LMFDB - Embedded newform 420.2.c.b.391.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(391,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 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("420.391");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 3x^14 - 4x^13 + 3x^12 + 2x^11 - 7x^10 + 12x^9 - 28x^8 + 24x^7 - 28x^6 + 16x^5 + 48x^4 - 128x^3 + 192x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			391.7
Root			$-0.102186 - 1.41052i$ of defining polynomial
Character	$\chi$	$=$	420.391
Dual form			420.2.c.b.391.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.102186 - 1.41052i) q^{2} +1.00000 q^{3} +(-1.97912 + 0.288270i) q^{4} +1.00000i q^{5} +(-0.102186 - 1.41052i) q^{6} +(0.178143 + 2.63975i) q^{7} +(0.608847 + 2.76212i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.102186 - 1.41052i) q^{2} +1.00000 q^{3} +(-1.97912 + 0.288270i) q^{4} +1.00000i q^{5} +(-0.102186 - 1.41052i) q^{6} +(0.178143 + 2.63975i) q^{7} +(0.608847 + 2.76212i) q^{8} +1.00000 q^{9} +(1.41052 - 0.102186i) q^{10} +5.22855i q^{11} +(-1.97912 + 0.288270i) q^{12} +4.52534i q^{13} +(3.70520 - 0.521019i) q^{14} +1.00000i q^{15} +(3.83380 - 1.14104i) q^{16} -6.70156i q^{17} +(-0.102186 - 1.41052i) q^{18} -2.81981 q^{19} +(-0.288270 - 1.97912i) q^{20} +(0.178143 + 2.63975i) q^{21} +(7.37496 - 0.534284i) q^{22} -0.858617i q^{23} +(0.608847 + 2.76212i) q^{24} -1.00000 q^{25} +(6.38308 - 0.462426i) q^{26} +1.00000 q^{27} +(-1.11353 - 5.17301i) q^{28} +6.47333 q^{29} +(1.41052 - 0.102186i) q^{30} -2.60723 q^{31} +(-2.00121 - 5.29104i) q^{32} +5.22855i q^{33} +(-9.45266 + 0.684805i) q^{34} +(-2.63975 + 0.178143i) q^{35} +(-1.97912 + 0.288270i) q^{36} +2.13976 q^{37} +(0.288144 + 3.97738i) q^{38} +4.52534i q^{39} +(-2.76212 + 0.608847i) q^{40} -8.71476i q^{41} +(3.70520 - 0.521019i) q^{42} +7.42042i q^{43} +(-1.50723 - 10.3479i) q^{44} +1.00000i q^{45} +(-1.21109 + 0.0877385i) q^{46} +9.82671 q^{47} +(3.83380 - 1.14104i) q^{48} +(-6.93653 + 0.940508i) q^{49} +(0.102186 + 1.41052i) q^{50} -6.70156i q^{51} +(-1.30452 - 8.95618i) q^{52} +3.69301 q^{53} +(-0.102186 - 1.41052i) q^{54} -5.22855 q^{55} +(-7.18284 + 2.09926i) q^{56} -2.81981 q^{57} +(-0.661483 - 9.13075i) q^{58} -4.27962 q^{59} +(-0.288270 - 1.97912i) q^{60} -10.7054i q^{61} +(0.266423 + 3.67755i) q^{62} +(0.178143 + 2.63975i) q^{63} +(-7.25861 + 3.36342i) q^{64} -4.52534 q^{65} +(7.37496 - 0.534284i) q^{66} -4.52269i q^{67} +(1.93186 + 13.2632i) q^{68} -0.858617i q^{69} +(0.521019 + 3.70520i) q^{70} +7.23513i q^{71} +(0.608847 + 2.76212i) q^{72} +9.24697i q^{73} +(-0.218653 - 3.01816i) q^{74} -1.00000 q^{75} +(5.58072 - 0.812865i) q^{76} +(-13.8020 + 0.931432i) q^{77} +(6.38308 - 0.462426i) q^{78} -2.68314i q^{79} +(1.14104 + 3.83380i) q^{80} +1.00000 q^{81} +(-12.2923 + 0.890525i) q^{82} +16.2812 q^{83} +(-1.11353 - 5.17301i) q^{84} +6.70156 q^{85} +(10.4666 - 0.758262i) q^{86} +6.47333 q^{87} +(-14.4419 + 3.18339i) q^{88} -8.53516i q^{89} +(1.41052 - 0.102186i) q^{90} +(-11.9458 + 0.806161i) q^{91} +(0.247513 + 1.69930i) q^{92} -2.60723 q^{93} +(-1.00415 - 13.8607i) q^{94} -2.81981i q^{95} +(-2.00121 - 5.29104i) q^{96} +10.5209i q^{97} +(2.03542 + 9.68799i) q^{98} +5.22855i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 16 q^{3} - 2 q^{4} + 2 q^{6} + 4 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 + 16 * q^3 - 2 * q^4 + 2 * q^6 + 4 * q^7 + 2 * q^8 + 16 * q^9	$ 16 q + 2 q^{2} + 16 q^{3} - 2 q^{4} + 2 q^{6} + 4 q^{7} + 2 q^{8} + 16 q^{9} - 2 q^{12} + 10 q^{14} + 6 q^{16} + 2 q^{18} + 24 q^{19} + 4 q^{21} - 12 q^{22} + 2 q^{24} - 16 q^{25} + 12 q^{26} + 16 q^{27} - 22 q^{28} + 16 q^{29} - 8 q^{31} - 18 q^{32} - 24 q^{34} - 2 q^{36} + 24 q^{37} - 28 q^{38} - 12 q^{40} + 10 q^{42} - 8 q^{44} - 20 q^{46} - 16 q^{47} + 6 q^{48} - 16 q^{49} - 2 q^{50} + 20 q^{52} - 32 q^{53} + 2 q^{54} - 2 q^{56} + 24 q^{57} - 32 q^{58} - 8 q^{59} - 16 q^{62} + 4 q^{63} - 2 q^{64} - 8 q^{65} - 12 q^{66} - 4 q^{68} - 20 q^{70} + 2 q^{72} - 4 q^{74} - 16 q^{75} - 16 q^{76} - 8 q^{77} + 12 q^{78} + 16 q^{80} + 16 q^{81} + 4 q^{82} - 8 q^{83} - 22 q^{84} + 64 q^{86} + 16 q^{87} - 52 q^{88} - 16 q^{91} + 64 q^{92} - 8 q^{93} - 16 q^{94} - 18 q^{96} + 2 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 + 16 * q^3 - 2 * q^4 + 2 * q^6 + 4 * q^7 + 2 * q^8 + 16 * q^9 - 2 * q^12 + 10 * q^14 + 6 * q^16 + 2 * q^18 + 24 * q^19 + 4 * q^21 - 12 * q^22 + 2 * q^24 - 16 * q^25 + 12 * q^26 + 16 * q^27 - 22 * q^28 + 16 * q^29 - 8 * q^31 - 18 * q^32 - 24 * q^34 - 2 * q^36 + 24 * q^37 - 28 * q^38 - 12 * q^40 + 10 * q^42 - 8 * q^44 - 20 * q^46 - 16 * q^47 + 6 * q^48 - 16 * q^49 - 2 * q^50 + 20 * q^52 - 32 * q^53 + 2 * q^54 - 2 * q^56 + 24 * q^57 - 32 * q^58 - 8 * q^59 - 16 * q^62 + 4 * q^63 - 2 * q^64 - 8 * q^65 - 12 * q^66 - 4 * q^68 - 20 * q^70 + 2 * q^72 - 4 * q^74 - 16 * q^75 - 16 * q^76 - 8 * q^77 + 12 * q^78 + 16 * q^80 + 16 * q^81 + 4 * q^82 - 8 * q^83 - 22 * q^84 + 64 * q^86 + 16 * q^87 - 52 * q^88 - 16 * q^91 + 64 * q^92 - 8 * q^93 - 16 * q^94 - 18 * q^96 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$-1$	$-1$	$1$	$1$

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 $

$2$	−0.102186	−	1.41052i	−0.0722563	−	0.997386i
$2$	−0.102186	−	1.41052i	−0.0722563	−	0.997386i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.97912	+	0.288270i	−0.989558	+	0.144135i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−0.102186	−	1.41052i	−0.0417172	−	0.575841i
$7$	0.178143	+	2.63975i	0.0673319	+	0.997731i
