LMFDB - Embedded newform 462.2.c.a.197.2

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			197.2
Root			$-2.18803i$ of defining polynomial
Character	$\chi$	$=$	462.197
Dual form			462.2.c.a.197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.64459 + 0.543441i) q^{3} +1.00000 q^{4} +0.118610i q^{5} +(1.64459 - 0.543441i) q^{6} -1.00000i q^{7} -1.00000 q^{8} +(2.40934 - 1.78747i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.64459 + 0.543441i) q^{3} +1.00000 q^{4} +0.118610i q^{5} +(1.64459 - 0.543441i) q^{6} -1.00000i q^{7} -1.00000 q^{8} +(2.40934 - 1.78747i) q^{9} -0.118610i q^{10} +(-2.10115 + 2.56616i) q^{11} +(-1.64459 + 0.543441i) q^{12} -0.913118i q^{13} +1.00000i q^{14} +(-0.0644573 - 0.195064i) q^{15} +1.00000 q^{16} +0.404381 q^{17} +(-2.40934 + 1.78747i) q^{18} -7.70348i q^{19} +0.118610i q^{20} +(0.543441 + 1.64459i) q^{21} +(2.10115 - 2.56616i) q^{22} +1.37265i q^{23} +(1.64459 - 0.543441i) q^{24} +4.98593 q^{25} +0.913118i q^{26} +(-2.99099 + 4.24900i) q^{27} -1.00000i q^{28} +3.20881 q^{29} +(0.0644573 + 0.195064i) q^{30} +8.74552 q^{31} -1.00000 q^{32} +(2.06097 - 5.36213i) q^{33} -0.404381 q^{34} +0.118610 q^{35} +(2.40934 - 1.78747i) q^{36} +4.13884 q^{37} +7.70348i q^{38} +(0.496226 + 1.50170i) q^{39} -0.118610i q^{40} +12.1630 q^{41} +(-0.543441 - 1.64459i) q^{42} +2.85361i q^{43} +(-2.10115 + 2.56616i) q^{44} +(0.212011 + 0.285771i) q^{45} -1.37265i q^{46} -10.3554i q^{47} +(-1.64459 + 0.543441i) q^{48} -1.00000 q^{49} -4.98593 q^{50} +(-0.665040 + 0.219757i) q^{51} -0.913118i q^{52} -8.81869i q^{53} +(2.99099 - 4.24900i) q^{54} +(-0.304371 - 0.249216i) q^{55} +1.00000i q^{56} +(4.18639 + 12.6691i) q^{57} -3.20881 q^{58} -5.49147i q^{59} +(-0.0644573 - 0.195064i) q^{60} -7.30675i q^{61} -8.74552 q^{62} +(-1.78747 - 2.40934i) q^{63} +1.00000 q^{64} +0.108304 q^{65} +(-2.06097 + 5.36213i) q^{66} -2.01758 q^{67} +0.404381 q^{68} +(-0.745956 - 2.25745i) q^{69} -0.118610 q^{70} +14.2157i q^{71} +(-2.40934 + 1.78747i) q^{72} +11.7838i q^{73} -4.13884 q^{74} +(-8.19981 + 2.70956i) q^{75} -7.70348i q^{76} +(2.56616 + 2.10115i) q^{77} +(-0.496226 - 1.50170i) q^{78} +4.34114i q^{79} +0.118610i q^{80} +(2.60987 - 8.61328i) q^{81} -12.1630 q^{82} -0.700078 q^{83} +(0.543441 + 1.64459i) q^{84} +0.0479634i q^{85} -2.85361i q^{86} +(-5.27718 + 1.74380i) q^{87} +(2.10115 - 2.56616i) q^{88} -10.7521i q^{89} +(-0.212011 - 0.285771i) q^{90} -0.913118 q^{91} +1.37265i q^{92} +(-14.3828 + 4.75267i) q^{93} +10.3554i q^{94} +0.913706 q^{95} +(1.64459 - 0.543441i) q^{96} -5.48096 q^{97} +1.00000 q^{98} +(-0.475441 + 9.93851i) 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
$3$	−1.64459	+	0.543441i	−0.949504	+	0.313756i
$3$	−1.64459	+	0.543441i	−0.949504	+	0.313756i
$4$	1.00000			0.500000
$5$			0.118610i			0.0530438i	0.999648	+	0.0265219i	$0.00844317\pi$
$5$			0.118610i			0.0530438i	−0.999648	+	0.0265219i	$0.991557\pi$
$6$	1.64459	−	0.543441i	0.671400	−	0.221859i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−1.00000			−0.353553
$9$	2.40934	−	1.78747i	0.803115	−	0.595825i
$10$		−	0.118610i		−	0.0375076i
$11$	−2.10115	+	2.56616i	−0.633520	+	0.773726i
$11$	−2.10115	+	2.56616i	−0.633520	+	0.773726i
$12$	−1.64459	+	0.543441i	−0.474752	+	0.156878i
$13$		−	0.913118i		−	0.253253i	−0.991950	−	0.126627i	$-0.959585\pi$
$13$		−	0.913118i		−	0.253253i	0.991950	−	0.126627i	$-0.0404150\pi$
$14$			1.00000i			0.267261i
$15$	−0.0644573	−	0.195064i	−0.0166428	−	0.0503653i
$16$	1.00000			0.250000
$17$	0.404381			0.0980767			0.0490383	−	0.998797i	$-0.484384\pi$
$17$	0.404381			0.0980767			0.0490383	+	0.998797i	$0.484384\pi$
$18$	−2.40934	+	1.78747i	−0.567888	+	0.421312i
$19$		−	7.70348i		−	1.76730i	−0.468148	−	0.883650i	$-0.655079\pi$
$19$		−	7.70348i		−	1.76730i	0.468148	−	0.883650i	$-0.344921\pi$
$20$			0.118610i			0.0265219i
$21$	0.543441	+	1.64459i	0.118589	+	0.358879i
$22$	2.10115	−	2.56616i	0.447966	−	0.547107i
$23$			1.37265i			0.286218i	0.989707	+	0.143109i	$0.0457099\pi$
$23$			1.37265i			0.286218i	−0.989707	+	0.143109i	$0.954290\pi$
$24$	1.64459	−	0.543441i	0.335700	−	0.110929i
$25$	4.98593			0.997186
$26$			0.913118i			0.179077i
$27$	−2.99099	+	4.24900i	−0.575617	+	0.817720i
$28$		−	1.00000i		−	0.188982i
$29$	3.20881			0.595862			0.297931	−	0.954587i	$-0.403703\pi$
$29$	3.20881			0.595862			0.297931	+	0.954587i	$0.403703\pi$
$30$	0.0644573	+	0.195064i	0.0117682	+	0.0356136i
$31$	8.74552			1.57074			0.785371	−	0.619026i	$-0.212472\pi$
$31$	8.74552			1.57074			0.785371	+	0.619026i	$0.212472\pi$
$32$	−1.00000			−0.176777
$33$	2.06097	−	5.36213i	0.358768	−	0.933427i
$34$	−0.404381			−0.0693507
$35$	0.118610			0.0200487
$36$	2.40934	−	1.78747i	0.401557	−	0.297912i
$37$	4.13884			0.680421			0.340211	−	0.940349i	$-0.389502\pi$
$37$	4.13884			0.680421			0.340211	+	0.940349i	$0.389502\pi$
$38$			7.70348i			1.24967i
$39$	0.496226	+	1.50170i	0.0794597	+	0.240465i
$40$		−	0.118610i		−	0.0187538i
$41$	12.1630			1.89954			0.949772	−	0.312942i	$-0.101315\pi$
$41$	12.1630			1.89954			0.949772	+	0.312942i	$0.101315\pi$
$42$	−0.543441	−	1.64459i	−0.0838548	−	0.253766i
$43$			2.85361i			0.435172i	0.976041	+	0.217586i	$0.0698182\pi$
$43$			2.85361i			0.435172i	−0.976041	+	0.217586i	$0.930182\pi$
$44$	−2.10115	+	2.56616i	−0.316760	+	0.386863i
$45$	0.212011	+	0.285771i	0.0316048	+	0.0426002i
$46$		−	1.37265i		−	0.202387i
$47$		−	10.3554i		−	1.51049i	−0.655443	−	0.755244i	$-0.727518\pi$
$47$		−	10.3554i		−	1.51049i	0.655443	−	0.755244i	$-0.272482\pi$
$48$	−1.64459	+	0.543441i	−0.237376	+	0.0784390i
$49$	−1.00000			−0.142857
$50$	−4.98593			−0.705117
$51$	−0.665040	+	0.219757i	−0.0931242	+	0.0307721i
$52$		−	0.913118i		−	0.126627i
$53$		−	8.81869i		−	1.21134i	−0.795716	−	0.605670i	$-0.792905\pi$
$53$		−	8.81869i		−	1.21134i	0.795716	−	0.605670i	$-0.207095\pi$
$54$	2.99099	−	4.24900i	0.407022	−	0.578215i
$55$	−0.304371	−	0.249216i	−0.0410414	−	0.0336043i
$56$			1.00000i			0.133631i
$57$	4.18639	+	12.6691i	0.554501	+	1.67806i
$58$	−3.20881			−0.421338
$59$		−	5.49147i		−	0.714929i	−0.933927	−	0.357464i	$-0.883641\pi$
$59$		−	5.49147i		−	0.714929i	0.933927	−	0.357464i	$-0.116359\pi$
$60$	−0.0644573	−	0.195064i	−0.00832140	−	0.0251826i
$61$		−	7.30675i		−	0.935534i	−0.883852	−	0.467767i	$-0.845059\pi$
$61$		−	7.30675i		−	0.935534i	0.883852	−	0.467767i	$-0.154941\pi$
$62$	−8.74552			−1.11068
$63$	−1.78747	−	2.40934i	−0.225201	−	0.303549i
$64$	1.00000			0.125000
$65$	0.108304			0.0134335
$66$	−2.06097	+	5.36213i	−0.253687	+	0.660032i
$67$	−2.01758			−0.246486			−0.123243	−	0.992377i	$-0.539329\pi$
$67$	−2.01758			−0.246486			−0.123243	+	0.992377i	$0.539329\pi$
$68$	0.404381			0.0490383
$69$	−0.745956	−	2.25745i	−0.0898026	−	0.271765i
$70$	−0.118610			−0.0141765
$71$			14.2157i			1.68710i	0.537053	+	0.843548i	$0.319537\pi$
$71$			14.2157i			1.68710i	−0.537053	+	0.843548i	$0.680463\pi$
$72$	−2.40934	+	1.78747i	−0.283944	+	0.210656i
$73$			11.7838i			1.37919i	0.724193	+	0.689597i	$0.242213\pi$
$73$			11.7838i			1.37919i	−0.724193	+	0.689597i	$0.757787\pi$
$74$	−4.13884			−0.481130
$75$	−8.19981	+	2.70956i	−0.946832	+	0.312873i
$76$		−	7.70348i		−	0.883650i
$77$	2.56616	+	2.10115i	0.292441	+	0.239448i
$78$	−0.496226	−	1.50170i	−0.0561865	−	0.170034i
$79$			4.34114i			0.488416i	0.969723	+	0.244208i	$0.0785279\pi$
$79$			4.34114i			0.488416i	−0.969723	+	0.244208i	$0.921472\pi$
