LMFDB - Embedded newform 462.2.c.b.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.b.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} +(-4.85008 - 3.07843i) 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} +(-4.85008 - 3.07843i) 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} +(9.64933 + 2.42701i) 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} + 20 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 + 20 * 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	$0.0404150\pi$
$13$			0.913118i			0.253253i	−0.991950	+	0.126627i	$0.959585\pi$
$14$			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	$-0.515616\pi$
$17$	−0.404381			−0.0980767			−0.0490383	+	0.998797i	$0.515616\pi$
$18$	2.40934	−	1.78747i	0.567888	−	0.421312i
$19$			7.70348i			1.76730i	0.468148	+	0.883650i	$0.344921\pi$
$19$			7.70348i			1.76730i	−0.468148	+	0.883650i	$0.655079\pi$
$20$			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	$-0.596297\pi$
$29$	−3.20881			−0.595862			−0.297931	+	0.954587i	$0.596297\pi$
$30$	−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
$33$	−4.85008	−	3.07843i	−0.844291	−	0.535886i
$34$	−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	$-0.898685\pi$
$41$	−12.1630			−1.89954			−0.949772	+	0.312942i	$0.898685\pi$
$42$	−0.543441	−	1.64459i	−0.0838548	−	0.253766i
$43$		−	2.85361i		−	0.435172i	−0.976041	−	0.217586i	$-0.930182\pi$
$43$		−	2.85361i		−	0.435172i	0.976041	−	0.217586i	$-0.0698182\pi$
$44$	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	$0.154941\pi$
$61$			7.30675i			0.935534i	−0.883852	+	0.467767i	$0.845059\pi$
$62$	8.74552			1.11068
$63$	1.78747	+	2.40934i	0.225201	+	0.303549i
$64$	1.00000			0.125000
$65$	−0.108304			−0.0134335
$66$	−4.85008	−	3.07843i	−0.597004	−	0.378928i
$67$	−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	$-0.757787\pi$
$73$		−	11.7838i		−	1.37919i	0.724193	−	0.689597i	$-0.242213\pi$
$74$	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	$-0.921472\pi$
$79$		−	4.34114i		−	0.488416i	0.969723	−	0.244208i	$-0.0785279\pi$
$80$			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	$-0.487767\pi$
$83$	0.700078			0.0768435			0.0384217	+	0.999262i	$0.487767\pi$
$84$	−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
$99$	9.64933	+	2.42701i	0.969794	+	0.243924i
$100$	4.98593			0.498593
$101$	6.44547			0.641348			0.320674	−	0.947190i	$-0.396091\pi$
$101$	6.44547			0.641348			0.320674	+	0.947190i	$0.396091\pi$
$102$	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	$-0.479603\pi$
$107$	1.32477			0.128070			0.0640351	+	0.997948i	$0.479603\pi$
$108$	−2.99099	+	4.24900i	−0.287808	+	0.408860i
$109$		−	11.5849i		−	1.10963i	−0.831974	−	0.554815i	$-0.812789\pi$
$109$		−	11.5849i		−	1.10963i	0.831974	−	0.554815i	$-0.187211\pi$
$110$	−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	$-0.892355\pi$
$127$		−	7.47768i		−	0.663537i	0.943361	−	0.331768i	$-0.107645\pi$
$128$	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	$-0.468404\pi$
$131$	2.26848			0.198198			0.0990992	+	0.995078i	$0.468404\pi$
$132$	−4.85008	−	3.07843i	−0.422145	−	0.267943i
$133$	−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	$0.224003\pi$
$139$			15.2576i			1.29413i	−0.762435	+	0.647064i	$0.775997\pi$
$140$	−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	$-0.807330\pi$
$149$	−20.0758			−1.64467			−0.822336	+	0.569002i	$0.807330\pi$
$150$	−8.19981	+	2.70956i	−0.669511	+	0.221235i