$7$	0.178143	+	2.63975i	0.0673319	+	0.997731i
$8$	0.608847	+	2.76212i	0.215260	+	0.976557i
$9$	1.00000			0.333333
$10$	1.41052	−	0.102186i	0.446045	−	0.0323140i
$11$			5.22855i			1.57647i	0.615376	+	0.788234i	$0.289004\pi$
$11$			5.22855i			1.57647i	−0.615376	+	0.788234i	$0.710996\pi$
$12$	−1.97912	+	0.288270i	−0.571322	+	0.0832163i
$13$			4.52534i			1.25510i	0.778574	+	0.627552i	$0.215943\pi$
$13$			4.52534i			1.25510i	−0.778574	+	0.627552i	$0.784057\pi$
$14$	3.70520	−	0.521019i	0.990258	−	0.139248i
$15$			1.00000i			0.258199i
$16$	3.83380	−	1.14104i	0.958450	−	0.285260i
$17$		−	6.70156i		−	1.62537i	−0.582705	−	0.812684i	$-0.698006\pi$
$17$		−	6.70156i		−	1.62537i	0.582705	−	0.812684i	$-0.301994\pi$
$18$	−0.102186	−	1.41052i	−0.0240854	−	0.332462i
$19$	−2.81981			−0.646908			−0.323454	−	0.946244i	$-0.604844\pi$
$19$	−2.81981			−0.646908			−0.323454	+	0.946244i	$0.604844\pi$
$20$	−0.288270	−	1.97912i	−0.0644591	−	0.442544i
$21$	0.178143	+	2.63975i	0.0388741	+	0.576040i
$22$	7.37496	−	0.534284i	1.57235	−	0.113910i
$23$		−	0.858617i		−	0.179034i	−0.995985	−	0.0895170i	$-0.971468\pi$
$23$		−	0.858617i		−	0.179034i	0.995985	−	0.0895170i	$-0.0285323\pi$
$24$	0.608847	+	2.76212i	0.124280	+	0.563815i
$25$	−1.00000			−0.200000
$26$	6.38308	−	0.462426i	1.25182	−	0.0906893i
$27$	1.00000			0.192450
$28$	−1.11353	−	5.17301i	−0.210437	−	0.977607i
$29$	6.47333			1.20207			0.601034	−	0.799224i	$-0.294756\pi$
$29$	6.47333			1.20207			0.601034	+	0.799224i	$0.294756\pi$
$30$	1.41052	−	0.102186i	0.257524	−	0.0186565i
$31$	−2.60723			−0.468273			−0.234137	−	0.972204i	$-0.575226\pi$
$31$	−2.60723			−0.468273			−0.234137	+	0.972204i	$0.575226\pi$
$32$	−2.00121	−	5.29104i	−0.353768	−	0.935333i
$33$			5.22855i			0.910174i
$34$	−9.45266	+	0.684805i	−1.62112	+	0.117443i
$35$	−2.63975	+	0.178143i	−0.446199	+	0.0301117i
$36$	−1.97912	+	0.288270i	−0.329853	+	0.0480450i
$37$	2.13976			0.351774			0.175887	−	0.984410i	$-0.443721\pi$
$37$	2.13976			0.351774			0.175887	+	0.984410i	$0.443721\pi$
$38$	0.288144	+	3.97738i	0.0467432	+	0.645217i
$39$			4.52534i			0.724635i
$40$	−2.76212	+	0.608847i	−0.436729	+	0.0962672i
$41$		−	8.71476i		−	1.36102i	−0.732740	−	0.680508i	$-0.761759\pi$
$41$		−	8.71476i		−	1.36102i	0.732740	−	0.680508i	$-0.238241\pi$
$42$	3.70520	−	0.521019i	0.571725	−	0.0803950i
$43$			7.42042i			1.13160i	0.824541	+	0.565802i	$0.191433\pi$
$43$			7.42042i			1.13160i	−0.824541	+	0.565802i	$0.808567\pi$
$44$	−1.50723	−	10.3479i	−0.227224	−	1.56001i
$45$			1.00000i			0.149071i
$46$	−1.21109	+	0.0877385i	−0.178566	+	0.0129363i
$47$	9.82671			1.43337			0.716686	−	0.697396i	$-0.245658\pi$
$47$	9.82671			1.43337			0.716686	+	0.697396i	$0.245658\pi$
$48$	3.83380	−	1.14104i	0.553362	−	0.164695i
$49$	−6.93653	+	0.940508i	−0.990933	+	0.134358i
$50$	0.102186	+	1.41052i	0.0144513	+	0.199477i
$51$		−	6.70156i		−	0.938406i
$52$	−1.30452	−	8.95618i	−0.180904	−	1.24200i
$53$	3.69301			0.507274			0.253637	−	0.967299i	$-0.418373\pi$
$53$	3.69301			0.507274			0.253637	+	0.967299i	$0.418373\pi$
$54$	−0.102186	−	1.41052i	−0.0139057	−	0.191947i
$55$	−5.22855			−0.705018
$56$	−7.18284	+	2.09926i	−0.959847	+	0.280525i
$57$	−2.81981			−0.373493
$58$	−0.661483	−	9.13075i	−0.0868570	−	1.19893i
$59$	−4.27962			−0.557159			−0.278579	−	0.960413i	$-0.589864\pi$
$59$	−4.27962			−0.557159			−0.278579	+	0.960413i	$0.589864\pi$
$60$	−0.288270	−	1.97912i	−0.0372155	−	0.255503i
$61$		−	10.7054i		−	1.37069i	−0.728221	−	0.685343i	$-0.759653\pi$
$61$		−	10.7054i		−	1.37069i	0.728221	−	0.685343i	$-0.240347\pi$
$62$	0.266423	+	3.67755i	0.0338357	+	0.467049i
$63$	0.178143	+	2.63975i	0.0224440	+	0.332577i
$64$	−7.25861	+	3.36342i	−0.907326	+	0.420427i
$65$	−4.52534			−0.561300
$66$	7.37496	−	0.534284i	0.907795	−	0.0657658i
$67$		−	4.52269i		−	0.552534i	−0.961081	−	0.276267i	$-0.910903\pi$
$67$		−	4.52269i		−	0.552534i	0.961081	−	0.276267i	$-0.0890975\pi$
$68$	1.93186	+	13.2632i	0.234272	+	1.60840i
$69$		−	0.858617i		−	0.103365i
$70$	0.521019	+	3.70520i	0.0622737	+	0.442857i
$71$			7.23513i			0.858652i	0.903150	+	0.429326i	$0.141249\pi$
$71$			7.23513i			0.858652i	−0.903150	+	0.429326i	$0.858751\pi$
$72$	0.608847	+	2.76212i	0.0717533	+	0.325519i
$73$			9.24697i			1.08228i	0.840934	+	0.541138i	$0.182006\pi$
$73$			9.24697i			1.08228i	−0.840934	+	0.541138i	$0.817994\pi$
$74$	−0.218653	−	3.01816i	−0.0254179	−	0.350854i
$75$	−1.00000			−0.115470
$76$	5.58072	−	0.812865i	0.640153	−	0.0932420i
$77$	−13.8020	+	0.931432i	−1.57289	+	0.106147i
$78$	6.38308	−	0.462426i	0.722741	−	0.0523595i
$79$		−	2.68314i		−	0.301877i	−0.988543	−	0.150938i	$-0.951770\pi$
$79$		−	2.68314i		−	0.301877i	0.988543	−	0.150938i	$-0.0482295\pi$
$80$	1.14104	+	3.83380i	0.127572	+	0.428632i
$81$	1.00000			0.111111
$82$	−12.2923	+	0.890525i	−1.35746	+	0.0983421i
$83$	16.2812			1.78710			0.893548	−	0.448967i	$-0.148208\pi$
$83$	16.2812			1.78710			0.893548	+	0.448967i	$0.148208\pi$
$84$	−1.11353	−	5.17301i	−0.121496	−	0.564422i
$85$	6.70156			0.726886
$86$	10.4666	−	0.758262i	1.12865	−	0.0817655i
$87$	6.47333			0.694014
$88$	−14.4419	+	3.18339i	−1.53951	+	0.339350i
$89$		−	8.53516i		−	0.904725i	−0.891834	−	0.452362i	$-0.850581\pi$
$89$		−	8.53516i		−	0.904725i	0.891834	−	0.452362i	$-0.149419\pi$
$90$	1.41052	−	0.102186i	0.148682	−	0.0107713i
$91$	−11.9458	+	0.806161i	−1.25226	+	0.0845086i
$92$	0.247513	+	1.69930i	0.0258051	+	0.177165i
$93$	−2.60723			−0.270358
$94$	−1.00415	−	13.8607i	−0.103570	−	1.42963i
