 690.2.j.b.367.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(367,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("690.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.j (of order $4$, degree $2$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			367.9
Character	$\chi$	$=$	690.367
Dual form			690.2.j.b.643.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-0.643329 - 2.14152i) q^{5} +1.00000 q^{6} +(-2.01701 + 2.01701i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-0.643329 - 2.14152i) q^{5} +1.00000 q^{6} +(-2.01701 + 2.01701i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(1.05938 - 1.96919i) q^{10} -5.11516i q^{11} +(0.707107 + 0.707107i) q^{12} +(4.36777 - 4.36777i) q^{13} -2.85248 q^{14} +(-1.96919 - 1.05938i) q^{15} -1.00000 q^{16} +(0.390995 - 0.390995i) q^{17} +(0.707107 - 0.707107i) q^{18} +6.15278 q^{19} +(2.14152 - 0.643329i) q^{20} +2.85248i q^{21} +(3.61696 - 3.61696i) q^{22} +(0.204508 - 4.79147i) q^{23} +1.00000i q^{24} +(-4.17226 + 2.75541i) q^{25} +6.17696 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.01701 - 2.01701i) q^{28} +5.15378i q^{29} +(-0.643329 - 2.14152i) q^{30} +5.55456 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.61696 - 3.61696i) q^{33} +0.552950 q^{34} +(5.61707 + 3.02187i) q^{35} +1.00000 q^{36} +(-1.66015 + 1.66015i) q^{37} +(4.35067 + 4.35067i) q^{38} -6.17696i q^{39} +(1.96919 + 1.05938i) q^{40} -8.20789 q^{41} +(-2.01701 + 2.01701i) q^{42} +(-3.51520 - 3.51520i) q^{43} +5.11516 q^{44} +(-2.14152 + 0.643329i) q^{45} +(3.53269 - 3.24347i) q^{46} +(-3.69444 - 3.69444i) q^{47} +(-0.707107 + 0.707107i) q^{48} -1.13662i q^{49} +(-4.89860 - 1.00186i) q^{50} -0.552950i q^{51} +(4.36777 + 4.36777i) q^{52} +(3.27229 + 3.27229i) q^{53} -1.00000i q^{54} +(-10.9542 + 3.29073i) q^{55} -2.85248i q^{56} +(4.35067 - 4.35067i) q^{57} +(-3.64427 + 3.64427i) q^{58} -9.42889i q^{59} +(1.05938 - 1.96919i) q^{60} +6.90926i q^{61} +(3.92767 + 3.92767i) q^{62} +(2.01701 + 2.01701i) q^{63} -1.00000i q^{64} +(-12.1636 - 6.54377i) q^{65} -5.11516i q^{66} +(-6.18692 + 6.18692i) q^{67} +(0.390995 + 0.390995i) q^{68} +(-3.24347 - 3.53269i) q^{69} +(1.83508 + 6.10865i) q^{70} +10.0403 q^{71} +(0.707107 + 0.707107i) q^{72} +(-9.69041 + 9.69041i) q^{73} -2.34781 q^{74} +(-1.00186 + 4.89860i) q^{75} +6.15278i q^{76} +(10.3173 + 10.3173i) q^{77} +(4.36777 - 4.36777i) q^{78} +0.836863 q^{79} +(0.643329 + 2.14152i) q^{80} -1.00000 q^{81} +(-5.80385 - 5.80385i) q^{82} +(7.68978 + 7.68978i) q^{83} -2.85248 q^{84} +(-1.08886 - 0.585786i) q^{85} -4.97125i q^{86} +(3.64427 + 3.64427i) q^{87} +(3.61696 + 3.61696i) q^{88} +8.61622 q^{89} +(-1.96919 - 1.05938i) q^{90} +17.6196i q^{91} +(4.79147 + 0.204508i) q^{92} +(3.92767 - 3.92767i) q^{93} -5.22472i q^{94} +(-3.95826 - 13.1763i) q^{95} -1.00000 q^{96} +(7.13357 - 7.13357i) q^{97} +(0.803714 - 0.803714i) q^{98} -5.11516 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{6}+O(q^{10}) $ 24 * q + 24 * q^6	$ 24 q + 24 q^{6} + 16 q^{13} - 24 q^{16} + 16 q^{23} - 16 q^{25} + 16 q^{31} + 24 q^{36} + 8 q^{46} + 40 q^{47} - 8 q^{50} + 16 q^{52} - 56 q^{55} - 16 q^{58} - 8 q^{62} + 32 q^{70} + 64 q^{71} - 16 q^{73} + 32 q^{75} + 16 q^{77} + 16 q^{78} - 24 q^{81} + 24 q^{82} - 48 q^{85} + 16 q^{87} + 16 q^{92} - 8 q^{93} + 24 q^{95} - 24 q^{96}+O(q^{100}) $ 24 * q + 24 * q^6 + 16 * q^13 - 24 * q^16 + 16 * q^23 - 16 * q^25 + 16 * q^31 + 24 * q^36 + 8 * q^46 + 40 * q^47 - 8 * q^50 + 16 * q^52 - 56 * q^55 - 16 * q^58 - 8 * q^62 + 32 * q^70 + 64 * q^71 - 16 * q^73 + 32 * q^75 + 16 * q^77 + 16 * q^78 - 24 * q^81 + 24 * q^82 - 48 * q^85 + 16 * q^87 + 16 * q^92 - 8 * q^93 + 24 * q^95 - 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$			1.00000i			0.500000i
$5$	−0.643329	−	2.14152i	−0.287706	−	0.957719i
$5$	−0.643329	−	2.14152i	−0.287706	−	0.957719i
$6$	1.00000			0.408248
$7$	−2.01701	+	2.01701i	−0.762356	+	0.762356i	−0.976748	−	0.214391i	$-0.931223\pi$
$7$	−2.01701	+	2.01701i	−0.762356	+	0.762356i	0.214391	+	0.976748i	$0.431223\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	1.05938	−	1.96919i	0.335007	−	0.622712i
$11$		−	5.11516i		−	1.54228i	−0.636666	−	0.771139i	$-0.719687\pi$
$11$		−	5.11516i		−	1.54228i	0.636666	−	0.771139i	$-0.280313\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	4.36777	−	4.36777i	1.21140	−	1.21140i	0.240836	−	0.970566i	$-0.422578\pi$
$13$	4.36777	−	4.36777i	1.21140	−	1.21140i	0.970566	−	0.240836i	$-0.0774215\pi$
$14$	−2.85248			−0.762356
$15$	−1.96919	−	1.05938i	−0.508442	−	0.273532i
$16$	−1.00000			−0.250000
$17$	0.390995	−	0.390995i	0.0948301	−	0.0948301i	−0.658100	−	0.752930i	$-0.728640\pi$
$17$	0.390995	−	0.390995i	0.0948301	−	0.0948301i	0.752930	+	0.658100i	$0.228640\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	6.15278			1.41154			0.705772	−	0.708439i	$-0.250600\pi$
$19$	6.15278			1.41154			0.705772	+	0.708439i	$0.250600\pi$
$20$	2.14152	−	0.643329i	0.478859	−	0.143853i
$21$			2.85248i			0.622461i
$22$	3.61696	−	3.61696i	0.771139	−	0.771139i
$23$	0.204508	−	4.79147i	0.0426429	−	0.999090i
$23$	0.204508	−	4.79147i	0.0426429	−	0.999090i
$24$			1.00000i			0.204124i
$25$	−4.17226	+	2.75541i	−0.834451	+	0.551082i
$26$	6.17696			1.21140
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−2.01701	−	2.01701i	−0.381178	−	0.381178i
$29$			5.15378i			0.957032i	0.878079	+	0.478516i	$0.158825\pi$
$29$			5.15378i			0.957032i	−0.878079	+	0.478516i	$0.841175\pi$
$30$	−0.643329	−	2.14152i	−0.117455	−	0.390987i
$31$	5.55456			0.997628			0.498814	−	0.866709i	$-0.333769\pi$
$31$	5.55456			0.997628			0.498814	+	0.866709i	$0.333769\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−3.61696	−	3.61696i	−0.629633	−	0.629633i
$34$	0.552950			0.0948301
$35$	5.61707	+	3.02187i	0.949457	+	0.510789i
$36$	1.00000			0.166667
$37$	−1.66015	+	1.66015i	−0.272927	+	0.272927i	−0.830277	−	0.557350i	$-0.811818\pi$
$37$	−1.66015	+	1.66015i	−0.272927	+	0.272927i	0.557350	+	0.830277i	$0.311818\pi$
$38$	4.35067	+	4.35067i	0.705772	+	0.705772i
$39$		−	6.17696i		−	0.989105i
$40$	1.96919	+	1.05938i	0.311356	+	0.167503i
$41$	−8.20789			−1.28186			−0.640928	−	0.767601i	$-0.721450\pi$
$41$	−8.20789			−1.28186			−0.640928	+	0.767601i	$0.721450\pi$
$42$	−2.01701	+	2.01701i	−0.311231	+	0.311231i
$43$	−3.51520	−	3.51520i	−0.536063	−	0.536063i	0.386307	−	0.922370i	$-0.373751\pi$
$43$	−3.51520	−	3.51520i	−0.536063	−	0.536063i	−0.922370	+	0.386307i	$0.873751\pi$
$44$	5.11516			0.771139
$45$	−2.14152	+	0.643329i	−0.319240	+	0.0959018i
$46$	3.53269	−	3.24347i	0.520867	−	0.478224i
$47$	−3.69444	−	3.69444i	−0.538889	−	0.538889i	0.384314	−	0.923203i	$-0.374438\pi$
$47$	−3.69444	−	3.69444i	−0.538889	−	0.538889i	−0.923203	+	0.384314i	$0.874438\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$		−	1.13662i		−	0.162375i
$50$	−4.89860	−	1.00186i	−0.692767	−	0.141684i
$51$		−	0.552950i		−	0.0774285i
$52$	4.36777	+	4.36777i	0.605701	+	0.605701i
$53$	3.27229	+	3.27229i	0.449484	+	0.449484i	0.895183	−	0.445699i	$-0.147045\pi$
$53$	3.27229	+	3.27229i	0.449484	+	0.449484i	−0.445699	+	0.895183i	$0.647045\pi$
$54$		−	1.00000i		−	0.136083i
$55$	−10.9542	+	3.29073i	−1.47707	+	0.443722i
$56$		−	2.85248i		−	0.381178i
$57$	4.35067	−	4.35067i	0.576261	−	0.576261i
$58$	−3.64427	+	3.64427i	−0.478516	+	0.478516i
$59$		−	9.42889i		−	1.22754i	−0.789486	−	0.613768i	$-0.789653\pi$
$59$		−	9.42889i		−	1.22754i	0.789486	−	0.613768i	$-0.210347\pi$
$60$	1.05938	−	1.96919i	0.136766	−	0.254221i
$61$			6.90926i			0.884639i	0.896857	+	0.442320i	$0.145844\pi$
$61$			6.90926i			0.884639i	−0.896857	+	0.442320i	$0.854156\pi$
$62$	3.92767	+	3.92767i	0.498814	+	0.498814i
$63$	2.01701	+	2.01701i	0.254119	+	0.254119i
$64$		−	1.00000i		−	0.125000i
$65$	−12.1636	−	6.54377i	−1.50871	−	0.811655i
$66$		−	5.11516i		−	0.629633i
$67$	−6.18692	+	6.18692i	−0.755853	+	0.755853i	−0.975565	−	0.219712i	$-0.929488\pi$
$67$	−6.18692	+	6.18692i	−0.755853	+	0.755853i	0.219712	+	0.975565i	$0.429488\pi$
$68$	0.390995	+	0.390995i	0.0474151	+	0.0474151i
$69$	−3.24347	−	3.53269i	−0.390468	−	0.425286i
$70$	1.83508	+	6.10865i	0.219334	+	0.730123i
$71$	10.0403			1.19157			0.595784	−	0.803144i	$-0.296841\pi$