$80$			0.118610i			0.0132609i
$81$	2.60987	−	8.61328i	0.289986	−	0.957031i
$82$	−12.1630			−1.34318
$83$	−0.700078			−0.0768435			−0.0384217	−	0.999262i	$-0.512233\pi$
$83$	−0.700078			−0.0768435			−0.0384217	+	0.999262i	$0.512233\pi$
$84$	0.543441	+	1.64459i	0.0592943	+	0.179439i
$85$			0.0479634i			0.00520236i
$86$		−	2.85361i		−	0.307713i
$87$	−5.27718	+	1.74380i	−0.565773	+	0.186955i
$88$	2.10115	−	2.56616i	0.223983	−	0.273554i
$89$		−	10.7521i		−	1.13972i	−0.821741	−	0.569861i	$-0.806997\pi$
$89$		−	10.7521i		−	1.13972i	0.821741	−	0.569861i	$-0.193003\pi$
$90$	−0.212011	−	0.285771i	−0.0223480	−	0.0301229i
$91$	−0.913118			−0.0957208
$92$			1.37265i			0.143109i
$93$	−14.3828	+	4.75267i	−1.49142	+	0.492829i
$94$			10.3554i			1.06808i
$95$	0.913706			0.0937443
$96$	1.64459	−	0.543441i	0.167850	−	0.0554647i
$97$	−5.48096			−0.556507			−0.278253	−	0.960508i	$-0.589756\pi$
$97$	−5.48096			−0.556507			−0.278253	+	0.960508i	$0.589756\pi$
$98$	1.00000			0.101015
$99$	−0.475441	+	9.93851i	−0.0477836	+	0.998858i
$100$	4.98593			0.498593
$101$	−6.44547			−0.641348			−0.320674	−	0.947190i	$-0.603909\pi$
$101$	−6.44547			−0.641348			−0.320674	+	0.947190i	$0.603909\pi$
$102$	0.665040	−	0.219757i	0.0658487	−	0.0217592i
$103$	−6.88546			−0.678445			−0.339222	−	0.940706i	$-0.610164\pi$
$103$	−6.88546			−0.678445			−0.339222	+	0.940706i	$0.610164\pi$
$104$			0.913118i			0.0895386i
$105$	−0.195064	+	0.0644573i	−0.0190363	+	0.00629039i
$106$			8.81869i			0.856547i
$107$	−1.32477			−0.128070			−0.0640351	−	0.997948i	$-0.520397\pi$
$107$	−1.32477			−0.128070			−0.0640351	+	0.997948i	$0.520397\pi$
$108$	−2.99099	+	4.24900i	−0.287808	+	0.408860i
$109$			11.5849i			1.10963i	0.831974	+	0.554815i	$0.187211\pi$
$109$			11.5849i			1.10963i	−0.831974	+	0.554815i	$0.812789\pi$
$110$	0.304371	+	0.249216i	0.0290206	+	0.0237618i
$111$	−6.80669	+	2.24922i	−0.646062	+	0.213486i
$112$		−	1.00000i		−	0.0944911i
$113$		−	15.5818i		−	1.46581i	−0.680332	−	0.732904i	$-0.738164\pi$
$113$		−	15.5818i		−	1.46581i	0.680332	−	0.732904i	$-0.261836\pi$
$114$	−4.18639	−	12.6691i	−0.392091	−	1.18657i
$115$	−0.162810			−0.0151821
$116$	3.20881			0.297931
$117$	−1.63217	−	2.20001i	−0.150895	−	0.203391i
$118$			5.49147i			0.505531i
$119$		−	0.404381i		−	0.0370695i
$120$	0.0644573	+	0.195064i	0.00588412	+	0.0178068i
$121$	−2.17036	−	10.7838i	−0.197305	−	0.980342i
$122$			7.30675i			0.661522i
$123$	−20.0032	+	6.60988i	−1.80362	+	0.595993i
$124$	8.74552			0.785371
$125$			1.18443i			0.105938i
$126$	1.78747	+	2.40934i	0.159241	+	0.214641i
$127$			7.47768i			0.663537i	0.943361	+	0.331768i	$0.107645\pi$
$127$			7.47768i			0.663537i	−0.943361	+	0.331768i	$0.892355\pi$
$128$	−1.00000			−0.0883883
$129$	−1.55077	−	4.69302i	−0.136538	−	0.413197i
$130$	−0.108304			−0.00949893
$131$	−2.26848			−0.198198			−0.0990992	−	0.995078i	$-0.531596\pi$
$131$	−2.26848			−0.198198			−0.0990992	+	0.995078i	$0.531596\pi$
$132$	2.06097	−	5.36213i	0.179384	−	0.466713i
$133$	−7.70348			−0.667977
$134$	2.01758			0.174292
$135$	−0.503971	−	0.354760i	−0.0433749	−	0.0305329i
$136$	−0.404381			−0.0346753
$137$			14.6823i			1.25439i	0.778862	+	0.627196i	$0.215797\pi$
$137$			14.6823i			1.25439i	−0.778862	+	0.627196i	$0.784203\pi$
$138$	0.745956	+	2.25745i	0.0635000	+	0.192167i
$139$		−	15.2576i		−	1.29413i	−0.762435	−	0.647064i	$-0.775997\pi$
$139$		−	15.2576i		−	1.29413i	0.762435	−	0.647064i	$-0.224003\pi$
$140$	0.118610			0.0100243
$141$	5.62754	+	17.0304i	0.473925	+	1.43421i
$142$		−	14.2157i		−	1.19296i
$143$	2.34321	+	1.91860i	0.195949	+	0.160441i
$144$	2.40934	−	1.78747i	0.200779	−	0.148956i
$145$			0.380596i			0.0316068i
$146$		−	11.7838i		−	0.975238i
$147$	1.64459	−	0.543441i	0.135643	−	0.0448223i
$148$	4.13884			0.340211
$149$	20.0758			1.64467			0.822336	−	0.569002i	$-0.192670\pi$
$149$	20.0758			1.64467			0.822336	+	0.569002i	$0.192670\pi$
$150$	8.19981	−	2.70956i	0.669511	−	0.221235i
$151$		−	11.7555i		−	0.956651i	−0.878183	−	0.478326i	$-0.841244\pi$
$151$		−	11.7555i		−	0.956651i	0.878183	−	0.478326i	$-0.158756\pi$
$152$			7.70348i			0.624835i
$153$	0.974292	−	0.722820i	0.0787668	−	0.0584365i
$154$	−2.56616	−	2.10115i	−0.206787	−	0.169315i
$155$			1.03730i			0.0833181i
$156$	0.496226	+	1.50170i	0.0397299	+	0.120232i
$157$	17.7004			1.41264			0.706322	−	0.707891i	$-0.250353\pi$
$157$	17.7004			1.41264			0.706322	+	0.707891i	$0.250353\pi$
$158$		−	4.34114i		−	0.345362i
$159$	4.79244	+	14.5031i	0.380065	+	1.15017i
$160$		−	0.118610i		−	0.00937691i
$161$	1.37265			0.108180
$162$	−2.60987	+	8.61328i	−0.205051	+	0.676723i
$163$	−10.9259			−0.855781			−0.427891	−	0.903831i	$-0.640743\pi$
$163$	−10.9259			−0.855781			−0.427891	+	0.903831i	$0.640743\pi$
$164$	12.1630			0.949772
$165$	0.635999	+	0.244450i	0.0495125	+	0.0190304i
$166$	0.700078			0.0543366
$167$	−3.89177			−0.301155			−0.150577	−	0.988598i	$-0.548113\pi$
$167$	−3.89177			−0.301155			−0.150577	+	0.988598i	$0.548113\pi$
$168$	−0.543441	−	1.64459i	−0.0419274	−	0.126883i
$169$	12.1662			0.935863
$170$		−	0.0479634i		−	0.00367862i
$171$	−13.7698	−	18.5603i	−1.05300	−	1.41934i
$172$			2.85361i			0.217586i
$173$	−15.0414			−1.14358			−0.571789	−	0.820401i	$-0.693750\pi$
$173$	−15.0414			−1.14358			−0.571789	+	0.820401i	$0.693750\pi$
$174$	5.27718	−	1.74380i	0.400062	−	0.132197i
$175$		−	4.98593i		−	0.376901i
$176$	−2.10115	+	2.56616i	−0.158380	+	0.193432i
$177$	2.98429	+	9.03121i	0.224313	+	0.678828i
$178$			10.7521i			0.805905i
$179$		−	4.42858i		−	0.331008i	−0.986209	−	0.165504i	$-0.947075\pi$
$179$		−	4.42858i		−	0.331008i	0.986209	−	0.165504i	$-0.0529251\pi$
$180$	0.212011	+	0.285771i	0.0158024	+	0.0213001i
$181$	−9.55361			−0.710114			−0.355057	−	0.934845i	$-0.615539\pi$
$181$	−9.55361			−0.710114			−0.355057	+	0.934845i	$0.615539\pi$
$182$	0.913118			0.0676848
$183$	3.97079	+	12.0166i	0.293529	+	0.888293i
$184$		−	1.37265i		−	0.101193i
$185$			0.490906i			0.0360921i
$186$	14.3828	−	4.75267i	1.05460	−	0.348483i
$187$	−0.849663	+	1.03771i	−0.0621335	+	0.0758845i
$188$		−	10.3554i		−	0.755244i
$189$	4.24900	+	2.99099i	0.309069	+	0.217563i
$190$	−0.913706			−0.0662872
$191$		−	2.91949i		−	0.211247i	−0.994406	−	0.105623i	$-0.966316\pi$
$191$		−	2.91949i		−	0.211247i	0.994406	−	0.105623i	$-0.0336838\pi$
$192$	−1.64459	+	0.543441i	−0.118688	+	0.0392195i
$193$			1.37905i			0.0992660i	0.998768	+	0.0496330i	$0.0158052\pi$
$193$			1.37905i			0.0992660i	−0.998768	+	0.0496330i	$0.984195\pi$
$194$	5.48096			0.393510
$195$	−0.178116	+	0.0588571i	−0.0127552	+	0.00421484i
$196$	−1.00000			−0.0714286
$197$	−18.6091			−1.32585			−0.662923	−	0.748688i	$-0.730684\pi$
$197$	−18.6091			−1.32585			−0.662923	+	0.748688i	$0.730684\pi$
$198$	0.475441	−	9.93851i	0.0337881	−	0.706299i
$199$	11.5227			0.816823			0.408412	−	0.912798i	$-0.366083\pi$
$199$	11.5227			0.816823			0.408412	+	0.912798i	$0.366083\pi$
$200$	−4.98593			−0.352559
$201$	3.31808	−	1.09643i	0.234039	−	0.0773365i
$202$	6.44547			0.453501
$203$		−	3.20881i		−	0.225215i
$204$	−0.665040	+	0.219757i	−0.0465621	+	0.0153861i
$205$			1.44265i			0.100759i
$206$	6.88546			0.479733
$207$	2.45358	+	3.30719i	0.170536	+	0.229866i
$208$		−	0.913118i		−	0.0633133i
$209$	19.7684	+	16.1862i	1.36741	+	1.11962i
$210$	0.195064	−	0.0644573i	0.0134607	−	0.00444798i
$211$			4.45606i			0.306768i	0.988167	+	0.153384i	$0.0490171\pi$