$95$		−	2.81981i		−	0.289306i
$96$	−2.00121	−	5.29104i	−0.204248	−	0.540015i
$97$			10.5209i			1.06824i	0.845410	+	0.534118i	$0.179356\pi$
$97$			10.5209i			1.06824i	−0.845410	+	0.534118i	$0.820644\pi$
$98$	2.03542	+	9.68799i	0.205608	+	0.978634i
$99$			5.22855i			0.525489i
$100$	1.97912	−	0.288270i	0.197912	−	0.0288270i
$101$		−	3.97836i		−	0.395861i	−0.980216	−	0.197931i	$-0.936578\pi$
$101$		−	3.97836i		−	0.395861i	0.980216	−	0.197931i	$-0.0634221\pi$
$102$	−9.45266	+	0.684805i	−0.935953	+	0.0678058i
$103$	−3.78934			−0.373375			−0.186688	−	0.982419i	$-0.559775\pi$
$103$	−3.78934			−0.373375			−0.186688	+	0.982419i	$0.559775\pi$
$104$	−12.4995	+	2.75524i	−1.22568	+	0.270174i
$105$	−2.63975	+	0.178143i	−0.257613	+	0.0173850i
$106$	−0.377374	−	5.20906i	−0.0366538	−	0.505948i
$107$		−	2.38868i		−	0.230922i	−0.993312	−	0.115461i	$-0.963165\pi$
$107$		−	2.38868i		−	0.230922i	0.993312	−	0.115461i	$-0.0368346\pi$
$108$	−1.97912	+	0.288270i	−0.190441	+	0.0277388i
$109$	5.79748			0.555298			0.277649	−	0.960683i	$-0.410445\pi$
$109$	5.79748			0.555298			0.277649	+	0.960683i	$0.410445\pi$
$110$	0.534284	+	7.37496i	0.0509420	+	0.703175i
$111$	2.13976			0.203097
$112$	3.69502	+	9.91700i	0.349147	+	0.937068i
$113$	−6.86598			−0.645897			−0.322948	−	0.946417i	$-0.604674\pi$
$113$	−6.86598			−0.645897			−0.322948	+	0.946417i	$0.604674\pi$
$114$	0.288144	+	3.97738i	0.0269872	+	0.372516i
$115$	0.858617			0.0800665
$116$	−12.8115	+	1.86607i	−1.18952	+	0.173260i
$117$			4.52534i			0.418368i
$118$	0.437316	+	6.03647i	0.0402582	+	0.555702i
$119$	17.6904	−	1.19384i	1.62168	−	0.109439i
$120$	−2.76212	+	0.608847i	−0.252146	+	0.0555799i
$121$	−16.3377			−1.48525
$122$	−15.1001	+	1.09394i	−1.36710	+	0.0990407i
$123$		−	8.71476i		−	0.785784i
$124$	5.16002	−	0.751587i	0.463384	−	0.0674945i
$125$		−	1.00000i		−	0.0894427i
$126$	3.70520	−	0.521019i	0.330086	−	0.0464161i
$127$			10.4834i			0.930250i	0.885245	+	0.465125i	$0.153991\pi$
$127$			10.4834i			0.930250i	−0.885245	+	0.465125i	$0.846009\pi$
$128$	5.48588	+	9.89470i	0.484888	+	0.874576i
$129$			7.42042i			0.653332i
$130$	0.462426	+	6.38308i	0.0405575	+	0.559833i
$131$	−19.0936			−1.66821			−0.834106	−	0.551604i	$-0.814016\pi$
$131$	−19.0936			−1.66821			−0.834106	+	0.551604i	$0.814016\pi$
$132$	−1.50723	−	10.3479i	−0.131188	−	0.900670i
$133$	−0.502330	−	7.44358i	−0.0435576	−	0.645440i
$134$	−6.37933	+	0.462155i	−0.551090	+	0.0399241i
$135$			1.00000i			0.0860663i
$136$	18.5105	−	4.08023i	1.58726	−	0.349876i
$137$	5.47214			0.467516			0.233758	−	0.972295i	$-0.424898\pi$
$137$	5.47214			0.467516			0.233758	+	0.972295i	$0.424898\pi$
$138$	−1.21109	+	0.0877385i	−0.103095	+	0.00746880i
$139$	2.83943			0.240838			0.120419	−	0.992723i	$-0.461576\pi$
$139$	2.83943			0.240838			0.120419	+	0.992723i	$0.461576\pi$
$140$	5.17301	−	1.11353i	0.437199	−	0.0941101i
$141$	9.82671			0.827558
$142$	10.2053	−	0.739328i	0.856407	−	0.0620430i
$143$	−23.6610			−1.97863
$144$	3.83380	−	1.14104i	0.319483	−	0.0950866i
$145$			6.47333i			0.537581i
$146$	13.0430	−	0.944910i	1.07945	−	0.0782013i
$147$	−6.93653	+	0.940508i	−0.572115	+	0.0775718i
$148$	−4.23483	+	0.616827i	−0.348101	+	0.0507029i
$149$	1.72856			0.141609			0.0708045	−	0.997490i	$-0.477443\pi$
$149$	1.72856			0.141609			0.0708045	+	0.997490i	$0.477443\pi$
$150$	0.102186	+	1.41052i	0.00834344	+	0.115168i
$151$		−	14.9532i		−	1.21687i	−0.793603	−	0.608436i	$-0.791797\pi$
$151$		−	14.9532i		−	1.21687i	0.793603	−	0.608436i	$-0.208203\pi$
$152$	−1.71683	−	7.78864i	−0.139253	−	0.631742i
$153$		−	6.70156i		−	0.541789i
$154$	2.72418	+	19.3728i	0.219520	+	1.56111i
$155$		−	2.60723i		−	0.209418i
$156$	−1.30452	−	8.95618i	−0.104445	−	0.717068i
$157$		−	11.0383i		−	0.880953i	−0.897764	−	0.440476i	$-0.854810\pi$
$157$		−	11.0383i		−	0.880953i	0.897764	−	0.440476i	$-0.145190\pi$
$158$	−3.78461	+	0.274179i	−0.301088	+	0.0218125i
$159$	3.69301			0.292875
$160$	5.29104	−	2.00121i	0.418294	−	0.158210i
$161$	2.26653	−	0.152957i	0.178628	−	0.0120547i
$162$	−0.102186	−	1.41052i	−0.00802848	−	0.110821i
$163$		−	18.7969i		−	1.47229i	−0.676826	−	0.736143i	$-0.736645\pi$
$163$		−	18.7969i		−	1.47229i	0.676826	−	0.736143i	$-0.263355\pi$
$164$	2.51220	+	17.2475i	0.196170	+	1.34681i
$165$	−5.22855			−0.407042
$166$	−1.66371	−	22.9649i	−0.129129	−	1.78243i
$167$	1.89315			0.146496			0.0732481	−	0.997314i	$-0.476663\pi$
$167$	1.89315			0.146496			0.0732481	+	0.997314i	$0.476663\pi$
$168$	−7.18284	+	2.09926i	−0.554168	+	0.161961i
$169$	−7.47874			−0.575288
$170$	−0.684805	−	9.45266i	−0.0525221	−	0.724986i
$171$	−2.81981			−0.215636
$172$	−2.13908	−	14.6859i	−0.163104	−	1.11979i
$173$			9.43306i			0.717182i	0.933495	+	0.358591i	$0.116743\pi$
$173$			9.43306i			0.717182i	−0.933495	+	0.358591i	$0.883257\pi$
$174$	−0.661483	−	9.13075i	−0.0501469	−	0.692200i
$175$	−0.178143	−	2.63975i	−0.0134664	−	0.199546i
$176$	5.96598	+	20.0452i	0.449703	+	1.51097i
$177$	−4.27962			−0.321676
$178$	−12.0390	+	0.872173i	−0.902360	+	0.0653721i
$179$		−	21.4618i		−	1.60413i	−0.597239	−	0.802063i	$-0.703736\pi$
$179$		−	21.4618i		−	1.60413i	0.597239	−	0.802063i	$-0.296264\pi$
$180$	−0.288270	−	1.97912i	−0.0214864	−	0.147515i
$181$			24.1736i			1.79681i	0.439171	+	0.898403i	$0.355272\pi$
$181$			24.1736i			1.79681i	−0.439171	+	0.898403i	$0.644728\pi$
$182$	2.35779	+	16.7673i	0.174771	+	1.24288i
$183$		−	10.7054i		−	0.791365i
$184$	2.37160	−	0.522767i	0.174837	−	0.0385389i
$185$			2.13976i			0.157318i