$71$	10.0403			1.19157			0.595784	+	0.803144i	$0.296841\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	−9.69041	+	9.69041i	−1.13418	+	1.13418i	−0.144702	+	0.989475i	$0.546222\pi$
$73$	−9.69041	+	9.69041i	−1.13418	+	1.13418i	−0.989475	+	0.144702i	$0.953778\pi$
$74$	−2.34781			−0.272927
$75$	−1.00186	+	4.89860i	−0.115685	+	0.565642i
$76$			6.15278i			0.705772i
$77$	10.3173	+	10.3173i	1.17577	+	1.17577i
$78$	4.36777	−	4.36777i	0.494553	−	0.494553i
$79$	0.836863			0.0941545			0.0470772	−	0.998891i	$-0.485009\pi$
$79$	0.836863			0.0941545			0.0470772	+	0.998891i	$0.485009\pi$
$80$	0.643329	+	2.14152i	0.0719264	+	0.239430i
$81$	−1.00000			−0.111111
$82$	−5.80385	−	5.80385i	−0.640928	−	0.640928i
$83$	7.68978	+	7.68978i	0.844063	+	0.844063i	0.989384	−	0.145322i	$-0.0464217\pi$
$83$	7.68978	+	7.68978i	0.844063	+	0.844063i	−0.145322	+	0.989384i	$0.546422\pi$
$84$	−2.85248			−0.311231
$85$	−1.08886	−	0.585786i	−0.118104	−	0.0635375i
$86$		−	4.97125i		−	0.536063i
$87$	3.64427	+	3.64427i	0.390707	+	0.390707i
$88$	3.61696	+	3.61696i	0.385570	+	0.385570i
$89$	8.61622			0.913317			0.456659	−	0.889642i	$-0.349046\pi$
$89$	8.61622			0.913317			0.456659	+	0.889642i	$0.349046\pi$
$90$	−1.96919	−	1.05938i	−0.207571	−	0.111669i
$91$			17.6196i			1.84704i
$92$	4.79147	+	0.204508i	0.499545	+	0.0213214i
$93$	3.92767	−	3.92767i	0.407280	−	0.407280i
$94$		−	5.22472i		−	0.538889i
$95$	−3.95826	−	13.1763i	−0.406109	−	1.35186i
$96$	−1.00000			−0.102062
$97$	7.13357	−	7.13357i	0.724304	−	0.724304i	−0.245175	−	0.969479i	$-0.578845\pi$
$97$	7.13357	−	7.13357i	0.724304	−	0.724304i	0.969479	+	0.245175i	$0.0788453\pi$
$98$	0.803714	−	0.803714i	0.0811874	−	0.0811874i
$99$	−5.11516			−0.514093
$100$	−2.75541	−	4.17226i	−0.275541	−	0.417226i
$101$	4.31730			0.429588			0.214794	−	0.976659i	$-0.431092\pi$
$101$	4.31730			0.429588			0.214794	+	0.976659i	$0.431092\pi$
$102$	0.390995	−	0.390995i	0.0387142	−	0.0387142i
$103$	12.0533	+	12.0533i	1.18765	+	1.18765i	0.977717	+	0.209929i	$0.0673234\pi$
$103$	12.0533	+	12.0533i	1.18765	+	1.18765i	0.209929	+	0.977717i	$0.432677\pi$
$104$			6.17696i			0.605701i
$105$	6.10865	−	1.83508i	0.596143	−	0.179086i
$106$			4.62772i			0.449484i
$107$	−5.43462	+	5.43462i	−0.525384	+	0.525384i	−0.919193	−	0.393808i	$-0.871157\pi$
$107$	−5.43462	+	5.43462i	−0.525384	+	0.525384i	0.393808	+	0.919193i	$0.371157\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	−1.98889			−0.190501			−0.0952507	−	0.995453i	$-0.530365\pi$
$109$	−1.98889			−0.190501			−0.0952507	+	0.995453i	$0.530365\pi$
$110$	−10.0727	−	5.41892i	−0.960396	−	0.516674i
$111$			2.34781i			0.222844i
$112$	2.01701	−	2.01701i	0.190589	−	0.190589i
$113$	−0.526241	−	0.526241i	−0.0495045	−	0.0495045i	0.681921	−	0.731426i	$-0.261145\pi$
$113$	−0.526241	−	0.526241i	−0.0495045	−	0.0495045i	−0.731426	+	0.681921i	$0.761145\pi$
$114$	6.15278			0.576261
$115$	−10.3926	+	2.64453i	−0.969116	+	0.246604i
$116$	−5.15378			−0.478516
$117$	−4.36777	−	4.36777i	−0.403801	−	0.403801i
$118$	6.66723	−	6.66723i	0.613768	−	0.613768i
$119$			1.57728i			0.144589i
$120$	2.14152	−	0.643329i	0.195494	−	0.0587276i
$121$	−15.1649			−1.37862
$122$	−4.88558	+	4.88558i	−0.442320	+	0.442320i
$123$	−5.80385	+	5.80385i	−0.523316	+	0.523316i
$124$			5.55456i			0.498814i
$125$	8.58491	+	7.16235i	0.767858	+	0.640620i
$126$			2.85248i			0.254119i
$127$	−15.6798	−	15.6798i	−1.39136	−	1.39136i	−0.822291	−	0.569068i	$-0.807304\pi$
$127$	−15.6798	−	15.6798i	−1.39136	−	1.39136i	−0.569068	−	0.822291i	$-0.692696\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−4.97125			−0.437694
$130$	−3.97382	−	13.2281i	−0.348527	−	1.16018i
$131$	−3.31192			−0.289364			−0.144682	−	0.989478i	$-0.546216\pi$
$131$	−3.31192			−0.289364			−0.144682	+	0.989478i	$0.546216\pi$
$132$	3.61696	−	3.61696i	0.314816	−	0.314816i
$133$	−12.4102	+	12.4102i	−1.07610	+	1.07610i
$134$	−8.74963			−0.755853
$135$	−1.05938	+	1.96919i	−0.0911773	+	0.169481i
$136$			0.552950i			0.0474151i
$137$	−2.13220	+	2.13220i	−0.182166	+	0.182166i	−0.792299	−	0.610133i	$-0.791116\pi$
$137$	−2.13220	+	2.13220i	−0.182166	+	0.182166i	0.610133	+	0.792299i	$0.291116\pi$
$138$	0.204508	−	4.79147i	0.0174089	−	0.407877i
$139$			8.40570i			0.712963i	0.934302	+	0.356481i	$0.116024\pi$
$139$			8.40570i			0.712963i	−0.934302	+	0.356481i	$0.883976\pi$
$140$	−3.02187	+	5.61707i	−0.255395	+	0.474729i
$141$	−5.22472			−0.440001
$142$	7.09959	+	7.09959i	0.595784	+	0.595784i
$143$	−22.3418	−	22.3418i	−1.86832	−	1.86832i
$144$			1.00000i			0.0833333i
$145$	11.0369	−	3.31558i	0.916568	−	0.275344i
$146$	−13.7043			−1.13418
$147$	−0.803714	−	0.803714i	−0.0662892	−	0.0662892i
$148$	−1.66015	−	1.66015i	−0.136464	−	0.136464i
$149$	18.0134			1.47572			0.737859	−	0.674955i	$-0.235837\pi$
$149$	18.0134			1.47572			0.737859	+	0.674955i	$0.235837\pi$
$150$	−4.17226	+	2.75541i	−0.340663	+	0.224978i
$151$	12.3312			1.00350			0.501749	−	0.865013i	$-0.332690\pi$
$151$	12.3312			1.00350			0.501749	+	0.865013i	$0.332690\pi$
$152$	−4.35067	+	4.35067i	−0.352886	+	0.352886i
$153$	−0.390995	−	0.390995i	−0.0316100	−	0.0316100i
$154$			14.5909i			1.17577i
$155$	−3.57341	−	11.8952i	−0.287023	−	0.955447i
$156$	6.17696			0.494553
$157$	−1.55503	+	1.55503i	−0.124105	+	0.124105i	−0.766431	−	0.642326i	$-0.777969\pi$
$157$	−1.55503	+	1.55503i	−0.124105	+	0.124105i	0.642326	+	0.766431i	$0.277969\pi$
$158$	0.591752	+	0.591752i	0.0470772	+	0.0470772i
$159$	4.62772			0.367002
$160$	−1.05938	+	1.96919i	−0.0837517	+	0.155678i
$161$	9.25193	+	10.0769i	0.729154	+	0.794172i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	5.61838	−	5.61838i	0.440065	−	0.440065i	−0.451968	−	0.892034i	$-0.649278\pi$
$163$	5.61838	−	5.61838i	0.440065	−	0.440065i	0.892034	+	0.451968i	$0.149278\pi$
$164$		−	8.20789i		−	0.640928i
$165$	−5.41892	+	10.0727i	−0.421862	+	0.784160i
$166$			10.8750i			0.844063i
$167$	5.78732	+	5.78732i	0.447836	+	0.447836i	0.894635	−	0.446798i	$-0.147436\pi$
$167$	5.78732	+	5.78732i	0.447836	+	0.447836i	−0.446798	+	0.894635i	$0.647436\pi$
$168$	−2.01701	−	2.01701i	−0.155615	−	0.155615i
$169$		−	25.1548i		−	1.93499i
$170$	−0.355729	−	1.18416i	−0.0272832	−	0.0908206i
$171$		−	6.15278i		−	0.470515i
$172$	3.51520	−	3.51520i	0.268032	−	0.268032i
$173$	−3.65117	+	3.65117i	−0.277593	+	0.277593i	−0.832147	−	0.554554i	$-0.812889\pi$
$173$	−3.65117	+	3.65117i	−0.277593	+	0.277593i	0.554554	+	0.832147i	$0.312889\pi$
$174$			5.15378i			0.390707i
$175$	2.85778	−	13.9731i	0.216028	−	1.05627i
$176$			5.11516i			0.385570i
$177$	−6.66723	−	6.66723i	−0.501140	−	0.501140i
$178$	6.09259	+	6.09259i	0.456659	+	0.456659i
$179$		−	18.7393i		−	1.40064i	−0.713830	−	0.700319i	$-0.753041\pi$
$179$		−	18.7393i		−	1.40064i	0.713830	−	0.700319i	$-0.246959\pi$
$180$	−0.643329	−	2.14152i	−0.0479509	−	0.159620i
$181$			20.7307i			1.54090i	0.637502	+	0.770449i	$0.279968\pi$
$181$			20.7307i			1.54090i	−0.637502	+	0.770449i	$0.720032\pi$
$182$	−12.4590	+	12.4590i	−0.923520	+	0.923520i
$183$	4.88558	+	4.88558i	0.361153	+	0.361153i
$184$	3.24347	+	3.53269i	0.239112	+	0.260433i
$185$	4.62328	+	2.48723i	0.339910	+	0.182865i
$186$	5.55456			0.407280
$187$	−2.00000	−	2.00000i	−0.146254	−	0.146254i
$188$	3.69444	−	3.69444i	0.269444	−	0.269444i
$189$	2.85248			0.207487
$190$	6.51816	−	12.1160i	0.472877	−	0.878986i
$191$		−	9.66249i		−	0.699153i	−0.936908	−	0.349577i	$-0.886325\pi$
$191$		−	9.66249i		−	0.699153i	0.936908	−	0.349577i	$-0.113675\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	−5.41019	+	5.41019i	−0.389434	+	0.389434i	−0.874486	−	0.485052i	$-0.838801\pi$
$193$	−5.41019	+	5.41019i	−0.389434	+	0.389434i	0.485052	+	0.874486i	$0.338801\pi$
$194$	10.0884			0.724304
$195$	−13.2281	+	3.97382i	−0.947285	+	0.284571i
$196$	1.13662			0.0811874
$197$	9.68778	+	9.68778i	0.690226	+	0.690226i	0.962282	−	0.272056i	$-0.0877035\pi$
$197$	9.68778	+	9.68778i	0.690226	+	0.690226i	−0.272056	+	0.962282i	$0.587703\pi$
$198$	−3.61696	−	3.61696i	−0.257046	−	0.257046i
$199$	1.92772			0.136652			0.0683262	−	0.997663i	$-0.478234\pi$
$199$	1.92772			0.136652			0.0683262	+	0.997663i	$0.478234\pi$
$200$	1.00186	−	4.89860i	0.0708422	−	0.346383i
$201$			8.74963i			0.617151i
$202$	3.05280	+	3.05280i	0.214794	+	0.214794i
$203$	−10.3952	−	10.3952i	−0.729600	−	0.729600i
$204$	0.552950			0.0387142
$205$	5.28037	+	17.5774i	0.368797	+	1.22766i