$211$			4.45606i			0.306768i	−0.988167	+	0.153384i	$0.950983\pi$
$212$		−	8.81869i		−	0.605670i
$213$	−7.72541	−	23.3790i	−0.529336	−	1.60190i
$214$	1.32477			0.0905594
$215$	−0.338465			−0.0230831
$216$	2.99099	−	4.24900i	0.203511	−	0.289108i
$217$		−	8.74552i		−	0.593684i
$218$		−	11.5849i		−	0.784627i
$219$	−6.40383	−	19.3796i	−0.432730	−	1.30955i
$220$	−0.304371	−	0.249216i	−0.0205207	−	0.0168021i
$221$		−	0.369247i		−	0.0248382i
$222$	6.80669	−	2.24922i	0.456835	−	0.150957i
$223$	−10.4573			−0.700273			−0.350136	−	0.936699i	$-0.613865\pi$
$223$	−10.4573			−0.700273			−0.350136	+	0.936699i	$0.613865\pi$
$224$			1.00000i			0.0668153i
$225$	12.0128	−	8.91222i	0.800855	−	0.594148i
$226$			15.5818i			1.03648i
$227$	−5.78740			−0.384123			−0.192062	−	0.981383i	$-0.561517\pi$
$227$	−5.78740			−0.384123			−0.192062	+	0.981383i	$0.561517\pi$
$228$	4.18639	+	12.6691i	0.277250	+	0.839029i
$229$	7.53283			0.497784			0.248892	−	0.968531i	$-0.419934\pi$
$229$	7.53283			0.497784			0.248892	+	0.968531i	$0.419934\pi$
$230$	0.162810			0.0107354
$231$	−5.36213	−	2.06097i	−0.352802	−	0.135602i
$232$	−3.20881			−0.210669
$233$	17.3347			1.13563			0.567817	−	0.823155i	$-0.307788\pi$
$233$	17.3347			1.13563			0.567817	+	0.823155i	$0.307788\pi$
$234$	1.63217	+	2.20001i	0.106699	+	0.143819i
$235$	1.22825			0.0801220
$236$		−	5.49147i		−	0.357464i
$237$	−2.35915	−	7.13938i	−0.153243	−	0.463753i
$238$			0.404381i			0.0262121i
$239$	12.0373			0.778631			0.389316	−	0.921104i	$-0.372712\pi$
$239$	12.0373			0.778631			0.389316	+	0.921104i	$0.372712\pi$
$240$	−0.0644573	−	0.195064i	−0.00416070	−	0.0125913i
$241$			24.9447i			1.60683i	0.595420	+	0.803415i	$0.296986\pi$
$241$			24.9447i			1.60683i	−0.595420	+	0.803415i	$0.703014\pi$
$242$	2.17036	+	10.7838i	0.139516	+	0.693207i
$243$	0.388643	+	15.5836i	0.0249315	+	0.999689i
$244$		−	7.30675i		−	0.467767i
$245$		−	0.118610i		−	0.00757768i
$246$	20.0032	−	6.60988i	1.27536	−	0.421431i
$247$	−7.03419			−0.447575
$248$	−8.74552			−0.555341
$249$	1.15134	−	0.380451i	0.0729632	−	0.0241101i
$250$		−	1.18443i		−	0.0749097i
$251$			11.3136i			0.714106i	0.934084	+	0.357053i	$0.116218\pi$
$251$			11.3136i			0.714106i	−0.934084	+	0.357053i	$0.883782\pi$
$252$	−1.78747	−	2.40934i	−0.112600	−	0.151774i
$253$	−3.52245	−	2.88415i	−0.221454	−	0.181325i
$254$		−	7.47768i		−	0.469191i
$255$	−0.0260653	−	0.0788800i	−0.00163227	−	0.00493966i
$256$	1.00000			0.0625000
$257$		−	24.6477i		−	1.53748i	−0.639559	−	0.768742i	$-0.720883\pi$
$257$		−	24.6477i		−	1.53748i	0.639559	−	0.768742i	$-0.279117\pi$
$258$	1.55077	+	4.69302i	0.0965467	+	0.292174i
$259$		−	4.13884i		−	0.257175i
$260$	0.108304			0.00671676
$261$	7.73114	−	5.73567i	0.478545	−	0.355029i
$262$	2.26848			0.140147
$263$	18.0728			1.11441			0.557207	−	0.830373i	$-0.311873\pi$
$263$	18.0728			1.11441			0.557207	+	0.830373i	$0.311873\pi$
$264$	−2.06097	+	5.36213i	−0.126844	+	0.330016i
$265$	1.04598			0.0642540
$266$	7.70348			0.472331
$267$	5.84314	+	17.6828i	0.357595	+	1.08217i
$268$	−2.01758			−0.123243
$269$			8.22269i			0.501346i	0.968072	+	0.250673i	$0.0806520\pi$
$269$			8.22269i			0.501346i	−0.968072	+	0.250673i	$0.919348\pi$
$270$	0.503971	+	0.354760i	0.0306707	+	0.0215900i
$271$			12.2822i			0.746093i	0.927813	+	0.373047i	$0.121687\pi$
$271$			12.2822i			0.746093i	−0.927813	+	0.373047i	$0.878313\pi$
$272$	0.404381			0.0245192
$273$	1.50170	−	0.496226i	0.0908872	−	0.0300329i
$274$		−	14.6823i		−	0.886988i
$275$	−10.4762	+	12.7947i	−0.631737	+	0.771549i
$276$	−0.745956	−	2.25745i	−0.0449013	−	0.135883i
$277$		−	27.2430i		−	1.63687i	−0.574596	−	0.818437i	$-0.694841\pi$
$277$		−	27.2430i		−	1.63687i	0.574596	−	0.818437i	$-0.305159\pi$
$278$			15.2576i			0.915087i
$279$	21.0710	−	15.6324i	1.26148	−	0.935886i
$280$	−0.118610			−0.00708827
$281$	−23.1187			−1.37914			−0.689572	−	0.724217i	$-0.742201\pi$
$281$	−23.1187			−1.37914			−0.689572	+	0.724217i	$0.742201\pi$
$282$	−5.62754	−	17.0304i	−0.335115	−	1.01414i
$283$			8.26048i			0.491035i	0.969392	+	0.245517i	$0.0789579\pi$
$283$			8.26048i			0.491035i	−0.969392	+	0.245517i	$0.921042\pi$
$284$			14.2157i			0.843548i
$285$	−1.50267	+	0.496546i	−0.0890106	+	0.0294128i
$286$	−2.34321	−	1.91860i	−0.138557	−	0.113449i
$287$		−	12.1630i		−	0.717960i
$288$	−2.40934	+	1.78747i	−0.141972	+	0.105328i
$289$	−16.8365			−0.990381
$290$		−	0.380596i		−	0.0223494i
$291$	9.01392	−	2.97858i	0.528405	−	0.174607i
$292$			11.7838i			0.689597i
$293$	−16.2502			−0.949348			−0.474674	−	0.880162i	$-0.657434\pi$
$293$	−16.2502			−0.949348			−0.474674	+	0.880162i	$0.657434\pi$
$294$	−1.64459	+	0.543441i	−0.0959144	+	0.0316941i
$295$	0.651341			0.0379225
$296$	−4.13884			−0.240565
$297$	−4.61909	−	16.6031i	−0.268027	−	0.963411i
$298$	−20.0758			−1.16296
$299$	1.25339			0.0724857
$300$	−8.19981	+	2.70956i	−0.473416	+	0.156437i
$301$	2.85361			0.164479
$302$			11.7555i			0.676454i
$303$	10.6001	−	3.50273i	0.608962	−	0.201227i
$304$		−	7.70348i		−	0.441825i
$305$	0.866650			0.0496243
$306$	−0.974292	+	0.722820i	−0.0556965	+	0.0413209i
$307$			10.5059i			0.599601i	0.954002	+	0.299800i	$0.0969201\pi$
$307$			10.5059i			0.599601i	−0.954002	+	0.299800i	$0.903080\pi$
$308$	2.56616	+	2.10115i	0.146221	+	0.119724i
$309$	11.3238	−	3.74184i	0.644186	−	0.212866i
$310$		−	1.03730i		−	0.0589148i
$311$		−	7.32826i		−	0.415547i	−0.978177	−	0.207774i	$-0.933378\pi$
$311$		−	7.32826i		−	0.415547i	0.978177	−	0.207774i	$-0.0666218\pi$
$312$	−0.496226	−	1.50170i	−0.0280933	−	0.0850172i
$313$	18.8781			1.06706			0.533528	−	0.845782i	$-0.320866\pi$
$313$	18.8781			1.06706			0.533528	+	0.845782i	$0.320866\pi$
$314$	−17.7004			−0.998890
$315$	0.285771	−	0.212011i	0.0161014	−	0.0119455i
$316$			4.34114i			0.244208i
$317$			25.1264i			1.41124i	0.708591	+	0.705620i	$0.249331\pi$
$317$			25.1264i			1.41124i	−0.708591	+	0.705620i	$0.750669\pi$
$318$	−4.79244	−	14.5031i	−0.268747	−	0.813294i
$319$	−6.74219	+	8.23433i	−0.377490	+	0.461034i
$320$			0.118610i			0.00663047i
$321$	2.17870	−	0.719934i	0.121603	−	0.0401828i
$322$	−1.37265			−0.0764950
$323$		−	3.11514i		−	0.173331i
$324$	2.60987	−	8.61328i	0.144993	−	0.478515i
$325$		−	4.55274i		−	0.252541i
$326$	10.9259			0.605129
$327$	−6.29570	−	19.0524i	−0.348153	−	1.05360i
$328$	−12.1630			−0.671590
$329$	−10.3554			−0.570911
$330$	−0.635999	−	0.244450i	−0.0350106	−	0.0134565i
$331$	22.5329			1.23852			0.619260	−	0.785186i	$-0.287433\pi$
$331$	22.5329			1.23852			0.619260	+	0.785186i	$0.287433\pi$
$332$	−0.700078			−0.0384217
$333$	9.97189	−	7.39807i	0.546456	−	0.405412i
$334$	3.89177			0.212948
$335$		−	0.239304i		−	0.0130746i
$336$	0.543441	+	1.64459i	0.0296471	+	0.0897197i
$337$			1.86013i			0.101328i	0.998716	+	0.0506639i	$0.0161337\pi$
$337$			1.86013i			0.101328i	−0.998716	+	0.0506639i	$0.983866\pi$
$338$	−12.1662			−0.661755
$339$	8.46777	+	25.6256i	0.459906	+	1.39179i
$340$			0.0479634i			0.00260118i
$341$	−18.3756	+	22.4424i	−0.995096	+	1.21532i
$342$	13.7698	+	18.5603i	0.744584	+	1.00363i
$343$			1.00000i			0.0539949i
$344$		−	2.85361i		−	0.153856i
$345$	0.267755	−	0.0884775i	0.0144154	−	0.00476347i
$346$	15.0414			0.808632
$347$	27.3110			1.46613			0.733067	−	0.680157i	$-0.238088\pi$
$347$	27.3110			1.46613			0.733067	+	0.680157i	$0.238088\pi$
$348$	−5.27718	+	1.74380i	−0.282887	+	0.0934776i
$349$			3.59647i			0.192515i	0.995356	+	0.0962574i	$0.0306872\pi$