$186$	0.266423	+	3.67755i	0.0195351	+	0.269651i
$187$	35.0394			2.56234
$188$	−19.4482	+	2.83274i	−1.41841	+	0.206599i
$189$	0.178143	+	2.63975i	0.0129580	+	0.192013i
$190$	−3.97738	+	0.288144i	−0.288550	+	0.0209042i
$191$		−	18.9822i		−	1.37350i	−0.726892	−	0.686751i	$-0.759036\pi$
$191$		−	18.9822i		−	1.37350i	0.726892	−	0.686751i	$-0.240964\pi$
$192$	−7.25861	+	3.36342i	−0.523845	+	0.242734i
$193$	26.5854			1.91366			0.956828	−	0.290654i	$-0.0938728\pi$
$193$	26.5854			1.91366			0.956828	+	0.290654i	$0.0938728\pi$
$194$	14.8399	−	1.07509i	1.06544	−	0.0771868i
$195$	−4.52534			−0.324067
$196$	13.4571	−	3.86097i	0.961220	−	0.275783i
$197$	23.2008			1.65299			0.826494	−	0.562945i	$-0.190332\pi$
$197$	23.2008			1.65299			0.826494	+	0.562945i	$0.190332\pi$
$198$	7.37496	−	0.534284i	0.524115	−	0.0379699i
$199$	19.8867			1.40973			0.704866	−	0.709341i	$-0.251007\pi$
$199$	19.8867			1.40973			0.704866	+	0.709341i	$0.251007\pi$
$200$	−0.608847	−	2.76212i	−0.0430520	−	0.195311i
$201$		−	4.52269i		−	0.319006i
$202$	−5.61154	+	0.406532i	−0.394827	+	0.0286035i
$203$	1.15318	+	17.0880i	0.0809375	+	1.19934i
$204$	1.93186	+	13.2632i	0.135257	+	0.928607i
$205$	8.71476			0.608665
$206$	0.387217	+	5.34493i	0.0269787	+	0.372399i
$207$		−	0.858617i		−	0.0596780i
$208$	5.16359	+	17.3493i	0.358031	+	1.20296i
$209$		−	14.7435i		−	1.01983i
$210$	0.521019	+	3.70520i	0.0359537	+	0.255683i
$211$		−	2.51318i		−	0.173014i	−0.996251	−	0.0865072i	$-0.972429\pi$
$211$		−	2.51318i		−	0.173014i	0.996251	−	0.0865072i	$-0.0275706\pi$
$212$	−7.30890	+	1.06458i	−0.501977	+	0.0731159i
$213$			7.23513i			0.495743i
$214$	−3.36927	+	0.244089i	−0.230319	+	0.0166856i
$215$	−7.42042			−0.506068
$216$	0.608847	+	2.76212i	0.0414268	+	0.187938i
$217$	−0.464462	−	6.88244i	−0.0315297	−	0.467211i
$218$	−0.592420	−	8.17744i	−0.0401238	−	0.553846i
$219$			9.24697i			0.624852i
$220$	10.3479	−	1.50723i	0.697656	−	0.101618i
$221$	30.3269			2.04001
$222$	−0.218653	−	3.01816i	−0.0146750	−	0.202566i
$223$	1.23567			0.0827463			0.0413732	−	0.999144i	$-0.486827\pi$
$223$	1.23567			0.0827463			0.0413732	+	0.999144i	$0.486827\pi$
$224$	13.6105	−	6.22527i	0.909391	−	0.415943i
$225$	−1.00000			−0.0666667
$226$	0.701606	+	9.68458i	0.0466701	+	0.644208i
$227$	−1.76552			−0.117182			−0.0585909	−	0.998282i	$-0.518661\pi$
$227$	−1.76552			−0.117182			−0.0585909	+	0.998282i	$0.518661\pi$
$228$	5.58072	−	0.812865i	0.369593	−	0.0538333i
$229$			8.94803i			0.591302i	0.955296	+	0.295651i	$0.0955366\pi$
$229$			8.94803i			0.591302i	−0.955296	+	0.295651i	$0.904463\pi$
$230$	−0.0877385	−	1.21109i	−0.00578531	−	0.0798572i
$231$	−13.8020	+	0.931432i	−0.908108	+	0.0612837i
$232$	3.94127	+	17.8801i	0.258757	+	1.17389i
$233$	−21.8087			−1.42874			−0.714368	−	0.699770i	$-0.753286\pi$
$233$	−21.8087			−1.42874			−0.714368	+	0.699770i	$0.753286\pi$
$234$	6.38308	−	0.462426i	0.417275	−	0.0302298i
$235$			9.82671i			0.641024i
$236$	8.46986	−	1.23368i	0.551341	−	0.0803060i
$237$		−	2.68314i		−	0.174289i
$238$	−3.49164	−	24.8306i	−0.226330	−	1.60953i
$239$		−	14.7558i		−	0.954471i	−0.878776	−	0.477235i	$-0.841639\pi$
$239$		−	14.7558i		−	0.954471i	0.878776	−	0.477235i	$-0.158361\pi$
$240$	1.14104	+	3.83380i	0.0736537	+	0.247471i
$241$		−	15.3302i		−	0.987503i	−0.869603	−	0.493751i	$-0.835625\pi$
$241$		−	15.3302i		−	0.987503i	0.869603	−	0.493751i	$-0.164375\pi$
$242$	1.66949	+	23.0447i	0.107319	+	1.48137i
$243$	1.00000			0.0641500
$244$	3.08604	+	21.1872i	0.197564	+	1.35637i
$245$	−0.940508	−	6.93653i	−0.0600868	−	0.443159i
$246$	−12.2923	+	0.890525i	−0.783730	+	0.0567778i
$247$		−	12.7606i		−	0.811937i
$248$	−1.58741	−	7.20149i	−0.100800	−	0.457295i
$249$	16.2812			1.03178
$250$	−1.41052	+	0.102186i	−0.0892089	+	0.00646280i
$251$	−15.4063			−0.972435			−0.486218	−	0.873838i	$-0.661624\pi$
$251$	−15.4063			−0.972435			−0.486218	+	0.873838i	$0.661624\pi$
$252$	−1.11353	−	5.17301i	−0.0701455	−	0.325869i
$253$	4.48932			0.282241
$254$	14.7870	−	1.07125i	0.927818	−	0.0672164i
$255$	6.70156			0.419668
$256$	13.3961	−	8.74903i	0.837254	−	0.546814i
$257$		−	11.6114i		−	0.724298i	−0.932120	−	0.362149i	$-0.882043\pi$
$257$		−	11.6114i		−	0.724298i	0.932120	−	0.362149i	$-0.117957\pi$
$258$	10.4666	−	0.758262i	0.651624	−	0.0472073i
$259$	0.381184	+	5.64842i	0.0236856	+	0.350976i
$260$	8.95618	−	1.30452i	0.555439	−	0.0809029i
$261$	6.47333			0.400689
$262$	1.95109	+	26.9318i	0.120539	+	1.66385i
$263$			14.4160i			0.888927i	0.895797	+	0.444463i	$0.146606\pi$
$263$			14.4160i			0.888927i	−0.895797	+	0.444463i	$0.853394\pi$
$264$	−14.4419	+	3.18339i	−0.888836	+	0.195924i
$265$			3.69301i			0.226860i
$266$	−10.4480	+	1.46917i	−0.640605	+	0.0900808i
$267$		−	8.53516i		−	0.522343i
$268$	1.30375	+	8.95093i	0.0796395	+	0.546765i
$269$			10.8482i			0.661425i	0.943732	+	0.330712i	$0.107289\pi$
$269$			10.8482i			0.661425i	−0.943732	+	0.330712i	$0.892711\pi$
$270$	1.41052	−	0.102186i	0.0858413	−	0.00621883i
$271$	−18.9758			−1.15270			−0.576349	−	0.817204i	$-0.695523\pi$
$271$	−18.9758			−1.15270			−0.576349	+	0.817204i	$0.695523\pi$
$272$	−7.64674	−	25.6924i	−0.463652	−	1.55783i
$273$	−11.9458	+	0.806161i	−0.722991	+	0.0487911i
$274$	−0.559175	−	7.71854i	−0.0337810	−	0.466294i
$275$		−	5.22855i		−	0.315293i
$276$	0.247513	+	1.69930i	0.0148986	+	0.102286i
$277$	11.0960			0.666692			0.333346	−	0.942804i	$-0.391822\pi$
$277$	11.0960			0.666692			0.333346	+	0.942804i	$0.391822\pi$
$278$	−0.290150	−	4.00507i	−0.0174020	−	0.240208i
$279$	−2.60723			−0.156091