$206$			17.0459i			1.18765i
$207$	−4.79147	−	0.204508i	−0.333030	−	0.0142143i
$208$	−4.36777	+	4.36777i	−0.302850	+	0.302850i
$209$		−	31.4724i		−	2.17699i
$210$	5.61707	+	3.02187i	0.387614	+	0.208529i
$211$	13.4119			0.923310			0.461655	−	0.887059i	$-0.347256\pi$
$211$	13.4119			0.923310			0.461655	+	0.887059i	$0.347256\pi$
$212$	−3.27229	+	3.27229i	−0.224742	+	0.224742i
$213$	7.09959	−	7.09959i	0.486456	−	0.486456i
$214$	−7.68571			−0.525384
$215$	−5.26646	+	9.78932i	−0.359169	+	0.667626i
$216$	1.00000			0.0680414
$217$	−11.2036	+	11.2036i	−0.760548	+	0.760548i
$218$	−1.40636	−	1.40636i	−0.0952507	−	0.0952507i
$219$			13.7043i			0.926052i
$220$	−3.29073	−	10.9542i	−0.221861	−	0.738535i
$221$		−	3.41555i		−	0.229755i
$222$	−1.66015	+	1.66015i	−0.111422	+	0.111422i
$223$	−7.77131	+	7.77131i	−0.520405	+	0.520405i	−0.917694	−	0.397289i	$-0.869951\pi$
$223$	−7.77131	+	7.77131i	−0.520405	+	0.520405i	0.397289	+	0.917694i	$0.369951\pi$
$224$	2.85248			0.190589
$225$	2.75541	+	4.17226i	0.183694	+	0.278150i
$226$		−	0.744216i		−	0.0495045i
$227$	−18.5374	+	18.5374i	−1.23037	+	1.23037i	−0.266550	+	0.963821i	$0.585884\pi$
$227$	−18.5374	+	18.5374i	−1.23037	+	1.23037i	−0.963821	+	0.266550i	$0.914116\pi$
$228$	4.35067	+	4.35067i	0.288130	+	0.288130i
$229$	9.30733			0.615046			0.307523	−	0.951541i	$-0.400500\pi$
$229$	9.30733			0.615046			0.307523	+	0.951541i	$0.400500\pi$
$230$	−9.21866	−	5.47872i	−0.607860	−	0.361256i
$231$	14.5909			0.960009
$232$	−3.64427	−	3.64427i	−0.239258	−	0.239258i
$233$	−12.4073	+	12.4073i	−0.812826	+	0.812826i	−0.985057	−	0.172230i	$-0.944903\pi$
$233$	−12.4073	+	12.4073i	−0.812826	+	0.812826i	0.172230	+	0.985057i	$0.444903\pi$
$234$		−	6.17696i		−	0.403801i
$235$	−5.53499	+	10.2885i	−0.361063	+	0.671145i
$236$	9.42889			0.613768
$237$	0.591752	−	0.591752i	0.0384384	−	0.0384384i
$238$	−1.11530	+	1.11530i	−0.0722944	+	0.0722944i
$239$			12.7394i			0.824041i	0.911174	+	0.412021i	$0.135177\pi$
$239$			12.7394i			0.824041i	−0.911174	+	0.412021i	$0.864823\pi$
$240$	1.96919	+	1.05938i	0.127111	+	0.0683830i
$241$		−	5.57785i		−	0.359301i	−0.983731	−	0.179650i	$-0.942503\pi$
$241$		−	5.57785i		−	0.359301i	0.983731	−	0.179650i	$-0.0574966\pi$
$242$	−10.7232	−	10.7232i	−0.689312	−	0.689312i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−6.90926			−0.442320
$245$	−2.43411	+	0.731223i	−0.155509	+	0.0467161i
$246$	−8.20789			−0.523316
$247$	26.8739	−	26.8739i	1.70995	−	1.70995i
$248$	−3.92767	+	3.92767i	−0.249407	+	0.249407i
$249$	10.8750			0.689174
$250$	1.00590	+	11.1350i	0.0636189	+	0.704239i
$251$		−	28.1668i		−	1.77787i	−0.458033	−	0.888935i	$-0.651446\pi$
$251$		−	28.1668i		−	1.77787i	0.458033	−	0.888935i	$-0.348554\pi$
$252$	−2.01701	+	2.01701i	−0.127059	+	0.127059i
$253$	−24.5091	−	1.04609i	−1.54088	−	0.0657672i
$254$		−	22.1746i		−	1.39136i
$255$	−1.18416	+	0.355729i	−0.0741547	+	0.0222766i
$256$	1.00000			0.0625000
$257$	−7.11158	−	7.11158i	−0.443608	−	0.443608i	0.449614	−	0.893223i	$-0.351561\pi$
$257$	−7.11158	−	7.11158i	−0.443608	−	0.443608i	−0.893223	+	0.449614i	$0.851561\pi$
$258$	−3.51520	−	3.51520i	−0.218847	−	0.218847i
$259$		−	6.69707i		−	0.416135i
$260$	6.54377	−	12.1636i	0.405828	−	0.754355i
$261$	5.15378			0.319011
$262$	−2.34188	−	2.34188i	−0.144682	−	0.144682i
$263$	−9.62249	−	9.62249i	−0.593348	−	0.593348i	0.345186	−	0.938534i	$-0.387816\pi$
$263$	−9.62249	−	9.62249i	−0.593348	−	0.593348i	−0.938534	+	0.345186i	$0.887816\pi$
$264$	5.11516			0.314816
$265$	4.90253	−	9.11286i	0.301160	−	0.559798i
$266$	−17.5507			−1.07610
$267$	6.09259	−	6.09259i	0.372860	−	0.372860i
$268$	−6.18692	−	6.18692i	−0.377926	−	0.377926i
$269$			6.89166i			0.420192i	0.977681	+	0.210096i	$0.0673776\pi$
$269$			6.89166i			0.420192i	−0.977681	+	0.210096i	$0.932622\pi$
$270$	−2.14152	+	0.643329i	−0.130329	+	0.0391518i
$271$	24.2167			1.47106			0.735530	−	0.677492i	$-0.236933\pi$
$271$	24.2167			1.47106			0.735530	+	0.677492i	$0.236933\pi$
$272$	−0.390995	+	0.390995i	−0.0237075	+	0.0237075i
$273$	12.4590	+	12.4590i	0.754051	+	0.754051i
$274$	−3.01539			−0.182166
$275$	14.0944	+	21.3418i	0.849922	+	1.28696i
$276$	3.53269	−	3.24347i	0.212643	−	0.195234i
$277$	19.0881	+	19.0881i	1.14690	+	1.14690i	0.987160	+	0.159736i	$0.0510642\pi$
$277$	19.0881	+	19.0881i	1.14690	+	1.14690i	0.159736	+	0.987160i	$0.448936\pi$
$278$	−5.94373	+	5.94373i	−0.356481	+	0.356481i
$279$		−	5.55456i		−	0.332543i
$280$	−6.10865	+	1.83508i	−0.365062	+	0.109667i
$281$			20.3366i			1.21318i	0.795015	+	0.606590i	$0.207463\pi$
$281$			20.3366i			1.21318i	−0.795015	+	0.606590i	$0.792537\pi$
$282$	−3.69444	−	3.69444i	−0.220000	−	0.220000i
$283$	−17.8450	−	17.8450i	−1.06078	−	1.06078i	−0.998029	−	0.0627483i	$-0.980013\pi$
$283$	−17.8450	−	17.8450i	−1.06078	−	1.06078i	−0.0627483	−	0.998029i	$-0.519987\pi$
$284$			10.0403i			0.595784i
$285$	−12.1160	−	6.51816i	−0.717689	−	0.386102i
$286$		−	31.5961i		−	1.86832i
$287$	16.5554	−	16.5554i	0.977232	−	0.977232i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$			16.6942i			0.982014i
$290$	10.1488	+	5.45983i	0.595956	+	0.320612i
$291$		−	10.0884i		−	0.591392i
$292$	−9.69041	−	9.69041i	−0.567088	−	0.567088i
$293$	−12.5889	−	12.5889i	−0.735454	−	0.735454i	0.236241	−	0.971695i	$-0.424085\pi$
$293$	−12.5889	−	12.5889i	−0.735454	−	0.735454i	−0.971695	+	0.236241i	$0.924085\pi$
$294$		−	1.13662i		−	0.0662892i
$295$	−20.1922	+	6.06588i	−1.17563	+	0.353169i
$296$		−	2.34781i		−	0.136464i
$297$	−3.61696	+	3.61696i	−0.209878	+	0.209878i
$298$	12.7374	+	12.7374i	0.737859	+	0.737859i
$299$	−20.0348	−	21.8213i	−1.15864	−	1.26196i
$300$	−4.89860	−	1.00186i	−0.282821	−	0.0578425i
$301$	14.1804			0.817342
$302$	8.71948	+	8.71948i	0.501749	+	0.501749i
$303$	3.05280	−	3.05280i	0.175379	−	0.175379i
$304$	−6.15278			−0.352886
$305$	14.7963	−	4.44493i	0.847236	−	0.254516i
$306$		−	0.552950i		−	0.0316100i
$307$	4.59148	+	4.59148i	0.262049	+	0.262049i	0.825886	−	0.563837i	$-0.190675\pi$
$307$	4.59148	+	4.59148i	0.262049	+	0.262049i	−0.563837	+	0.825886i	$0.690675\pi$
$308$	−10.3173	+	10.3173i	−0.587883	+	0.587883i
$309$	17.0459			0.969709
$310$	5.88441	−	10.9380i	0.334212	−	0.621235i
$311$	−16.9139			−0.959097			−0.479549	−	0.877515i	$-0.659200\pi$
$311$	−16.9139			−0.959097			−0.479549	+	0.877515i	$0.659200\pi$
$312$	4.36777	+	4.36777i	0.247276	+	0.247276i
$313$	8.92881	+	8.92881i	0.504686	+	0.504686i	0.912891	−	0.408204i	$-0.133845\pi$
$313$	8.92881	+	8.92881i	0.504686	+	0.504686i	−0.408204	+	0.912891i	$0.633845\pi$
$314$	−2.19914			−0.124105
$315$	3.02187	−	5.61707i	0.170263	−	0.316486i
$316$			0.836863i			0.0470772i
$317$	2.16941	+	2.16941i	0.121846	+	0.121846i	0.765400	−	0.643554i	$-0.222541\pi$
$317$	2.16941	+	2.16941i	0.121846	+	0.121846i	−0.643554	+	0.765400i	$0.722541\pi$
$318$	3.27229	+	3.27229i	0.183501	+	0.183501i
$319$	26.3624			1.47601
$320$	−2.14152	+	0.643329i	−0.119715	+	0.0359632i
$321$			7.68571i			0.428974i
$322$	−0.583354	+	13.6676i	−0.0325091	+	0.761663i
$323$	2.40570	−	2.40570i	0.133857	−	0.133857i
$324$		−	1.00000i		−	0.0555556i
$325$	−6.18845	+	30.2585i	−0.343274	+	1.67844i
$326$	7.94559			0.440065
$327$	−1.40636	+	1.40636i	−0.0777719	+	0.0777719i
$328$	5.80385	−	5.80385i	0.320464	−	0.320464i
$329$	14.9034			0.821651
$330$	−10.9542	+	3.29073i	−0.603011	+	0.181149i
$331$	−4.44874			−0.244525			−0.122262	−	0.992498i	$-0.539015\pi$
$331$	−4.44874			−0.244525			−0.122262	+	0.992498i	$0.539015\pi$
$332$	−7.68978	+	7.68978i	−0.422031	+	0.422031i
$333$	1.66015	+	1.66015i	0.0909757	+	0.0909757i
$334$			8.18451i			0.447836i
$335$	17.2297	+	9.26921i	0.941357	+	0.506431i
$336$		−	2.85248i		−	0.155615i
$337$	−0.387079	+	0.387079i	−0.0210856	+	0.0210856i	−0.717571	−	0.696485i	$-0.754746\pi$
$337$	−0.387079	+	0.387079i	−0.0210856	+	0.0210856i	0.696485	+	0.717571i	$0.254746\pi$
$338$	17.7872	−	17.7872i	0.967494	−	0.967494i
$339$	−0.744216			−0.0404203
$340$	0.585786	−	1.08886i	0.0317687	−	0.0590519i
$341$		−	28.4124i		−	1.53862i
$342$	4.35067	−	4.35067i	0.235257	−	0.235257i
$343$	−11.8265	−	11.8265i	−0.638569	−	0.638569i
$344$	4.97125			0.268032
$345$	−5.47872	+	9.21866i	−0.294964	+	0.496316i
$346$	−5.16353			−0.277593
$347$	21.9216	+	21.9216i	1.17681	+	1.17681i	0.980551	+	0.196262i	$0.0628804\pi$
