LMFDB - Embedded newform 462.2.c.a.197.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(197,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("462.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.c (of order $2$, degree $1$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 16x^{10} + 94x^{8} + 246x^{6} + 277x^{4} + 114x^{2} + 9 $ x^12 + 16x^10 + 94x^8 + 246x^6 + 277x^4 + 114*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			197.3
Root			$0.822410i$ of defining polynomial
Character	$\chi$	$=$	462.197
Dual form			462.2.c.a.197.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.742446 - 1.56486i) q^{3} +1.00000 q^{4} +3.23163i q^{5} +(0.742446 + 1.56486i) q^{6} -1.00000i q^{7} -1.00000 q^{8} +(-1.89755 + 2.32364i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.742446 - 1.56486i) q^{3} +1.00000 q^{4} +3.23163i q^{5} +(0.742446 + 1.56486i) q^{6} -1.00000i q^{7} -1.00000 q^{8} +(-1.89755 + 2.32364i) q^{9} -3.23163i q^{10} +(-3.30730 - 0.248504i) q^{11} +(-0.742446 - 1.56486i) q^{12} -5.12971i q^{13} +1.00000i q^{14} +(5.05704 - 2.39931i) q^{15} +1.00000 q^{16} -2.90054 q^{17} +(1.89755 - 2.32364i) q^{18} -0.590340i q^{19} +3.23163i q^{20} +(-1.56486 + 0.742446i) q^{21} +(3.30730 + 0.248504i) q^{22} -9.26189i q^{23} +(0.742446 + 1.56486i) q^{24} -5.44344 q^{25} +5.12971i q^{26} +(5.04499 + 1.24421i) q^{27} -1.00000i q^{28} -0.996472 q^{29} +(-5.05704 + 2.39931i) q^{30} -4.39402 q^{31} -1.00000 q^{32} +(2.06662 + 5.35995i) q^{33} +2.90054 q^{34} +3.23163 q^{35} +(-1.89755 + 2.32364i) q^{36} -8.10808 q^{37} +0.590340i q^{38} +(-8.02726 + 3.80853i) q^{39} -3.23163i q^{40} -9.80126 q^{41} +(1.56486 - 0.742446i) q^{42} -1.94644i q^{43} +(-3.30730 - 0.248504i) q^{44} +(-7.50916 - 6.13218i) q^{45} +9.26189i q^{46} +7.19265i q^{47} +(-0.742446 - 1.56486i) q^{48} -1.00000 q^{49} +5.44344 q^{50} +(2.15350 + 4.53893i) q^{51} -5.12971i q^{52} -0.204904i q^{53} +(-5.04499 - 1.24421i) q^{54} +(0.803073 - 10.6880i) q^{55} +1.00000i q^{56} +(-0.923798 + 0.438296i) q^{57} +0.996472 q^{58} -6.09950i q^{59} +(5.05704 - 2.39931i) q^{60} +5.31267i q^{61} +4.39402 q^{62} +(2.32364 + 1.89755i) q^{63} +1.00000 q^{64} +16.5773 q^{65} +(-2.06662 - 5.35995i) q^{66} +8.79756 q^{67} -2.90054 q^{68} +(-14.4935 + 6.87645i) q^{69} -3.23163 q^{70} -6.62041i q^{71} +(1.89755 - 2.32364i) q^{72} +7.07170i q^{73} +8.10808 q^{74} +(4.04146 + 8.51821i) q^{75} -0.590340i q^{76} +(-0.248504 + 3.30730i) q^{77} +(8.02726 - 3.80853i) q^{78} -5.49348i q^{79} +3.23163i q^{80} +(-1.79862 - 8.81844i) q^{81} +9.80126 q^{82} +11.0267 q^{83} +(-1.56486 + 0.742446i) q^{84} -9.37349i q^{85} +1.94644i q^{86} +(0.739826 + 1.55933i) q^{87} +(3.30730 + 0.248504i) q^{88} +1.28964i q^{89} +(7.50916 + 6.13218i) q^{90} -5.12971 q^{91} -9.26189i q^{92} +(3.26233 + 6.87601i) q^{93} -7.19265i q^{94} +1.90776 q^{95} +(0.742446 + 1.56486i) q^{96} -11.3155 q^{97} +1.00000 q^{98} +(6.85320 - 7.21344i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 4 q^{3} + 12 q^{4} - 4 q^{6} - 12 q^{8}+O(q^{10}) $ 12 * q - 12 * q^2 + 4 * q^3 + 12 * q^4 - 4 * q^6 - 12 * q^8	$ 12 q - 12 q^{2} + 4 q^{3} + 12 q^{4} - 4 q^{6} - 12 q^{8} - 8 q^{11} + 4 q^{12} + 4 q^{15} + 12 q^{16} - 4 q^{17} + 8 q^{22} - 4 q^{24} - 28 q^{25} - 8 q^{27} + 8 q^{29} - 4 q^{30} + 12 q^{31} - 12 q^{32} + 16 q^{33} + 4 q^{34} - 4 q^{35} - 36 q^{39} + 20 q^{41} - 8 q^{44} - 12 q^{45} + 4 q^{48} - 12 q^{49} + 28 q^{50} + 8 q^{51} + 8 q^{54} + 4 q^{55} + 28 q^{57} - 8 q^{58} + 4 q^{60} - 12 q^{62} + 4 q^{63} + 12 q^{64} - 16 q^{66} + 24 q^{67} - 4 q^{68} - 20 q^{69} + 4 q^{70} - 40 q^{75} + 4 q^{77} + 36 q^{78} + 4 q^{81} - 20 q^{82} + 44 q^{83} + 8 q^{87} + 8 q^{88} + 12 q^{90} - 24 q^{91} - 24 q^{93} - 4 q^{96} - 48 q^{97} + 12 q^{98} + 36 q^{99}+O(q^{100}) $ 12 * q - 12 * q^2 + 4 * q^3 + 12 * q^4 - 4 * q^6 - 12 * q^8 - 8 * q^11 + 4 * q^12 + 4 * q^15 + 12 * q^16 - 4 * q^17 + 8 * q^22 - 4 * q^24 - 28 * q^25 - 8 * q^27 + 8 * q^29 - 4 * q^30 + 12 * q^31 - 12 * q^32 + 16 * q^33 + 4 * q^34 - 4 * q^35 - 36 * q^39 + 20 * q^41 - 8 * q^44 - 12 * q^45 + 4 * q^48 - 12 * q^49 + 28 * q^50 + 8 * q^51 + 8 * q^54 + 4 * q^55 + 28 * q^57 - 8 * q^58 + 4 * q^60 - 12 * q^62 + 4 * q^63 + 12 * q^64 - 16 * q^66 + 24 * q^67 - 4 * q^68 - 20 * q^69 + 4 * q^70 - 40 * q^75 + 4 * q^77 + 36 * q^78 + 4 * q^81 - 20 * q^82 + 44 * q^83 + 8 * q^87 + 8 * q^88 + 12 * q^90 - 24 * q^91 - 24 * q^93 - 4 * q^96 - 48 * q^97 + 12 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.742446	−	1.56486i	−0.428651	−	0.903470i
$3$	−0.742446	−	1.56486i	−0.428651	−	0.903470i
$4$	1.00000			0.500000
$5$			3.23163i			1.44523i	0.691251	+	0.722615i	$0.257060\pi$
$5$			3.23163i			1.44523i	−0.691251	+	0.722615i	$0.742940\pi$
$6$	0.742446	+	1.56486i	0.303102	+	0.638850i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−1.00000			−0.353553
$9$	−1.89755	+	2.32364i	−0.632516	+	0.774547i
$10$		−	3.23163i		−	1.02193i
$11$	−3.30730	−	0.248504i	−0.997189	−	0.0749268i
$11$	−3.30730	−	0.248504i	−0.997189	−	0.0749268i
$12$	−0.742446	−	1.56486i	−0.214326	−	0.451735i
$13$		−	5.12971i		−	1.42273i	−0.702825	−	0.711363i	$-0.748078\pi$
$13$		−	5.12971i		−	1.42273i	0.702825	−	0.711363i	$-0.251922\pi$
$14$			1.00000i			0.267261i
$15$	5.05704	−	2.39931i	1.30572	−	0.619500i
$16$	1.00000			0.250000
$17$	−2.90054			−0.703485			−0.351743	−	0.936097i	$-0.614411\pi$
$17$	−2.90054			−0.703485			−0.351743	+	0.936097i	$0.614411\pi$
$18$	1.89755	−	2.32364i	0.447256	−	0.547688i
$19$		−	0.590340i		−	0.135433i	−0.997705	−	0.0677167i	$-0.978429\pi$
$19$		−	0.590340i		−	0.135433i	0.997705	−	0.0677167i	$-0.0215714\pi$
$20$			3.23163i			0.722615i
$21$	−1.56486	+	0.742446i	−0.341480	+	0.162015i
$22$	3.30730	+	0.248504i	0.705119	+	0.0529812i
$23$		−	9.26189i		−	1.93124i	−0.259963	−	0.965619i	$-0.583710\pi$
$23$		−	9.26189i		−	1.93124i	0.259963	−	0.965619i	$-0.416290\pi$
$24$	0.742446	+	1.56486i	0.151551	+	0.319425i
$25$	−5.44344			−1.08869
$26$			5.12971i			1.00602i
$27$	5.04499	+	1.24421i	0.970909	+	0.239448i
$28$		−	1.00000i		−	0.188982i
$29$	−0.996472			−0.185040			−0.0925201	−	0.995711i	$-0.529492\pi$
$29$	−0.996472			−0.185040			−0.0925201	+	0.995711i	$0.529492\pi$
$30$	−5.05704	+	2.39931i	−0.923285	+	0.438052i
$31$	−4.39402			−0.789190			−0.394595	−	0.918855i	$-0.629115\pi$
$31$	−4.39402			−0.789190			−0.394595	+	0.918855i	$0.629115\pi$
$32$	−1.00000			−0.176777
$33$	2.06662	+	5.35995i	0.359752	+	0.933048i
$34$	2.90054			0.497439
$35$	3.23163			0.546245
$36$	−1.89755	+	2.32364i	−0.316258	+	0.387274i
$37$	−8.10808			−1.33296			−0.666480	−	0.745523i	$-0.732200\pi$
$37$	−8.10808			−1.33296			−0.666480	+	0.745523i	$0.732200\pi$
$38$			0.590340i			0.0957659i
$39$	−8.02726	+	3.80853i	−1.28539	+	0.609854i
$40$		−	3.23163i		−	0.510966i
$41$	−9.80126			−1.53070			−0.765350	−	0.643615i	$-0.777434\pi$
$41$	−9.80126			−1.53070			−0.765350	+	0.643615i	$0.777434\pi$
$42$	1.56486	−	0.742446i	0.241463	−	0.114562i
$43$		−	1.94644i		−	0.296829i	−0.988925	−	0.148414i	$-0.952583\pi$
$43$		−	1.94644i		−	0.296829i	0.988925	−	0.148414i	$-0.0474169\pi$
$44$	−3.30730	−	0.248504i	−0.498595	−	0.0374634i
$45$	−7.50916	−	6.13218i	−1.11940	−	0.914131i
$46$			9.26189i			1.36559i
$47$			7.19265i			1.04916i	0.851363	+	0.524578i	$0.175777\pi$
$47$			7.19265i			1.04916i	−0.851363	+	0.524578i	$0.824223\pi$
$48$	−0.742446	−	1.56486i	−0.107163	−	0.225867i
$49$	−1.00000			−0.142857
$50$	5.44344			0.769819
$51$	2.15350	+	4.53893i	0.301550	+	0.635578i
$52$		−	5.12971i		−	0.711363i
$53$		−	0.204904i		−	0.0281458i	−0.999901	−	0.0140729i	$-0.995520\pi$
$53$		−	0.204904i		−	0.0281458i	0.999901	−	0.0140729i	$-0.00447969\pi$
$54$	−5.04499	−	1.24421i	−0.686536	−	0.169316i
$55$	0.803073	−	10.6880i	0.108286	−	1.44117i