$349$			3.59647i			0.192515i	−0.995356	+	0.0962574i	$0.969313\pi$
$350$			4.98593i			0.266509i
$351$	3.87983	+	2.73113i	0.207090	+	0.145777i
$352$	2.10115	−	2.56616i	0.111992	−	0.136777i
$353$		−	10.4939i		−	0.558532i	−0.960214	−	0.279266i	$-0.909909\pi$
$353$		−	10.4939i		−	0.558532i	0.960214	−	0.279266i	$-0.0900912\pi$
$354$	−2.98429	−	9.03121i	−0.158613	−	0.480004i
$355$	−1.68612			−0.0894900
$356$		−	10.7521i		−	0.569861i
$357$	0.219757	+	0.665040i	0.0116308	+	0.0351976i
$358$			4.42858i			0.234058i
$359$	7.78386			0.410817			0.205408	−	0.978676i	$-0.434148\pi$
$359$	7.78386			0.410817			0.205408	+	0.978676i	$0.434148\pi$
$360$	−0.212011	−	0.285771i	−0.0111740	−	0.0150615i
$361$	−40.3437			−2.12335
$362$	9.55361			0.502127
$363$	9.42969	+	16.5554i	0.494930	+	0.868933i
$364$	−0.913118			−0.0478604
$365$	−1.39768			−0.0731577
$366$	−3.97079	−	12.0166i	−0.207557	−	0.628118i
$367$	5.02069			0.262078			0.131039	−	0.991377i	$-0.458169\pi$
$367$	5.02069			0.262078			0.131039	+	0.991377i	$0.458169\pi$
$368$			1.37265i			0.0715545i
$369$	29.3049	−	21.7411i	1.52555	−	1.13180i
$370$		−	0.490906i		−	0.0255210i
$371$	−8.81869			−0.457843
$372$	−14.3828	+	4.75267i	−0.745712	+	0.246415i
$373$			35.0542i			1.81504i	0.420012	+	0.907519i	$0.362026\pi$
$373$			35.0542i			1.81504i	−0.420012	+	0.907519i	$0.637974\pi$
$374$	0.849663	−	1.03771i	0.0439350	−	0.0536585i
$375$	−0.643666	−	1.94789i	−0.0332388	−	0.100589i
$376$			10.3554i			0.534038i
$377$		−	2.93003i		−	0.150904i
$378$	−4.24900	−	2.99099i	−0.218545	−	0.153840i
$379$	−21.9708			−1.12856			−0.564282	−	0.825582i	$-0.690847\pi$
$379$	−21.9708			−1.12856			−0.564282	+	0.825582i	$0.690847\pi$
$380$	0.913706			0.0468722
$381$	−4.06368	−	12.2977i	−0.208189	−	0.630030i
$382$			2.91949i			0.149374i
$383$		−	14.3769i		−	0.734624i	−0.930098	−	0.367312i	$-0.880278\pi$
$383$		−	14.3769i		−	0.734624i	0.930098	−	0.367312i	$-0.119722\pi$
$384$	1.64459	−	0.543441i	0.0839251	−	0.0277324i
$385$	−0.249216	+	0.304371i	−0.0127012	+	0.0155122i
$386$		−	1.37905i		−	0.0701916i
$387$	5.10076	+	6.87533i	0.259286	+	0.349493i
$388$	−5.48096			−0.278253
$389$			19.5795i			0.992719i	0.868117	+	0.496360i	$0.165330\pi$
$389$			19.5795i			0.992719i	−0.868117	+	0.496360i	$0.834670\pi$
$390$	0.178116	−	0.0588571i	0.00901927	−	0.00298034i
$391$			0.555074i			0.0280713i
$392$	1.00000			0.0505076
$393$	3.73072	−	1.23279i	0.188190	−	0.0621859i
$394$	18.6091			0.937515
$395$	−0.514900			−0.0259074
$396$	−0.475441	+	9.93851i	−0.0238918	+	0.499429i
$397$	−23.8328			−1.19613			−0.598067	−	0.801446i	$-0.704064\pi$
$397$	−23.8328			−1.19613			−0.598067	+	0.801446i	$0.704064\pi$
$398$	−11.5227			−0.577581
$399$	12.6691	−	4.18639i	0.634246	−	0.209582i
$400$	4.98593			0.249297
$401$			8.49515i			0.424228i	0.977245	+	0.212114i	$0.0680348\pi$
$401$			8.49515i			0.424228i	−0.977245	+	0.212114i	$0.931965\pi$
$402$	−3.31808	+	1.09643i	−0.165491	+	0.0546851i
$403$		−	7.98569i		−	0.397795i
$404$	−6.44547			−0.320674
$405$	1.02162	+	0.309556i	0.0507645	+	0.0153819i
$406$			3.20881i			0.159251i
$407$	−8.69631	+	10.6209i	−0.431060	+	0.526460i
$408$	0.665040	−	0.219757i	0.0329244	−	0.0108796i
$409$		−	11.3806i		−	0.562734i	−0.959600	−	0.281367i	$-0.909212\pi$
$409$		−	11.3806i		−	0.562734i	0.959600	−	0.281367i	$-0.0907878\pi$
$410$		−	1.44265i		−	0.0712474i
$411$	−7.97895	−	24.1463i	−0.393573	−	1.19105i
$412$	−6.88546			−0.339222
$413$	−5.49147			−0.270218
$414$	−2.45358	−	3.30719i	−0.120587	−	0.162540i
$415$		−	0.0830359i		−	0.00407607i
$416$			0.913118i			0.0447693i
$417$	8.29158	+	25.0924i	0.406040	+	1.22878i
$418$	−19.7684	−	16.1862i	−0.966903	−	0.791691i
$419$		−	21.4535i		−	1.04807i	−0.851696	−	0.524036i	$-0.824426\pi$
$419$		−	21.4535i		−	1.04807i	0.851696	−	0.524036i	$-0.175574\pi$
$420$	−0.195064	+	0.0644573i	−0.00951814	+	0.00314519i
$421$	−13.4081			−0.653470			−0.326735	−	0.945116i	$-0.605948\pi$
$421$	−13.4081			−0.653470			−0.326735	+	0.945116i	$0.605948\pi$
$422$		−	4.45606i		−	0.216918i
$423$	−18.5100	−	24.9497i	−0.899986	−	1.21310i
$424$			8.81869i			0.428273i
$425$	2.01621			0.0978007
$426$	7.72541	+	23.3790i	0.374297	+	1.13272i
$427$	−7.30675			−0.353599
$428$	−1.32477			−0.0640351
$429$	−4.89625	−	1.88190i	−0.236393	−	0.0908592i
$430$	0.338465			0.0163223
$431$	−34.8775			−1.67999			−0.839996	−	0.542593i	$-0.817443\pi$
$431$	−34.8775			−1.67999			−0.839996	+	0.542593i	$0.817443\pi$
$432$	−2.99099	+	4.24900i	−0.143904	+	0.204430i
$433$	−11.8022			−0.567180			−0.283590	−	0.958946i	$-0.591525\pi$
$433$	−11.8022			−0.567180			−0.283590	+	0.958946i	$0.591525\pi$
$434$			8.74552i			0.419798i
$435$	−0.206831	−	0.625924i	−0.00991681	−	0.0300107i
$436$			11.5849i			0.554815i
$437$	10.5742			0.505833
$438$	6.40383	+	19.3796i	0.305987	+	0.925992i
$439$			15.8251i			0.755291i	0.925950	+	0.377645i	$0.123266\pi$
$439$			15.8251i			0.755291i	−0.925950	+	0.377645i	$0.876734\pi$
$440$	0.304371	+	0.249216i	0.0145103	+	0.0118809i
$441$	−2.40934	+	1.78747i	−0.114731	+	0.0851178i
$442$			0.369247i			0.0175633i
$443$		−	12.2185i		−	0.580520i	−0.956948	−	0.290260i	$-0.906258\pi$
$443$		−	12.2185i		−	0.580520i	0.956948	−	0.290260i	$-0.0937418\pi$
$444$	−6.80669	+	2.24922i	−0.323031	+	0.106743i
$445$	1.27530			0.0604552
$446$	10.4573			0.495167
$447$	−33.0164	+	10.9100i	−1.56162	+	0.516025i
$448$		−	1.00000i		−	0.0472456i
$449$		−	25.9020i		−	1.22239i	−0.791479	−	0.611196i	$-0.790689\pi$
$449$		−	25.9020i		−	1.22239i	0.791479	−	0.611196i	$-0.209311\pi$
$450$	−12.0128	+	8.91222i	−0.566290	+	0.420126i
$451$	−25.5563	+	31.2123i	−1.20340	+	1.46973i
$452$		−	15.5818i		−	0.732904i
$453$	6.38844	+	19.3330i	0.300155	+	0.908344i
$454$	5.78740			0.271616
$455$		−	0.108304i		−	0.00507739i
$456$	−4.18639	−	12.6691i	−0.196046	−	0.593283i
$457$			10.3890i			0.485977i	0.970029	+	0.242988i	$0.0781277\pi$
$457$			10.3890i			0.485977i	−0.970029	+	0.242988i	$0.921872\pi$
$458$	−7.53283			−0.351986
$459$	−1.20950	+	1.71821i	−0.0564546	+	0.0801992i
$460$	−0.162810			−0.00759104
$461$	−15.9146			−0.741215			−0.370607	−	0.928790i	$-0.620850\pi$
$461$	−15.9146			−0.741215			−0.370607	+	0.928790i	$0.620850\pi$
$462$	5.36213	+	2.06097i	0.249469	+	0.0958848i
$463$	−6.33871			−0.294585			−0.147292	−	0.989093i	$-0.547056\pi$
$463$	−6.33871			−0.294585			−0.147292	+	0.989093i	$0.547056\pi$
$464$	3.20881			0.148965
$465$	−0.563712	−	1.70593i	−0.0261415	−	0.0791108i
$466$	−17.3347			−0.803014
$467$			7.94706i			0.367746i	0.982950	+	0.183873i	$0.0588635\pi$
$467$			7.94706i			0.367746i	−0.982950	+	0.183873i	$0.941136\pi$
$468$	−1.63217	−	2.20001i	−0.0754473	−	0.101696i
$469$			2.01758i			0.0931630i
$470$	−1.22825			−0.0566548
$471$	−29.1098	+	9.61911i	−1.34131	+	0.443225i
$472$			5.49147i			0.252765i
$473$	−7.32282	−	5.99586i	−0.336704	−	0.275690i
$474$	2.35915	+	7.13938i	0.108359	+	0.327923i
$475$		−	38.4090i		−	1.76233i
$476$		−	0.404381i		−	0.0185348i
$477$	−15.7632	−	21.2472i	−0.721746	−	0.972845i
$478$	−12.0373			−0.550576
$479$	−21.7287			−0.992808			−0.496404	−	0.868092i	$-0.665347\pi$
$479$	−21.7287			−0.992808			−0.496404	+	0.868092i	$0.665347\pi$
$480$	0.0644573	+	0.195064i	0.00294206	+	0.00890341i
$481$		−	3.77925i		−	0.172319i
$482$		−	24.9447i		−	1.13620i
$483$	−2.25745	+	0.745956i	−0.102718	+	0.0339422i
$484$	−2.17036	−	10.7838i	−0.0986526	−	0.490171i
$485$		−	0.650094i		−	0.0295192i