$347$	21.9216	+	21.9216i	1.17681	+	1.17681i	0.196262	+	0.980551i	$0.437120\pi$
$348$	−3.64427	+	3.64427i	−0.195353	+	0.195353i
$349$		−	29.6703i		−	1.58821i	−0.607779	−	0.794106i	$-0.707939\pi$
$349$		−	29.6703i		−	1.58821i	0.607779	−	0.794106i	$-0.292061\pi$
$350$	11.9013	−	7.85974i	0.636149	−	0.420121i
$351$	−6.17696			−0.329702
$352$	−3.61696	+	3.61696i	−0.192785	+	0.192785i
$353$	−1.26153	+	1.26153i	−0.0671442	+	0.0671442i	−0.739881	−	0.672737i	$-0.765118\pi$
$353$	−1.26153	+	1.26153i	−0.0671442	+	0.0671442i	0.672737	+	0.739881i	$0.265118\pi$
$354$		−	9.42889i		−	0.501140i
$355$	−6.45924	−	21.5016i	−0.342821	−	1.14119i
$356$			8.61622i			0.456659i
$357$	1.11530	+	1.11530i	0.0590281	+	0.0590281i
$358$	13.2507	−	13.2507i	0.700319	−	0.700319i
$359$	9.95032			0.525158			0.262579	−	0.964911i	$-0.415427\pi$
$359$	9.95032			0.525158			0.262579	+	0.964911i	$0.415427\pi$
$360$	1.05938	−	1.96919i	0.0558344	−	0.103785i
$361$	18.8567			0.992458
$362$	−14.6588	+	14.6588i	−0.770449	+	0.770449i
$363$	−10.7232	+	10.7232i	−0.562821	+	0.562821i
$364$	−17.6196			−0.923520
$365$	26.9864	+	14.5181i	1.41253	+	0.759914i
$366$			6.90926i			0.361153i
$367$	22.7067	−	22.7067i	1.18528	−	1.18528i	0.206922	−	0.978358i	$-0.433655\pi$
$367$	22.7067	−	22.7067i	1.18528	−	1.18528i	0.978358	−	0.206922i	$-0.0663445\pi$
$368$	−0.204508	+	4.79147i	−0.0106607	+	0.249773i
$369$			8.20789i			0.427286i
$370$	1.51041	+	5.02789i	0.0785226	+	0.261387i
$371$	−13.2005			−0.685334
$372$	3.92767	+	3.92767i	0.203640	+	0.203640i
$373$	−17.7101	−	17.7101i	−0.916992	−	0.916992i	0.0798177	−	0.996809i	$-0.474566\pi$
$373$	−17.7101	−	17.7101i	−0.916992	−	0.916992i	−0.996809	+	0.0798177i	$0.974566\pi$
$374$		−	2.82843i		−	0.146254i
$375$	11.1350	−	1.00590i	0.575009	−	0.0519446i
$376$	5.22472			0.269444
$377$	22.5105	+	22.5105i	1.15935	+	1.15935i
$378$	2.01701	+	2.01701i	0.103744	+	0.103744i
$379$	11.5472			0.593142			0.296571	−	0.955011i	$-0.404157\pi$
$379$	11.5472			0.593142			0.296571	+	0.955011i	$0.404157\pi$
$380$	13.1763	−	3.95826i	0.675931	−	0.203055i
$381$	−22.1746			−1.13604
$382$	6.83241	−	6.83241i	0.349577	−	0.349577i
$383$	21.9574	+	21.9574i	1.12197	+	1.12197i	0.991445	+	0.130527i	$0.0416668\pi$
$383$	21.9574	+	21.9574i	1.12197	+	1.12197i	0.130527	+	0.991445i	$0.458333\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	15.4573	−	28.7322i	0.787779	−	1.46433i
$386$	−7.65117			−0.389434
$387$	−3.51520	+	3.51520i	−0.178688	+	0.178688i
$388$	7.13357	+	7.13357i	0.362152	+	0.362152i
$389$	20.6283			1.04589			0.522947	−	0.852365i	$-0.324832\pi$
$389$	20.6283			1.04589			0.522947	+	0.852365i	$0.324832\pi$
$390$	−12.1636	−	6.54377i	−0.615928	−	0.331357i
$391$	−1.79348	−	1.95340i	−0.0907000	−	0.0987877i
$392$	0.803714	+	0.803714i	0.0405937	+	0.0405937i
$393$	−2.34188	+	2.34188i	−0.118132	+	0.118132i
$394$			13.7006i			0.690226i
$395$	−0.538379	−	1.79216i	−0.0270888	−	0.0901735i
$396$		−	5.11516i		−	0.257046i
$397$	−1.70732	−	1.70732i	−0.0856879	−	0.0856879i	0.662964	−	0.748652i	$-0.269298\pi$
$397$	−1.70732	−	1.70732i	−0.0856879	−	0.0856879i	−0.748652	+	0.662964i	$0.769298\pi$
$398$	1.36310	+	1.36310i	0.0683262	+	0.0683262i
$399$			17.5507i			0.878632i
$400$	4.17226	−	2.75541i	0.208613	−	0.137771i
$401$		−	30.6848i		−	1.53233i	−0.642646	−	0.766163i	$-0.722164\pi$
$401$		−	30.6848i		−	1.53233i	0.642646	−	0.766163i	$-0.277836\pi$
$402$	−6.18692	+	6.18692i	−0.308575	+	0.308575i
$403$	24.2610	−	24.2610i	1.20853	−	1.20853i
$404$			4.31730i			0.214794i
$405$	0.643329	+	2.14152i	0.0319673	+	0.106413i
$406$		−	14.7010i		−	0.729600i
$407$	8.49194	+	8.49194i	0.420930	+	0.420930i
$408$	0.390995	+	0.390995i	0.0193571	+	0.0193571i
$409$			9.11463i			0.450689i	0.974279	+	0.225345i	$0.0723508\pi$
$409$			9.11463i			0.450689i	−0.974279	+	0.225345i	$0.927649\pi$
$410$	−8.69531	+	16.1629i	−0.429431	+	0.798228i
$411$			3.01539i			0.148738i
$412$	−12.0533	+	12.0533i	−0.593823	+	0.593823i
$413$	19.0181	+	19.0181i	0.935820	+	0.935820i
$414$	−3.24347	−	3.53269i	−0.159408	−	0.173622i
$415$	11.5208	−	21.4149i	0.565533	−	1.05122i
$416$	−6.17696			−0.302850
$417$	5.94373	+	5.94373i	0.291066	+	0.291066i
$418$	22.2544	−	22.2544i	1.08850	−	1.08850i
$419$	−8.58413			−0.419362			−0.209681	−	0.977770i	$-0.567243\pi$
$419$	−8.58413			−0.419362			−0.209681	+	0.977770i	$0.567243\pi$
$420$	1.83508	+	6.10865i	0.0895428	+	0.298072i
$421$		−	7.06186i		−	0.344174i	−0.985082	−	0.172087i	$-0.944949\pi$
$421$		−	7.06186i		−	0.344174i	0.985082	−	0.172087i	$-0.0550510\pi$
$422$	9.48362	+	9.48362i	0.461655	+	0.461655i
$423$	−3.69444	+	3.69444i	−0.179630	+	0.179630i
$424$	−4.62772			−0.224742
$425$	−0.553979	+	2.70868i	−0.0268719	+	0.131390i
$426$	10.0403			0.486456
$427$	−13.9360	−	13.9360i	−0.674411	−	0.674411i
$428$	−5.43462	−	5.43462i	−0.262692	−	0.262692i
$429$	−31.5961			−1.52548
$430$	−10.6460	+	3.19815i	−0.513398	+	0.154228i
$431$			19.9570i			0.961296i	0.876914	+	0.480648i	$0.159599\pi$
$431$			19.9570i			0.961296i	−0.876914	+	0.480648i	$0.840401\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	−15.9071	−	15.9071i	−0.764447	−	0.764447i	0.212676	−	0.977123i	$-0.431782\pi$
$433$	−15.9071	−	15.9071i	−0.764447	−	0.764447i	−0.977123	+	0.212676i	$0.931782\pi$
$434$	−15.8442			−0.760548
$435$	5.45983	−	10.1488i	0.261779	−	0.486596i
$436$		−	1.98889i		−	0.0952507i
$437$	1.25829	−	29.4809i	0.0601923	−	1.41026i
$438$	−9.69041	+	9.69041i	−0.463026	+	0.463026i
$439$			15.0024i			0.716028i	0.933716	+	0.358014i	$0.116546\pi$
$439$			15.0024i			0.716028i	−0.933716	+	0.358014i	$0.883454\pi$
$440$	5.41892	−	10.0727i	0.258337	−	0.480198i
$441$	−1.13662			−0.0541249
$442$	2.41516	−	2.41516i	0.114877	−	0.114877i
$443$	13.3100	−	13.3100i	0.632377	−	0.632377i	−0.316287	−	0.948664i	$-0.602436\pi$
$443$	13.3100	−	13.3100i	0.632377	−	0.632377i	0.948664	+	0.316287i	$0.102436\pi$
$444$	−2.34781			−0.111422
$445$	−5.54306	−	18.4518i	−0.262766	−	0.874701i
$446$	−10.9903			−0.520405
$447$	12.7374	−	12.7374i	0.602459	−	0.602459i
$448$	2.01701	+	2.01701i	0.0952946	+	0.0952946i
$449$			29.8217i			1.40737i	0.710510	+	0.703687i	$0.248464\pi$
$449$			29.8217i			1.40737i	−0.710510	+	0.703687i	$0.751536\pi$
$450$	−1.00186	+	4.89860i	−0.0472282	+	0.230922i
$451$			41.9847i			1.97698i
$452$	0.526241	−	0.526241i	0.0247523	−	0.0247523i
$453$	8.71948	−	8.71948i	0.409677	−	0.409677i
$454$	−26.2159			−1.23037
$455$	37.7329	−	11.3352i	1.76894	−	0.531404i
$456$			6.15278i			0.288130i
$457$	−28.1085	+	28.1085i	−1.31486	+	1.31486i	−0.397074	+	0.917787i	$0.629974\pi$
$457$	−28.1085	+	28.1085i	−1.31486	+	1.31486i	−0.917787	+	0.397074i	$0.870026\pi$
$458$	6.58128	+	6.58128i	0.307523	+	0.307523i
$459$	−0.552950			−0.0258095
$460$	−2.64453	−	10.3926i	−0.123302	−	0.484558i
$461$	−30.4481			−1.41811			−0.709054	−	0.705154i	$-0.750878\pi$
$461$	−30.4481			−1.41811			−0.709054	+	0.705154i	$0.750878\pi$
$462$	10.3173	+	10.3173i	0.480004	+	0.480004i
$463$	2.16221	−	2.16221i	0.100486	−	0.100486i	−0.655076	−	0.755563i	$-0.727364\pi$
$463$	2.16221	−	2.16221i	0.100486	−	0.100486i	0.755563	+	0.655076i	$0.227364\pi$
$464$		−	5.15378i		−	0.239258i
$465$	−10.9380	−	5.88441i	−0.507236	−	0.272883i
$466$	−17.5465			−0.812826
$467$	10.3427	−	10.3427i	0.478604	−	0.478604i	−0.426081	−	0.904685i	$-0.640106\pi$
$467$	10.3427	−	10.3427i	0.478604	−	0.478604i	0.904685	+	0.426081i	$0.140106\pi$
$468$	4.36777	−	4.36777i	0.201900	−	0.201900i
$469$		−	24.9581i		−	1.15246i
$470$	−11.1889	+	3.36121i	−0.516104	+	0.155041i
$471$			2.19914i			0.101331i
$472$	6.66723	+	6.66723i	0.306884	+	0.306884i
$473$	−17.9808	+	17.9808i	−0.826759	+	0.826759i
$474$	0.836863			0.0384384
$475$	−25.6710	+	16.9534i	−1.17786	+	0.777877i
$476$	−1.57728			−0.0722944
$477$	3.27229	−	3.27229i	0.149828	−	0.149828i
$478$	−9.00810	+	9.00810i	−0.412021	+	0.412021i
$479$	−27.5688			−1.25965			−0.629826	−	0.776736i	$-0.716874\pi$
$479$	−27.5688			−1.25965			−0.629826	+	0.776736i	$0.716874\pi$
$480$	0.643329	+	2.14152i	0.0293638	+	0.0977468i
$481$			14.5023i			0.661249i
$482$	3.94413	−	3.94413i	0.179650	−	0.179650i
$483$	13.6676	+	0.583354i	0.621895	+	0.0265435i
$484$		−	15.1649i		−	0.689312i
$485$	−19.8659	−	10.6875i	−0.902066	−	0.485293i
$486$	−1.00000			−0.0453609
$487$	−11.1321	−	11.1321i	−0.504442	−	0.504442i	0.408373	−	0.912815i	$-0.366096\pi$