$56$			1.00000i			0.133631i
$57$	−0.923798	+	0.438296i	−0.122360	+	0.0580537i
$58$	0.996472			0.130843
$59$		−	6.09950i		−	0.794087i	−0.917800	−	0.397043i	$-0.870036\pi$
$59$		−	6.09950i		−	0.794087i	0.917800	−	0.397043i	$-0.129964\pi$
$60$	5.05704	−	2.39931i	0.652861	−	0.309750i
$61$			5.31267i			0.680217i	0.940386	+	0.340109i	$0.110464\pi$
$61$			5.31267i			0.680217i	−0.940386	+	0.340109i	$0.889536\pi$
$62$	4.39402			0.558042
$63$	2.32364	+	1.89755i	0.292751	+	0.239069i
$64$	1.00000			0.125000
$65$	16.5773			2.05617
$66$	−2.06662	−	5.35995i	−0.254383	−	0.659764i
$67$	8.79756			1.07479			0.537397	−	0.843330i	$-0.319408\pi$
$67$	8.79756			1.07479			0.537397	+	0.843330i	$0.319408\pi$
$68$	−2.90054			−0.351743
$69$	−14.4935	+	6.87645i	−1.74481	+	0.827827i
$70$	−3.23163			−0.386254
$71$		−	6.62041i		−	0.785698i	−0.919603	−	0.392849i	$-0.871490\pi$
$71$		−	6.62041i		−	0.785698i	0.919603	−	0.392849i	$-0.128510\pi$
$72$	1.89755	−	2.32364i	0.223628	−	0.273844i
$73$			7.07170i			0.827680i	0.910350	+	0.413840i	$0.135813\pi$
$73$			7.07170i			0.827680i	−0.910350	+	0.413840i	$0.864187\pi$
$74$	8.10808			0.942546
$75$	4.04146	+	8.51821i	0.466668	+	0.983598i
$76$		−	0.590340i		−	0.0677167i
$77$	−0.248504	+	3.30730i	−0.0283197	+	0.376902i
$78$	8.02726	−	3.80853i	0.908908	−	0.431232i
$79$		−	5.49348i		−	0.618065i	−0.951052	−	0.309032i	$-0.899995\pi$
$79$		−	5.49348i		−	0.618065i	0.951052	−	0.309032i	$-0.100005\pi$
$80$			3.23163i			0.361307i
$81$	−1.79862	−	8.81844i	−0.199847	−	0.979827i
$82$	9.80126			1.08237
$83$	11.0267			1.21034			0.605170	−	0.796096i	$-0.293105\pi$
$83$	11.0267			1.21034			0.605170	+	0.796096i	$0.293105\pi$
$84$	−1.56486	+	0.742446i	−0.170740	+	0.0810075i
$85$		−	9.37349i		−	1.01670i
$86$			1.94644i			0.209890i
$87$	0.739826	+	1.55933i	0.0793177	+	0.167178i
$88$	3.30730	+	0.248504i	0.352560	+	0.0264906i
$89$			1.28964i			0.136702i	0.997661	+	0.0683508i	$0.0217737\pi$
$89$			1.28964i			0.136702i	−0.997661	+	0.0683508i	$0.978226\pi$
$90$	7.50916	+	6.13218i	0.791534	+	0.646388i
$91$	−5.12971			−0.537740
$92$		−	9.26189i		−	0.965619i
$93$	3.26233	+	6.87601i	0.338287	+	0.713009i
$94$		−	7.19265i		−	0.741865i
$95$	1.90776			0.195732
$96$	0.742446	+	1.56486i	0.0757756	+	0.159712i
$97$	−11.3155			−1.14891			−0.574455	−	0.818536i	$-0.694786\pi$
$97$	−11.3155			−1.14891			−0.574455	+	0.818536i	$0.694786\pi$
$98$	1.00000			0.101015
$99$	6.85320	−	7.21344i	0.688772	−	0.724978i
$100$	−5.44344			−0.544344
$101$	18.8350			1.87416			0.937078	−	0.349119i	$-0.113519\pi$
$101$	18.8350			1.87416			0.937078	+	0.349119i	$0.113519\pi$
$102$	−2.15350	−	4.53893i	−0.213228	−	0.449421i
$103$	−9.82920			−0.968500			−0.484250	−	0.874930i	$-0.660907\pi$
$103$	−9.82920			−0.968500			−0.484250	+	0.874930i	$0.660907\pi$
$104$			5.12971i			0.503010i
$105$	−2.39931	−	5.05704i	−0.234149	−	0.493516i
$106$			0.204904i			0.0199021i
$107$	−4.77732			−0.461841			−0.230920	−	0.972973i	$-0.574174\pi$
$107$	−4.77732			−0.461841			−0.230920	+	0.972973i	$0.574174\pi$
$108$	5.04499	+	1.24421i	0.485455	+	0.119724i
$109$			1.35871i			0.130141i	0.997881	+	0.0650703i	$0.0207272\pi$
$109$			1.35871i			0.130141i	−0.997881	+	0.0650703i	$0.979273\pi$
$110$	−0.803073	+	10.6880i	−0.0765700	+	1.01906i
$111$	6.01981	+	12.6880i	0.571375	+	1.20429i
$112$		−	1.00000i		−	0.0944911i
$113$		−	16.5869i		−	1.56036i	−0.625555	−	0.780180i	$-0.715128\pi$
$113$		−	16.5869i		−	1.56036i	0.625555	−	0.780180i	$-0.284872\pi$
$114$	0.923798	−	0.438296i	0.0865216	−	0.0410502i
$115$	29.9310			2.79108
$116$	−0.996472			−0.0925201
$117$	11.9196	+	9.73387i	1.10197	+	0.899897i
$118$			6.09950i			0.561504i
$119$			2.90054i			0.265892i
$120$	−5.05704	+	2.39931i	−0.461642	+	0.219026i
$121$	10.8765	+	1.64376i	0.988772	+	0.149432i
$122$		−	5.31267i		−	0.480986i
$123$	7.27691	+	15.3376i	0.656136	+	1.38294i
$124$	−4.39402			−0.394595
$125$		−	1.43305i		−	0.128176i
$126$	−2.32364	−	1.89755i	−0.207006	−	0.169047i
$127$			9.11268i			0.808619i	0.914622	+	0.404310i	$0.132488\pi$
$127$			9.11268i			0.808619i	−0.914622	+	0.404310i	$0.867512\pi$
$128$	−1.00000			−0.0883883
$129$	−3.04589	+	1.44512i	−0.268176	+	0.127236i
$130$	−16.5773			−1.45393
$131$	−19.4608			−1.70030			−0.850151	−	0.526539i	$-0.823489\pi$
$131$	−19.4608			−1.70030			−0.850151	+	0.526539i	$0.823489\pi$
$132$	2.06662	+	5.35995i	0.179876	+	0.466524i
$133$	−0.590340			−0.0511890
$134$	−8.79756			−0.759993
$135$	−4.02083	+	16.3036i	−0.346058	+	1.40319i
$136$	2.90054			0.248720
$137$		−	4.98696i		−	0.426065i	−0.977045	−	0.213032i	$-0.931666\pi$
$137$		−	4.98696i		−	0.426065i	0.977045	−	0.213032i	$-0.0683340\pi$
$138$	14.4935	−	6.87645i	1.23377	−	0.585362i
$139$			19.7345i			1.67386i	0.547310	+	0.836930i	$0.315652\pi$
$139$			19.7345i			1.67386i	−0.547310	+	0.836930i	$0.684348\pi$
$140$	3.23163			0.273123
$141$	11.2555	−	5.34015i	0.947881	−	0.449722i
$142$			6.62041i			0.555572i
$143$	−1.27475	+	16.9655i	−0.106600	+	1.41873i
$144$	−1.89755	+	2.32364i	−0.158129	+	0.193637i
$145$		−	3.22023i		−	0.267425i
$146$		−	7.07170i		−	0.585258i
$147$	0.742446	+	1.56486i	0.0612359	+	0.129067i
$148$	−8.10808			−0.666480
$149$	−16.8436			−1.37988			−0.689942	−	0.723865i	$-0.742364\pi$
$149$	−16.8436			−1.37988			−0.689942	+	0.723865i	$0.742364\pi$
$150$	−4.04146	−	8.51821i	−0.329984	−	0.695509i
$151$		−	4.32743i		−	0.352161i	−0.984376	−	0.176081i	$-0.943658\pi$
$151$		−	4.32743i		−	0.352161i	0.984376	−	0.176081i	$-0.0563419\pi$
$152$			0.590340i			0.0478829i
$153$	5.50392	−	6.73983i	0.444966	−	0.544883i
$154$	0.248504	−	3.30730i	0.0200250	−	0.266510i
$155$		−	14.1999i		−	1.14056i
$156$	−8.02726	+	3.80853i	−0.642695	+	0.304927i
$157$	21.8185			1.74130			0.870652	−	0.491899i	$-0.163697\pi$
$157$	21.8185			1.74130			0.870652	+	0.491899i	$0.163697\pi$
$158$			5.49348i			0.437038i
$159$	−0.320646	+	0.152130i	−0.0254289	+	0.0120647i
$160$		−	3.23163i		−	0.255483i
$161$	−9.26189			−0.729939
$162$	1.79862	+	8.81844i	0.141313	+	0.692842i
$163$	9.54906			0.747940			0.373970	−	0.927441i	$-0.377996\pi$
$163$	9.54906			0.747940			0.373970	+	0.927441i	$0.377996\pi$
$164$	−9.80126			−0.765350
$165$	−17.3214	+	6.67856i	−1.34847	+	0.519925i
$166$	−11.0267			−0.855840
$167$	7.91163			0.612220			0.306110	−	0.951996i	$-0.400972\pi$
$167$	7.91163			0.612220			0.306110	+	0.951996i	$0.400972\pi$
$168$	1.56486	−	0.742446i	0.120731	−	0.0572810i
$169$	−13.3139			−1.02415
$170$			9.37349i			0.718914i
$171$	1.37174	+	1.12020i	0.104900	+	0.0856638i
$172$		−	1.94644i		−	0.148414i
$173$	−1.60954			−0.122371			−0.0611857	−	0.998126i	$-0.519488\pi$
$173$	−1.60954			−0.122371			−0.0611857	+	0.998126i	$0.519488\pi$
$174$	−0.739826	−	1.55933i	−0.0560861	−	0.118213i
$175$			5.44344i			0.411486i
$176$	−3.30730	−	0.248504i	−0.249297	−	0.0187317i
$177$	−9.54483	+	4.52855i	−0.717433	+	0.340386i
$178$		−	1.28964i		−	0.0966626i
$179$		−	17.6786i		−	1.32136i	−0.750666	−	0.660682i	$-0.770267\pi$
$179$		−	17.6786i		−	1.32136i	0.750666	−	0.660682i	$-0.229733\pi$
$180$	−7.50916	−	6.13218i	−0.559699	−	0.457065i
$181$	11.6389			0.865111			0.432555	−	0.901607i	$-0.357612\pi$
$181$	11.6389			0.865111			0.432555	+	0.901607i	$0.357612\pi$
$182$	5.12971			0.380240
$183$	8.31356	−	3.94437i	0.614556	−	0.291576i
$184$			9.26189i			0.682795i
$185$		−	26.2023i		−	1.92643i
$186$	−3.26233	−	6.87601i	−0.239205	−	0.504174i
$187$	9.59298	+	0.720797i	0.701508	+	0.0527099i
$188$			7.19265i			0.524578i
$189$	1.24421	−	5.04499i	0.0905030	−	0.366969i
$190$	−1.90776			−0.138404
$191$			10.5237i			0.761468i	0.924685	+	0.380734i	$0.124329\pi$
$191$			10.5237i			0.761468i	−0.924685	+	0.380734i	$0.875671\pi$
$192$	−0.742446	−	1.56486i	−0.0535814	−	0.112934i
$193$		−	16.2873i		−	1.17238i	−0.810173	−	0.586191i	$-0.800627\pi$