$151$			11.7555i			0.956651i	0.878183	+	0.478326i	$0.158756\pi$
$151$			11.7555i			0.956651i	−0.878183	+	0.478326i	$0.841244\pi$
$152$			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
$165$	0.365131	−	0.575266i	0.0284254	−	0.0447844i
$166$	0.700078			0.0543366
$167$	3.89177			0.301155			0.150577	−	0.988598i	$-0.451887\pi$
$167$	3.89177			0.301155			0.150577	+	0.988598i	$0.451887\pi$
$168$	−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	$-0.306250\pi$
$173$	15.0414			1.14358			0.571789	+	0.820401i	$0.306250\pi$
$174$	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	$-0.984195\pi$
$193$		−	1.37905i		−	0.0992660i	0.998768	−	0.0496330i	$-0.0158052\pi$
$194$	−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	$-0.269316\pi$
$197$	18.6091			1.32585			0.662923	+	0.748688i	$0.269316\pi$
$198$	9.64933	+	2.42701i	0.685748	+	0.172480i
$199$	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	$-0.950983\pi$
$211$		−	4.45606i		−	0.306768i	0.988167	−	0.153384i	$-0.0490171\pi$
$212$		−	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	$-0.438483\pi$
$227$	5.78740			0.384123			0.192062	+	0.981383i	$0.438483\pi$
$228$	−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
$231$	3.07843	−	4.85008i	0.202546	−	0.319112i
$232$	−3.20881			−0.210669
$233$	−17.3347			−1.13563			−0.567817	−	0.823155i	$-0.692212\pi$
$233$	−17.3347			−1.13563			−0.567817	+	0.823155i	$0.692212\pi$
$234$	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	$-0.627288\pi$
$239$	−12.0373			−0.778631			−0.389316	+	0.921104i	$0.627288\pi$
$240$	−0.0644573	−	0.195064i	−0.00416070	−	0.0125913i
$241$		−	24.9447i		−	1.60683i	−0.595420	−	0.803415i	$-0.703014\pi$
$241$		−	24.9447i		−	1.60683i	0.595420	−	0.803415i	$-0.296986\pi$
$242$	−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	$-0.688127\pi$
$263$	−18.0728			−1.11441			−0.557207	+	0.830373i	$0.688127\pi$
$264$	−4.85008	−	3.07843i	−0.298502	−	0.189464i
$265$	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	$-0.878313\pi$
$271$		−	12.2822i		−	0.746093i	0.927813	−	0.373047i	$-0.121687\pi$
$272$	−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	$0.305159\pi$
$277$			27.2430i			1.63687i	−0.574596	+	0.818437i	$0.694841\pi$
$278$			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	$-0.257799\pi$
$281$	23.1187			1.37914			0.689572	+	0.724217i	$0.257799\pi$
$282$	5.62754	+	17.0304i	0.335115	+	1.01414i
$283$		−	8.26048i		−	0.491035i	−0.969392	−	0.245517i	$-0.921042\pi$
$283$		−	8.26048i		−	0.491035i	0.969392	−	0.245517i	$-0.0789579\pi$
$284$			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	$-0.342566\pi$
$293$	16.2502			0.949348			0.474674	+	0.880162i	$0.342566\pi$
$294$	1.64459	−	0.543441i	0.0959144	−	0.0316941i
$295$	0.651341			0.0379225
$296$	4.13884			0.240565
$297$	−17.1881	+	1.25240i	−0.997356	+	0.0726717i
$298$	−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	$-0.903080\pi$
$307$		−	10.5059i		−	0.599601i	0.954002	−	0.299800i	$-0.0969201\pi$
$308$	−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
$330$	0.365131	−	0.575266i	0.0200998	−	0.0316673i
$331$	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	$-0.983866\pi$
$337$		−	1.86013i		−	0.101328i	0.998716	−	0.0506639i	$-0.0161337\pi$
$338$	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	$-0.761912\pi$
$347$	−27.3110			−1.46613			−0.733067	+	0.680157i	$0.761912\pi$
$348$	5.27718	−	1.74380i	0.282887	−	0.0934776i