$280$	−2.09926	−	7.18284i	−0.125455	−	0.429257i
$281$	−26.1397			−1.55937			−0.779683	−	0.626175i	$-0.784620\pi$
$281$	−26.1397			−1.55937			−0.779683	+	0.626175i	$0.784620\pi$
$282$	−1.00415	−	13.8607i	−0.0597963	−	0.825395i
$283$	15.0023			0.891793			0.445897	−	0.895084i	$-0.352885\pi$
$283$	15.0023			0.891793			0.445897	+	0.895084i	$0.352885\pi$
$284$	−2.08567	−	14.3192i	−0.123762	−	0.849686i
$285$		−	2.81981i		−	0.167031i
$286$	2.41782	+	33.3742i	0.142969	+	1.97346i
$287$	23.0048	−	1.55248i	1.35793	−	0.0916399i
$288$	−2.00121	−	5.29104i	−0.117923	−	0.311778i
$289$	−27.9109			−1.64182
$290$	9.13075	−	0.661483i	0.536176	−	0.0388436i
$291$			10.5209i			0.616747i
$292$	−2.66562	−	18.3008i	−0.155994	−	1.07097i
$293$		−	30.1766i		−	1.76293i	−0.472245	−	0.881467i	$-0.656556\pi$
$293$		−	30.1766i		−	1.76293i	0.472245	−	0.881467i	$-0.343444\pi$
$294$	2.03542	+	9.68799i	0.118708	+	0.565015i
$295$		−	4.27962i		−	0.249169i
$296$	1.30278	+	5.91026i	0.0757228	+	0.343527i
$297$			5.22855i			0.303391i
$298$	−0.176634	−	2.43816i	−0.0102321	−	0.141239i
$299$	3.88554			0.224706
$300$	1.97912	−	0.288270i	0.114264	−	0.0166433i
$301$	−19.5880	+	1.32190i	−1.12904	+	0.0761930i
$302$	−21.0917	+	1.52800i	−1.21369	+	0.0879267i
$303$		−	3.97836i		−	0.228551i
$304$	−10.8106	+	3.21751i	−0.620029	+	0.184537i
$305$	10.7054			0.612989
$306$	−9.45266	+	0.684805i	−0.540373	+	0.0391477i
$307$	−6.17458			−0.352402			−0.176201	−	0.984354i	$-0.556381\pi$
$307$	−6.17458			−0.352402			−0.176201	+	0.984354i	$0.556381\pi$
$308$	27.0474	−	5.82213i	1.54117	−	0.331746i
$309$	−3.78934			−0.215568
$310$	−3.67755	+	0.266423i	−0.208871	+	0.0151318i
$311$	3.80564			0.215798			0.107899	−	0.994162i	$-0.465588\pi$
$311$	3.80564			0.215798			0.107899	+	0.994162i	$0.465588\pi$
$312$	−12.4995	+	2.75524i	−0.707647	+	0.155985i
$313$			16.5774i			0.937011i	0.883461	+	0.468506i	$0.155207\pi$
$313$			16.5774i			0.937011i	−0.883461	+	0.468506i	$0.844793\pi$
$314$	−15.5697	+	1.12796i	−0.878650	+	0.0636544i
$315$	−2.63975	+	0.178143i	−0.148733	+	0.0100372i
$316$	0.773468	+	5.31025i	0.0435110	+	0.298725i
$317$	−11.1118			−0.624098			−0.312049	−	0.950066i	$-0.601015\pi$
$317$	−11.1118			−0.624098			−0.312049	+	0.950066i	$0.601015\pi$
$318$	−0.377374	−	5.20906i	−0.0211621	−	0.292109i
$319$			33.8461i			1.89502i
$320$	−3.36342	−	7.25861i	−0.188021	−	0.405769i
$321$		−	2.38868i		−	0.133323i
$322$	−0.447356	−	3.18135i	−0.0249302	−	0.177290i
$323$			18.8971i			1.05146i
$324$	−1.97912	+	0.288270i	−0.109951	+	0.0160150i
$325$		−	4.52534i		−	0.251021i
$326$	−26.5133	+	1.92078i	−1.46844	+	0.106382i
$327$	5.79748			0.320601
$328$	24.0712	−	5.30596i	1.32911	−	0.292972i
$329$	1.75056	+	25.9400i	0.0965117	+	1.43012i
$330$	0.534284	+	7.37496i	0.0294114	+	0.405978i
$331$			22.4709i			1.23511i	0.786526	+	0.617557i	$0.211877\pi$
$331$			22.4709i			1.23511i	−0.786526	+	0.617557i	$0.788123\pi$
$332$	−32.2224	+	4.69339i	−1.76844	+	0.257583i
$333$	2.13976			0.117258
$334$	−0.193453	−	2.67032i	−0.0105853	−	0.146113i
$335$	4.52269			0.247101
$336$	3.69502	+	9.91700i	0.201580	+	0.541017i
$337$	−6.02729			−0.328328			−0.164164	−	0.986433i	$-0.552493\pi$
$337$	−6.02729			−0.328328			−0.164164	+	0.986433i	$0.552493\pi$
$338$	0.764222	+	10.5489i	0.0415682	+	0.573784i
$339$	−6.86598			−0.372909
$340$	−13.2632	+	1.93186i	−0.719296	+	0.104770i
$341$		−	13.6321i		−	0.738217i
$342$	0.288144	+	3.97738i	0.0155811	+	0.215072i
$343$	−3.71840	−	18.1431i	−0.200775	−	0.979637i
$344$	−20.4961	+	4.51790i	−1.10508	+	0.243589i
$345$	0.858617			0.0462264
$346$	13.3055	−	0.963925i	0.715307	−	0.0518209i
$347$			9.57093i			0.513794i	0.966439	+	0.256897i	$0.0827001\pi$
$347$			9.57093i			0.513794i	−0.966439	+	0.256897i	$0.917300\pi$
$348$	−12.8115	+	1.86607i	−0.686767	+	0.100032i
$349$		−	12.9442i		−	0.692884i	−0.938071	−	0.346442i	$-0.887390\pi$
$349$		−	12.9442i		−	0.692884i	0.938071	−	0.346442i	$-0.112610\pi$
$350$	−3.70520	+	0.521019i	−0.198052	+	0.0278497i
$351$			4.52534i			0.241545i
$352$	27.6645	−	10.4635i	1.47452	−	0.557704i
$353$			11.6209i			0.618520i	0.950978	+	0.309260i	$0.100081\pi$
$353$			11.6209i			0.618520i	−0.950978	+	0.309260i	$0.899919\pi$
$354$	0.437316	+	6.03647i	0.0232431	+	0.320835i
$355$	−7.23513			−0.384001
$356$	2.46043	+	16.8921i	0.130402	+	0.895278i
$357$	17.6904	−	1.19384i	0.936277	−	0.0631847i
$358$	−30.2722	+	2.19309i	−1.59993	+	0.115908i
$359$			5.42483i			0.286312i	0.989700	+	0.143156i	$0.0457250\pi$
$359$			5.42483i			0.286312i	−0.989700	+	0.143156i	$0.954275\pi$
$360$	−2.76212	+	0.608847i	−0.145576	+	0.0320891i
$361$	−11.0487			−0.581510
$362$	34.0972	−	2.47020i	1.79211	−	0.129831i
$363$	−16.3377			−0.857509
$364$	23.4097	−	5.03909i	1.22700	−	0.264120i
$365$	−9.24697			−0.484009
$366$	−15.1001	+	1.09394i	−0.789297	+	0.0571811i
$367$	−28.4203			−1.48353			−0.741763	−	0.670662i	$-0.766010\pi$
$367$	−28.4203			−1.48353			−0.741763	+	0.670662i	$0.766010\pi$
$368$	−0.979715	−	3.29177i	−0.0510712	−	0.171595i
$369$		−	8.71476i		−	0.453672i
$370$	3.01816	−	0.218653i	0.156907	−	0.0113672i
$371$	0.657886	+	9.74862i	0.0341557	+	0.506123i
$372$	5.16002	−	0.751587i	0.267535	−	0.0389680i
$373$	23.0923			1.19568			0.597838	−	0.801617i	$-0.296027\pi$
$373$	23.0923			1.19568			0.597838	+	0.801617i	$0.296027\pi$
$374$	−3.58054	−	49.4237i	−0.185145	−	2.55564i
$375$		−	1.00000i		−	0.0516398i
$376$	5.98296	+	27.1425i	0.308548	+	1.39977i
$377$			29.2941i			1.50872i
$378$	3.70520	−	0.521019i	0.190575	−	0.0267983i