$193$		−	16.2873i		−	1.17238i	0.810173	−	0.586191i	$-0.199373\pi$
$194$	11.3155			0.812402
$195$	−12.3078	−	25.9411i	−0.881378	−	1.85768i
$196$	−1.00000			−0.0714286
$197$	−6.38099			−0.454627			−0.227313	−	0.973822i	$-0.572994\pi$
$197$	−6.38099			−0.454627			−0.227313	+	0.973822i	$0.572994\pi$
$198$	−6.85320	+	7.21344i	−0.487036	+	0.512637i
$199$	−3.17528			−0.225090			−0.112545	−	0.993647i	$-0.535900\pi$
$199$	−3.17528			−0.225090			−0.112545	+	0.993647i	$0.535900\pi$
$200$	5.44344			0.384910
$201$	−6.53171	−	13.7669i	−0.460712	−	0.971043i
$202$	−18.8350			−1.32523
$203$			0.996472i			0.0699386i
$204$	2.15350	+	4.53893i	0.150775	+	0.317789i
$205$		−	31.6741i		−	2.21221i
$206$	9.82920			0.684833
$207$	21.5213	+	17.5749i	1.49583	+	1.22154i
$208$		−	5.12971i		−	0.355682i
$209$	−0.146702	+	1.95243i	−0.0101476	+	0.135053i
$210$	2.39931	+	5.05704i	0.165568	+	0.348969i
$211$		−	21.3853i		−	1.47222i	−0.676860	−	0.736112i	$-0.736660\pi$
$211$		−	21.3853i		−	1.47222i	0.676860	−	0.736112i	$-0.263340\pi$
$212$		−	0.204904i		−	0.0140729i
$213$	−10.3600	+	4.91530i	−0.709854	+	0.336790i
$214$	4.77732			0.326571
$215$	6.29016			0.428986
$216$	−5.04499	−	1.24421i	−0.343268	−	0.0846578i
$217$			4.39402i			0.298286i
$218$		−	1.35871i		−	0.0920234i
$219$	11.0662	−	5.25036i	0.747784	−	0.354786i
$220$	0.803073	−	10.6880i	0.0541432	−	0.720584i
$221$			14.8790i			1.00087i
$222$	−6.01981	−	12.6880i	−0.404023	−	0.851562i
$223$	−16.4101			−1.09890			−0.549449	−	0.835527i	$-0.685162\pi$
$223$	−16.4101			−1.09890			−0.549449	+	0.835527i	$0.685162\pi$
$224$			1.00000i			0.0668153i
$225$	10.3292	−	12.6486i	0.688613	−	0.843241i
$226$			16.5869i			1.10334i
$227$	−16.7311			−1.11048			−0.555241	−	0.831689i	$-0.687374\pi$
$227$	−16.7311			−1.11048			−0.555241	+	0.831689i	$0.687374\pi$
$228$	−0.923798	+	0.438296i	−0.0611800	+	0.0290269i
$229$	−2.37838			−0.157168			−0.0785839	−	0.996908i	$-0.525040\pi$
$229$	−2.37838			−0.157168			−0.0785839	+	0.996908i	$0.525040\pi$
$230$	−29.9310			−1.97359
$231$	5.35995	−	2.06662i	0.352659	−	0.135974i
$232$	0.996472			0.0654216
$233$	18.7833			1.23054			0.615268	−	0.788318i	$-0.289048\pi$
$233$	18.7833			1.23054			0.615268	+	0.788318i	$0.289048\pi$
$234$	−11.9196	−	9.73387i	−0.779210	−	0.636323i
$235$	−23.2440			−1.51627
$236$		−	6.09950i		−	0.397043i
$237$	−8.59650	+	4.07861i	−0.558403	+	0.264934i
$238$		−	2.90054i		−	0.188014i
$239$	−7.45129			−0.481984			−0.240992	−	0.970527i	$-0.577473\pi$
$239$	−7.45129			−0.481984			−0.240992	+	0.970527i	$0.577473\pi$
$240$	5.05704	−	2.39931i	0.326430	−	0.154875i
$241$			25.4487i			1.63930i	0.572867	+	0.819648i	$0.305831\pi$
$241$			25.4487i			1.63930i	−0.572867	+	0.819648i	$0.694169\pi$
$242$	−10.8765	−	1.64376i	−0.699167	−	0.105665i
$243$	−12.4642	+	9.36181i	−0.799580	+	0.600560i
$244$			5.31267i			0.340109i
$245$		−	3.23163i		−	0.206461i
$246$	−7.27691	−	15.3376i	−0.463959	−	0.977887i
$247$	−3.02828			−0.192685
$248$	4.39402			0.279021
$249$	−8.18675	−	17.2552i	−0.518814	−	1.09351i
$250$			1.43305i			0.0906339i
$251$			7.92147i			0.499999i	0.968246	+	0.249999i	$0.0804304\pi$
$251$			7.92147i			0.499999i	−0.968246	+	0.249999i	$0.919570\pi$
$252$	2.32364	+	1.89755i	0.146376	+	0.119534i
$253$	−2.30162	+	30.6319i	−0.144701	+	1.92581i
$254$		−	9.11268i		−	0.571780i
$255$	−14.6682	+	6.95931i	−0.918556	+	0.435809i
$256$	1.00000			0.0625000
$257$			8.84848i			0.551953i	0.961164	+	0.275976i	$0.0890012\pi$
$257$			8.84848i			0.551953i	−0.961164	+	0.275976i	$0.910999\pi$
$258$	3.04589	−	1.44512i	0.189629	−	0.0899695i
$259$			8.10808i			0.503812i
$260$	16.5773			1.02808
$261$	1.89085	−	2.31544i	0.117041	−	0.143322i
$262$	19.4608			1.20230
$263$	23.3226			1.43813			0.719066	−	0.694942i	$-0.244570\pi$
$263$	23.3226			1.43813			0.719066	+	0.694942i	$0.244570\pi$
$264$	−2.06662	−	5.35995i	−0.127192	−	0.329882i
$265$	0.662175			0.0406771
$266$	0.590340			0.0361961
$267$	2.01810	−	0.957488i	0.123506	−	0.0585973i
$268$	8.79756			0.537397
$269$			10.7058i			0.652745i	0.945241	+	0.326372i	$0.105826\pi$
$269$			10.7058i			0.652745i	−0.945241	+	0.326372i	$0.894174\pi$
$270$	4.02083	−	16.3036i	0.244700	−	0.992203i
$271$			16.4808i			1.00114i	0.865697	+	0.500568i	$0.166876\pi$
$271$			16.4808i			1.00114i	−0.865697	+	0.500568i	$0.833124\pi$
$272$	−2.90054			−0.175871
$273$	3.80853	+	8.02726i	0.230503	+	0.485832i
$274$			4.98696i			0.301273i
$275$	18.0031	+	1.35272i	1.08563	+	0.0815719i
$276$	−14.4935	+	6.87645i	−0.872407	+	0.413914i
$277$			11.4920i			0.690486i	0.938513	+	0.345243i	$0.112204\pi$
$277$			11.4920i			0.690486i	−0.938513	+	0.345243i	$0.887796\pi$
$278$		−	19.7345i		−	1.18360i
$279$	8.33787	−	10.2101i	0.499175	−	0.611265i
$280$	−3.23163			−0.193127
$281$	−23.3191			−1.39110			−0.695549	−	0.718479i	$-0.744839\pi$
$281$	−23.3191			−1.39110			−0.695549	+	0.718479i	$0.744839\pi$
$282$	−11.2555	+	5.34015i	−0.670253	+	0.318001i
$283$		−	16.7703i		−	0.996891i	−0.866921	−	0.498446i	$-0.833904\pi$
$283$		−	16.7703i		−	0.996891i	0.866921	−	0.498446i	$-0.166096\pi$
$284$		−	6.62041i		−	0.392849i
$285$	−1.41641	−	2.98537i	−0.0839009	−	0.176838i
$286$	1.27475	−	16.9655i	0.0753778	−	1.00319i
$287$			9.80126i			0.578550i
$288$	1.89755	−	2.32364i	0.111814	−	0.136922i
$289$	−8.58684			−0.505108
$290$			3.22023i			0.189098i
$291$	8.40111	+	17.7071i	0.492482	+	1.03801i
$292$			7.07170i			0.413840i
$293$	27.6593			1.61587			0.807937	−	0.589270i	$-0.200584\pi$
$293$	27.6593			1.61587			0.807937	+	0.589270i	$0.200584\pi$
$294$	−0.742446	−	1.56486i	−0.0433003	−	0.0912642i
$295$	19.7113			1.14764
$296$	8.10808			0.471273
$297$	−16.3761	−	5.36868i	−0.950239	−	0.311522i
$298$	16.8436			0.975725
$299$	−47.5108			−2.74762
$300$	4.04146	+	8.51821i	0.233334	+	0.491799i
$301$	−1.94644			−0.112191
$302$			4.32743i			0.249016i
$303$	−13.9840	−	29.4741i	−0.803360	−	1.69324i
$304$		−	0.590340i		−	0.0338583i
$305$	−17.1686			−0.983070
$306$	−5.50392	+	6.73983i	−0.314638	+	0.385290i
$307$			3.81462i			0.217712i	0.994058	+	0.108856i	$0.0347187\pi$
$307$			3.81462i			0.217712i	−0.994058	+	0.108856i	$0.965281\pi$
$308$	−0.248504	+	3.30730i	−0.0141598	+	0.188451i
$309$	7.29765	+	15.3813i	0.415149	+	0.875011i
$310$			14.1999i			0.806498i
$311$		−	23.1098i		−	1.31044i	−0.755439	−	0.655219i	$-0.772576\pi$
$311$		−	23.1098i		−	1.31044i	0.755439	−	0.655219i	$-0.227424\pi$
$312$	8.02726	−	3.80853i	0.454454	−	0.215616i
$313$	−17.6194			−0.995905			−0.497952	−	0.867204i	$-0.665915\pi$
$313$	−17.6194			−0.995905			−0.497952	+	0.867204i	$0.665915\pi$
$314$	−21.8185			−1.23129
$315$	−6.13218	+	7.50916i	−0.345509	+	0.423093i
$316$		−	5.49348i		−	0.309032i
$317$			21.1812i			1.18966i	0.803853	+	0.594828i	$0.202780\pi$
$317$			21.1812i			1.18966i	−0.803853	+	0.594828i	$0.797220\pi$
$318$	0.320646	−	0.152130i	0.0179809	−	0.00853105i
$319$	3.29563	+	0.247627i	0.184520	+	0.0138645i
$320$			3.23163i			0.180654i
$321$	3.54690	+	7.47581i	0.197969	+	0.417259i
$322$	9.26189			0.516145
$323$			1.71231i			0.0952754i
$324$	−1.79862	−	8.81844i	−0.0999236	−	0.489914i
$325$			27.9233i			1.54891i
$326$	−9.54906			−0.528874
$327$	2.12618	−	1.00877i	0.117578	−	0.0557850i
$328$	9.80126			0.541184
$329$	7.19265			0.396544
$330$	17.3214	−	6.67856i	0.953511	−	0.367642i
$331$	9.70904			0.533657			0.266829	−	0.963744i	$-0.414024\pi$
$331$	9.70904			0.533657			0.266829	+	0.963744i	$0.414024\pi$
$332$	11.0267			0.605170
$333$	15.3855	−	18.8403i	0.843119	−	1.03244i
$334$	−7.91163			−0.432905
$335$			28.4305i			1.55332i
$336$	−1.56486	+	0.742446i	−0.0853699	+	0.0405038i
$337$		−	9.55751i		−	0.520631i	−0.965524	−	0.260315i	$-0.916173\pi$
$337$		−	9.55751i		−	0.520631i	0.965524	−	0.260315i	$-0.0838265\pi$