$486$	−0.388643	−	15.5836i	−0.0176292	−	0.706887i
$487$	7.48422			0.339142			0.169571	−	0.985518i	$-0.445762\pi$
$487$	7.48422			0.339142			0.169571	+	0.985518i	$0.445762\pi$
$488$			7.30675i			0.330761i
$489$	17.9686	−	5.93757i	0.812567	−	0.268506i
$490$			0.118610i			0.00535823i
$491$	39.2685			1.77216			0.886082	−	0.463529i	$-0.153417\pi$
$491$	39.2685			1.77216			0.886082	+	0.463529i	$0.153417\pi$
$492$	−20.0032	+	6.60988i	−0.901812	+	0.297997i
$493$	1.29758			0.0584402
$494$	7.03419			0.316483
$495$	−1.17880	−	0.0563918i	−0.0529832	−	0.00253462i
$496$	8.74552			0.392685
$497$	14.2157			0.637663
$498$	−1.15134	+	0.380451i	−0.0515928	+	0.0170484i
$499$	24.1232			1.07990			0.539950	−	0.841697i	$-0.318443\pi$
$499$	24.1232			1.07990			0.539950	+	0.841697i	$0.318443\pi$
$500$			1.18443i			0.0529692i
$501$	6.40037	−	2.11495i	0.285947	−	0.0944890i
$502$		−	11.3136i		−	0.504949i
$503$	38.8817			1.73365			0.866825	−	0.498612i	$-0.166157\pi$
$503$	38.8817			1.73365			0.866825	+	0.498612i	$0.166157\pi$
$504$	1.78747	+	2.40934i	0.0796204	+	0.107321i
$505$		−	0.764494i		−	0.0340195i
$506$	3.52245	+	2.88415i	0.156592	+	0.128216i
$507$	−20.0084	+	6.61162i	−0.888605	+	0.293632i
$508$			7.47768i			0.331768i
$509$			9.25429i			0.410189i	0.978742	+	0.205095i	$0.0657502\pi$
$509$			9.25429i			0.410189i	−0.978742	+	0.205095i	$0.934250\pi$
$510$	0.0260653	+	0.0788800i	0.00115419	+	0.00349287i
$511$	11.7838			0.521287
$512$	−1.00000			−0.0441942
$513$	32.7321	+	23.0411i	1.44516	+	1.01729i
$514$			24.6477i			1.08717i
$515$		−	0.816682i		−	0.0359873i
$516$	−1.55077	−	4.69302i	−0.0682688	−	0.206599i
$517$	26.5736	+	21.7582i	1.16871	+	0.956924i
$518$			4.13884i			0.181850i
$519$	24.7370	−	8.17413i	1.08583	−	0.358804i
$520$	−0.108304			−0.00474946
$521$			8.91059i			0.390380i	0.980765	+	0.195190i	$0.0625324\pi$
$521$			8.91059i			0.390380i	−0.980765	+	0.195190i	$0.937468\pi$
$522$	−7.73114	+	5.73567i	−0.338383	+	0.251044i
$523$			40.3572i			1.76470i	0.470596	+	0.882349i	$0.344039\pi$
$523$			40.3572i			1.76470i	−0.470596	+	0.882349i	$0.655961\pi$
$524$	−2.26848			−0.0990992
$525$	2.70956	+	8.19981i	0.118255	+	0.357869i
$526$	−18.0728			−0.788010
$527$	3.53652			0.154053
$528$	2.06097	−	5.36213i	0.0896920	−	0.233357i
$529$	21.1158			0.918079
$530$	−1.04598			−0.0454345
$531$	−9.81586	−	13.2308i	−0.425972	−	0.574170i
$532$	−7.70348			−0.333988
$533$		−	11.1063i		−	0.481066i
$534$	−5.84314	−	17.6828i	−0.252858	−	0.765210i
$535$		−	0.157130i		−	0.00679333i
$536$	2.01758			0.0871460
$537$	2.40667	+	7.28320i	0.103856	+	0.314293i
$538$		−	8.22269i		−	0.354505i
$539$	2.10115	−	2.56616i	0.0905028	−	0.110532i
$540$	−0.503971	−	0.354760i	−0.0216875	−	0.0152664i
$541$			11.8497i			0.509460i	0.967012	+	0.254730i	$0.0819866\pi$
$541$			11.8497i			0.509460i	−0.967012	+	0.254730i	$0.918013\pi$
$542$		−	12.2822i		−	0.527567i
$543$	15.7118	−	5.19182i	0.674256	−	0.222802i
$544$	−0.404381			−0.0173377
$545$	−1.37408			−0.0588590
$546$	−1.50170	+	0.496226i	−0.0642670	+	0.0212365i
$547$		−	34.3815i		−	1.47005i	−0.678042	−	0.735023i	$-0.737171\pi$
$547$		−	34.3815i		−	1.47005i	0.678042	−	0.735023i	$-0.262829\pi$
$548$			14.6823i			0.627196i
$549$	−13.0606	−	17.6045i	−0.557414	−	0.751341i
$550$	10.4762	−	12.7947i	0.446706	−	0.545568i
$551$		−	24.7191i		−	1.05307i
$552$	0.745956	+	2.25745i	0.0317500	+	0.0960835i
$553$	4.34114			0.184604
$554$			27.2430i			1.15745i
$555$	−0.266778	−	0.807338i	−0.0113241	−	0.0342696i
$556$		−	15.2576i		−	0.647064i
$557$	−19.0572			−0.807478			−0.403739	−	0.914874i	$-0.632290\pi$
$557$	−19.0572			−0.807478			−0.403739	+	0.914874i	$0.632290\pi$
$558$	−21.0710	+	15.6324i	−0.892005	+	0.661772i
$559$	2.60568			0.110209
$560$	0.118610			0.00501217
$561$	0.833415	−	2.16834i	0.0351868	−	0.0915474i
$562$	23.1187			0.975202
$563$	36.5587			1.54076			0.770382	−	0.637583i	$-0.220066\pi$
$563$	36.5587			1.54076			0.770382	+	0.637583i	$0.220066\pi$
$564$	5.62754	+	17.0304i	0.236962	+	0.717107i
$565$	1.84814			0.0777520
$566$		−	8.26048i		−	0.347214i
$567$	−8.61328	−	2.60987i	−0.361724	−	0.109604i
$568$		−	14.2157i		−	0.596479i
$569$	−31.4344			−1.31780			−0.658899	−	0.752231i	$-0.728978\pi$
$569$	−31.4344			−1.31780			−0.658899	+	0.752231i	$0.728978\pi$
$570$	1.50267	−	0.496546i	0.0629400	−	0.0207980i
$571$		−	12.2759i		−	0.513731i	−0.966447	−	0.256865i	$-0.917310\pi$
$571$		−	12.2759i		−	0.513731i	0.966447	−	0.256865i	$-0.0826897\pi$
$572$	2.34321	+	1.91860i	0.0979744	+	0.0802205i
$573$	1.58657	+	4.80136i	0.0662800	+	0.200580i
$574$			12.1630i			0.507675i
$575$			6.84396i			0.285413i
$576$	2.40934	−	1.78747i	0.100389	−	0.0744781i
$577$	16.7874			0.698870			0.349435	−	0.936961i	$-0.386374\pi$
$577$	16.7874			0.698870			0.349435	+	0.936961i	$0.386374\pi$
$578$	16.8365			0.700305
$579$	−0.749431	−	2.26796i	−0.0311453	−	0.0942534i
$580$			0.380596i			0.0158034i
$581$			0.700078i			0.0290441i
$582$	−9.01392	+	2.97858i	−0.373639	+	0.123466i
$583$	22.6302	+	18.5294i	0.937246	+	0.767408i
$584$		−	11.7838i		−	0.487619i
$585$	0.260943	−	0.193591i	0.0107886	−	0.00800402i
$586$	16.2502			0.671290
$587$			23.6991i			0.978165i	0.872238	+	0.489082i	$0.162668\pi$
$587$			23.6991i			0.978165i	−0.872238	+	0.489082i	$0.837332\pi$
$588$	1.64459	−	0.543441i	0.0678217	−	0.0224111i
$589$		−	67.3709i		−	2.77597i
$590$	−0.651341			−0.0268153
$591$	30.6044	−	10.1130i	1.25890	−	0.415992i
$592$	4.13884			0.170105
$593$	16.9830			0.697408			0.348704	−	0.937233i	$-0.386622\pi$
$593$	16.9830			0.697408			0.348704	+	0.937233i	$0.386622\pi$
$594$	4.61909	+	16.6031i	0.189524	+	0.681235i
$595$	0.0479634			0.00196631
$596$	20.0758			0.822336
$597$	−18.9501	+	6.26192i	−0.775577	+	0.256283i
$598$	−1.25339			−0.0512551
$599$			9.37140i			0.382905i	0.981502	+	0.191452i	$0.0613198\pi$
$599$			9.37140i			0.382905i	−0.981502	+	0.191452i	$0.938680\pi$
$600$	8.19981	−	2.70956i	0.334756	−	0.110617i
$601$		−	23.6313i		−	0.963940i	−0.876188	−	0.481970i	$-0.839921\pi$
$601$		−	23.6313i		−	0.963940i	0.876188	−	0.481970i	$-0.160079\pi$
$602$	−2.85361			−0.116305
$603$	−4.86103	+	3.60636i	−0.197957	+	0.146863i
$604$		−	11.7555i		−	0.478326i
$605$	1.27906	−	0.257425i	0.0520011	−	0.0104658i
$606$	−10.6001	+	3.50273i	−0.430601	+	0.142289i
$607$		−	40.2500i		−	1.63370i	−0.576853	−	0.816848i	$-0.695720\pi$
$607$		−	40.2500i		−	1.63370i	0.576853	−	0.816848i	$-0.304280\pi$
$608$			7.70348i			0.312418i
$609$	1.74380	+	5.27718i	0.0706624	+	0.213842i
$610$	−0.866650			−0.0350896
$611$	−9.45569			−0.382536
$612$	0.974292	−	0.722820i	0.0393834	−	0.0292183i
$613$			13.9207i			0.562253i	0.959671	+	0.281126i	$0.0907080\pi$
$613$			13.9207i			0.562253i	−0.959671	+	0.281126i	$0.909292\pi$
$614$		−	10.5059i		−	0.423982i
$615$	−0.783995	−	2.37257i	−0.0316137	−	0.0956711i
$616$	−2.56616	−	2.10115i	−0.103394	−	0.0846576i
$617$		−	22.8716i		−	0.920776i	−0.887718	−	0.460388i	$-0.847710\pi$
$617$		−	22.8716i		−	0.920776i	0.887718	−	0.460388i	$-0.152290\pi$
$618$	−11.3238	+	3.74184i	−0.455508	+	0.150519i
$619$	37.5142			1.50782			0.753912	−	0.656975i	$-0.228165\pi$
$619$	37.5142			1.50782			0.753912	+	0.656975i	$0.228165\pi$
$620$			1.03730i			0.0416590i
$621$	−5.83240	−	4.10559i	−0.234046	−	0.164752i
$622$			7.32826i			0.293836i
$623$	−10.7521			−0.430775
$624$	0.496226	+	1.50170i	0.0198649	+	0.0601162i
$625$	24.7892			0.991567