$349$		−	3.59647i		−	0.192515i	−0.995356	−	0.0962574i	$-0.969313\pi$
$349$		−	3.59647i		−	0.192515i	0.995356	−	0.0962574i	$-0.0306872\pi$
$350$			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	$-0.565852\pi$
$359$	−7.78386			−0.410817			−0.205408	+	0.978676i	$0.565852\pi$
$360$	0.212011	+	0.285771i	0.0111740	+	0.0150615i
$361$	−40.3437			−2.12335
$362$	−9.55361			−0.502127
$363$	−2.29099	−	18.9143i	−0.120246	−	0.992744i
$364$	−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	$-0.637974\pi$
$373$		−	35.0542i		−	1.81504i	0.420012	−	0.907519i	$-0.362026\pi$
$374$	−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
$396$	9.64933	+	2.42701i	0.484897	+	0.121962i
$397$	−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	$0.0907878\pi$
$409$			11.3806i			0.562734i	−0.959600	+	0.281367i	$0.909212\pi$
$410$		−	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
$429$	2.81097	−	4.42869i	0.135715	−	0.213819i
$430$	0.338465			0.0163223
$431$	34.8775			1.67999			0.839996	−	0.542593i	$-0.182557\pi$
$431$	34.8775			1.67999			0.839996	+	0.542593i	$0.182557\pi$
$432$	−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	$-0.876734\pi$
$439$		−	15.8251i		−	0.755291i	0.925950	−	0.377645i	$-0.123266\pi$
$440$	−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	$-0.921872\pi$
$457$		−	10.3890i		−	0.485977i	0.970029	−	0.242988i	$-0.0781277\pi$
$458$	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	$-0.379150\pi$
$461$	15.9146			0.741215			0.370607	+	0.928790i	$0.379150\pi$
$462$	3.07843	−	4.85008i	0.143221	−	0.225646i
$463$	−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	$-0.334653\pi$
$479$	21.7287			0.992808			0.496404	+	0.868092i	$0.334653\pi$
$480$	−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	$-0.846583\pi$
$491$	−39.2685			−1.77216			−0.886082	+	0.463529i	$0.846583\pi$
$492$	20.0032	−	6.60988i	0.901812	−	0.297997i
$493$	1.29758			0.0584402
$494$	−7.03419			−0.316483
$495$	−0.287867	+	1.14450i	−0.0129387	+	0.0514416i
$496$	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	$-0.833843\pi$
$503$	−38.8817			−1.73365			−0.866825	+	0.498612i	$0.833843\pi$
$504$	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	$-0.655961\pi$
$523$		−	40.3572i		−	1.76470i	0.470596	−	0.882349i	$-0.344039\pi$
$524$	2.26848			0.0990992
$525$	−2.70956	−	8.19981i	−0.118255	−	0.357869i
$526$	−18.0728			−0.788010
$527$	−3.53652			−0.154053
$528$	−4.85008	−	3.07843i	−0.211073	−	0.133971i
$529$	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	$-0.918013\pi$
$541$		−	11.8497i		−	0.509460i	0.967012	−	0.254730i	$-0.0819866\pi$
$542$		−	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	$0.262829\pi$
$547$			34.3815i			1.47005i	−0.678042	+	0.735023i	$0.737171\pi$
$548$			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	$-0.367710\pi$
$557$	19.0572			0.807478			0.403739	+	0.914874i	$0.367710\pi$
$558$	21.0710	−	15.6324i	0.892005	−	0.661772i
$559$	2.60568			0.110209
$560$	−0.118610			−0.00501217
$561$	1.96128	+	1.24486i	0.0828052	+	0.0525579i
$562$	23.1187			0.975202
$563$	−36.5587			−1.54076			−0.770382	−	0.637583i	$-0.779934\pi$
$563$	−36.5587			−1.54076			−0.770382	+	0.637583i	$0.779934\pi$
$564$	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	$-0.271022\pi$
$569$	31.4344			1.31780			0.658899	+	0.752231i	$0.271022\pi$
$570$	1.50267	−	0.496546i	0.0629400	−	0.0207980i
$571$			12.2759i			0.513731i	0.966447	+	0.256865i	$0.0826897\pi$