$487$	−11.1321	−	11.1321i	−0.504442	−	0.504442i	−0.912815	+	0.408373i	$0.866096\pi$
$488$	−4.88558	−	4.88558i	−0.221160	−	0.221160i
$489$		−	7.94559i		−	0.359312i
$490$	−2.23823	−	1.20412i	−0.101113	−	0.0543966i
$491$	12.2648			0.553501			0.276750	−	0.960942i	$-0.410742\pi$
$491$	12.2648			0.553501			0.276750	+	0.960942i	$0.410742\pi$
$492$	−5.80385	−	5.80385i	−0.261658	−	0.261658i
$493$	2.01510	+	2.01510i	0.0907555	+	0.0907555i
$494$	38.0055			1.70995
$495$	3.29073	+	10.9542i	0.147907	+	0.492356i
$496$	−5.55456			−0.249407
$497$	−20.2514	+	20.2514i	−0.908400	+	0.908400i
$498$	7.68978	+	7.68978i	0.344587	+	0.344587i
$499$			10.1093i			0.452555i	0.974063	+	0.226277i	$0.0726556\pi$
$499$			10.1093i			0.452555i	−0.974063	+	0.226277i	$0.927344\pi$
$500$	−7.16235	+	8.58491i	−0.320310	+	0.383929i
$501$	8.18451			0.365657
$502$	19.9169	−	19.9169i	0.888935	−	0.888935i
$503$	−25.5661	−	25.5661i	−1.13994	−	1.13994i	−0.988461	−	0.151476i	$-0.951597\pi$
$503$	−25.5661	−	25.5661i	−1.13994	−	1.13994i	−0.151476	−	0.988461i	$-0.548403\pi$
$504$	−2.85248			−0.127059
$505$	−2.77745	−	9.24561i	−0.123595	−	0.411424i
$506$	−16.5909	−	18.0703i	−0.737554	−	0.803321i
$507$	−17.7872	−	17.7872i	−0.789955	−	0.789955i
$508$	15.6798	−	15.6798i	0.695679	−	0.695679i
$509$			23.2951i			1.03254i	0.856427	+	0.516268i	$0.172679\pi$
$509$			23.2951i			1.03254i	−0.856427	+	0.516268i	$0.827321\pi$
$510$	−1.08886	−	0.585786i	−0.0482157	−	0.0259391i
$511$		−	39.0912i		−	1.72929i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−4.35067	−	4.35067i	−0.192087	−	0.192087i
$514$		−	10.0573i		−	0.443608i
$515$	18.0582	−	33.5666i	0.795739	−	1.47912i
$516$		−	4.97125i		−	0.218847i
$517$	−18.8976	+	18.8976i	−0.831117	+	0.831117i
$518$	4.73554	−	4.73554i	0.208068	−	0.208068i
$519$			5.16353i			0.226654i
$520$	13.2281	−	3.97382i	0.580091	−	0.174263i
$521$		−	22.1829i		−	0.971850i	−0.874001	−	0.485925i	$-0.838483\pi$
$521$		−	22.1829i		−	0.971850i	0.874001	−	0.485925i	$-0.161517\pi$
$522$	3.64427	+	3.64427i	0.159505	+	0.159505i
$523$	14.7292	+	14.7292i	0.644064	+	0.644064i	0.951552	−	0.307488i	$-0.0994883\pi$
$523$	14.7292	+	14.7292i	0.644064	+	0.644064i	−0.307488	+	0.951552i	$0.599488\pi$
$524$		−	3.31192i		−	0.144682i
$525$	−7.85974	−	11.9013i	−0.343027	−	0.519414i
$526$		−	13.6083i		−	0.593348i
$527$	2.17180	−	2.17180i	0.0946052	−	0.0946052i
$528$	3.61696	+	3.61696i	0.157408	+	0.157408i
$529$	−22.9164	−	1.95979i	−0.996363	−	0.0852082i
$530$	9.91038	−	2.97715i	0.430479	−	0.129319i
$531$	−9.42889			−0.409179
$532$	−12.4102	−	12.4102i	−0.538050	−	0.538050i
$533$	−35.8502	+	35.8502i	−1.55284	+	1.55284i
$534$	8.61622			0.372860
$535$	15.1346	+	8.14212i	0.654326	+	0.352014i
$536$		−	8.74963i		−	0.377926i
$537$	−13.2507	−	13.2507i	−0.571808	−	0.571808i
$538$	−4.87314	+	4.87314i	−0.210096	+	0.210096i
$539$	−5.81401			−0.250427
$540$	−1.96919	−	1.05938i	−0.0847404	−	0.0455886i
$541$	25.8534			1.11152			0.555762	−	0.831341i	$-0.312426\pi$
$541$	25.8534			1.11152			0.555762	+	0.831341i	$0.312426\pi$
$542$	17.1238	+	17.1238i	0.735530	+	0.735530i
$543$	14.6588	+	14.6588i	0.629069	+	0.629069i
$544$	−0.552950			−0.0237075
$545$	1.27951	+	4.25926i	0.0548083	+	0.182447i
$546$			17.6196i			0.754051i
$547$	−9.64881	−	9.64881i	−0.412553	−	0.412553i	0.470074	−	0.882627i	$-0.344227\pi$
$547$	−9.64881	−	9.64881i	−0.412553	−	0.412553i	−0.882627	+	0.470074i	$0.844227\pi$
$548$	−2.13220	−	2.13220i	−0.0910831	−	0.0910831i
$549$	6.90926			0.294880
$550$	−5.12468	+	25.0571i	−0.218517	+	1.06844i
$551$			31.7101i			1.35089i
$552$	4.79147	+	0.204508i	0.203938	+	0.00870444i
$553$	−1.68796	+	1.68796i	−0.0717793	+	0.0717793i
$554$			26.9947i			1.14690i
$555$	5.02789	−	1.51041i	0.213422	−	0.0641135i
$556$	−8.40570			−0.356481
$557$	2.29468	−	2.29468i	0.0972289	−	0.0972289i	−0.656819	−	0.754048i	$-0.728099\pi$
$557$	2.29468	−	2.29468i	0.0972289	−	0.0972289i	0.754048	+	0.656819i	$0.228099\pi$
$558$	3.92767	−	3.92767i	0.166271	−	0.166271i
$559$	−30.7072			−1.29878
$560$	−5.61707	−	3.02187i	−0.237364	−	0.127697i
$561$	−2.82843			−0.119416
$562$	−14.3801	+	14.3801i	−0.606590	+	0.606590i
$563$	9.31814	+	9.31814i	0.392713	+	0.392713i	0.875653	−	0.482941i	$-0.160431\pi$
$563$	9.31814	+	9.31814i	0.392713	+	0.392713i	−0.482941	+	0.875653i	$0.660431\pi$
$564$		−	5.22472i		−	0.220000i
$565$	−0.788411	+	1.46550i	−0.0331687	+	0.0616542i
$566$		−	25.2367i		−	1.06078i
$567$	2.01701	−	2.01701i	0.0847063	−	0.0847063i
$568$	−7.09959	+	7.09959i	−0.297892	+	0.297892i
$569$	28.0086			1.17418			0.587090	−	0.809522i	$-0.300273\pi$
$569$	28.0086			1.17418			0.587090	+	0.809522i	$0.300273\pi$
$570$	−3.95826	−	13.1763i	−0.165793	−	0.551896i
$571$		−	36.3711i		−	1.52208i	−0.648703	−	0.761042i	$-0.724688\pi$
$571$		−	36.3711i		−	1.52208i	0.648703	−	0.761042i	$-0.275312\pi$
$572$	22.3418	−	22.3418i	0.934159	−	0.934159i
$573$	−6.83241	−	6.83241i	−0.285428	−	0.285428i
$574$	23.4128			0.977232
$575$	12.3492	+	20.5547i	0.514997	+	0.857192i
$576$	−1.00000			−0.0416667
$577$	−19.8564	−	19.8564i	−0.826634	−	0.826634i	0.160416	−	0.987050i	$-0.448716\pi$
$577$	−19.8564	−	19.8564i	−0.826634	−	0.826634i	−0.987050	+	0.160416i	$0.948716\pi$
$578$	−11.8046	+	11.8046i	−0.491007	+	0.491007i
$579$			7.65117i			0.317972i
$580$	3.31558	+	11.0369i	0.137672	+	0.458284i
$581$	−31.0206			−1.28695
$582$	7.13357	−	7.13357i	0.295696	−	0.295696i
$583$	16.7383	−	16.7383i	0.693229	−	0.693229i
$584$		−	13.7043i		−	0.567088i
$585$	−6.54377	+	12.1636i	−0.270552	+	0.502903i
$586$		−	17.8035i		−	0.735454i
$587$	−26.7004	−	26.7004i	−1.10204	−	1.10204i	−0.994164	−	0.107879i	$-0.965594\pi$
$587$	−26.7004	−	26.7004i	−1.10204	−	1.10204i	−0.107879	−	0.994164i	$-0.534406\pi$
$588$	0.803714	−	0.803714i	0.0331446	−	0.0331446i
$589$	34.1760			1.40820
$590$	−18.5673	−	9.98881i	−0.764402	−	0.411233i
$591$	13.7006			0.563567
$592$	1.66015	−	1.66015i	0.0682318	−	0.0682318i
$593$	−3.37233	+	3.37233i	−0.138485	+	0.138485i	−0.772951	−	0.634466i	$-0.781220\pi$
$593$	−3.37233	+	3.37233i	−0.138485	+	0.138485i	0.634466	+	0.772951i	$0.281220\pi$
$594$	−5.11516			−0.209878
$595$	3.37778	−	1.01471i	0.138475	−	0.0415990i
$596$			18.0134i			0.737859i
$597$	1.36310	−	1.36310i	0.0557881	−	0.0557881i
$598$	1.26324	−	29.5967i	0.0516576	−	1.21030i
$599$		−	16.1347i		−	0.659248i	−0.944112	−	0.329624i	$-0.893078\pi$
$599$		−	16.1347i		−	0.659248i	0.944112	−	0.329624i	$-0.106922\pi$
$600$	−2.75541	−	4.17226i	−0.112489	−	0.170332i
$601$	22.7683			0.928740			0.464370	−	0.885641i	$-0.346281\pi$
$601$	22.7683			0.928740			0.464370	+	0.885641i	$0.346281\pi$
$602$	10.0270	+	10.0270i	0.408671	+	0.408671i
$603$	6.18692	+	6.18692i	0.251951	+	0.251951i
$604$			12.3312i			0.501749i
$605$	9.75599	+	32.4759i	0.396638	+	1.32033i
$606$	4.31730			0.175379
$607$	22.8209	+	22.8209i	0.926273	+	0.926273i	0.997463	−	0.0711898i	$-0.0226796\pi$
$607$	22.8209	+	22.8209i	0.926273	+	0.926273i	−0.0711898	+	0.997463i	$0.522680\pi$
$608$	−4.35067	−	4.35067i	−0.176443	−	0.176443i
$609$	−14.7010			−0.595716
$610$	13.6056	+	7.31956i	0.550876	+	0.296360i
$611$	−32.2729			−1.30562
$612$	0.390995	−	0.390995i	0.0158050	−	0.0158050i
$613$	−15.0940	−	15.0940i	−0.609639	−	0.609639i	0.333213	−	0.942852i	$-0.391867\pi$
$613$	−15.0940	−	15.0940i	−0.609639	−	0.609639i	−0.942852	+	0.333213i	$0.891867\pi$
$614$			6.49333i			0.262049i
$615$	16.1629	+	8.69531i	0.651750	+	0.350629i
$616$	−14.5909			−0.587883
$617$	−13.3305	+	13.3305i	−0.536665	+	0.536665i	−0.922548	−	0.385883i	$-0.873897\pi$
$617$	−13.3305	+	13.3305i	−0.536665	+	0.536665i	0.385883	+	0.922548i	$0.373897\pi$
$618$	12.0533	+	12.0533i	0.484854	+	0.484854i
$619$	−31.9076			−1.28247			−0.641236	−	0.767343i	$-0.721578\pi$
$619$	−31.9076			−1.28247			−0.641236	+	0.767343i	$0.721578\pi$
$620$	11.8952	−	3.57341i	0.477724	−	0.143512i
$621$	−3.53269	+	3.24347i	−0.141762	+	0.130156i
$622$	−11.9599	−	11.9599i	−0.479549	−	0.479549i
$623$	−17.3790	+	17.3790i	−0.696273	+	0.696273i
$624$			6.17696i			0.247276i
$625$	9.81543	−	22.9926i	0.392617	−	0.919702i
$626$			12.6272i			0.504686i
$627$	−22.2544	−	22.2544i	−0.888754	−	0.888754i
$628$	−1.55503	−	1.55503i	−0.0620523	−	0.0620523i
$629$			1.29822i			0.0517634i
$630$	6.10865	−	1.83508i	0.243374	−	0.0731114i