$338$	13.3139			0.724183
$339$	−25.9560	+	12.3148i	−1.40974	+	0.668850i
$340$		−	9.37349i		−	0.508349i
$341$	14.5324	+	1.09193i	0.786972	+	0.0591315i
$342$	−1.37174	−	1.12020i	−0.0741752	−	0.0605734i
$343$			1.00000i			0.0539949i
$344$			1.94644i			0.104945i
$345$	−22.2222	−	46.8377i	−1.19640	−	2.52166i
$346$	1.60954			0.0865297
$347$	31.9277			1.71397			0.856983	−	0.515344i	$-0.172336\pi$
$347$	31.9277			1.71397			0.856983	+	0.515344i	$0.172336\pi$
$348$	0.739826	+	1.55933i	0.0396589	+	0.0835891i
$349$		−	9.79830i		−	0.524491i	−0.965001	−	0.262246i	$-0.915537\pi$
$349$		−	9.79830i		−	0.524491i	0.965001	−	0.262246i	$-0.0844631\pi$
$350$		−	5.44344i		−	0.290964i
$351$	6.38244	−	25.8794i	0.340669	−	1.38134i
$352$	3.30730	+	0.248504i	0.176280	+	0.0132453i
$353$		−	2.67901i		−	0.142589i	−0.997455	−	0.0712946i	$-0.977287\pi$
$353$		−	2.67901i		−	0.142589i	0.997455	−	0.0712946i	$-0.0227131\pi$
$354$	9.54483	−	4.52855i	0.507302	−	0.240690i
$355$	21.3947			1.13551
$356$			1.28964i			0.0683508i
$357$	4.53893	−	2.15350i	0.240226	−	0.113975i
$358$			17.6786i			0.934345i
$359$	−30.5018			−1.60982			−0.804912	−	0.593394i	$-0.797788\pi$
$359$	−30.5018			−1.60982			−0.804912	+	0.593394i	$0.797788\pi$
$360$	7.50916	+	6.13218i	0.395767	+	0.323194i
$361$	18.6515			0.981658
$362$	−11.6389			−0.611726
$363$	−5.50297	−	18.2405i	−0.288831	−	0.957380i
$364$	−5.12971			−0.268870
$365$	−22.8531			−1.19619
$366$	−8.31356	+	3.94437i	−0.434557	+	0.206175i
$367$	−13.9760			−0.729539			−0.364769	−	0.931098i	$-0.618852\pi$
$367$	−13.9760			−0.729539			−0.364769	+	0.931098i	$0.618852\pi$
$368$		−	9.26189i		−	0.482809i
$369$	18.5984	−	22.7746i	0.968192	−	1.18560i
$370$			26.2023i			1.36219i
$371$	−0.204904			−0.0106381
$372$	3.26233	+	6.87601i	0.169144	+	0.356505i
$373$		−	3.06923i		−	0.158919i	−0.996838	−	0.0794594i	$-0.974681\pi$
$373$		−	3.06923i		−	0.158919i	0.996838	−	0.0794594i	$-0.0253194\pi$
$374$	−9.59298	−	0.720797i	−0.496041	−	0.0372715i
$375$	−2.24251	+	1.06396i	−0.115803	+	0.0549427i
$376$		−	7.19265i		−	0.370932i
$377$			5.11161i			0.263261i
$378$	−1.24421	+	5.04499i	−0.0639953	+	0.259486i
$379$	0.945831			0.0485841			0.0242920	−	0.999705i	$-0.492267\pi$
$379$	0.945831			0.0485841			0.0242920	+	0.999705i	$0.492267\pi$
$380$	1.90776			0.0978662
$381$	14.2600	−	6.76567i	0.730563	−	0.346616i
$382$		−	10.5237i		−	0.538439i
$383$		−	23.8910i		−	1.22077i	−0.792103	−	0.610387i	$-0.791014\pi$
$383$		−	23.8910i		−	1.22077i	0.792103	−	0.610387i	$-0.208986\pi$
$384$	0.742446	+	1.56486i	0.0378878	+	0.0798562i
$385$	−10.6880	−	0.803073i	−0.544710	−	0.0409284i
$386$			16.2873i			0.828999i
$387$	4.52282	+	3.69346i	0.229908	+	0.187749i
$388$	−11.3155			−0.574455
$389$			13.7773i			0.698537i	0.937023	+	0.349269i	$0.113570\pi$
$389$			13.7773i			0.698537i	−0.937023	+	0.349269i	$0.886430\pi$
$390$	12.3078	+	25.9411i	0.623229	+	1.31358i
$391$			26.8645i			1.35860i
$392$	1.00000			0.0505076
$393$	14.4486	+	30.4534i	0.728837	+	1.53617i
$394$	6.38099			0.321470
$395$	17.7529			0.893245
$396$	6.85320	−	7.21344i	0.344386	−	0.362489i
$397$	3.53660			0.177497			0.0887483	−	0.996054i	$-0.471713\pi$
$397$	3.53660			0.177497			0.0887483	+	0.996054i	$0.471713\pi$
$398$	3.17528			0.159163
$399$	0.438296	+	0.923798i	0.0219422	+	0.0462477i
$400$	−5.44344			−0.272172
$401$			25.1732i			1.25709i	0.777774	+	0.628545i	$0.216349\pi$
$401$			25.1732i			1.25709i	−0.777774	+	0.628545i	$0.783651\pi$
$402$	6.53171	+	13.7669i	0.325772	+	0.686631i
$403$			22.5401i			1.12280i
$404$	18.8350			0.937078
$405$	28.4980	−	5.81249i	1.41608	−	0.288825i
$406$		−	0.996472i		−	0.0494541i
$407$	26.8159	+	2.01489i	1.32921	+	0.0998744i
$408$	−2.15350	−	4.53893i	−0.106614	−	0.224711i
$409$		−	4.73002i		−	0.233885i	−0.993139	−	0.116942i	$-0.962691\pi$
$409$		−	4.73002i		−	0.233885i	0.993139	−	0.116942i	$-0.0373093\pi$
$410$			31.6741i			1.56427i
$411$	−7.80387	+	3.70255i	−0.384937	+	0.182633i
$412$	−9.82920			−0.484250
$413$	−6.09950			−0.300137
$414$	−21.5213	−	17.5749i	−1.05771	−	0.863758i
$415$			35.6343i			1.74922i
$416$			5.12971i			0.251505i
$417$	30.8817	−	14.6518i	1.51228	−	0.717503i
$418$	0.146702	−	1.95243i	0.00717543	−	0.0954967i
$419$		−	34.1447i		−	1.66808i	−0.551706	−	0.834039i	$-0.686023\pi$
$419$		−	34.1447i		−	1.66808i	0.551706	−	0.834039i	$-0.313977\pi$
$420$	−2.39931	−	5.05704i	−0.117074	−	0.246758i
$421$	−27.5120			−1.34085			−0.670426	−	0.741976i	$-0.733889\pi$
$421$	−27.5120			−1.34085			−0.670426	+	0.741976i	$0.733889\pi$
$422$			21.3853i			1.04102i
$423$	−16.7131	−	13.6484i	−0.812621	−	0.663608i
$424$			0.204904i			0.00995103i
$425$	15.7889			0.765877
$426$	10.3600	−	4.91530i	0.501943	−	0.238147i
$427$	5.31267			0.257098
$428$	−4.77732			−0.230920
$429$	27.4950	−	10.6012i	1.32747	−	0.511829i
$430$	−6.29016			−0.303339
$431$	9.02544			0.434740			0.217370	−	0.976089i	$-0.430252\pi$
$431$	9.02544			0.434740			0.217370	+	0.976089i	$0.430252\pi$
$432$	5.04499	+	1.24421i	0.242727	+	0.0598621i
$433$	−11.8100			−0.567552			−0.283776	−	0.958891i	$-0.591587\pi$
$433$	−11.8100			−0.567552			−0.283776	+	0.958891i	$0.591587\pi$
$434$		−	4.39402i		−	0.210920i
$435$	−5.03919	+	2.39085i	−0.241611	+	0.114632i
$436$			1.35871i			0.0650703i
$437$	−5.46767			−0.261554
$438$	−11.0662	+	5.25036i	−0.528763	+	0.250872i
$439$		−	30.3442i		−	1.44825i	−0.689668	−	0.724126i	$-0.742243\pi$
$439$		−	30.3442i		−	1.44825i	0.689668	−	0.724126i	$-0.257757\pi$
$440$	−0.803073	+	10.6880i	−0.0382850	+	0.509530i
$441$	1.89755	−	2.32364i	0.0903594	−	0.110650i
$442$		−	14.8790i		−	0.707720i
$443$		−	0.929517i		−	0.0441627i	−0.999756	−	0.0220813i	$-0.992971\pi$
$443$		−	0.929517i		−	0.0441627i	0.999756	−	0.0220813i	$-0.00702928\pi$
$444$	6.01981	+	12.6880i	0.285688	+	0.602145i
$445$	−4.16764			−0.197565
$446$	16.4101			0.777039
$447$	12.5055	+	26.3579i	0.591489	+	1.24668i
$448$		−	1.00000i		−	0.0472456i
$449$			2.58421i			0.121956i	0.998139	+	0.0609781i	$0.0194220\pi$
$449$			2.58421i			0.121956i	−0.998139	+	0.0609781i	$0.980578\pi$
$450$	−10.3292	+	12.6486i	−0.486923	+	0.596261i
$451$	32.4157	+	2.43565i	1.52640	+	0.114690i
$452$		−	16.5869i		−	0.780180i
$453$	−6.77180	+	3.21288i	−0.318167	+	0.150954i
$454$	16.7311			0.785230
$455$		−	16.5773i		−	0.777158i
$456$	0.923798	−	0.438296i	0.0432608	−	0.0205251i
$457$		−	39.8050i		−	1.86200i	−0.365017	−	0.931001i	$-0.618937\pi$
$457$		−	39.8050i		−	1.86200i	0.365017	−	0.931001i	$-0.381063\pi$
$458$	2.37838			0.111134
$459$	−14.6332	−	3.60889i	−0.683020	−	0.168448i
$460$	29.9310			1.39554
$461$	11.8192			0.550475			0.275238	−	0.961376i	$-0.411243\pi$
$461$	11.8192			0.550475			0.275238	+	0.961376i	$0.411243\pi$
$462$	−5.35995	+	2.06662i	−0.249368	+	0.0961479i
$463$	−19.8065			−0.920485			−0.460242	−	0.887793i	$-0.652237\pi$
$463$	−19.8065			−0.920485			−0.460242	+	0.887793i	$0.652237\pi$
$464$	−0.996472			−0.0462600
$465$	−22.2207	+	10.5426i	−1.03046	+	0.488903i
$466$	−18.7833			−0.870120
$467$		−	11.9386i		−	0.552455i	−0.961092	−	0.276227i	$-0.910916\pi$
$467$		−	11.9386i		−	0.552455i	0.961092	−	0.276227i	$-0.0890842\pi$
$468$	11.9196	+	9.73387i	0.550984	+	0.449948i
$469$		−	8.79756i		−	0.406234i
$470$	23.2440			1.07217
$471$	−16.1990	−	34.1428i	−0.746413	−	1.57322i
$472$			6.09950i			0.280752i
$473$	−0.483697	+	6.43745i	−0.0222404	+	0.295994i
$474$	8.59650	−	4.07861i	0.394850	−	0.187337i
$475$			3.21349i			0.147445i
$476$			2.90054i			0.132946i
$477$	0.476124	+	0.388816i	0.0218002	+	0.0178026i
$478$	7.45129			0.340814
$479$	−17.9347			−0.819458			−0.409729	−	0.912207i	$-0.634377\pi$
$479$	−17.9347			−0.819458			−0.409729	+	0.912207i	$0.634377\pi$
$480$	−5.05704	+	2.39931i	−0.230821	+	0.109513i
$481$			41.5921i			1.89644i
$482$		−	25.4487i		−	1.15916i