$379$		−	12.0804i		−	0.620527i	−0.950651	−	0.310263i	$-0.899583\pi$
$379$		−	12.0804i		−	0.620527i	0.950651	−	0.310263i	$-0.100417\pi$
$380$	0.812865	+	5.58072i	0.0416991	+	0.286285i
$381$			10.4834i			0.537080i
$382$	−26.7747	+	1.93971i	−1.36991	+	0.0992443i
$383$	−4.05602			−0.207253			−0.103626	−	0.994616i	$-0.533045\pi$
$383$	−4.05602			−0.207253			−0.103626	+	0.994616i	$0.533045\pi$
$384$	5.48588	+	9.89470i	0.279950	+	0.504937i
$385$	−0.931432	−	13.8020i	−0.0474702	−	0.703418i
$386$	−2.71665	−	37.4991i	−0.138274	−	1.90865i
$387$			7.42042i			0.377201i
$388$	−3.03286	−	20.8221i	−0.153970	−	1.05708i
$389$	5.28804			0.268114			0.134057	−	0.990974i	$-0.457199\pi$
$389$	5.28804			0.268114			0.134057	+	0.990974i	$0.457199\pi$
$390$	0.462426	+	6.38308i	0.0234159	+	0.323220i
$391$	−5.75407			−0.290996
$392$	−6.82108	−	18.5869i	−0.344517	−	0.938780i
$393$	−19.0936			−0.963143
$394$	−2.37079	−	32.7251i	−0.119439	−	1.64867i
$395$	2.68314			0.135003
$396$	−1.50723	−	10.3479i	−0.0757413	−	0.520002i
$397$			15.0058i			0.753121i	0.926392	+	0.376561i	$0.122893\pi$
$397$			15.0058i			0.753121i	−0.926392	+	0.376561i	$0.877107\pi$
$398$	−2.03214	−	28.0505i	−0.101862	−	1.40605i
$399$	−0.502330	−	7.44358i	−0.0251480	−	0.372645i
$400$	−3.83380	+	1.14104i	−0.191690	+	0.0570519i
$401$	19.3630			0.966942			0.483471	−	0.875360i	$-0.339376\pi$
$401$	19.3630			0.966942			0.483471	+	0.875360i	$0.339376\pi$
$402$	−6.37933	+	0.462155i	−0.318172	+	0.0230502i
$403$		−	11.7986i		−	0.587732i
$404$	1.14684	+	7.87363i	0.0570574	+	0.391728i
$405$			1.00000i			0.0496904i
$406$	23.9850	−	3.37273i	1.19036	−	0.167386i
$407$			11.1878i			0.554560i
$408$	18.5105	−	4.08023i	0.916407	−	0.202001i
$409$			0.432474i			0.0213845i	0.999943	+	0.0106922i	$0.00340351\pi$
$409$			0.432474i			0.0213845i	−0.999943	+	0.0106922i	$0.996596\pi$
$410$	−0.890525	−	12.2923i	−0.0439799	−	0.607074i
$411$	5.47214			0.269921
$412$	7.49955	−	1.09235i	0.369476	−	0.0538164i
$413$	−0.762386	−	11.2971i	−0.0375146	−	0.555894i
$414$	−1.21109	+	0.0877385i	−0.0595220	+	0.00431211i
$415$			16.2812i			0.799214i
$416$	23.9438	−	9.05619i	1.17394	−	0.444016i
$417$	2.83943			0.139048
$418$	−20.7960	+	1.50658i	−1.01716	+	0.0736891i
$419$	5.56216			0.271729			0.135865	−	0.990727i	$-0.456619\pi$
$419$	5.56216			0.271729			0.135865	+	0.990727i	$0.456619\pi$
$420$	5.17301	−	1.11353i	0.252417	−	0.0543345i
$421$	−1.97874			−0.0964379			−0.0482190	−	0.998837i	$-0.515355\pi$
$421$	−1.97874			−0.0964379			−0.0482190	+	0.998837i	$0.515355\pi$
$422$	−3.54488	+	0.256811i	−0.172562	+	0.0125014i
$423$	9.82671			0.477791
$424$	2.24848	+	10.2005i	0.109196	+	0.495382i
$425$			6.70156i			0.325073i
$426$	10.2053	−	0.739328i	0.494447	−	0.0358206i
$427$	28.2595	−	1.90710i	1.36757	−	0.0922908i
$428$	0.688584	+	4.72747i	0.0332840	+	0.228511i
$429$	−23.6610			−1.14236
$430$	0.758262	+	10.4666i	0.0365666	+	0.504746i
$431$			14.0974i			0.679048i	0.940597	+	0.339524i	$0.110266\pi$
$431$			14.0974i			0.679048i	−0.940597	+	0.339524i	$0.889734\pi$
$432$	3.83380	−	1.14104i	0.184454	−	0.0548983i
$433$		−	18.3496i		−	0.881826i	−0.897550	−	0.440913i	$-0.854655\pi$
$433$		−	18.3496i		−	0.881826i	0.897550	−	0.440913i	$-0.145345\pi$
$434$	−9.66034	+	1.35842i	−0.463711	+	0.0652062i
$435$			6.47333i			0.310373i
$436$	−11.4739	+	1.67124i	−0.549499	+	0.0800378i
$437$			2.42113i			0.115819i
$438$	13.0430	−	0.944910i	0.623219	−	0.0451495i
$439$	8.36492			0.399236			0.199618	−	0.979874i	$-0.436030\pi$
$439$	8.36492			0.399236			0.199618	+	0.979874i	$0.436030\pi$
$440$	−3.18339	−	14.4419i	−0.151762	−	0.688490i
$441$	−6.93653	+	0.940508i	−0.330311	+	0.0447861i
$442$	−3.09898	−	42.7766i	−0.147403	−	2.03467i
$443$			1.47488i			0.0700737i	0.999386	+	0.0350368i	$0.0111549\pi$
$443$			1.47488i			0.0700737i	−0.999386	+	0.0350368i	$0.988845\pi$
$444$	−4.23483	+	0.616827i	−0.200976	+	0.0292733i
$445$	8.53516			0.404605
$446$	−0.126268	−	1.74293i	−0.00597895	−	0.0825300i
$447$	1.72856			0.0817580
$448$	−10.1716	−	18.5617i	−0.480565	−	0.876959i
$449$	−16.1871			−0.763918			−0.381959	−	0.924179i	$-0.624750\pi$
$449$	−16.1871			−0.763918			−0.381959	+	0.924179i	$0.624750\pi$
$450$	0.102186	+	1.41052i	0.00481709	+	0.0664924i
$451$	45.5656			2.14560
$452$	13.5886	−	1.97925i	0.639152	−	0.0930963i
$453$		−	14.9532i		−	0.702562i
$454$	0.180411	+	2.49030i	0.00846713	+	0.116876i
$455$	−0.806161	−	11.9458i	−0.0377934	−	0.560026i
$456$	−1.71683	−	7.78864i	−0.0803980	−	0.364737i
$457$	−26.6551			−1.24687			−0.623435	−	0.781875i	$-0.714264\pi$
$457$	−26.6551			−1.24687			−0.623435	+	0.781875i	$0.714264\pi$
$458$	12.6213	−	0.914362i	0.589757	−	0.0427253i
$459$		−	6.70156i		−	0.312802i
$460$	−1.69930	+	0.247513i	−0.0792304	+	0.0115404i
$461$			34.3308i			1.59895i	0.600703	+	0.799473i	$0.294888\pi$
$461$			34.3308i			1.59895i	−0.600703	+	0.799473i	$0.705112\pi$
$462$	2.72418	+	19.3728i	0.126740	+	0.901306i
$463$			16.8787i			0.784421i	0.919875	+	0.392210i	$0.128290\pi$
$463$			16.8787i			0.784421i	−0.919875	+	0.392210i	$0.871710\pi$
$464$	24.8175	−	7.38632i	1.15212	−	0.342902i
$465$		−	2.60723i		−	0.120908i
$466$	2.22854	+	30.7615i	0.103235	+	1.42500i
$467$	−33.4884			−1.54966			−0.774829	−	0.632171i	$-0.782164\pi$
$467$	−33.4884			−1.54966			−0.774829	+	0.632171i	$0.782164\pi$
$468$	−1.30452	−	8.95618i	−0.0603015	−	0.414000i
$469$	11.9388	−	0.805688i	0.551280	−	0.0372032i
$470$	13.8607	−	1.00415i	0.639348	−	0.0463180i
$471$		−	11.0383i		−	0.508618i