$626$	−18.8781			−0.754523
$627$	−41.3071	−	15.8766i	−1.64965	−	0.634051i
$628$	17.7004			0.706322
$629$	1.67367			0.0667335
$630$	−0.285771	+	0.212011i	−0.0113854	+	0.00844674i
$631$	−30.9362			−1.23155			−0.615775	−	0.787922i	$-0.711157\pi$
$631$	−30.9362			−1.23155			−0.615775	+	0.787922i	$0.711157\pi$
$632$		−	4.34114i		−	0.172681i
$633$	−2.42161	−	7.32839i	−0.0962502	−	0.291277i
$634$		−	25.1264i		−	0.997897i
$635$	−0.886924			−0.0351965
$636$	4.79244	+	14.5031i	0.190032	+	0.575086i
$637$			0.913118i			0.0361790i
$638$	6.74219	−	8.23433i	0.266926	−	0.326000i
$639$	25.4102	+	34.2506i	1.00521	+	1.35493i
$640$		−	0.118610i		−	0.00468845i
$641$			7.09428i			0.280207i	0.990137	+	0.140104i	$0.0447436\pi$
$641$			7.09428i			0.280207i	−0.990137	+	0.140104i	$0.955256\pi$
$642$	−2.17870	+	0.719934i	−0.0859864	+	0.0284135i
$643$	−3.26857			−0.128900			−0.0644499	−	0.997921i	$-0.520529\pi$
$643$	−3.26857			−0.128900			−0.0644499	+	0.997921i	$0.520529\pi$
$644$	1.37265			0.0540901
$645$	0.556636	−	0.183936i	0.0219175	−	0.00724247i
$646$			3.11514i			0.122564i
$647$		−	13.1991i		−	0.518910i	−0.965755	−	0.259455i	$-0.916457\pi$
$647$		−	13.1991i		−	0.518910i	0.965755	−	0.259455i	$-0.0835429\pi$
$648$	−2.60987	+	8.61328i	−0.102525	+	0.338362i
$649$	14.0920	+	11.5384i	0.553159	+	0.452922i
$650$			4.55274i			0.178573i
$651$	4.75267	+	14.3828i	0.186272	+	0.563705i
$652$	−10.9259			−0.427891
$653$			48.7540i			1.90789i	0.299980	+	0.953945i	$0.403020\pi$
$653$			48.7540i			1.90789i	−0.299980	+	0.953945i	$0.596980\pi$
$654$	6.29570	+	19.0524i	0.246181	+	0.745006i
$655$		−	0.269064i		−	0.0105132i
$656$	12.1630			0.474886
$657$	21.0633	+	28.3913i	0.821758	+	1.10765i
$658$	10.3554			0.403695
$659$	8.53676			0.332545			0.166272	−	0.986080i	$-0.446827\pi$
$659$	8.53676			0.332545			0.166272	+	0.986080i	$0.446827\pi$
$660$	0.635999	+	0.244450i	0.0247562	+	0.00951521i
$661$	0.899894			0.0350018			0.0175009	−	0.999847i	$-0.494429\pi$
$661$	0.899894			0.0350018			0.0175009	+	0.999847i	$0.494429\pi$
$662$	−22.5329			−0.875766
$663$	0.200664	+	0.607260i	0.00779315	+	0.0235840i
$664$	0.700078			0.0271683
$665$		−	0.913706i		−	0.0354320i
$666$	−9.97189	+	7.39807i	−0.386403	+	0.286669i
$667$			4.40459i			0.170546i
$668$	−3.89177			−0.150577
$669$	17.1980	−	5.68293i	0.664911	−	0.219715i
$670$			0.239304i			0.00924511i
$671$	18.7503	+	15.3526i	0.723847	+	0.592679i
$672$	−0.543441	−	1.64459i	−0.0209637	−	0.0634414i
$673$		−	22.2082i		−	0.856062i	−0.903764	−	0.428031i	$-0.859207\pi$
$673$		−	22.2082i		−	0.856062i	0.903764	−	0.428031i	$-0.140793\pi$
$674$		−	1.86013i		−	0.0716496i
$675$	−14.9129	+	21.1852i	−0.573997	+	0.815419i
$676$	12.1662			0.467931
$677$	16.5325			0.635394			0.317697	−	0.948192i	$-0.397091\pi$
$677$	16.5325			0.635394			0.317697	+	0.948192i	$0.397091\pi$
$678$	−8.46777	−	25.6256i	−0.325203	−	0.984145i
$679$			5.48096i			0.210340i
$680$		−	0.0479634i		−	0.00183931i
$681$	9.51789	−	3.14511i	0.364726	−	0.120521i
$682$	18.3756	−	22.4424i	0.703639	−	0.859364i
$683$		−	20.8460i		−	0.797649i	−0.917027	−	0.398824i	$-0.869418\pi$
$683$		−	20.8460i		−	0.797649i	0.917027	−	0.398824i	$-0.130582\pi$
$684$	−13.7698	−	18.5603i	−0.526501	−	0.709672i
$685$	−1.74146			−0.0665377
$686$		−	1.00000i		−	0.0381802i
$687$	−12.3884	+	4.09365i	−0.472647	+	0.156183i
$688$			2.85361i			0.108793i
$689$	−8.05250			−0.306776
$690$	−0.267755	+	0.0884775i	−0.0101933	+	0.00336828i
$691$	23.4259			0.891164			0.445582	−	0.895241i	$-0.352997\pi$
$691$	23.4259			0.891164			0.445582	+	0.895241i	$0.352997\pi$
$692$	−15.0414			−0.571789
$693$	9.93851	+	0.475441i	0.377533	+	0.0180605i
$694$	−27.3110			−1.03671
$695$	1.80969			0.0686455
$696$	5.27718	−	1.74380i	0.200031	−	0.0660986i
$697$	4.91849			0.186301
$698$		−	3.59647i		−	0.136128i
$699$	−28.5084	+	9.42039i	−1.07829	+	0.356312i
$700$		−	4.98593i		−	0.188451i
$701$	−35.8804			−1.35518			−0.677591	−	0.735439i	$-0.736976\pi$
$701$	−35.8804			−1.35518			−0.677591	+	0.735439i	$0.736976\pi$
$702$	−3.87983	−	2.73113i	−0.146435	−	0.103080i
$703$		−	31.8835i		−	1.20251i
$704$	−2.10115	+	2.56616i	−0.0791900	+	0.0967158i
$705$	−2.01996	+	0.667480i	−0.0760762	+	0.0251388i
$706$			10.4939i			0.394942i
$707$			6.44547i			0.242407i
$708$	2.98429	+	9.03121i	0.112157	+	0.339414i
$709$	−13.6999			−0.514512			−0.257256	−	0.966343i	$-0.582818\pi$
$709$	−13.6999			−0.514512			−0.257256	+	0.966343i	$0.582818\pi$
$710$	1.68612			0.0632790
$711$	7.75967	+	10.4593i	0.291010	+	0.392254i
$712$			10.7521i			0.402953i
$713$			12.0046i			0.449574i
$714$	−0.219757	−	0.665040i	−0.00822420	−	0.0248885i
$715$	−0.227564	+	0.277927i	−0.00851040	+	0.0103939i
$716$		−	4.42858i		−	0.165504i
$717$	−19.7965	+	6.54159i	−0.739313	+	0.244300i
$718$	−7.78386			−0.290491
$719$			31.0063i			1.15634i	0.815917	+	0.578169i	$0.196233\pi$
$719$			31.0063i			1.15634i	−0.815917	+	0.578169i	$0.803767\pi$
$720$	0.212011	+	0.285771i	0.00790120	+	0.0106501i
$721$			6.88546i			0.256428i
$722$	40.3437			1.50144
$723$	−13.5560	−	41.0238i	−0.504152	−	1.52569i
$724$	−9.55361			−0.355057
$725$	15.9989			0.594185
$726$	−9.42969	−	16.5554i	−0.349968	−	0.614428i
$727$	0.0445612			0.00165268			0.000826341	−	1.00000i	$-0.499737\pi$
$727$	0.0445612			0.00165268			0.000826341		1.00000i	$0.499737\pi$
$728$	0.913118			0.0338424
$729$	−9.10793	−	25.4174i	−0.337331	−	0.941386i
$730$	1.39768			0.0517303
$731$			1.15394i			0.0426802i
$732$	3.97079	+	12.0166i	0.146765	+	0.444146i
$733$			2.79394i			0.103196i	0.998668	+	0.0515982i	$0.0164315\pi$
$733$			2.79394i			0.103196i	−0.998668	+	0.0515982i	$0.983568\pi$
$734$	−5.02069			−0.185317
$735$	0.0644573	+	0.195064i	0.00237754	+	0.00719504i
$736$		−	1.37265i		−	0.0505967i
$737$	4.23922	−	5.17742i	0.156154	−	0.190713i
$738$	−29.3049	+	21.7411i	−1.07873	+	0.800300i
$739$		−	43.5261i		−	1.60113i	−0.599244	−	0.800566i	$-0.704532\pi$
$739$		−	43.5261i		−	1.60113i	0.599244	−	0.800566i	$-0.295468\pi$
$740$			0.490906i			0.0180461i
$741$	11.5683	−	3.82267i	0.424974	−	0.140429i
$742$	8.81869			0.323744
$743$	−7.61997			−0.279550			−0.139775	−	0.990183i	$-0.544638\pi$
$743$	−7.61997			−0.279550			−0.139775	+	0.990183i	$0.544638\pi$
$744$	14.3828	−	4.75267i	0.527298	−	0.174241i
$745$			2.38118i			0.0872396i
$746$		−	35.0542i		−	1.28343i
$747$	−1.68673	+	1.25137i	−0.0617141	+	0.0457853i
$748$	−0.849663	+	1.03771i	−0.0310668	+	0.0379423i
$749$			1.32477i			0.0484060i
$750$	0.643666	+	1.94789i	0.0235034	+	0.0711270i
$751$	−19.2400			−0.702078			−0.351039	−	0.936361i	$-0.614172\pi$
$751$	−19.2400			−0.702078			−0.351039	+	0.936361i	$0.614172\pi$
$752$		−	10.3554i		−	0.377622i
$753$	−6.14826	−	18.6062i	−0.224055	−	0.678046i
$754$			2.93003i			0.106705i
$755$	1.39432			0.0507444
$756$	4.24900	+	2.99099i	0.154534	+	0.108781i
$757$	26.9612			0.979922			0.489961	−	0.871744i	$-0.337011\pi$
$757$	26.9612			0.979922			0.489961	+	0.871744i	$0.337011\pi$
$758$	21.9708			0.798015
$759$	7.36034	+	2.82899i	0.267164	+	0.102686i
$760$	−0.913706			−0.0331436
$761$	−37.3077			−1.35240			−0.676201	−	0.736717i	$-0.736375\pi$
$761$	−37.3077			−1.35240			−0.676201	+	0.736717i	$0.736375\pi$
$762$	4.06368	+	12.2977i	0.147212	+	0.445499i
$763$	11.5849			0.419401
$764$		−	2.91949i		−	0.105623i
$765$	0.0857333	+	0.115560i	0.00309969	+	0.00417809i
$766$			14.3769i			0.519458i
$767$	−5.01436			−0.181058
$768$	−1.64459	+	0.543441i	−0.0593440	+	0.0196097i