$483$	6.87645	+	14.4935i	0.312889	+	0.659478i
$484$	10.8765	+	1.64376i	0.494386	+	0.0747162i
$485$		−	36.5674i		−	1.66044i
$486$	12.4642	−	9.36181i	0.565388	−	0.424660i
$487$	−28.0222			−1.26981			−0.634903	−	0.772592i	$-0.718960\pi$
$487$	−28.0222			−1.26981			−0.634903	+	0.772592i	$0.718960\pi$
$488$		−	5.31267i		−	0.240493i
$489$	−7.08966	−	14.9429i	−0.320606	−	0.675742i
$490$			3.23163i			0.145990i
$491$	27.2759			1.23094			0.615472	−	0.788159i	$-0.288965\pi$
$491$	27.2759			1.23094			0.615472	+	0.788159i	$0.288965\pi$
$492$	7.27691	+	15.3376i	0.328068	+	0.691471i
$493$	2.89031			0.130173
$494$	3.02828			0.136249
$495$	23.3112	+	22.1470i	1.04776	+	0.995434i
$496$	−4.39402			−0.197297
$497$	−6.62041			−0.296966
$498$	8.18675	+	17.2552i	0.366857	+	0.773226i
$499$	30.9951			1.38753			0.693765	−	0.720202i	$-0.255951\pi$
$499$	30.9951			1.38753			0.693765	+	0.720202i	$0.255951\pi$
$500$		−	1.43305i		−	0.0640878i
$501$	−5.87396	−	12.3806i	−0.262429	−	0.553122i
$502$		−	7.92147i		−	0.353552i
$503$	−14.1946			−0.632908			−0.316454	−	0.948608i	$-0.602492\pi$
$503$	−14.1946			−0.632908			−0.316454	+	0.948608i	$0.602492\pi$
$504$	−2.32364	−	1.89755i	−0.103503	−	0.0845235i
$505$			60.8679i			2.70859i
$506$	2.30162	−	30.6319i	0.102319	−	1.36175i
$507$	9.88488	+	20.8344i	0.439003	+	0.925288i
$508$			9.11268i			0.404310i
$509$			15.6031i			0.691596i	0.938309	+	0.345798i	$0.112392\pi$
$509$			15.6031i			0.691596i	−0.938309	+	0.345798i	$0.887608\pi$
$510$	14.6682	−	6.95931i	0.649517	−	0.308163i
$511$	7.07170			0.312834
$512$	−1.00000			−0.0441942
$513$	0.734508	−	2.97826i	0.0324293	−	0.131494i
$514$		−	8.84848i		−	0.390290i
$515$		−	31.7644i		−	1.39970i
$516$	−3.04589	+	1.44512i	−0.134088	+	0.0636180i
$517$	1.78740	−	23.7883i	0.0786098	−	1.04621i
$518$		−	8.10808i		−	0.356249i
$519$	1.19500	+	2.51871i	0.0524547	+	0.110559i
$520$	−16.5773			−0.726964
$521$			21.1359i			0.925981i	0.886363	+	0.462990i	$0.153224\pi$
$521$			21.1359i			0.925981i	−0.886363	+	0.462990i	$0.846776\pi$
$522$	−1.89085	+	2.31544i	−0.0827604	+	0.101344i
$523$		−	23.5430i		−	1.02946i	−0.857351	−	0.514732i	$-0.827891\pi$
$523$		−	23.5430i		−	1.02946i	0.857351	−	0.514732i	$-0.172109\pi$
$524$	−19.4608			−0.850151
$525$	8.51821	−	4.04146i	0.371765	−	0.176384i
$526$	−23.3226			−1.01691
$527$	12.7451			0.555184
$528$	2.06662	+	5.35995i	0.0899381	+	0.233262i
$529$	−62.7826			−2.72968
$530$	−0.662175			−0.0287631
$531$	14.1730	+	11.5741i	0.615058	+	0.502273i
$532$	−0.590340			−0.0255945
$533$			50.2776i			2.17777i
$534$	−2.01810	+	0.957488i	−0.0873317	+	0.0414345i
$535$		−	15.4385i		−	0.667466i
$536$	−8.79756			−0.379997
$537$	−27.6645	+	13.1254i	−1.19381	+	0.566404i
$538$		−	10.7058i		−	0.461560i
$539$	3.30730	+	0.248504i	0.142456	+	0.0107038i
$540$	−4.02083	+	16.3036i	−0.173029	+	0.701593i
$541$		−	35.0791i		−	1.50817i	−0.656778	−	0.754084i	$-0.728081\pi$
$541$		−	35.0791i		−	1.50817i	0.656778	−	0.754084i	$-0.271919\pi$
$542$		−	16.4808i		−	0.707910i
$543$	−8.64124	−	18.2132i	−0.370831	−	0.781602i
$544$	2.90054			0.124360
$545$	−4.39085			−0.188083
$546$	−3.80853	−	8.02726i	−0.162990	−	0.343535i
$547$		−	41.6921i		−	1.78263i	−0.453388	−	0.891313i	$-0.649785\pi$
$547$		−	41.6921i		−	1.78263i	0.453388	−	0.891313i	$-0.350215\pi$
$548$		−	4.98696i		−	0.213032i
$549$	−12.3447	−	10.0810i	−0.526861	−	0.430248i
$550$	−18.0031	−	1.35272i	−0.767655	−	0.0576801i
$551$			0.588257i			0.0250606i
$552$	14.4935	−	6.87645i	0.616885	−	0.292681i
$553$	−5.49348			−0.233607
$554$		−	11.4920i		−	0.488247i
$555$	−41.0029	+	19.4538i	−1.74048	+	0.825769i
$556$			19.7345i			0.836930i
$557$	−14.8900			−0.630909			−0.315454	−	0.948941i	$-0.602157\pi$
$557$	−14.8900			−0.630909			−0.315454	+	0.948941i	$0.602157\pi$
$558$	−8.33787	+	10.2101i	−0.352970	+	0.432230i
$559$	−9.98466			−0.422306
$560$	3.23163			0.136561
$561$	−5.99432	−	15.5468i	−0.253081	−	0.656385i
$562$	23.3191			0.983655
$563$	−6.89072			−0.290409			−0.145205	−	0.989402i	$-0.546384\pi$
$563$	−6.89072			−0.290409			−0.145205	+	0.989402i	$0.546384\pi$
$564$	11.2555	−	5.34015i	0.473940	−	0.224861i
$565$	53.6026			2.25508
$566$			16.7703i			0.704909i
$567$	−8.81844	+	1.79862i	−0.370340	+	0.0755351i
$568$			6.62041i			0.277786i
$569$	0.276599			0.0115956			0.00579781	−	0.999983i	$-0.498154\pi$
$569$	0.276599			0.0115956			0.00579781	+	0.999983i	$0.498154\pi$
$570$	1.41641	+	2.98537i	0.0593269	+	0.125044i
$571$		−	1.89950i		−	0.0794918i	−0.999210	−	0.0397459i	$-0.987345\pi$
$571$		−	1.89950i		−	0.0794918i	0.999210	−	0.0397459i	$-0.0126548\pi$
$572$	−1.27475	+	16.9655i	−0.0533001	+	0.709363i
$573$	16.4681	−	7.81328i	0.687963	−	0.326404i
$574$		−	9.80126i		−	0.409097i
$575$			50.4166i			2.10252i
$576$	−1.89755	+	2.32364i	−0.0790645	+	0.0968184i
$577$	−1.45384			−0.0605242			−0.0302621	−	0.999542i	$-0.509634\pi$
$577$	−1.45384			−0.0605242			−0.0302621	+	0.999542i	$0.509634\pi$
$578$	8.58684			0.357166
$579$	−25.4872	+	12.0924i	−1.05921	+	0.502543i
$580$		−	3.22023i		−	0.133713i
$581$		−	11.0267i		−	0.457466i
$582$	−8.40111	−	17.7071i	−0.348237	−	0.733981i
$583$	−0.0509195	+	0.677680i	−0.00210887	+	0.0280666i
$584$		−	7.07170i		−	0.292629i
$585$	−31.4563	+	38.5198i	−1.30056	+	1.59260i
$586$	−27.6593			−1.14259
$587$		−	8.64257i		−	0.356717i	−0.983966	−	0.178359i	$-0.942921\pi$
$587$		−	8.64257i		−	0.356717i	0.983966	−	0.178359i	$-0.0570787\pi$
$588$	0.742446	+	1.56486i	0.0306180	+	0.0645336i
$589$			2.59397i			0.106883i
$590$	−19.7113			−0.811502
$591$	4.73754	+	9.98533i	0.194876	+	0.410742i
$592$	−8.10808			−0.333240
$593$	10.8978			0.447520			0.223760	−	0.974644i	$-0.428167\pi$
$593$	10.8978			0.447520			0.223760	+	0.974644i	$0.428167\pi$
$594$	16.3761	+	5.36868i	0.671920	+	0.220280i
$595$	−9.37349			−0.384276
$596$	−16.8436			−0.689942
$597$	2.35748	+	4.96886i	0.0964851	+	0.203362i
$598$	47.5108			1.94286
$599$			0.516297i			0.0210953i	0.999944	+	0.0105477i	$0.00335749\pi$
$599$			0.516297i			0.0210953i	−0.999944	+	0.0105477i	$0.996643\pi$
$600$	−4.04146	−	8.51821i	−0.164992	−	0.347754i
$601$		−	32.3301i		−	1.31877i	−0.751804	−	0.659387i	$-0.770816\pi$
$601$		−	32.3301i		−	1.31877i	0.751804	−	0.659387i	$-0.229184\pi$
$602$	1.94644			0.0793308
$603$	−16.6938	+	20.4424i	−0.679824	+	0.832478i
$604$		−	4.32743i		−	0.176081i
$605$	−5.31201	+	35.1488i	−0.215964	+	1.42900i
$606$	13.9840	+	29.4741i	0.568061	+	1.19730i
$607$		−	11.1564i		−	0.452826i	−0.974031	−	0.226413i	$-0.927300\pi$
$607$		−	11.1564i		−	0.452826i	0.974031	−	0.226413i	$-0.0726999\pi$
$608$			0.590340i			0.0239415i
$609$	1.55933	−	0.739826i	0.0631874	−	0.0299793i
$610$	17.1686			0.695136
$611$	36.8962			1.49266
$612$	5.50392	−	6.73983i	0.222483	−	0.272441i
$613$			29.2219i			1.18026i	0.807308	+	0.590131i	$0.200924\pi$
$613$			29.2219i			1.18026i	−0.807308	+	0.590131i	$0.799076\pi$
$614$		−	3.81462i		−	0.153946i
$615$	−49.5653	+	23.5163i	−1.99867	+	0.948268i
$616$	0.248504	−	3.30730i	0.0100125	−	0.133255i
$617$		−	23.5155i		−	0.946699i	−0.880875	−	0.473349i	$-0.843045\pi$
$617$		−	23.5155i		−	0.946699i	0.880875	−	0.473349i	$-0.156955\pi$
$618$	−7.29765	−	15.3813i	−0.293555	−	0.618726i
$619$	5.46439			0.219632			0.109816	−	0.993952i	$-0.464974\pi$
$619$	5.46439			0.219632			0.109816	+	0.993952i	$0.464974\pi$
$620$		−	14.1999i		−	0.570280i
$621$	11.5237	−	46.7261i	0.462432	−	1.87506i
$622$			23.1098i			0.926620i
$623$	1.28964			0.0516683
$624$	−8.02726	+	3.80853i	−0.321348	+	0.152463i
$625$	−22.5861			−0.903446
$626$	17.6194			0.704211
$627$	3.16420	−	1.22001i	0.126366	−	0.0487225i
$628$	21.8185			0.870652
$629$	23.5179			0.937718
$630$	6.13218	−	7.50916i	0.244312	−	0.299172i
$631$	1.55593			0.0619406			0.0309703	−	0.999520i	$-0.490140\pi$