$631$			12.7919i			0.509238i	0.967041	+	0.254619i	$0.0819500\pi$
$631$			12.7919i			0.509238i	−0.967041	+	0.254619i	$0.918050\pi$
$632$	−0.591752	+	0.591752i	−0.0235386	+	0.0235386i
$633$	9.48362	−	9.48362i	0.376940	−	0.376940i
$634$			3.06801i			0.121846i
$635$	−23.4914	+	43.6660i	−0.932229	+	1.73283i
$636$			4.62772i			0.183501i
$637$	−4.96451	−	4.96451i	−0.196701	−	0.196701i
$638$	18.6410	+	18.6410i	0.738005	+	0.738005i
$639$		−	10.0403i		−	0.397190i
$640$	−1.96919	−	1.05938i	−0.0778390	−	0.0418758i
$641$			17.4191i			0.688014i	0.938967	+	0.344007i	$0.111784\pi$
$641$			17.4191i			0.688014i	−0.938967	+	0.344007i	$0.888216\pi$
$642$	−5.43462	+	5.43462i	−0.214487	+	0.214487i
$643$	27.1429	+	27.1429i	1.07041	+	1.07041i	0.997326	+	0.0730859i	$0.0232847\pi$
$643$	27.1429	+	27.1429i	1.07041	+	1.07041i	0.0730859	+	0.997326i	$0.476715\pi$
$644$	−10.0769	+	9.25193i	−0.397086	+	0.364577i
$645$	3.19815	+	10.6460i	0.125927	+	0.419188i
$646$	3.40218			0.133857
$647$	−26.3595	−	26.3595i	−1.03630	−	1.03630i	−0.999316	−	0.0369830i	$-0.988225\pi$
$647$	−26.3595	−	26.3595i	−1.03630	−	1.03630i	−0.0369830	−	0.999316i	$-0.511775\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	−48.2303			−1.89320
$650$	−25.7719	+	17.0201i	−1.01086	+	0.667582i
$651$			15.8442i			0.620985i
$652$	5.61838	+	5.61838i	0.220033	+	0.220033i
$653$	13.2363	−	13.2363i	0.517978	−	0.517978i	−0.398981	−	0.916959i	$-0.630636\pi$
$653$	13.2363	−	13.2363i	0.517978	−	0.517978i	0.916959	+	0.398981i	$0.130636\pi$
$654$	−1.98889			−0.0777719
$655$	2.13065	+	7.09255i	0.0832515	+	0.277129i
$656$	8.20789			0.320464
$657$	9.69041	+	9.69041i	0.378059	+	0.378059i
$658$	10.5383	+	10.5383i	0.410825	+	0.410825i
$659$	−26.8438			−1.04569			−0.522843	−	0.852429i	$-0.675129\pi$
$659$	−26.8438			−1.04569			−0.522843	+	0.852429i	$0.675129\pi$
$660$	−10.0727	−	5.41892i	−0.392080	−	0.210931i
$661$			29.5722i			1.15023i	0.818074	+	0.575113i	$0.195042\pi$
$661$			29.5722i			1.15023i	−0.818074	+	0.575113i	$0.804958\pi$
$662$	−3.14573	−	3.14573i	−0.122262	−	0.122262i
$663$	−2.41516	−	2.41516i	−0.0937970	−	0.0937970i
$664$	−10.8750			−0.422031
$665$	34.5606	+	18.5929i	1.34020	+	0.721001i
$666$			2.34781i			0.0909757i
$667$	24.6942	+	1.05399i	0.956162	+	0.0408106i
$668$	−5.78732	+	5.78732i	−0.223918	+	0.223918i
$669$			10.9903i			0.424909i
$670$	5.62889	+	18.7375i	0.217463	+	0.723894i
$671$	35.3419			1.36436
$672$	2.01701	−	2.01701i	0.0778077	−	0.0778077i
$673$	−11.0151	+	11.0151i	−0.424602	+	0.424602i	−0.886785	−	0.462182i	$-0.847067\pi$
$673$	−11.0151	+	11.0151i	−0.424602	+	0.424602i	0.462182	+	0.886785i	$0.347067\pi$
$674$	−0.547413			−0.0210856
$675$	4.89860	+	1.00186i	0.188547	+	0.0385616i
$676$	25.1548			0.967494
$677$	−5.28014	+	5.28014i	−0.202932	+	0.202932i	−0.801255	−	0.598323i	$-0.795834\pi$
$677$	−5.28014	+	5.28014i	−0.202932	+	0.202932i	0.598323	+	0.801255i	$0.295834\pi$
$678$	−0.526241	−	0.526241i	−0.0202101	−	0.0202101i
$679$			28.7769i			1.10436i
$680$	1.18416	−	0.355729i	0.0454103	−	0.0136416i
$681$			26.2159i			1.00459i
$682$	20.0906	−	20.0906i	0.769310	−	0.769310i
$683$	−9.53627	+	9.53627i	−0.364895	+	0.364895i	−0.865611	−	0.500716i	$-0.833070\pi$
$683$	−9.53627	+	9.53627i	−0.364895	+	0.364895i	0.500716	+	0.865611i	$0.333070\pi$
$684$	6.15278			0.235257
$685$	5.93787	+	3.19445i	0.226874	+	0.122054i
$686$		−	16.7251i		−	0.638569i
$687$	6.58128	−	6.58128i	0.251091	−	0.251091i
$688$	3.51520	+	3.51520i	0.134016	+	0.134016i
$689$	28.5852			1.08901
$690$	−10.3926	+	2.64453i	−0.395640	+	0.100676i
$691$	−40.3146			−1.53364			−0.766820	−	0.641862i	$-0.778162\pi$
$691$	−40.3146			−1.53364			−0.766820	+	0.641862i	$0.778162\pi$
$692$	−3.65117	−	3.65117i	−0.138796	−	0.138796i
$693$	10.3173	−	10.3173i	0.391922	−	0.391922i
$694$			31.0018i			1.17681i
$695$	18.0010	−	5.40763i	0.682818	−	0.205123i
$696$	−5.15378			−0.195353
$697$	−3.20924	+	3.20924i	−0.121559	+	0.121559i
$698$	20.9800	−	20.9800i	0.794106	−	0.794106i
$699$			17.5465i			0.663670i
$700$	13.9731	+	2.85778i	0.528135	+	0.108014i
$701$			10.9576i			0.413862i	0.978356	+	0.206931i	$0.0663476\pi$
$701$			10.9576i			0.413862i	−0.978356	+	0.206931i	$0.933652\pi$
$702$	−4.36777	−	4.36777i	−0.164851	−	0.164851i
$703$	−10.2145	+	10.2145i	−0.385249	+	0.385249i
$704$	−5.11516			−0.192785
$705$	3.36121	+	11.1889i	0.126591	+	0.421397i
$706$	−1.78407			−0.0671442
$707$	−8.70803	+	8.70803i	−0.327499	+	0.327499i
$708$	6.66723	−	6.66723i	0.250570	−	0.250570i
$709$	11.6600			0.437899			0.218950	−	0.975736i	$-0.429737\pi$
$709$	11.6600			0.437899			0.218950	+	0.975736i	$0.429737\pi$
$710$	10.6366	−	19.7713i	0.399184	−	0.742004i
$711$		−	0.836863i		−	0.0313848i
$712$	−6.09259	+	6.09259i	−0.228329	+	0.228329i
$713$	1.13595	−	26.6145i	0.0425417	−	0.996721i
$714$			1.57728i			0.0590281i
$715$	−33.4724	+	62.2188i	−1.25180	+	2.32685i
$716$	18.7393			0.700319
$717$	9.00810	+	9.00810i	0.336414	+	0.336414i
$718$	7.03594	+	7.03594i	0.262579	+	0.262579i
$719$			17.1352i			0.639036i	0.947580	+	0.319518i	$0.103521\pi$
$719$			17.1352i			0.639036i	−0.947580	+	0.319518i	$0.896479\pi$
$720$	2.14152	−	0.643329i	0.0798099	−	0.0239755i
$721$	−48.6231			−1.81082
$722$	13.3337	+	13.3337i	0.496229	+	0.496229i
$723$	−3.94413	−	3.94413i	−0.146684	−	0.146684i
$724$	−20.7307			−0.770449
$725$	−14.2008	−	21.5029i	−0.527403	−	0.798597i
$726$	−15.1649			−0.562821
$727$	−11.2875	+	11.2875i	−0.418630	+	0.418630i	−0.884731	−	0.466101i	$-0.845658\pi$
$727$	−11.2875	+	11.2875i	−0.418630	+	0.418630i	0.466101	+	0.884731i	$0.345658\pi$
$728$	−12.4590	−	12.4590i	−0.461760	−	0.461760i
$729$			1.00000i			0.0370370i
$730$	8.81638	+	29.3481i	0.326309	+	1.08622i
$731$	−2.74885			−0.101670
$732$	−4.88558	+	4.88558i	−0.180576	+	0.180576i
$733$	26.0488	+	26.0488i	0.962134	+	0.962134i	0.999309	−	0.0371743i	$-0.0118357\pi$
$733$	26.0488	+	26.0488i	0.962134	+	0.962134i	−0.0371743	+	0.999309i	$0.511836\pi$
$734$	32.1121			1.18528
$735$	−1.20412	+	2.23823i	−0.0444147	+	0.0825582i
$736$	−3.53269	+	3.24347i	−0.130217	+	0.119556i
$737$	31.6471	+	31.6471i	1.16574	+	1.16574i
$738$	−5.80385	+	5.80385i	−0.213643	+	0.213643i
$739$		−	27.4713i		−	1.01055i	−0.862959	−	0.505275i	$-0.831391\pi$
$739$		−	27.4713i		−	1.01055i	0.862959	−	0.505275i	$-0.168609\pi$
$740$	−2.48723	+	4.62328i	−0.0914324	+	0.169955i
$741$		−	38.0055i		−	1.39617i
$742$	−9.33414	−	9.33414i	−0.342667	−	0.342667i
$743$	−17.8846	−	17.8846i	−0.656122	−	0.656122i	0.298338	−	0.954460i	$-0.403568\pi$
$743$	−17.8846	−	17.8846i	−0.656122	−	0.656122i	−0.954460	+	0.298338i	$0.903568\pi$
$744$			5.55456i			0.203640i
$745$	−11.5886	−	38.5762i	−0.424572	−	1.41332i
$746$		−	25.0458i		−	0.916992i
$747$	7.68978	−	7.68978i	0.281354	−	0.281354i
$748$	2.00000	−	2.00000i	0.0731272	−	0.0731272i
$749$		−	21.9233i		−	0.801060i
$750$	8.58491	+	7.16235i	0.313477	+	0.261532i
$751$			9.57596i			0.349432i	0.984619	+	0.174716i	$0.0559007\pi$
$751$			9.57596i			0.349432i	−0.984619	+	0.174716i	$0.944099\pi$
$752$	3.69444	+	3.69444i	0.134722	+	0.134722i
$753$	−19.9169	−	19.9169i	−0.725812	−	0.725812i
$754$			31.8347i			1.15935i
$755$	−7.93302	−	26.4076i	−0.288712	−	0.961070i
$756$			2.85248i			0.103744i
$757$	34.4079	−	34.4079i	1.25058	−	1.25058i	0.295116	−	0.955461i	$-0.404642\pi$
$757$	34.4079	−	34.4079i	1.25058	−	1.25058i	0.955461	−	0.295116i	$-0.0953584\pi$
$758$	8.16513	+	8.16513i	0.296571	+	0.296571i
$759$	−18.0703	+	16.5909i	−0.655909	+	0.602211i
$760$	12.1160	+	6.51816i	0.439493	+	0.236438i
$761$	−26.3481			−0.955116			−0.477558	−	0.878600i	$-0.658478\pi$
$761$	−26.3481			−0.955116			−0.477558	+	0.878600i	$0.658478\pi$
$762$	−15.6798	−	15.6798i	−0.568020	−	0.568020i
$763$	4.01161	−	4.01161i	0.145230	−	0.145230i
$764$	9.66249			0.349577
$765$	−0.585786	+	1.08886i	−0.0211792	+	0.0393679i
$766$			31.0525i			1.12197i
$767$	−41.1832	−	41.1832i	−1.48704	−	1.48704i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−24.2043			−0.872830			−0.436415	−	0.899745i	$-0.643752\pi$
$769$	−24.2043			−0.872830			−0.436415	+	0.899745i	$0.643752\pi$
$770$	31.2467	−	9.38673i	1.12605	−	0.338274i
$771$	−10.0573			−0.362205
$772$	−5.41019	−	5.41019i	−0.194717	−	0.194717i
$773$	15.8801	+	15.8801i	0.571168	+	0.571168i	0.932455	−	0.361286i	$-0.117662\pi$
$773$	15.8801	+	15.8801i	0.571168	+	0.571168i	−0.361286	+	0.932455i	$0.617662\pi$