$769$			42.6052i			1.53638i	0.640221	+	0.768191i	$0.278843\pi$
$769$			42.6052i			1.53638i	−0.640221	+	0.768191i	$0.721157\pi$
$770$	0.249216	−	0.304371i	0.00898112	−	0.0109688i
$771$	13.3946	+	40.5354i	0.482395	+	1.45985i
$772$			1.37905i			0.0496330i
$773$			41.7823i			1.50281i	0.659844	+	0.751403i	$0.270622\pi$
$773$			41.7823i			1.50281i	−0.659844	+	0.751403i	$0.729378\pi$
$774$	−5.10076	−	6.87533i	−0.183343	−	0.247129i
$775$	43.6045			1.56632
$776$	5.48096			0.196755
$777$	2.24922	+	6.80669i	0.0806902	+	0.244189i
$778$		−	19.5795i		−	0.701959i
$779$		−	93.6976i		−	3.35707i
$780$	−0.178116	+	0.0588571i	−0.00637759	+	0.00210742i
$781$	−36.4798	−	29.8693i	−1.30535	−	1.06881i
$782$		−	0.555074i		−	0.0198494i
$783$	−9.59754	+	13.6342i	−0.342988	+	0.487248i
$784$	−1.00000			−0.0357143
$785$			2.09943i			0.0749319i
$786$	−3.73072	+	1.23279i	−0.133070	+	0.0439721i
$787$			23.9969i			0.855397i	0.903922	+	0.427698i	$0.140675\pi$
$787$			23.9969i			0.855397i	−0.903922	+	0.427698i	$0.859325\pi$
$788$	−18.6091			−0.662923
$789$	−29.7223	+	9.82149i	−1.05814	+	0.349654i
$790$	0.514900			0.0183193
$791$	−15.5818			−0.554024
$792$	0.475441	−	9.93851i	0.0168941	−	0.353150i
$793$	−6.67193			−0.236927
$794$	23.8328			0.845794
$795$	−1.72021	+	0.568429i	−0.0610095	+	0.0201601i
$796$	11.5227			0.408412
$797$			43.9574i			1.55705i	0.627614	+	0.778525i	$0.284032\pi$
$797$			43.9574i			1.55705i	−0.627614	+	0.778525i	$0.715968\pi$
$798$	−12.6691	+	4.18639i	−0.448480	+	0.148197i
$799$		−	4.18752i		−	0.148144i
$800$	−4.98593			−0.176279
$801$	−19.2191	−	25.9055i	−0.679075	−	0.915328i
$802$		−	8.49515i		−	0.299974i
$803$	−30.2392	−	24.7596i	−1.06712	−	0.873747i
$804$	3.31808	−	1.09643i	0.117020	−	0.0386682i
$805$			0.162810i			0.00573829i
$806$			7.98569i			0.281284i
$807$	−4.46855	−	13.5229i	−0.157300	−	0.476030i
$808$	6.44547			0.226751
$809$	56.5063			1.98666			0.993328	−	0.115322i	$-0.0367898\pi$
$809$	56.5063			1.98666			0.993328	+	0.115322i	$0.0367898\pi$
$810$	−1.02162	−	0.309556i	−0.0358960	−	0.0108767i
$811$			25.7590i			0.904521i	0.891886	+	0.452260i	$0.149382\pi$
$811$			25.7590i			0.904521i	−0.891886	+	0.452260i	$0.850618\pi$
$812$		−	3.20881i		−	0.112607i
$813$	−6.67468	−	20.1992i	−0.234091	−	0.708418i
$814$	8.69631	−	10.6209i	0.304806	−	0.372263i
$815$		−	1.29591i		−	0.0453939i
$816$	−0.665040	+	0.219757i	−0.0232810	+	0.00769303i
$817$	21.9827			0.769079
$818$			11.3806i			0.397913i
$819$	−2.20001	+	1.63217i	−0.0768747	+	0.0570328i
$820$			1.44265i			0.0503795i
$821$	−39.3526			−1.37341			−0.686707	−	0.726934i	$-0.740945\pi$
$821$	−39.3526			−1.37341			−0.686707	+	0.726934i	$0.740945\pi$
$822$	7.97895	+	24.1463i	0.278298	+	0.842199i
$823$	38.4208			1.33927			0.669633	−	0.742692i	$-0.266451\pi$
$823$	38.4208			1.33927			0.669633	+	0.742692i	$0.266451\pi$
$824$	6.88546			0.239867
$825$	10.2758	−	26.7352i	0.357759	−	0.930800i
$826$	5.49147			0.191073
$827$	44.6041			1.55104			0.775519	−	0.631324i	$-0.217488\pi$
$827$	44.6041			1.55104			0.775519	+	0.631324i	$0.217488\pi$
$828$	2.45358	+	3.30719i	0.0852679	+	0.114933i
$829$	−34.6669			−1.20403			−0.602015	−	0.798485i	$-0.705635\pi$
$829$	−34.6669			−1.20403			−0.602015	+	0.798485i	$0.705635\pi$
$830$			0.0830359i			0.00288222i
$831$	14.8050	+	44.8036i	0.513579	+	1.55422i
$832$		−	0.913118i		−	0.0316567i
$833$	−0.404381			−0.0140110
$834$	−8.29158	−	25.0924i	−0.287114	−	0.868879i
$835$		−	0.461601i		−	0.0159744i
$836$	19.7684	+	16.1862i	0.683704	+	0.559810i
$837$	−26.1578	+	37.1597i	−0.904145	+	1.28443i
$838$			21.4535i			0.741099i
$839$			13.2539i			0.457577i	0.973476	+	0.228788i	$0.0734764\pi$
$839$			13.2539i			0.457577i	−0.973476	+	0.228788i	$0.926524\pi$
$840$	0.195064	−	0.0644573i	0.00673034	−	0.00222399i
$841$	−18.7035			−0.644949
$842$	13.4081			0.462073
$843$	38.0207	−	12.5636i	1.30950	−	0.432715i
$844$			4.45606i			0.153384i
$845$			1.44303i			0.0496417i
$846$	18.5100	+	24.9497i	0.636387	+	0.857788i
$847$	−10.7838	+	2.17036i	−0.370534	+	0.0745744i
$848$		−	8.81869i		−	0.302835i
$849$	−4.48909	−	13.5851i	−0.154065	−	0.466239i
$850$	−2.01621			−0.0691556
$851$			5.68119i			0.194749i
$852$	−7.72541	−	23.3790i	−0.264668	−	0.800952i
$853$		−	55.0590i		−	1.88519i	−0.333945	−	0.942593i	$-0.608380\pi$
$853$		−	55.0590i		−	1.88519i	0.333945	−	0.942593i	$-0.391620\pi$
$854$	7.30675			0.250032
$855$	2.20143	−	1.63323i	0.0752874	−	0.0558552i
$856$	1.32477			0.0452797
$857$	−24.1166			−0.823808			−0.411904	−	0.911227i	$-0.635136\pi$
$857$	−24.1166			−0.823808			−0.411904	+	0.911227i	$0.635136\pi$
$858$	4.89625	+	1.88190i	0.167155	+	0.0642472i
$859$	−26.9578			−0.919787			−0.459894	−	0.887974i	$-0.652113\pi$
$859$	−26.9578			−0.919787			−0.459894	+	0.887974i	$0.652113\pi$
$860$	−0.338465			−0.0115416
$861$	6.60988	+	20.0032i	0.225264	+	0.681706i
$862$	34.8775			1.18793
$863$		−	26.2227i		−	0.892631i	−0.894876	−	0.446316i	$-0.852736\pi$
$863$		−	26.2227i		−	0.892631i	0.894876	−	0.446316i	$-0.147264\pi$
$864$	2.99099	−	4.24900i	0.101756	−	0.144554i
$865$		−	1.78406i		−	0.0606597i
$866$	11.8022			0.401056
$867$	27.6891	−	9.14963i	0.940370	−	0.310738i
$868$		−	8.74552i		−	0.296842i
$869$	−11.1400	−	9.12137i	−0.377900	−	0.309421i
$870$	0.206831	+	0.625924i	0.00701224	+	0.0212208i
$871$			1.84228i			0.0624234i
$872$		−	11.5849i		−	0.392313i
$873$	−13.2055	+	9.79707i	−0.446939	+	0.331581i
$874$	−10.5742			−0.357678
$875$	1.18443			0.0400409
$876$	−6.40383	−	19.3796i	−0.216365	−	0.654775i
$877$		−	24.6717i		−	0.833105i	−0.909112	−	0.416553i	$-0.863238\pi$
$877$		−	24.6717i		−	0.833105i	0.909112	−	0.416553i	$-0.136762\pi$
$878$		−	15.8251i		−	0.534071i
$879$	26.7249	−	8.83103i	0.901409	−	0.297863i
$880$	−0.304371	−	0.249216i	−0.0102603	−	0.00840107i
$881$			22.0033i			0.741310i	0.928771	+	0.370655i	$0.120867\pi$
$881$			22.0033i			0.741310i	−0.928771	+	0.370655i	$0.879133\pi$
$882$	2.40934	−	1.78747i	0.0811268	−	0.0601874i
$883$	−41.1984			−1.38644			−0.693219	−	0.720727i	$-0.743808\pi$
$883$	−41.1984			−1.38644			−0.693219	+	0.720727i	$0.743808\pi$
$884$		−	0.369247i		−	0.0124191i
$885$	−1.07119	+	0.353965i	−0.0360076	+	0.0118984i
$886$			12.2185i			0.410490i
$887$	1.98579			0.0666764			0.0333382	−	0.999444i	$-0.489386\pi$
$887$	1.98579			0.0666764			0.0333382	+	0.999444i	$0.489386\pi$
$888$	6.80669	−	2.24922i	0.228418	−	0.0754787i
$889$	7.47768			0.250793
$890$	−1.27530			−0.0427483
$891$	16.6193	+	24.7951i	0.556768	+	0.830668i
$892$	−10.4573			−0.350136
$893$	−79.7726			−2.66949
$894$	33.0164	−	10.9100i	1.10423	−	0.364885i
$895$	0.525272			0.0175579
$896$			1.00000i			0.0334077i
$897$	−2.06132	+	0.681146i	−0.0688254	+	0.0227428i
$898$			25.9020i			0.864361i
$899$	28.0627			0.935945
$900$	12.0128	−	8.91222i	0.400427	−	0.297074i
$901$		−	3.56611i		−	0.118804i
$902$	25.5563	−	31.2123i	0.850932	−	1.03925i
$903$	−4.69302	+	1.55077i	−0.156174	+	0.0516064i
$904$			15.5818i			0.518242i
$905$		−	1.13315i		−	0.0376671i
$906$	−6.38844	−	19.3330i	−0.212242	−	0.642296i
$907$	−12.9729			−0.430759			−0.215380	−	0.976530i	$-0.569099\pi$
$907$	−12.9729			−0.430759			−0.215380	+	0.976530i	$0.569099\pi$
$908$	−5.78740			−0.192062
$909$	−15.5293	+	11.5211i	−0.515076	+	0.382131i
$910$			0.108304i			0.00359026i
$911$			41.2945i			1.36815i	0.729412	+	0.684074i	$0.239794\pi$
$911$			41.2945i			1.36815i	−0.729412	+	0.684074i	$0.760206\pi$