$631$	1.55593			0.0619406			0.0309703	+	0.999520i	$0.490140\pi$
$632$			5.49348i			0.218519i
$633$	−33.4649	+	15.8774i	−1.33011	+	0.631071i
$634$		−	21.1812i		−	0.841213i
$635$	−29.4488			−1.16864
$636$	−0.320646	+	0.152130i	−0.0127144	+	0.00603236i
$637$			5.12971i			0.203247i
$638$	−3.29563	−	0.247627i	−0.130475	−	0.00980365i
$639$	15.3835	+	12.5625i	0.608560	+	0.496966i
$640$		−	3.23163i		−	0.127741i
$641$			8.88248i			0.350837i	0.984494	+	0.175418i	$0.0561278\pi$
$641$			8.88248i			0.350837i	−0.984494	+	0.175418i	$0.943872\pi$
$642$	−3.54690	−	7.47581i	−0.139985	−	0.295047i
$643$	−28.1763			−1.11117			−0.555583	−	0.831461i	$-0.687505\pi$
$643$	−28.1763			−1.11117			−0.555583	+	0.831461i	$0.687505\pi$
$644$	−9.26189			−0.364970
$645$	−4.67011	−	9.84320i	−0.183885	−	0.387576i
$646$		−	1.71231i		−	0.0673699i
$647$		−	19.1273i		−	0.751971i	−0.926625	−	0.375986i	$-0.877304\pi$
$647$		−	19.1273i		−	0.751971i	0.926625	−	0.375986i	$-0.122696\pi$
$648$	1.79862	+	8.81844i	0.0706566	+	0.346421i
$649$	−1.51575	+	20.1729i	−0.0594984	+	0.791855i
$650$		−	27.9233i		−	1.09524i
$651$	6.87601	−	3.26233i	0.269492	−	0.127861i
$652$	9.54906			0.373970
$653$		−	15.6023i		−	0.610566i	−0.952262	−	0.305283i	$-0.901249\pi$
$653$		−	15.6023i		−	0.610566i	0.952262	−	0.305283i	$-0.0987511\pi$
$654$	−2.12618	+	1.00877i	−0.0831403	+	0.0394459i
$655$		−	62.8903i		−	2.45733i
$656$	−9.80126			−0.382675
$657$	−16.4321	−	13.4189i	−0.641078	−	0.523521i
$658$	−7.19265			−0.280399
$659$	−18.9545			−0.738361			−0.369180	−	0.929358i	$-0.620362\pi$
$659$	−18.9545			−0.738361			−0.369180	+	0.929358i	$0.620362\pi$
$660$	−17.3214	+	6.67856i	−0.674234	+	0.259962i
$661$	36.4945			1.41947			0.709735	−	0.704468i	$-0.248815\pi$
$661$	36.4945			1.41947			0.709735	+	0.704468i	$0.248815\pi$
$662$	−9.70904			−0.377353
$663$	23.2834	−	11.0468i	0.904253	−	0.429023i
$664$	−11.0267			−0.427920
$665$		−	1.90776i		−	0.0739799i
$666$	−15.3855	+	18.8403i	−0.596175	+	0.730046i
$667$			9.22921i			0.357356i
$668$	7.91163			0.306110
$669$	12.1836	+	25.6794i	0.471045	+	0.992822i
$670$		−	28.4305i		−	1.09837i
$671$	1.32022	−	17.5706i	0.0509665	−	0.678305i
$672$	1.56486	−	0.742446i	0.0603656	−	0.0286405i
$673$		−	14.8489i		−	0.572381i	−0.958173	−	0.286191i	$-0.907611\pi$
$673$		−	14.8489i		−	0.572381i	0.958173	−	0.286191i	$-0.0923891\pi$
$674$			9.55751i			0.368142i
$675$	−27.4621	−	6.77279i	−1.05702	−	0.260685i
$676$	−13.3139			−0.512075
$677$	−23.1785			−0.890822			−0.445411	−	0.895326i	$-0.646942\pi$
$677$	−23.1785			−0.890822			−0.445411	+	0.895326i	$0.646942\pi$
$678$	25.9560	−	12.3148i	0.996835	−	0.472949i
$679$			11.3155i			0.434247i
$680$			9.37349i			0.359457i
$681$	12.4219	+	26.1818i	0.476010	+	1.00329i
$682$	−14.5324	−	1.09193i	−0.556473	−	0.0418123i
$683$		−	24.8571i		−	0.951131i	−0.879680	−	0.475566i	$-0.842243\pi$
$683$		−	24.8571i		−	0.951131i	0.879680	−	0.475566i	$-0.157757\pi$
$684$	1.37174	+	1.12020i	0.0524498	+	0.0428319i
$685$	16.1160			0.615761
$686$		−	1.00000i		−	0.0381802i
$687$	1.76582	+	3.72182i	0.0673702	+	0.141996i
$688$		−	1.94644i		−	0.0742072i
$689$	−1.05110			−0.0400437
$690$	22.2222	+	46.8377i	0.845983	+	1.78308i
$691$	17.9982			0.684683			0.342342	−	0.939576i	$-0.388780\pi$
$691$	17.9982			0.684683			0.342342	+	0.939576i	$0.388780\pi$
$692$	−1.60954			−0.0611857
$693$	−7.21344	−	6.85320i	−0.274016	−	0.260331i
$694$	−31.9277			−1.21196
$695$	−63.7747			−2.41911
$696$	−0.739826	−	1.55933i	−0.0280430	−	0.0591064i
$697$	28.4290			1.07682
$698$			9.79830i			0.370871i
$699$	−13.9456	−	29.3932i	−0.527471	−	1.11175i
$700$			5.44344i			0.205743i
$701$	35.0988			1.32566			0.662832	−	0.748768i	$-0.269355\pi$
$701$	35.0988			1.32566			0.662832	+	0.748768i	$0.269355\pi$
$702$	−6.38244	+	25.8794i	−0.240890	+	0.976753i
$703$			4.78653i			0.180527i
$704$	−3.30730	−	0.248504i	−0.124649	−	0.00936585i
$705$	17.2574	+	36.3735i	0.649952	+	1.36991i
$706$			2.67901i			0.100826i
$707$		−	18.8350i		−	0.708365i
$708$	−9.54483	+	4.52855i	−0.358717	+	0.170193i
$709$	42.6426			1.60148			0.800738	−	0.599015i	$-0.204441\pi$
$709$	42.6426			1.60148			0.800738	+	0.599015i	$0.204441\pi$
$710$	−21.3947			−0.802930
$711$	12.7649	+	10.4241i	0.478720	+	0.390936i
$712$		−	1.28964i		−	0.0483313i
$713$			40.6970i			1.52411i
$714$	−4.53893	+	2.15350i	−0.169865	+	0.0805926i
$715$	−54.8263	−	4.11954i	−2.05039	−	0.154062i
$716$		−	17.6786i		−	0.660682i
$717$	5.53218	+	11.6602i	0.206603	+	0.435458i
$718$	30.5018			1.13832
$719$			14.2711i			0.532224i	0.963942	+	0.266112i	$0.0857391\pi$
$719$			14.2711i			0.532224i	−0.963942	+	0.266112i	$0.914261\pi$
$720$	−7.50916	−	6.13218i	−0.279850	−	0.228533i
$721$			9.82920i			0.366059i
$722$	−18.6515			−0.694137
$723$	39.8236	−	18.8943i	1.48106	−	0.702687i
$724$	11.6389			0.432555
$725$	5.42424			0.201451
$726$	5.50297	+	18.2405i	0.204234	+	0.676970i
$727$	−10.9408			−0.405772			−0.202886	−	0.979202i	$-0.565032\pi$
$727$	−10.9408			−0.405772			−0.202886	+	0.979202i	$0.565032\pi$
$728$	5.12971			0.190120
$729$	23.9039	+	12.5541i	0.885329	+	0.464965i
$730$	22.8531			0.845833
$731$			5.64572i			0.208815i
$732$	8.31356	−	3.94437i	0.307278	−	0.145788i
$733$		−	26.4535i		−	0.977082i	−0.872541	−	0.488541i	$-0.837529\pi$
$733$		−	26.4535i		−	0.977082i	0.872541	−	0.488541i	$-0.162471\pi$
$734$	13.9760			0.515862
$735$	−5.05704	+	2.39931i	−0.186532	+	0.0885000i
$736$			9.26189i			0.341398i
$737$	−29.0962	−	2.18623i	−1.07177	−	0.0805308i
$738$	−18.5984	+	22.7746i	−0.684615	+	0.838345i
$739$			50.3991i			1.85396i	0.375109	+	0.926981i	$0.377605\pi$
$739$			50.3991i			1.85396i	−0.375109	+	0.926981i	$0.622395\pi$
$740$		−	26.2023i		−	0.963217i
$741$	2.24833	+	4.73882i	0.0825945	+	0.174085i
$742$	0.204904			0.00752227
$743$	2.62976			0.0964765			0.0482383	−	0.998836i	$-0.484639\pi$
$743$	2.62976			0.0964765			0.0482383	+	0.998836i	$0.484639\pi$
$744$	−3.26233	−	6.87601i	−0.119603	−	0.252087i
$745$		−	54.4324i		−	1.99425i
$746$			3.06923i			0.112372i
$747$	−20.9237	+	25.6222i	−0.765560	+	0.937466i
$748$	9.59298	+	0.720797i	0.350754	+	0.0263549i
$749$			4.77732i			0.174559i
$750$	2.24251	−	1.06396i	0.0818850	−	0.0388503i
$751$	−22.6742			−0.827395			−0.413697	−	0.910414i	$-0.635763\pi$
$751$	−22.6742			−0.827395			−0.413697	+	0.910414i	$0.635763\pi$
$752$			7.19265i			0.262289i
$753$	12.3960	−	5.88126i	0.451734	−	0.214325i
$754$		−	5.11161i		−	0.186154i
$755$	13.9847			0.508954
$756$	1.24421	−	5.04499i	0.0452515	−	0.183485i
$757$	0.286736			0.0104216			0.00521080	−	0.999986i	$-0.498341\pi$
$757$	0.286736			0.0104216			0.00521080	+	0.999986i	$0.498341\pi$
$758$	−0.945831			−0.0343541
$759$	49.6433	−	19.1408i	1.80194	−	0.694767i
$760$	−1.90776			−0.0692018
$761$	15.5922			0.565218			0.282609	−	0.959235i	$-0.408800\pi$
$761$	15.5922			0.565218			0.282609	+	0.959235i	$0.408800\pi$
$762$	−14.2600	+	6.76567i	−0.516586	+	0.245094i
$763$	1.35871			0.0491886
$764$			10.5237i			0.380734i
$765$	21.7806	+	17.7866i	0.787481	+	0.643078i
$766$			23.8910i			0.863218i
$767$	−31.2887			−1.12977
$768$	−0.742446	−	1.56486i	−0.0267907	−	0.0564669i
$769$		−	19.4671i		−	0.702002i	−0.936375	−	0.351001i	$-0.885841\pi$
$769$		−	19.4671i		−	0.702002i	0.936375	−	0.351001i	$-0.114159\pi$
$770$	10.6880	+	0.803073i	0.385168	+	0.0289408i
$771$	13.8466	−	6.56952i	0.498673	−	0.236595i
$772$		−	16.2873i		−	0.586191i
$773$			8.12522i			0.292244i	0.989267	+	0.146122i	$0.0466792\pi$
$773$			8.12522i			0.292244i	−0.989267	+	0.146122i	$0.953321\pi$
$774$	−4.52282	−	3.69346i	−0.162569	−	0.132759i
$775$	23.9186			0.859182
$776$	11.3155			0.406201
$777$	12.6880	−	6.01981i	0.455179	−	0.215960i
$778$		−	13.7773i		−	0.493940i
$779$			5.78608i			0.207308i
$780$	−12.3078	−	25.9411i	−0.440689	−	0.928842i