$774$	−4.97125			−0.178688
$775$	−23.1750	+	15.3051i	−0.832472	+	0.549775i
$776$			10.0884i			0.362152i
$777$	−4.73554	−	4.73554i	−0.169887	−	0.169887i
$778$	14.5864	+	14.5864i	0.522947	+	0.522947i
$779$	−50.5013			−1.80940
$780$	−3.97382	−	13.2281i	−0.142286	−	0.473642i
$781$		−	51.3579i		−	1.83773i
$782$	0.113083	−	2.64944i	0.00404383	−	0.0947439i
$783$	3.64427	−	3.64427i	0.130236	−	0.130236i
$784$			1.13662i			0.0405937i
$785$	4.33052	+	2.32973i	0.154563	+	0.0831518i
$786$	−3.31192			−0.118132
$787$	−7.43774	+	7.43774i	−0.265127	+	0.265127i	−0.827133	−	0.562006i	$-0.810030\pi$
$787$	−7.43774	+	7.43774i	−0.265127	+	0.265127i	0.562006	+	0.827133i	$0.310030\pi$
$788$	−9.68778	+	9.68778i	−0.345113	+	0.345113i
$789$	−13.6083			−0.484467
$790$	0.886560	−	1.64794i	0.0315424	−	0.0586311i
$791$	2.12286			0.0754802
$792$	3.61696	−	3.61696i	0.128523	−	0.128523i
$793$	30.1780	+	30.1780i	1.07165	+	1.07165i
$794$		−	2.41452i		−	0.0856879i
$795$	−2.97715	−	9.91038i	−0.105589	−	0.351485i
$796$			1.92772i			0.0683262i
$797$	−34.2834	+	34.2834i	−1.21438	+	1.21438i	−0.244807	+	0.969572i	$0.578724\pi$
$797$	−34.2834	+	34.2834i	−1.21438	+	1.21438i	−0.969572	+	0.244807i	$0.921276\pi$
$798$	−12.4102	+	12.4102i	−0.439316	+	0.439316i
$799$	−2.88901			−0.102206
$800$	4.89860	+	1.00186i	0.173192	+	0.0354211i
$801$		−	8.61622i		−	0.304439i
$802$	21.6974	−	21.6974i	0.766163	−	0.766163i
$803$	49.5680	+	49.5680i	1.74922	+	1.74922i
$804$	−8.74963			−0.308575
$805$	15.6279	−	26.2960i	0.550812	−	0.926812i
$806$	34.3103			1.20853
$807$	4.87314	+	4.87314i	0.171543	+	0.171543i
$808$	−3.05280	+	3.05280i	−0.107397	+	0.107397i
$809$			13.7935i			0.484953i	0.970157	+	0.242476i	$0.0779597\pi$
$809$			13.7935i			0.484953i	−0.970157	+	0.242476i	$0.922040\pi$
$810$	−1.05938	+	1.96919i	−0.0372230	+	0.0691902i
$811$	−20.9214			−0.734650			−0.367325	−	0.930093i	$-0.619726\pi$
$811$	−20.9214			−0.734650			−0.367325	+	0.930093i	$0.619726\pi$
$812$	10.3952	−	10.3952i	0.364800	−	0.364800i
$813$	17.1238	−	17.1238i	0.600558	−	0.600558i
$814$			12.0094i			0.420930i
$815$	−15.6464	−	8.41743i	−0.548068	−	0.294850i
$816$			0.552950i			0.0193571i
$817$	−21.6283	−	21.6283i	−0.756677	−	0.756677i
$818$	−6.44502	+	6.44502i	−0.225345	+	0.225345i
$819$	17.6196			0.615680
$820$	−17.5774	+	5.28037i	−0.613829	+	0.184399i
$821$	−6.90808			−0.241094			−0.120547	−	0.992708i	$-0.538465\pi$
$821$	−6.90808			−0.241094			−0.120547	+	0.992708i	$0.538465\pi$
$822$	−2.13220	+	2.13220i	−0.0743691	+	0.0743691i
$823$	−12.3135	+	12.3135i	−0.429223	+	0.429223i	−0.888364	−	0.459141i	$-0.848157\pi$
$823$	−12.3135	+	12.3135i	−0.429223	+	0.429223i	0.459141	+	0.888364i	$0.348157\pi$
$824$	−17.0459			−0.593823
$825$	25.0571	+	5.12468i	0.872377	+	0.178418i
$826$			26.8957i			0.935820i
$827$	−3.25744	+	3.25744i	−0.113272	+	0.113272i	−0.761471	−	0.648199i	$-0.775523\pi$
$827$	−3.25744	+	3.25744i	−0.113272	+	0.113272i	0.648199	+	0.761471i	$0.275523\pi$
$828$	0.204508	−	4.79147i	0.00710714	−	0.166515i
$829$		−	52.0135i		−	1.80650i	−0.429111	−	0.903252i	$-0.641173\pi$
$829$		−	52.0135i		−	1.80650i	0.429111	−	0.903252i	$-0.358827\pi$
$830$	23.2891	−	6.99620i	0.808375	−	0.242841i
$831$	26.9947			0.936436
$832$	−4.36777	−	4.36777i	−0.151425	−	0.151425i
$833$	−0.444414	−	0.444414i	−0.0153980	−	0.0153980i
$834$			8.40570i			0.291066i
$835$	8.67054	−	16.1168i	0.300056	−	0.557746i
$836$	31.4724			1.08850
$837$	−3.92767	−	3.92767i	−0.135760	−	0.135760i
$838$	−6.06990	−	6.06990i	−0.209681	−	0.209681i
$839$	−1.25549			−0.0433444			−0.0216722	−	0.999765i	$-0.506899\pi$
$839$	−1.25549			−0.0433444			−0.0216722	+	0.999765i	$0.506899\pi$
$840$	−3.02187	+	5.61707i	−0.104264	+	0.193807i
$841$	2.43858			0.0840888
$842$	4.99349	−	4.99349i	0.172087	−	0.172087i
$843$	14.3801	+	14.3801i	0.495278	+	0.495278i
$844$			13.4119i			0.461655i
$845$	−53.8697	+	16.1828i	−1.85317	+	0.556707i
$846$	−5.22472			−0.179630
$847$	30.5876	−	30.5876i	1.05100	−	1.05100i
$848$	−3.27229	−	3.27229i	−0.112371	−	0.112371i
$849$	−25.2367			−0.866121
$850$	−2.30705	+	1.52360i	−0.0791311	+	0.0522592i
$851$	7.61505	+	8.29408i	0.261040	+	0.284317i
$852$	7.09959	+	7.09959i	0.243228	+	0.243228i
$853$	30.5170	−	30.5170i	1.04488	−	1.04488i	0.0459389	−	0.998944i	$-0.485372\pi$
$853$	30.5170	−	30.5170i	1.04488	−	1.04488i	0.998944	−	0.0459389i	$-0.0146279\pi$
$854$		−	19.7085i		−	0.674411i
$855$	−13.1763	+	3.95826i	−0.450621	+	0.135370i
$856$		−	7.68571i		−	0.262692i
$857$	−14.6537	−	14.6537i	−0.500562	−	0.500562i	0.411051	−	0.911613i	$-0.365162\pi$
$857$	−14.6537	−	14.6537i	−0.500562	−	0.500562i	−0.911613	+	0.411051i	$0.865162\pi$
$858$	−22.3418	−	22.3418i	−0.762738	−	0.762738i
$859$			43.2161i			1.47451i	0.675613	+	0.737256i	$0.263879\pi$
$859$			43.2161i			1.47451i	−0.675613	+	0.737256i	$0.736121\pi$
$860$	−9.78932	−	5.26646i	−0.333813	−	0.179585i
$861$		−	23.4128i		−	0.797906i
$862$	−14.1117	+	14.1117i	−0.480648	+	0.480648i
$863$	3.46294	−	3.46294i	0.117880	−	0.117880i	−0.645706	−	0.763586i	$-0.723437\pi$
$863$	3.46294	−	3.46294i	0.117880	−	0.117880i	0.763586	+	0.645706i	$0.223437\pi$
$864$			1.00000i			0.0340207i
$865$	10.1680	+	5.47016i	0.345721	+	0.185991i
$866$		−	22.4960i		−	0.764447i
$867$	11.8046	+	11.8046i	0.400906	+	0.400906i
$868$	−11.2036	−	11.2036i	−0.380274	−	0.380274i
$869$		−	4.28069i		−	0.145212i
$870$	11.0369	−	3.31558i	0.374187	−	0.112409i
$871$			54.0461i			1.83128i
$872$	1.40636	−	1.40636i	0.0476253	−	0.0476253i
$873$	−7.13357	−	7.13357i	−0.241435	−	0.241435i
$874$	21.7359	−	19.9564i	0.735226	−	0.675034i
$875$	−31.7623	+	2.86931i	−1.07376	+	0.0970005i
$876$	−13.7043			−0.463026
$877$	−5.55079	−	5.55079i	−0.187437	−	0.187437i	0.607150	−	0.794587i	$-0.292313\pi$
$877$	−5.55079	−	5.55079i	−0.187437	−	0.187437i	−0.794587	+	0.607150i	$0.792313\pi$
$878$	−10.6083	+	10.6083i	−0.358014	+	0.358014i
$879$	−17.8035			−0.600496
$880$	10.9542	−	3.29073i	0.369267	−	0.110931i
$881$		−	51.9461i		−	1.75011i	−0.484024	−	0.875055i	$-0.660825\pi$
$881$		−	51.9461i		−	1.75011i	0.484024	−	0.875055i	$-0.339175\pi$
$882$	−0.803714	−	0.803714i	−0.0270625	−	0.0270625i
$883$	13.6444	−	13.6444i	0.459170	−	0.459170i	−0.439213	−	0.898383i	$-0.644743\pi$
$883$	13.6444	−	13.6444i	0.459170	−	0.459170i	0.898383	+	0.439213i	$0.144743\pi$
$884$	3.41555			0.114877
$885$	−9.98881	+	18.5673i	−0.335770	+	0.624132i
$886$	18.8232			0.632377
$887$	−1.93479	−	1.93479i	−0.0649638	−	0.0649638i	0.673878	−	0.738842i	$-0.264627\pi$
$887$	−1.93479	−	1.93479i	−0.0649638	−	0.0649638i	−0.738842	+	0.673878i	$0.764627\pi$
$888$	−1.66015	−	1.66015i	−0.0557110	−	0.0557110i
$889$	63.2525			2.12142
$890$	9.12789	−	16.9670i	0.305967	−	0.568734i
$891$			5.11516i			0.171364i
$892$	−7.77131	−	7.77131i	−0.260203	−	0.260203i
$893$	−22.7310	−	22.7310i	−0.760665	−	0.760665i
$894$	18.0134			0.602459
$895$	−40.1306	+	12.0555i	−1.34142	+	0.402971i
$896$			2.85248i			0.0952946i
$897$	−29.5967	−	1.26324i	−0.988206	−	0.0421783i
$898$	−21.0871	+	21.0871i	−0.703687	+	0.703687i
$899$			28.6270i			0.954762i
$900$	−4.17226	+	2.75541i	−0.139075	+	0.0918470i
$901$	2.55890			0.0852492
$902$	−29.6876	+	29.6876i	−0.988490	+	0.988490i
$903$	10.0270	−	10.0270i	0.333679	−	0.333679i
$904$	0.744216			0.0247523
$905$	44.3952	−	13.3366i	1.47575	−	0.443325i
$906$	12.3312			0.409677
$907$	−1.67221	+	1.67221i	−0.0555247	+	0.0555247i	−0.734324	−	0.678799i	$-0.762501\pi$
$907$	−1.67221	+	1.67221i	−0.0555247	+	0.0555247i	0.678799	+	0.734324i	$0.262501\pi$
$908$	−18.5374	−	18.5374i	−0.615186	−	0.615186i
$909$		−	4.31730i		−	0.143196i
$910$	34.6964	+	18.6660i	1.15017	+	0.618771i
$911$			8.95458i			0.296678i	0.988937	+	0.148339i	$0.0473927\pi$
$911$			8.95458i			0.296678i	−0.988937	+	0.148339i	$0.952607\pi$
$912$	−4.35067	+	4.35067i	−0.144065	+	0.144065i
$913$	39.3344	−	39.3344i	1.30178	−	1.30178i
$914$	−39.7514			−1.31486
$915$	7.31956	−	13.6056i	0.241977	−	0.449788i
$916$			9.30733i			0.307523i
$917$	6.68016	−	6.68016i	0.220598	−	0.220598i
$918$	−0.390995	−	0.390995i	−0.0129047	−	0.0129047i
$919$	13.4943			0.445136			0.222568	−	0.974917i	$-0.428556\pi$
$919$	13.4943			0.445136			0.222568	+	0.974917i	$0.428556\pi$
$920$	5.47872	−	9.21866i	0.180628	−	0.303930i
$921$	6.49333			0.213962