$571$			12.2759i			0.513731i	−0.966447	+	0.256865i	$0.917310\pi$
$572$	−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	$-0.613378\pi$
$593$	−16.9830			−0.697408			−0.348704	+	0.937233i	$0.613378\pi$
$594$	−17.1881	+	1.25240i	−0.705237	+	0.0513867i
$595$	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	$0.160079\pi$
$601$			23.6313i			0.963940i	−0.876188	+	0.481970i	$0.839921\pi$
$602$	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	$0.304280\pi$
$607$			40.2500i			1.63370i	−0.576853	+	0.816848i	$0.695720\pi$
$608$			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	$-0.909292\pi$
$613$		−	13.9207i		−	0.562253i	0.959671	−	0.281126i	$-0.0907080\pi$
$614$		−	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
$627$	23.7146	−	37.3625i	0.947071	−	1.49212i
$628$	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	$-0.553173\pi$
$659$	−8.53676			−0.332545			−0.166272	+	0.986080i	$0.553173\pi$
$660$	0.365131	−	0.575266i	0.0142127	−	0.0223922i
$661$	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	$0.140793\pi$
$673$			22.2082i			0.856062i	−0.903764	+	0.428031i	$0.859207\pi$
$674$		−	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	$-0.602909\pi$
$677$	−16.5325			−0.635394			−0.317697	+	0.948192i	$0.602909\pi$
$678$	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
$693$	−2.42701	+	9.64933i	−0.0921947	+	0.366548i
$694$	−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	$-0.263024\pi$
$701$	35.8804			1.35518			0.677591	+	0.735439i	$0.263024\pi$
$702$	−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
$726$	−2.29099	−	18.9143i	−0.0850268	−	0.701976i
$727$	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	$-0.983568\pi$
$733$		−	2.79394i		−	0.103196i	0.998668	−	0.0515982i	$-0.0164315\pi$
$734$	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	$0.295468\pi$
$739$			43.5261i			1.60113i	−0.599244	+	0.800566i	$0.704532\pi$
$740$			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	$-0.455362\pi$
$743$	7.61997			0.279550			0.139775	+	0.990183i	$0.455362\pi$
$744$	−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
$759$	4.22561	−	6.65748i	0.153380	−	0.241651i
$760$	−0.913706			−0.0331436
$761$	37.3077			1.35240			0.676201	−	0.736717i	$-0.263625\pi$
$761$	37.3077			1.35240			0.676201	+	0.736717i	$0.263625\pi$
$762$	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	$-0.721157\pi$
$769$		−	42.6052i		−	1.53638i	0.640221	−	0.768191i	$-0.278843\pi$
$770$	−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	$-0.859325\pi$
$787$		−	23.9969i		−	0.855397i	0.903922	−	0.427698i	$-0.140675\pi$
$788$	18.6091			0.662923
$789$	29.7223	−	9.82149i	1.05814	−	0.349654i
$790$	0.514900			0.0183193
$791$	15.5818			0.554024
$792$	9.64933	+	2.42701i	0.342874	+	0.0862402i
$793$	−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	$-0.963210\pi$
$809$	−56.5063			−1.98666			−0.993328	+	0.115322i	$0.963210\pi$
$810$	1.02162	+	0.309556i	0.0358960	+	0.0108767i
$811$		−	25.7590i		−	0.904521i	−0.891886	−	0.452260i	$-0.850618\pi$
$811$		−	25.7590i		−	0.904521i	0.891886	−	0.452260i	$-0.149382\pi$
$812$		−	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	$-0.259055\pi$
$821$	39.3526			1.37341			0.686707	+	0.726934i	$0.259055\pi$
$822$	−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
$825$	−24.1822	−	15.3488i	−0.841915	−	0.534378i
$826$	5.49147			0.191073
$827$	−44.6041			−1.55104			−0.775519	−	0.631324i	$-0.782512\pi$