$781$	−1.64520	+	21.8957i	−0.0588698	+	0.783489i
$782$		−	26.8645i		−	0.960673i
$783$	−5.02719	−	1.23982i	−0.179657	−	0.0443076i
$784$	−1.00000			−0.0357143
$785$			70.5093i			2.51659i
$786$	−14.4486	−	30.4534i	−0.515366	−	1.08624i
$787$		−	8.97343i		−	0.319868i	−0.987128	−	0.159934i	$-0.948872\pi$
$787$		−	8.97343i		−	0.319868i	0.987128	−	0.159934i	$-0.0511282\pi$
$788$	−6.38099			−0.227313
$789$	−17.3158	−	36.4965i	−0.616457	−	1.29931i
$790$	−17.7529			−0.631620
$791$	−16.5869			−0.589761
$792$	−6.85320	+	7.21344i	−0.243518	+	0.256318i
$793$	27.2525			0.967763
$794$	−3.53660			−0.125509
$795$	−0.491629	−	1.03621i	−0.0174363	−	0.0367505i
$796$	−3.17528			−0.112545
$797$		−	47.7914i		−	1.69286i	−0.532501	−	0.846429i	$-0.678748\pi$
$797$		−	47.7914i		−	1.69286i	0.532501	−	0.846429i	$-0.321252\pi$
$798$	−0.438296	−	0.923798i	−0.0155155	−	0.0327021i
$799$		−	20.8626i		−	0.738065i
$800$	5.44344			0.192455
$801$	−2.99666	−	2.44715i	−0.105882	−	0.0864659i
$802$		−	25.1732i		−	0.888896i
$803$	1.75735	−	23.3883i	0.0620154	−	0.825354i
$804$	−6.53171	−	13.7669i	−0.230356	−	0.485522i
$805$		−	29.9310i		−	1.05493i
$806$		−	22.5401i		−	0.793940i
$807$	16.7530	−	7.94848i	0.589735	−	0.279800i
$808$	−18.8350			−0.662615
$809$	−8.71247			−0.306314			−0.153157	−	0.988202i	$-0.548944\pi$
$809$	−8.71247			−0.306314			−0.153157	+	0.988202i	$0.548944\pi$
$810$	−28.4980	+	5.81249i	−1.00132	+	0.204230i
$811$		−	30.5248i		−	1.07187i	−0.844259	−	0.535935i	$-0.819959\pi$
$811$		−	30.5248i		−	1.07187i	0.844259	−	0.535935i	$-0.180041\pi$
$812$			0.996472i			0.0349693i
$813$	25.7901	−	12.2361i	0.904497	−	0.429139i
$814$	−26.8159	−	2.01489i	−0.939896	−	0.0706219i
$815$			30.8591i			1.08095i
$816$	2.15350	+	4.53893i	0.0753875	+	0.158894i
$817$	−1.14906			−0.0402005
$818$			4.73002i			0.165381i
$819$	9.73387	−	11.9196i	0.340129	−	0.416505i
$820$		−	31.6741i		−	1.10611i
$821$	−15.3072			−0.534224			−0.267112	−	0.963665i	$-0.586069\pi$
$821$	−15.3072			−0.534224			−0.267112	+	0.963665i	$0.586069\pi$
$822$	7.80387	−	3.70255i	0.272191	−	0.129141i
$823$	−13.3186			−0.464258			−0.232129	−	0.972685i	$-0.574569\pi$
$823$	−13.3186			−0.464258			−0.232129	+	0.972685i	$0.574569\pi$
$824$	9.82920			0.342416
$825$	−11.2495	−	29.1766i	−0.391658	−	1.01580i
$826$	6.09950			0.212229
$827$	−7.55918			−0.262858			−0.131429	−	0.991326i	$-0.541957\pi$
$827$	−7.55918			−0.262858			−0.131429	+	0.991326i	$0.541957\pi$
$828$	21.5213	+	17.5749i	0.747917	+	0.610769i
$829$	−3.02091			−0.104921			−0.0524603	−	0.998623i	$-0.516706\pi$
$829$	−3.02091			−0.104921			−0.0524603	+	0.998623i	$0.516706\pi$
$830$		−	35.6343i		−	1.23689i
$831$	17.9833	−	8.53217i	0.623833	−	0.295978i
$832$		−	5.12971i		−	0.177841i
$833$	2.90054			0.100498
$834$	−30.8817	+	14.6518i	−1.06935	+	0.507351i
$835$			25.5675i			0.884799i
$836$	−0.146702	+	1.95243i	−0.00507379	+	0.0675263i
$837$	−22.1678	−	5.46709i	−0.766232	−	0.188970i
$838$			34.1447i			1.17951i
$839$		−	15.7873i		−	0.545037i	−0.962151	−	0.272519i	$-0.912143\pi$
$839$		−	15.7873i		−	0.545037i	0.962151	−	0.272519i	$-0.0878566\pi$
$840$	2.39931	+	5.05704i	0.0827841	+	0.174484i
$841$	−28.0070			−0.965760
$842$	27.5120			0.948126
$843$	17.3131	+	36.4910i	0.596296	+	1.25682i
$844$		−	21.3853i		−	0.736112i
$845$		−	43.0258i		−	1.48013i
$846$	16.7131	+	13.6484i	0.574610	+	0.469241i
$847$	1.64376	−	10.8765i	0.0564801	−	0.373721i
$848$		−	0.204904i		−	0.00703644i
$849$	−26.2431	+	12.4510i	−0.900661	+	0.427319i
$850$	−15.7889			−0.541557
$851$			75.0962i			2.57426i
$852$	−10.3600	+	4.91530i	−0.354927	+	0.168395i
$853$			45.3134i			1.55150i	0.631039	+	0.775751i	$0.282629\pi$
$853$			45.3134i			1.55150i	−0.631039	+	0.775751i	$0.717371\pi$
$854$	−5.31267			−0.181796
$855$	−3.62007	+	4.43296i	−0.123804	+	0.151604i
$856$	4.77732			0.163285
$857$	19.9624			0.681902			0.340951	−	0.940081i	$-0.389251\pi$
$857$	19.9624			0.681902			0.340951	+	0.940081i	$0.389251\pi$
$858$	−27.4950	+	10.6012i	−0.938664	+	0.361918i
$859$	−41.8378			−1.42749			−0.713743	−	0.700407i	$-0.753002\pi$
$859$	−41.8378			−1.42749			−0.713743	+	0.700407i	$0.753002\pi$
$860$	6.29016			0.214493
$861$	15.3376	−	7.27691i	0.522703	−	0.247996i
$862$	−9.02544			−0.307408
$863$		−	30.0446i		−	1.02273i	−0.859363	−	0.511366i	$-0.829140\pi$
$863$		−	30.0446i		−	1.02273i	0.859363	−	0.511366i	$-0.170860\pi$
$864$	−5.04499	−	1.24421i	−0.171634	−	0.0423289i
$865$		−	5.20146i		−	0.176855i
$866$	11.8100			0.401320
$867$	6.37527	+	13.4372i	0.216515	+	0.456350i
$868$			4.39402i			0.149143i
$869$	−1.36515	+	18.1686i	−0.0463096	+	0.616327i
$870$	5.03919	−	2.39085i	0.170845	−	0.0810573i
$871$		−	45.1289i		−	1.52914i
$872$		−	1.35871i		−	0.0460117i
$873$	21.4716	−	26.2931i	0.726704	−	0.889885i
$874$	5.46767			0.184947
$875$	−1.43305			−0.0484458
$876$	11.0662	−	5.25036i	0.373892	−	0.177393i
$877$			0.399043i			0.0134747i	0.999977	+	0.00673736i	$0.00214458\pi$
$877$			0.399043i			0.0134747i	−0.999977	+	0.00673736i	$0.997855\pi$
$878$			30.3442i			1.02407i
$879$	−20.5355	−	43.2828i	−0.692646	−	1.45989i
$880$	0.803073	−	10.6880i	0.0270716	−	0.360292i
$881$		−	16.6600i		−	0.561288i	−0.959812	−	0.280644i	$-0.909452\pi$
$881$		−	16.6600i		−	0.561288i	0.959812	−	0.280644i	$-0.0905481\pi$
$882$	−1.89755	+	2.32364i	−0.0638938	+	0.0782411i
$883$	−20.7500			−0.698293			−0.349147	−	0.937068i	$-0.613528\pi$
$883$	−20.7500			−0.698293			−0.349147	+	0.937068i	$0.613528\pi$
$884$			14.8790i			0.500433i
$885$	−14.6346	−	30.8454i	−0.491936	−	1.03686i
$886$			0.929517i			0.0312277i
$887$	36.7439			1.23374			0.616870	−	0.787065i	$-0.288400\pi$
$887$	36.7439			1.23374			0.616870	+	0.787065i	$0.288400\pi$
$888$	−6.01981	−	12.6880i	−0.202012	−	0.425781i
$889$	9.11268			0.305629
$890$	4.16764			0.139700
$891$	3.75717	+	29.6122i	0.125870	+	0.992047i
$892$	−16.4101			−0.549449
$893$	4.24611			0.142091
$894$	−12.5055	−	26.3579i	−0.418246	−	0.881539i
$895$	57.1309			1.90967
$896$			1.00000i			0.0334077i
$897$	35.2742	+	74.3476i	1.17777	+	2.48239i
$898$		−	2.58421i		−	0.0862361i
$899$	4.37852			0.146032
$900$	10.3292	−	12.6486i	0.344307	−	0.421620i
$901$			0.594334i			0.0198001i
$902$	−32.4157	−	2.43565i	−1.07933	−	0.0810983i
$903$	1.44512	+	3.04589i	0.0480907	+	0.101361i
$904$			16.5869i			0.551670i
$905$			37.6126i			1.25028i
$906$	6.77180	−	3.21288i	0.224978	−	0.106741i
$907$	−5.42779			−0.180227			−0.0901134	−	0.995932i	$-0.528723\pi$
$907$	−5.42779			−0.180227			−0.0901134	+	0.995932i	$0.528723\pi$
$908$	−16.7311			−0.555241
$909$	−35.7404	+	43.7659i	−1.18543	+	1.45162i
$910$			16.5773i			0.549533i
$911$		−	1.83411i		−	0.0607668i	−0.999538	−	0.0303834i	$-0.990327\pi$
$911$		−	1.83411i		−	0.0607668i	0.999538	−	0.0303834i	$-0.00967282\pi$
$912$	−0.923798	+	0.438296i	−0.0305900	+	0.0145134i
$913$	−36.4687	−	2.74019i	−1.20694	−	0.0906869i
$914$			39.8050i			1.31663i
$915$	12.7467	+	26.8664i	0.421395	+	0.888175i
$916$	−2.37838			−0.0785839
$917$			19.4608i			0.642654i
$918$	14.6332	+	3.60889i	0.482968	+	0.119111i
$919$			50.1346i			1.65379i	0.562358	+	0.826894i	$0.309894\pi$
$919$			50.1346i			1.65379i	−0.562358	+	0.826894i	$0.690106\pi$
$920$	−29.9310			−0.986796
$921$	5.96933	−	2.83215i	0.196696	−	0.0933225i
$922$	−11.8192			−0.389245
$923$	−33.9608			−1.11783
$924$	5.35995	−	2.06662i	0.176329	−	0.0679868i
$925$	44.1359			1.45118
$926$	19.8065			0.650881
$927$	18.6514	−	22.8395i	0.612592	−	0.750149i
$928$	0.996472			0.0327108
$929$		−	42.8505i		−	1.40588i	−0.711250	−	0.702939i	$-0.751871\pi$
$929$		−	42.8505i		−	1.40588i	0.711250	−	0.702939i	$-0.248129\pi$
$930$	22.2207	−	10.5426i	0.728647	−	0.345707i
$931$			0.590340i			0.0193476i
$932$	18.7833			0.615268
$933$	−36.1636	+	17.1578i	−1.18394	+	0.561721i
$934$			11.9386i			0.390644i