$922$	−21.5300	−	21.5300i	−0.709054	−	0.709054i
$923$	43.8539	−	43.8539i	1.44347	−	1.44347i
$924$			14.5909i			0.480004i
$925$	2.35218	−	11.5010i	0.0773391	−	0.378150i
$926$	3.05783			0.100486
$927$	12.0533	−	12.0533i	0.395882	−	0.395882i
$928$	3.64427	−	3.64427i	0.119629	−	0.119629i
$929$			23.6746i			0.776740i	0.921504	+	0.388370i	$0.126962\pi$
$929$			23.6746i			0.776740i	−0.921504	+	0.388370i	$0.873038\pi$
$930$	−3.57341	−	11.8952i	−0.117177	−	0.390060i
$931$		−	6.99339i		−	0.229199i
$932$	−12.4073	−	12.4073i	−0.406413	−	0.406413i
$933$	−11.9599	+	11.9599i	−0.391550	+	0.391550i
$934$	14.6268			0.478604
$935$	−2.99639	+	5.56971i	−0.0979925	+	0.182149i
$936$	6.17696			0.201900
$937$	32.6658	−	32.6658i	1.06715	−	1.06715i	0.0695692	−	0.997577i	$-0.477838\pi$
$937$	32.6658	−	32.6658i	1.06715	−	1.06715i	0.997577	−	0.0695692i	$-0.0221625\pi$
$938$	17.6480	−	17.6480i	0.576229	−	0.576229i
$939$	12.6272			0.412075
$940$	−10.2885	−	5.53499i	−0.335573	−	0.180531i
$941$		−	12.4003i		−	0.404238i	−0.979361	−	0.202119i	$-0.935217\pi$
$941$		−	12.4003i		−	0.404238i	0.979361	−	0.202119i	$-0.0647827\pi$
$942$	−1.55503	+	1.55503i	−0.0506655	+	0.0506655i
$943$	−1.67858	+	39.3278i	−0.0546620	+	1.28069i
$944$			9.42889i			0.306884i
$945$	−1.83508	−	6.10865i	−0.0596952	−	0.198714i
$946$	−25.4287			−0.826759
$947$	−25.3756	−	25.3756i	−0.824595	−	0.824595i	0.162168	−	0.986763i	$-0.448151\pi$
$947$	−25.3756	−	25.3756i	−0.824595	−	0.824595i	−0.986763	+	0.162168i	$0.948151\pi$
$948$	0.591752	+	0.591752i	0.0192192	+	0.0192192i
$949$			84.6510i			2.74789i
$950$	−30.1400	−	6.16423i	−0.977871	−	0.199994i
$951$	3.06801			0.0994869
$952$	−1.11530	−	1.11530i	−0.0361472	−	0.0361472i
$953$	−2.72751	−	2.72751i	−0.0883527	−	0.0883527i	0.661549	−	0.749902i	$-0.269899\pi$
$953$	−2.72751	−	2.72751i	−0.0883527	−	0.0883527i	−0.749902	+	0.661549i	$0.769899\pi$
$954$	4.62772			0.149828
$955$	−20.6925	+	6.21616i	−0.669592	+	0.201150i
$956$	−12.7394			−0.412021
$957$	18.6410	−	18.6410i	0.602579	−	0.602579i
$958$	−19.4941	−	19.4941i	−0.629826	−	0.629826i
$959$		−	8.60132i		−	0.277751i
$960$	−1.05938	+	1.96919i	−0.0341915	+	0.0635553i
$961$	−0.146886			−0.00473826
$962$	−10.2547	+	10.2547i	−0.330624	+	0.330624i
$963$	5.43462	+	5.43462i	0.175128	+	0.175128i
$964$	5.57785			0.179650
$965$	15.0666	+	8.10552i	0.485011	+	0.260926i
$966$	9.25193	+	10.0769i	0.297676	+	0.324219i
$967$	29.5079	+	29.5079i	0.948911	+	0.948911i	0.998757	−	0.0498460i	$-0.0158730\pi$
$967$	29.5079	+	29.5079i	0.948911	+	0.948911i	−0.0498460	+	0.998757i	$0.515873\pi$
$968$	10.7232	−	10.7232i	0.344656	−	0.344656i
$969$		−	3.40218i		−	0.109294i
$970$	−6.49015	−	21.6045i	−0.208386	−	0.693680i
$971$			18.8170i			0.603868i	0.953329	+	0.301934i	$0.0976322\pi$
$971$			18.8170i			0.603868i	−0.953329	+	0.301934i	$0.902368\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	−16.9544	−	16.9544i	−0.543532	−	0.543532i
$974$		−	15.7431i		−	0.504442i
$975$	17.0201	+	25.7719i	0.545078	+	0.825360i
$976$		−	6.90926i		−	0.221160i
$977$	12.0016	−	12.0016i	0.383966	−	0.383966i	−0.488563	−	0.872529i	$-0.662479\pi$
$977$	12.0016	−	12.0016i	0.383966	−	0.383966i	0.872529	+	0.488563i	$0.162479\pi$
$978$	5.61838	−	5.61838i	0.179656	−	0.179656i
$979$		−	44.0733i		−	1.40859i
$980$	−0.731223	−	2.43411i	−0.0233581	−	0.0777547i
$981$			1.98889i			0.0635005i
$982$	8.67249	+	8.67249i	0.276750	+	0.276750i
$983$	−25.4709	−	25.4709i	−0.812395	−	0.812395i	0.172597	−	0.984992i	$-0.444784\pi$
$983$	−25.4709	−	25.4709i	−0.812395	−	0.812395i	−0.984992	+	0.172597i	$0.944784\pi$
$984$		−	8.20789i		−	0.261658i
$985$	14.5142	−	26.9791i	0.462461	−	0.859624i
$986$			2.84978i			0.0907555i
$987$	10.5383	−	10.5383i	0.335437	−	0.335437i
$988$	26.8739	+	26.8739i	0.854974	+	0.854974i
$989$	−17.5619	+	16.1241i	−0.558435	+	0.512716i
$990$	−5.41892	+	10.0727i	−0.172225	+	0.320132i
$991$	−24.2368			−0.769909			−0.384954	−	0.922936i	$-0.625783\pi$
$991$	−24.2368			−0.769909			−0.384954	+	0.922936i	$0.625783\pi$
$992$	−3.92767	−	3.92767i	−0.124704	−	0.124704i
$993$	−3.14573	+	3.14573i	−0.0998268	+	0.0998268i
$994$	−28.6398			−0.908400
$995$	−1.24016	−	4.12826i	−0.0393157	−	0.130875i
$996$			10.8750i			0.344587i
$997$	31.0953	+	31.0953i	0.984797	+	0.984797i	0.999886	−	0.0150892i	$-0.00480322\pi$
$997$	31.0953	+	31.0953i	0.984797	+	0.984797i	−0.0150892	+	0.999886i	$0.504803\pi$
$998$	−7.14836	+	7.14836i	−0.226277	+	0.226277i
$999$	2.34781			0.0742813

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.j.b.367.9	✓	24
5.3	odd	4	inner	690.2.j.b.643.10	yes	24
23.22	odd	2	inner	690.2.j.b.367.10	yes	24
115.68	even	4	inner	690.2.j.b.643.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.j.b.367.9	✓	24	1.1	even	1	trivial
690.2.j.b.367.10	yes	24	23.22	odd	2	inner
690.2.j.b.643.9	yes	24	115.68	even	4	inner
690.2.j.b.643.10	yes	24	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-0.643329 - 2.14152i) q^{5} +1.00000 q^{6} +(-2.01701 + 2.01701i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-0.643329 - 2.14152i) q^{5} +1.00000 q^{6} +(-2.01701 + 2.01701i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(1.05938 - 1.96919i) q^{10} -5.11516i q^{11} +(0.707107 + 0.707107i) q^{12} +(4.36777 - 4.36777i) q^{13} -2.85248 q^{14} +(-1.96919 - 1.05938i) q^{15} -1.00000 q^{16} +(0.390995 - 0.390995i) q^{17} +(0.707107 - 0.707107i) q^{18} +6.15278 q^{19} +(2.14152 - 0.643329i) q^{20} +2.85248i q^{21} +(3.61696 - 3.61696i) q^{22} +(0.204508 - 4.79147i) q^{23} +1.00000i q^{24} +(-4.17226 + 2.75541i) q^{25} +6.17696 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.01701 - 2.01701i) q^{28} +5.15378i q^{29} +(-0.643329 - 2.14152i) q^{30} +5.55456 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.61696 - 3.61696i) q^{33} +0.552950 q^{34} +(5.61707 + 3.02187i) q^{35} +1.00000 q^{36} +(-1.66015 + 1.66015i) q^{37} +(4.35067 + 4.35067i) q^{38} -6.17696i q^{39} +(1.96919 + 1.05938i) q^{40} -8.20789 q^{41} +(-2.01701 + 2.01701i) q^{42} +(-3.51520 - 3.51520i) q^{43} +5.11516 q^{44} +(-2.14152 + 0.643329i) q^{45} +(3.53269 - 3.24347i) q^{46} +(-3.69444 - 3.69444i) q^{47} +(-0.707107 + 0.707107i) q^{48} -1.13662i q^{49} +(-4.89860 - 1.00186i) q^{50} -0.552950i q^{51} +(4.36777 + 4.36777i) q^{52} +(3.27229 + 3.27229i) q^{53} -1.00000i q^{54} +(-10.9542 + 3.29073i) q^{55} -2.85248i q^{56} +(4.35067 - 4.35067i) q^{57} +(-3.64427 + 3.64427i) q^{58} -9.42889i q^{59} +(1.05938 - 1.96919i) q^{60} +6.90926i q^{61} +(3.92767 + 3.92767i) q^{62} +(2.01701 + 2.01701i) q^{63} -1.00000i q^{64} +(-12.1636 - 6.54377i) q^{65} -5.11516i q^{66} +(-6.18692 + 6.18692i) q^{67} +(0.390995 + 0.390995i) q^{68} +(-3.24347 - 3.53269i) q^{69} +(1.83508 + 6.10865i) q^{70} +10.0403 q^{71} +(0.707107 + 0.707107i) q^{72} +(-9.69041 + 9.69041i) q^{73} -2.34781 q^{74} +(-1.00186 + 4.89860i) q^{75} +6.15278i q^{76} +(10.3173 + 10.3173i) q^{77} +(4.36777 - 4.36777i) q^{78} +0.836863 q^{79} +(0.643329 + 2.14152i) q^{80} -1.00000 q^{81} +(-5.80385 - 5.80385i) q^{82} +(7.68978 + 7.68978i) q^{83} -2.85248 q^{84} +(-1.08886 - 0.585786i) q^{85} -4.97125i q^{86} +(3.64427 + 3.64427i) q^{87} +(3.61696 + 3.61696i) q^{88} +8.61622 q^{89} +(-1.96919 - 1.05938i) q^{90} +17.6196i q^{91} +(4.79147 + 0.204508i) q^{92} +(3.92767 - 3.92767i) q^{93} -5.22472i q^{94} +(-3.95826 - 13.1763i) q^{95} -1.00000 q^{96} +(7.13357 - 7.13357i) q^{97} +(0.803714 - 0.803714i) q^{98} -5.11516 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{6}+O(q^{10}) \) 24 * q + 24 * q^6	\( 24 q + 24 q^{6} + 16 q^{13} - 24 q^{16} + 16 q^{23} - 16 q^{25} + 16 q^{31} + 24 q^{36} + 8 q^{46} + 40 q^{47} - 8 q^{50} + 16 q^{52} - 56 q^{55} - 16 q^{58} - 8 q^{62} + 32 q^{70} + 64 q^{71} - 16 q^{73} + 32 q^{75} + 16 q^{77} + 16 q^{78} - 24 q^{81} + 24 q^{82} - 48 q^{85} + 16 q^{87} + 16 q^{92} - 8 q^{93} + 24 q^{95} - 24 q^{96}+O(q^{100}) \) 24 * q + 24 * q^6 + 16 * q^13 - 24 * q^16 + 16 * q^23 - 16 * q^25 + 16 * q^31 + 24 * q^36 + 8 * q^46 + 40 * q^47 - 8 * q^50 + 16 * q^52 - 56 * q^55 - 16 * q^58 - 8 * q^62 + 32 * q^70 + 64 * q^71 - 16 * q^73 + 32 * q^75 + 16 * q^77 + 16 * q^78 - 24 * q^81 + 24 * q^82 - 48 * q^85 + 16 * q^87 + 16 * q^92 - 8 * q^93 + 24 * q^95 - 24 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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