$472$	−2.60563	−	11.8208i	−0.119934	−	0.544097i
$473$	−38.7980			−1.78394
$474$	−3.78461	+	0.274179i	−0.173833	+	0.0125935i
$475$	2.81981			0.129382
$476$	−34.6673	+	7.46236i	−1.58897	+	0.342037i
$477$	3.69301			0.169091
$478$	−20.8132	+	1.50783i	−0.951976	+	0.0689665i
$479$	−21.1342			−0.965644			−0.482822	−	0.875718i	$-0.660388\pi$
$479$	−21.1342			−0.965644			−0.482822	+	0.875718i	$0.660388\pi$
$480$	5.29104	−	2.00121i	0.241502	−	0.0913425i
$481$			9.68314i			0.441513i
$482$	−21.6235	+	1.56653i	−0.984921	+	0.0713533i
$483$	2.26653	−	0.152957i	0.103131	−	0.00695979i
$484$	32.3343	−	4.70968i	1.46974	−	0.214076i
$485$	−10.5209			−0.477730
$486$	−0.102186	−	1.41052i	−0.00463525	−	0.0639823i
$487$			13.3600i			0.605399i	0.953086	+	0.302699i	$0.0978878\pi$
$487$			13.3600i			0.605399i	−0.953086	+	0.302699i	$0.902112\pi$
$488$	29.5696	−	6.51795i	1.33855	−	0.295054i
$489$		−	18.7969i		−	0.850025i
$490$	−9.68799	+	2.03542i	−0.437659	+	0.0919508i
$491$		−	10.6077i		−	0.478717i	−0.970931	−	0.239359i	$-0.923063\pi$
$491$		−	10.6077i		−	0.478717i	0.970931	−	0.239359i	$-0.0769372\pi$
$492$	2.51220	+	17.2475i	0.113259	+	0.777578i
$493$		−	43.3814i		−	1.95380i
$494$	−17.9990	+	1.30395i	−0.809815	+	0.0586676i
$495$	−5.22855			−0.235006
$496$	−9.99562	+	2.97496i	−0.448817	+	0.133579i
$497$	−19.0989	+	1.28889i	−0.856703	+	0.0578147i
$498$	−1.66371	−	22.9649i	−0.0745527	−	1.02908i
$499$			22.9131i			1.02573i	0.858470	+	0.512865i	$0.171416\pi$
$499$			22.9131i			1.02573i	−0.858470	+	0.512865i	$0.828584\pi$
$500$	0.288270	+	1.97912i	0.0128918	+	0.0885088i
$501$	1.89315			0.0845796
$502$	1.57430	+	21.7308i	0.0702646	+	0.969893i
$503$	15.2517			0.680040			0.340020	−	0.940418i	$-0.389566\pi$
$503$	15.2517			0.680040			0.340020	+	0.940418i	$0.389566\pi$
$504$	−7.18284	+	2.09926i	−0.319949	+	0.0935083i
$505$	3.97836			0.177035
$506$	−0.458745	−	6.33227i	−0.0203937	−	0.281504i
$507$	−7.47874			−0.332143
$508$	−3.02204	−	20.7478i	−0.134081	−	0.920536i
$509$			6.06153i			0.268673i	0.990936	+	0.134336i	$0.0428902\pi$
$509$			6.06153i			0.268673i	−0.990936	+	0.134336i	$0.957110\pi$
$510$	−0.684805	−	9.45266i	−0.0303237	−	0.418571i
$511$	−24.4097	+	1.64729i	−1.07982	+	0.0728717i
$512$	−13.7095	−	18.0013i	−0.605882	−	0.795555i
$513$	−2.81981			−0.124498
$514$	−16.3781	+	1.18652i	−0.722405	+	0.0523351i
$515$		−	3.78934i		−	0.166978i
$516$	−2.13908	−	14.6859i	−0.0941679	−	0.646510i
$517$			51.3794i			2.25967i
$518$	7.92824	−	1.11485i	0.348347	−	0.0489839i
$519$			9.43306i			0.414065i
$520$	−2.75524	−	12.4995i	−0.120825	−	0.548141i
$521$			33.7238i			1.47747i	0.673998	+	0.738733i	$0.264576\pi$
$521$			33.7238i			1.47747i	−0.673998	+	0.738733i	$0.735424\pi$
$522$	−0.661483	−	9.13075i	−0.0289523	−	0.399642i
$523$	17.5830			0.768852			0.384426	−	0.923156i	$-0.374399\pi$
$523$	17.5830			0.768852			0.384426	+	0.923156i	$0.374399\pi$
$524$	37.7884	−	5.50410i	1.65079	−	0.240448i
$525$	−0.178143	−	2.63975i	−0.00777482	−	0.115208i
$526$	20.3340	−	1.47311i	0.886603	−	0.0642306i
$527$			17.4725i			0.761116i
$528$	5.96598	+	20.0452i	0.259636	+	0.872356i
$529$	22.2628			0.967947
$530$	5.20906	−	0.377374i	0.226267	−	0.0163921i
$531$	−4.27962			−0.185720
$532$	3.13993	+	14.5869i	0.136133	+	0.632422i
$533$	39.4373			1.70822
$534$	−12.0390	+	0.872173i	−0.520978	+	0.0377426i
$535$	2.38868			0.103272
$536$	12.4922	−	2.75363i	0.539581	−	0.118939i
$537$		−	21.4618i		−	0.926143i
$538$	15.3015	−	1.10853i	0.659696	−	0.0477921i
$539$	−4.91749	−	36.2680i	−0.211811	−	1.56217i
$540$	−0.288270	−	1.97912i	−0.0124052	−	0.0851676i
$541$	−22.7960			−0.980079			−0.490039	−	0.871700i	$-0.663018\pi$
$541$	−22.7960			−0.980079			−0.490039	+	0.871700i	$0.663018\pi$
$542$	1.93906	+	26.7657i	0.0832897	+	1.14968i
$543$			24.1736i			1.03739i
$544$	−35.4582	+	13.4113i	−1.52026	+	0.575003i
$545$			5.79748i			0.248337i
$546$	2.35779	+	16.7673i	0.100904	+	0.717575i
$547$		−	14.4784i		−	0.619053i	−0.950891	−	0.309527i	$-0.899829\pi$
$547$		−	14.4784i		−	0.619053i	0.950891	−	0.309527i	$-0.100171\pi$
$548$	−10.8300	+	1.57745i	−0.462635	+	0.0673854i
$549$		−	10.7054i		−	0.456895i
$550$	−7.37496	+	0.534284i	−0.314469	+	0.0227819i
$551$	−18.2535			−0.777627
$552$	2.37160	−	0.522767i	0.100942	−	0.0222504i
$553$	7.08281	−	0.477984i	0.301192	−	0.0203259i
$554$	−1.13385	−	15.6511i	−0.0481727	−	0.664950i
$555$			2.13976i			0.0908276i
$556$	−5.61957	+	0.818523i	−0.238323	+	0.0347131i
$557$	14.9697			0.634288			0.317144	−	0.948377i	$-0.397276\pi$
$557$	14.9697			0.634288			0.317144	+	0.948377i	$0.397276\pi$
$558$	0.266423	+	3.67755i	0.0112786	+	0.155683i
$559$	−33.5800			−1.42028
$560$	−9.91700	+	3.69502i	−0.419070	+	0.156143i
$561$	35.0394			1.47937
$562$	2.67111	+	36.8705i	0.112674	+	1.55529i
$563$	6.81282			0.287126			0.143563	−	0.989641i	$-0.454144\pi$
$563$	6.81282			0.287126			0.143563	+	0.989641i	$0.454144\pi$
$564$	−19.4482	+	2.83274i	−0.818917	+	0.119280i
$565$		−	6.86598i		−	0.288854i
$566$	−1.53302	−	21.1610i	−0.0644377	−	0.889462i
$567$	0.178143	+	2.63975i	0.00748132	+	0.110859i
$568$	−19.9843	+	4.40509i	−0.838522	+	0.184833i
$569$	15.3819			0.644841			0.322421	−	0.946597i	$-0.395503\pi$
$569$	15.3819			0.644841			0.322421	+	0.946597i	$0.395503\pi$
$570$	−3.97738	+	0.288144i	−0.166594	+	0.0120690i
$571$		−	33.9875i		−	1.42233i	−0.703024	−	0.711167i	$-0.748167\pi$
$571$		−	33.9875i		−	1.42233i	0.703024	−	0.711167i	$-0.251833\pi$
$572$	46.8278	−	6.82075i	1.95797	−	0.285190i
$573$		−	18.9822i		−	0.792992i