$827$	−44.6041			−1.55104			−0.775519	+	0.631324i	$0.782512\pi$
$828$	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	$0.391620\pi$
$853$			55.0590i			1.88519i	−0.333945	+	0.942593i	$0.608380\pi$
$854$	−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	$-0.364864\pi$
$857$	24.1166			0.823808			0.411904	+	0.911227i	$0.364864\pi$
$858$	2.81097	−	4.42869i	0.0959648	−	0.151193i
$859$	−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	$0.136762\pi$
$877$			24.6717i			0.833105i	−0.909112	+	0.416553i	$0.863238\pi$
$878$		−	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	$-0.510614\pi$
$887$	−1.98579			−0.0666764			−0.0333382	+	0.999444i	$0.510614\pi$
$888$	−6.80669	+	2.24922i	−0.228418	+	0.0754787i
$889$	7.47768			0.250793
$890$	1.27530			0.0427483
$891$	27.5868	−	11.4004i	0.924192	−	0.381928i
$892$	−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	$0.0574491\pi$
$919$			10.8833i			0.359007i	−0.983757	+	0.179503i	$0.942551\pi$
$920$	−0.162810			−0.00536768
$921$	5.70931	+	17.2778i	0.188128	+	0.569323i
$922$	15.9146			0.524118
$923$	−12.9806			−0.427263
$924$	3.07843	−	4.85008i	0.101273	−	0.159556i
$925$	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	$-0.942470\pi$
$937$		−	11.0048i		−	0.359510i	0.983711	−	0.179755i	$-0.0575305\pi$
$938$		−	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	$-0.250095\pi$
$941$	43.3691			1.41379			0.706897	+	0.707317i	$0.250095\pi$
$942$	−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	$-0.423066\pi$
$953$	14.7778			0.478700			0.239350	+	0.970933i	$0.423066\pi$
$954$	−15.7632	−	21.2472i	−0.510352	−	0.687905i
$955$	0.346279			0.0112053
$956$	−12.0373			−0.389316
$957$	15.5630	+	9.87811i	0.503081	+	0.319314i
$958$	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	$0.101831\pi$
$967$			19.5588i			0.628968i	−0.949263	+	0.314484i	$0.898169\pi$
$968$	−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
$990$	−0.287867	+	1.14450i	−0.00914902	+	0.0363747i
$991$	−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	$0.119778\pi$
$997$			23.2063i			0.734950i	−0.930033	+	0.367475i	$0.880222\pi$
$998$	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.b.197.2	yes	12
3.2	odd	2		462.2.c.a.197.1	✓	12
11.10	odd	2		462.2.c.a.197.2	yes	12
33.32	even	2	inner	462.2.c.b.197.1	yes	12

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

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} +(-4.85008 - 3.07843i) 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} +(-4.85008 - 3.07843i) 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} +(9.64933 + 2.42701i) 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	\( 12 q + 12 q^{2} + 4 q^{3} + 12 q^{4} + 4 q^{6} + 12 q^{8} + 8 q^{11} + 4 q^{12} + 4 q^{15} + 12 q^{16} + 4 q^{17} + 8 q^{22} + 4 q^{24} - 28 q^{25} - 8 q^{27} - 8 q^{29} + 4 q^{30} + 12 q^{31} + 12 q^{32} - 16 q^{33} + 4 q^{34} + 4 q^{35} + 36 q^{39} - 20 q^{41} + 8 q^{44} - 12 q^{45} + 4 q^{48} - 12 q^{49} - 28 q^{50} - 8 q^{51} - 8 q^{54} + 4 q^{55} - 28 q^{57} - 8 q^{58} + 4 q^{60} + 12 q^{62} - 4 q^{63} + 12 q^{64} - 16 q^{66} + 24 q^{67} + 4 q^{68} - 20 q^{69} + 4 q^{70} - 40 q^{75} - 4 q^{77} + 36 q^{78} + 4 q^{81} - 20 q^{82} - 44 q^{83} - 8 q^{87} + 8 q^{88} - 12 q^{90} - 24 q^{91} - 24 q^{93} + 4 q^{96} - 48 q^{97} - 12 q^{98} + 20 q^{99}+O(q^{100}) \) 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 + 20 * q^99

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