$935$	−2.32935	+	31.0010i	−0.0761779	+	1.01384i
$936$	−11.9196	−	9.73387i	−0.389605	−	0.318162i
$937$		−	24.0473i		−	0.785591i	−0.919626	−	0.392796i	$-0.871508\pi$
$937$		−	24.0473i		−	0.785591i	0.919626	−	0.392796i	$-0.128492\pi$
$938$			8.79756i			0.287251i
$939$	13.0814	+	27.5717i	0.426896	+	0.899770i
$940$	−23.2440			−0.758135
$941$	−19.7564			−0.644040			−0.322020	−	0.946733i	$-0.604362\pi$
$941$	−19.7564			−0.644040			−0.322020	+	0.946733i	$0.604362\pi$
$942$	16.1990	+	34.1428i	0.527793	+	1.11243i
$943$			90.7782i			2.95614i
$944$		−	6.09950i		−	0.198522i
$945$	16.3036	+	4.02083i	0.530355	+	0.130798i
$946$	0.483697	−	6.43745i	0.0157264	−	0.209300i
$947$		−	18.8203i		−	0.611577i	−0.952099	−	0.305789i	$-0.901080\pi$
$947$		−	18.8203i		−	0.611577i	0.952099	−	0.305789i	$-0.0989201\pi$
$948$	−8.59650	+	4.07861i	−0.279201	+	0.132467i
$949$	36.2758			1.17756
$950$		−	3.21349i		−	0.104259i
$951$	33.1455	−	15.7259i	1.07482	−	0.509947i
$952$		−	2.90054i		−	0.0940072i
$953$	−25.6411			−0.830597			−0.415299	−	0.909685i	$-0.636323\pi$
$953$	−25.6411			−0.830597			−0.415299	+	0.909685i	$0.636323\pi$
$954$	−0.476124	−	0.388816i	−0.0154151	−	0.0125884i
$955$	−34.0087			−1.10050
$956$	−7.45129			−0.240992
$957$	−2.05933	−	5.34104i	−0.0665686	−	0.172651i
$958$	17.9347			0.579444
$959$	−4.98696			−0.161037
$960$	5.05704	−	2.39931i	0.163215	−	0.0774375i
$961$	−11.6926			−0.377179
$962$		−	41.5921i		−	1.34098i
$963$	9.06518	−	11.1008i	0.292121	−	0.357717i
$964$			25.4487i			0.819648i
$965$	52.6344			1.69436
$966$	−6.87645	−	14.4935i	−0.221246	−	0.466321i
$967$			24.8153i			0.798005i	0.916950	+	0.399003i	$0.130644\pi$
$967$			24.8153i			0.798005i	−0.916950	+	0.399003i	$0.869356\pi$
$968$	−10.8765	−	1.64376i	−0.349584	−	0.0528323i
$969$	2.67952	−	1.27130i	0.0860785	−	0.0408399i
$970$			36.5674i			1.17411i
$971$		−	7.81834i		−	0.250902i	−0.992100	−	0.125451i	$-0.959962\pi$
$971$		−	7.81834i		−	0.250902i	0.992100	−	0.125451i	$-0.0400379\pi$
$972$	−12.4642	+	9.36181i	−0.399790	+	0.300280i
$973$	19.7345			0.632660
$974$	28.0222			0.897889
$975$	43.6959	−	20.7315i	1.39939	−	0.663941i
$976$			5.31267i			0.170054i
$977$			8.19837i			0.262289i	0.991363	+	0.131145i	$0.0418652\pi$
$977$			8.19837i			0.262289i	−0.991363	+	0.131145i	$0.958135\pi$
$978$	7.08966	+	14.9429i	0.226702	+	0.477821i
$979$	0.320481	−	4.26523i	0.0102426	−	0.136317i
$980$		−	3.23163i		−	0.103231i
$981$	−3.15715	−	2.57821i	−0.100800	−	0.0823161i
$982$	−27.2759			−0.870409
$983$			8.85468i			0.282420i	0.989980	+	0.141210i	$0.0450993\pi$
$983$			8.85468i			0.282420i	−0.989980	+	0.141210i	$0.954901\pi$
$984$	−7.27691	−	15.3376i	−0.231979	−	0.488943i
$985$		−	20.6210i		−	0.657040i
$986$	−2.89031			−0.0920462
$987$	−5.34015	−	11.2555i	−0.169979	−	0.358265i
$988$	−3.02828			−0.0963423
$989$	−18.0277			−0.573247
$990$	−23.3112	−	22.1470i	−0.740878	−	0.703878i
$991$	51.0136			1.62050			0.810251	−	0.586083i	$-0.199331\pi$
$991$	51.0136			1.62050			0.810251	+	0.586083i	$0.199331\pi$
$992$	4.39402			0.139510
$993$	−7.20844	−	15.1932i	−0.228753	−	0.482143i
$994$	6.62041			0.209987
$995$		−	10.2613i		−	0.325307i
$996$	−8.18675	−	17.2552i	−0.259407	−	0.546753i
$997$		−	0.737359i		−	0.0233524i	−0.999932	−	0.0116762i	$-0.996283\pi$
$997$		−	0.737359i		−	0.0233524i	0.999932	−	0.0116762i	$-0.00371673\pi$
$998$	−30.9951			−0.981132
$999$	−40.9052	−	10.0882i	−1.29418	−	0.319175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.c.a.197.3	✓	12
3.2	odd	2		462.2.c.b.197.4	yes	12
11.10	odd	2		462.2.c.b.197.3	yes	12
33.32	even	2	inner	462.2.c.a.197.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.c.a.197.3	✓	12	1.1	even	1	trivial
462.2.c.a.197.4	yes	12	33.32	even	2	inner
462.2.c.b.197.3	yes	12	11.10	odd	2
462.2.c.b.197.4	yes	12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.742446 - 1.56486i) q^{3} +1.00000 q^{4} +3.23163i q^{5} +(0.742446 + 1.56486i) q^{6} -1.00000i q^{7} -1.00000 q^{8} +(-1.89755 + 2.32364i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.742446 - 1.56486i) q^{3} +1.00000 q^{4} +3.23163i q^{5} +(0.742446 + 1.56486i) q^{6} -1.00000i q^{7} -1.00000 q^{8} +(-1.89755 + 2.32364i) q^{9} -3.23163i q^{10} +(-3.30730 - 0.248504i) q^{11} +(-0.742446 - 1.56486i) q^{12} -5.12971i q^{13} +1.00000i q^{14} +(5.05704 - 2.39931i) q^{15} +1.00000 q^{16} -2.90054 q^{17} +(1.89755 - 2.32364i) q^{18} -0.590340i q^{19} +3.23163i q^{20} +(-1.56486 + 0.742446i) q^{21} +(3.30730 + 0.248504i) q^{22} -9.26189i q^{23} +(0.742446 + 1.56486i) q^{24} -5.44344 q^{25} +5.12971i q^{26} +(5.04499 + 1.24421i) q^{27} -1.00000i q^{28} -0.996472 q^{29} +(-5.05704 + 2.39931i) q^{30} -4.39402 q^{31} -1.00000 q^{32} +(2.06662 + 5.35995i) q^{33} +2.90054 q^{34} +3.23163 q^{35} +(-1.89755 + 2.32364i) q^{36} -8.10808 q^{37} +0.590340i q^{38} +(-8.02726 + 3.80853i) q^{39} -3.23163i q^{40} -9.80126 q^{41} +(1.56486 - 0.742446i) q^{42} -1.94644i q^{43} +(-3.30730 - 0.248504i) q^{44} +(-7.50916 - 6.13218i) q^{45} +9.26189i q^{46} +7.19265i q^{47} +(-0.742446 - 1.56486i) q^{48} -1.00000 q^{49} +5.44344 q^{50} +(2.15350 + 4.53893i) q^{51} -5.12971i q^{52} -0.204904i q^{53} +(-5.04499 - 1.24421i) q^{54} +(0.803073 - 10.6880i) q^{55} +1.00000i q^{56} +(-0.923798 + 0.438296i) q^{57} +0.996472 q^{58} -6.09950i q^{59} +(5.05704 - 2.39931i) q^{60} +5.31267i q^{61} +4.39402 q^{62} +(2.32364 + 1.89755i) q^{63} +1.00000 q^{64} +16.5773 q^{65} +(-2.06662 - 5.35995i) q^{66} +8.79756 q^{67} -2.90054 q^{68} +(-14.4935 + 6.87645i) q^{69} -3.23163 q^{70} -6.62041i q^{71} +(1.89755 - 2.32364i) q^{72} +7.07170i q^{73} +8.10808 q^{74} +(4.04146 + 8.51821i) q^{75} -0.590340i q^{76} +(-0.248504 + 3.30730i) q^{77} +(8.02726 - 3.80853i) q^{78} -5.49348i q^{79} +3.23163i q^{80} +(-1.79862 - 8.81844i) q^{81} +9.80126 q^{82} +11.0267 q^{83} +(-1.56486 + 0.742446i) q^{84} -9.37349i q^{85} +1.94644i q^{86} +(0.739826 + 1.55933i) q^{87} +(3.30730 + 0.248504i) q^{88} +1.28964i q^{89} +(7.50916 + 6.13218i) q^{90} -5.12971 q^{91} -9.26189i q^{92} +(3.26233 + 6.87601i) q^{93} -7.19265i q^{94} +1.90776 q^{95} +(0.742446 + 1.56486i) q^{96} -11.3155 q^{97} +1.00000 q^{98} +(6.85320 - 7.21344i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 4 q^{3} + 12 q^{4} - 4 q^{6} - 12 q^{8}+O(q^{10}) \) 12 * q - 12 * q^2 + 4 * q^3 + 12 * q^4 - 4 * q^6 - 12 * q^8	\( 12 q - 12 q^{2} + 4 q^{3} + 12 q^{4} - 4 q^{6} - 12 q^{8} - 8 q^{11} + 4 q^{12} + 4 q^{15} + 12 q^{16} - 4 q^{17} + 8 q^{22} - 4 q^{24} - 28 q^{25} - 8 q^{27} + 8 q^{29} - 4 q^{30} + 12 q^{31} - 12 q^{32} + 16 q^{33} + 4 q^{34} - 4 q^{35} - 36 q^{39} + 20 q^{41} - 8 q^{44} - 12 q^{45} + 4 q^{48} - 12 q^{49} + 28 q^{50} + 8 q^{51} + 8 q^{54} + 4 q^{55} + 28 q^{57} - 8 q^{58} + 4 q^{60} - 12 q^{62} + 4 q^{63} + 12 q^{64} - 16 q^{66} + 24 q^{67} - 4 q^{68} - 20 q^{69} + 4 q^{70} - 40 q^{75} + 4 q^{77} + 36 q^{78} + 4 q^{81} - 20 q^{82} + 44 q^{83} + 8 q^{87} + 8 q^{88} + 12 q^{90} - 24 q^{91} - 24 q^{93} - 4 q^{96} - 48 q^{97} + 12 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 4 * q^3 + 12 * q^4 - 4 * q^6 - 12 * q^8 - 8 * q^11 + 4 * q^12 + 4 * q^15 + 12 * q^16 - 4 * q^17 + 8 * q^22 - 4 * q^24 - 28 * q^25 - 8 * q^27 + 8 * q^29 - 4 * q^30 + 12 * q^31 - 12 * q^32 + 16 * q^33 + 4 * q^34 - 4 * q^35 - 36 * q^39 + 20 * q^41 - 8 * q^44 - 12 * q^45 + 4 * q^48 - 12 * q^49 + 28 * q^50 + 8 * q^51 + 8 * q^54 + 4 * q^55 + 28 * q^57 - 8 * q^58 + 4 * q^60 - 12 * q^62 + 4 * q^63 + 12 * q^64 - 16 * q^66 + 24 * q^67 - 4 * q^68 - 20 * q^69 + 4 * q^70 - 40 * q^75 + 4 * q^77 + 36 * q^78 + 4 * q^81 - 20 * q^82 + 44 * q^83 + 8 * q^87 + 8 * q^88 + 12 * q^90 - 24 * q^91 - 24 * q^93 - 4 * q^96 - 48 * q^97 + 12 * q^98 + 36 * q^99

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