$912$	4.18639	+	12.6691i	0.138625	+	0.419515i
$913$	1.47097	−	1.79651i	0.0486819	−	0.0594558i
$914$		−	10.3890i		−	0.343637i
$915$	−1.42528	+	0.470973i	−0.0471184	+	0.0155699i
$916$	7.53283			0.248892
$917$			2.26848i			0.0749119i
$918$	1.20950	−	1.71821i	0.0399194	−	0.0567094i
$919$		−	10.8833i		−	0.359007i	−0.983757	−	0.179503i	$-0.942551\pi$
$919$		−	10.8833i		−	0.359007i	0.983757	−	0.179503i	$-0.0574491\pi$
$920$	0.162810			0.00536768
$921$	−5.70931	−	17.2778i	−0.188128	−	0.569323i
$922$	15.9146			0.524118
$923$	12.9806			0.427263
$924$	−5.36213	−	2.06097i	−0.176401	−	0.0678008i
$925$	20.6360			0.678507
$926$	6.33871			0.208303
$927$	−16.5894	+	12.3076i	−0.544869	+	0.404234i
$928$	−3.20881			−0.105335
$929$			42.1657i			1.38341i	0.722180	+	0.691706i	$0.243140\pi$
$929$			42.1657i			1.38341i	−0.722180	+	0.691706i	$0.756860\pi$
$930$	0.563712	+	1.70593i	0.0184849	+	0.0559398i
$931$			7.70348i			0.252471i
$932$	17.3347			0.567817
$933$	3.98248	+	12.0520i	0.130380	+	0.394564i
$934$		−	7.94706i		−	0.260036i
$935$	−0.123082	−	0.100778i	−0.00402520	−	0.00329580i
$936$	1.63217	+	2.20001i	0.0533493	+	0.0719097i
$937$			11.0048i			0.359510i	0.983711	+	0.179755i	$0.0575305\pi$
$937$			11.0048i			0.359510i	−0.983711	+	0.179755i	$0.942470\pi$
$938$		−	2.01758i		−	0.0658762i
$939$	−31.0468	+	10.2592i	−1.01317	+	0.334795i
$940$	1.22825			0.0400610
$941$	−43.3691			−1.41379			−0.706897	−	0.707317i	$-0.749905\pi$
$941$	−43.3691			−1.41379			−0.706897	+	0.707317i	$0.749905\pi$
$942$	29.1098	−	9.61911i	0.948449	−	0.313408i
$943$			16.6956i			0.543684i
$944$		−	5.49147i		−	0.178732i
$945$	−0.354760	+	0.503971i	−0.0115403	+	0.0163942i
$946$	7.32282	+	5.99586i	0.238086	+	0.194942i
$947$		−	16.8067i		−	0.546143i	−0.961994	−	0.273071i	$-0.911960\pi$
$947$		−	16.8067i		−	0.546143i	0.961994	−	0.273071i	$-0.0880395\pi$
$948$	−2.35915	−	7.13938i	−0.0766217	−	0.231876i
$949$	10.7600			0.349286
$950$			38.4090i			1.24615i
$951$	−13.6547	−	41.3226i	−0.442785	−	1.33998i
$952$			0.404381i			0.0131060i
$953$	−14.7778			−0.478700			−0.239350	−	0.970933i	$-0.576934\pi$
$953$	−14.7778			−0.478700			−0.239350	+	0.970933i	$0.576934\pi$
$954$	15.7632	+	21.2472i	0.510352	+	0.687905i
$955$	0.346279			0.0112053
$956$	12.0373			0.389316
$957$	6.61326	−	17.2061i	0.213776	−	0.556193i
$958$	21.7287			0.702021
$959$	14.6823			0.474115
$960$	−0.0644573	−	0.195064i	−0.00208035	−	0.00629566i
$961$	45.4841			1.46723
$962$			3.77925i			0.121848i
$963$	−3.19182	+	2.36799i	−0.102855	+	0.0763074i
$964$			24.9447i			0.803415i
$965$	−0.163568			−0.00526544
$966$	2.25745	−	0.745956i	0.0726323	−	0.0240007i
$967$		−	19.5588i		−	0.628968i	−0.949263	−	0.314484i	$-0.898169\pi$
$967$		−	19.5588i		−	0.628968i	0.949263	−	0.314484i	$-0.101831\pi$
$968$	2.17036	+	10.7838i	0.0697580	+	0.346603i
$969$	1.69289	+	5.12312i	0.0543836	+	0.164578i
$970$			0.650094i			0.0208733i
$971$		−	28.1654i		−	0.903870i	−0.892051	−	0.451935i	$-0.850734\pi$
$971$		−	28.1654i		−	0.903870i	0.892051	−	0.451935i	$-0.149266\pi$
$972$	0.388643	+	15.5836i	0.0124657	+	0.499845i
$973$	−15.2576			−0.489135
$974$	−7.48422			−0.239810
$975$	2.47415	+	7.48739i	0.0792361	+	0.239788i
$976$		−	7.30675i		−	0.233883i
$977$		−	29.4997i		−	0.943779i	−0.881658	−	0.471889i	$-0.843572\pi$
$977$		−	29.4997i		−	0.943779i	0.881658	−	0.471889i	$-0.156428\pi$
$978$	−17.9686	+	5.93757i	−0.574572	+	0.189863i
$979$	27.5917	+	22.5918i	0.881833	+	0.722037i
$980$		−	0.118610i		−	0.00378884i
$981$	20.7077	+	27.9119i	0.661145	+	0.891160i
$982$	−39.2685			−1.25311
$983$			27.1328i			0.865403i	0.901537	+	0.432702i	$0.142440\pi$
$983$			27.1328i			0.865403i	−0.901537	+	0.432702i	$0.857560\pi$
$984$	20.0032	−	6.60988i	0.637678	−	0.210715i
$985$		−	2.20722i		−	0.0703279i
$986$	−1.29758			−0.0413234
$987$	17.0304	−	5.62754i	0.542082	−	0.179127i
$988$	−7.03419			−0.223787
$989$	−3.91702			−0.124554
$990$	1.17880	+	0.0563918i	0.0374648	+	0.00179225i
$991$	−37.4980			−1.19116			−0.595581	−	0.803295i	$-0.703078\pi$
$991$	−37.4980			−1.19116			−0.595581	+	0.803295i	$0.703078\pi$
$992$	−8.74552			−0.277670
$993$	−37.0573	+	12.2453i	−1.17598	+	0.388593i
$994$	−14.2157			−0.450896
$995$			1.36670i			0.0433274i
$996$	1.15134	−	0.380451i	0.0364816	−	0.0120550i
$997$		−	23.2063i		−	0.734950i	−0.930033	−	0.367475i	$-0.880222\pi$
$997$		−	23.2063i		−	0.734950i	0.930033	−	0.367475i	$-0.119778\pi$
$998$	−24.1232			−0.763605
$999$	−12.3792	+	17.5859i	−0.391662	+	0.556394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.c.a.197.2	yes	12
3.2	odd	2		462.2.c.b.197.1	yes	12
11.10	odd	2		462.2.c.b.197.2	yes	12
33.32	even	2	inner	462.2.c.a.197.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.c.a.197.1	✓	12	33.32	even	2	inner
462.2.c.a.197.2	yes	12	1.1	even	1	trivial
462.2.c.b.197.1	yes	12	3.2	odd	2
462.2.c.b.197.2	yes	12	11.10	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.64459 + 0.543441i) q^{3} +1.00000 q^{4} +0.118610i q^{5} +(1.64459 - 0.543441i) q^{6} -1.00000i q^{7} -1.00000 q^{8} +(2.40934 - 1.78747i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.64459 + 0.543441i) q^{3} +1.00000 q^{4} +0.118610i q^{5} +(1.64459 - 0.543441i) q^{6} -1.00000i q^{7} -1.00000 q^{8} +(2.40934 - 1.78747i) q^{9} -0.118610i q^{10} +(-2.10115 + 2.56616i) q^{11} +(-1.64459 + 0.543441i) q^{12} -0.913118i q^{13} +1.00000i q^{14} +(-0.0644573 - 0.195064i) q^{15} +1.00000 q^{16} +0.404381 q^{17} +(-2.40934 + 1.78747i) q^{18} -7.70348i q^{19} +0.118610i q^{20} +(0.543441 + 1.64459i) q^{21} +(2.10115 - 2.56616i) q^{22} +1.37265i q^{23} +(1.64459 - 0.543441i) q^{24} +4.98593 q^{25} +0.913118i q^{26} +(-2.99099 + 4.24900i) q^{27} -1.00000i q^{28} +3.20881 q^{29} +(0.0644573 + 0.195064i) q^{30} +8.74552 q^{31} -1.00000 q^{32} +(2.06097 - 5.36213i) q^{33} -0.404381 q^{34} +0.118610 q^{35} +(2.40934 - 1.78747i) q^{36} +4.13884 q^{37} +7.70348i q^{38} +(0.496226 + 1.50170i) q^{39} -0.118610i q^{40} +12.1630 q^{41} +(-0.543441 - 1.64459i) q^{42} +2.85361i q^{43} +(-2.10115 + 2.56616i) q^{44} +(0.212011 + 0.285771i) q^{45} -1.37265i q^{46} -10.3554i q^{47} +(-1.64459 + 0.543441i) q^{48} -1.00000 q^{49} -4.98593 q^{50} +(-0.665040 + 0.219757i) q^{51} -0.913118i q^{52} -8.81869i q^{53} +(2.99099 - 4.24900i) q^{54} +(-0.304371 - 0.249216i) q^{55} +1.00000i q^{56} +(4.18639 + 12.6691i) q^{57} -3.20881 q^{58} -5.49147i q^{59} +(-0.0644573 - 0.195064i) q^{60} -7.30675i q^{61} -8.74552 q^{62} +(-1.78747 - 2.40934i) q^{63} +1.00000 q^{64} +0.108304 q^{65} +(-2.06097 + 5.36213i) q^{66} -2.01758 q^{67} +0.404381 q^{68} +(-0.745956 - 2.25745i) q^{69} -0.118610 q^{70} +14.2157i q^{71} +(-2.40934 + 1.78747i) q^{72} +11.7838i q^{73} -4.13884 q^{74} +(-8.19981 + 2.70956i) q^{75} -7.70348i q^{76} +(2.56616 + 2.10115i) q^{77} +(-0.496226 - 1.50170i) q^{78} +4.34114i q^{79} +0.118610i q^{80} +(2.60987 - 8.61328i) q^{81} -12.1630 q^{82} -0.700078 q^{83} +(0.543441 + 1.64459i) q^{84} +0.0479634i q^{85} -2.85361i q^{86} +(-5.27718 + 1.74380i) q^{87} +(2.10115 - 2.56616i) q^{88} -10.7521i q^{89} +(-0.212011 - 0.285771i) q^{90} -0.913118 q^{91} +1.37265i q^{92} +(-14.3828 + 4.75267i) q^{93} +10.3554i q^{94} +0.913706 q^{95} +(1.64459 - 0.543441i) q^{96} -5.48096 q^{97} +1.00000 q^{98} +(-0.475441 + 9.93851i) 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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