$574$	−4.54056	−	32.2900i	−0.189519	−	1.34776i
$575$			0.858617i			0.0358068i
$576$	−7.25861	+	3.36342i	−0.302442	+	0.140142i
$577$		−	41.9819i		−	1.74773i	−0.486170	−	0.873864i	$-0.661606\pi$
$577$		−	41.9819i		−	1.74773i	0.486170	−	0.873864i	$-0.338394\pi$
$578$	2.85210	+	39.3688i	0.118632	+	1.63753i
$579$	26.5854			1.10485
$580$	−1.86607	−	12.8115i	−0.0774842	−	0.531968i
$581$	2.90039	+	42.9783i	0.120329	+	1.78304i
$582$	14.8399	−	1.07509i	0.615135	−	0.0445638i
$583$			19.3091i			0.799701i
$584$	−25.5412	+	5.62999i	−1.05690	+	0.232971i
$585$	−4.52534			−0.187100
$586$	−42.5646	+	3.08362i	−1.75833	+	0.127383i
$587$	12.5442			0.517756			0.258878	−	0.965910i	$-0.416647\pi$
$587$	12.5442			0.517756			0.258878	+	0.965910i	$0.416647\pi$
$588$	13.4571	−	3.86097i	0.554961	−	0.159224i
$589$	7.35190			0.302930
$590$	−6.03647	+	0.437316i	−0.248518	+	0.0180040i
$591$	23.2008			0.954353
$592$	8.20340	−	2.44155i	0.337158	−	0.100347i
$593$			9.26081i			0.380296i	0.981755	+	0.190148i	$0.0608968\pi$
$593$			9.26081i			0.380296i	−0.981755	+	0.190148i	$0.939103\pi$
$594$	7.37496	−	0.534284i	0.302598	−	0.0219219i
$595$	1.19384	+	17.6904i	0.0489426	+	0.725237i
$596$	−3.42102	+	0.498291i	−0.140130	+	0.0204108i
$597$	19.8867			0.813909
$598$	−0.397047	−	5.48062i	−0.0162365	−	0.224119i
$599$			15.8991i			0.649618i	0.945780	+	0.324809i	$0.105300\pi$
$599$			15.8991i			0.649618i	−0.945780	+	0.324809i	$0.894700\pi$
$600$	−0.608847	−	2.76212i	−0.0248561	−	0.112763i
$601$		−	31.4061i		−	1.28108i	−0.767925	−	0.640540i	$-0.778711\pi$
$601$		−	31.4061i		−	1.28108i	0.767925	−	0.640540i	$-0.221289\pi$
$602$	3.86618	+	27.4942i	0.157574	+	1.12058i
$603$		−	4.52269i		−	0.184178i
$604$	4.31055	+	29.5941i	0.175394	+	1.20417i
$605$		−	16.3377i		−	0.664223i
$606$	−5.61154	+	0.406532i	−0.227953	+	0.0165142i
$607$	−14.6628			−0.595147			−0.297573	−	0.954699i	$-0.596177\pi$
$607$	−14.6628			−0.595147			−0.297573	+	0.954699i	$0.596177\pi$
$608$	5.64304	+	14.9197i	0.228855	+	0.605074i
$609$	1.15318	+	17.0880i	0.0467293	+	0.692439i
$610$	−1.09394	−	15.1001i	−0.0442923	−	0.611387i
$611$			44.4692i			1.79903i
$612$	1.93186	+	13.2632i	0.0780907	+	0.536132i
$613$	35.6120			1.43836			0.719178	−	0.694826i	$-0.244519\pi$
$613$	35.6120			1.43836			0.719178	+	0.694826i	$0.244519\pi$
$614$	0.630955	+	8.70935i	0.0254633	+	0.351481i
$615$	8.71476			0.351413
$616$	−10.9761	−	37.5558i	−0.442238	−	1.51317i
$617$	22.0702			0.888513			0.444256	−	0.895900i	$-0.353468\pi$
$617$	22.0702			0.888513			0.444256	+	0.895900i	$0.353468\pi$
$618$	0.387217	+	5.34493i	0.0155762	+	0.215005i
$619$	−29.1671			−1.17232			−0.586162	−	0.810194i	$-0.699362\pi$
$619$	−29.1671			−1.17232			−0.586162	+	0.810194i	$0.699362\pi$
$620$	0.751587	+	5.16002i	0.0301845	+	0.207231i
$621$		−	0.858617i		−	0.0344551i
$622$	−0.388882	−	5.36792i	−0.0155928	−	0.215234i
$623$	22.5307	−	1.52048i	0.902672	−	0.0609169i
$624$	5.16359	+	17.3493i	0.206709	+	0.694527i
$625$	1.00000			0.0400000
$626$	23.3827	−	1.69398i	0.934562	−	0.0677050i
$627$		−	14.7435i		−	0.588799i
$628$	3.18201	+	21.8461i	0.126976	+	0.871754i
$629$		−	14.3397i		−	0.571762i
$630$	0.521019	+	3.70520i	0.0207579	+	0.147619i
$631$			0.162149i			0.00645504i	0.999995	+	0.00322752i	$0.00102735\pi$
$631$			0.162149i			0.00645504i	−0.999995	+	0.00322752i	$0.998973\pi$
$632$	7.41115	−	1.63362i	0.294800	−	0.0649820i
$633$		−	2.51318i		−	0.0998899i
$634$	1.13546	+	15.6733i	0.0450950	+	0.622467i
$635$	−10.4834			−0.416020
$636$	−7.30890	+	1.06458i	−0.289817	+	0.0422135i
$637$	−4.25612	−	31.3902i	−0.168634	−	1.24372i
$638$	47.7406	−	3.45860i	1.89007	−	0.136927i
$639$			7.23513i			0.286217i
$640$	−9.89470	+	5.48588i	−0.391122	+	0.216849i
$641$	12.4758			0.492766			0.246383	−	0.969173i	$-0.420758\pi$
$641$	12.4758			0.492766			0.246383	+	0.969173i	$0.420758\pi$
$642$	−3.36927	+	0.244089i	−0.132975	+	0.00963343i
$643$	−28.4881			−1.12346			−0.561731	−	0.827320i	$-0.689864\pi$
$643$	−28.4881			−1.12346			−0.561731	+	0.827320i	$0.689864\pi$
$644$	−4.44164	+	0.956093i	−0.175025	+	0.0376753i
$645$	−7.42042			−0.292179
$646$	26.6547	−	1.93102i	1.04871	−	0.0759748i
$647$	−24.4328			−0.960554			−0.480277	−	0.877117i	$-0.659464\pi$
$647$	−24.4328			−0.960554			−0.480277	+	0.877117i	$0.659464\pi$
$648$	0.608847	+	2.76212i	0.0239178	+	0.108506i
$649$		−	22.3762i		−	0.878342i
$650$	−6.38308	+	0.462426i	−0.250365	+	0.0181379i
$651$	−0.464462	−	6.88244i	−0.0182037	−	0.269744i
$652$	5.41858	+	37.2012i	0.212208	+	1.45691i
$653$	−39.9022			−1.56149			−0.780746	−	0.624848i	$-0.785161\pi$
$653$	−39.9022			−1.56149			−0.780746	+	0.624848i	$0.785161\pi$
$654$	−0.592420	−	8.17744i	−0.0231655	−	0.319763i
$655$		−	19.0936i		−	0.746047i
$656$	−9.94388	−	33.4107i	−0.388243	−	1.30447i
$657$			9.24697i			0.360759i
$658$	36.4100	−	5.11990i	1.41941	−	0.199595i
$659$		−	2.24981i		−	0.0876403i	−0.999039	−	0.0438202i	$-0.986047\pi$
$659$		−	2.24981i		−	0.0876403i	0.999039	−	0.0438202i	$-0.0139529\pi$
$660$	10.3479	−	1.50723i	0.402792	−	0.0586690i
$661$			26.0267i			1.01232i	0.862439	+	0.506162i	$0.168936\pi$
$661$			26.0267i			1.01232i	−0.862439	+	0.506162i	$0.831064\pi$
$662$	31.6956	−	2.29621i	1.23188	−	0.0892447i
$663$	30.3269			1.17780
$664$	9.91278	+	44.9707i	0.384690	+	1.74520i
$665$	7.44358	−	0.502330i	0.288650	−	0.0194795i
$666$	−0.218653	−	3.01816i	−0.00847263	−	0.116951i
$667$		−	5.55812i		−	0.215211i
$668$	−3.74676	+	0.545738i	−0.144967	+	0.0211152i
$669$	1.23567			0.0477736
$670$	−0.462155	−	6.37933i	−0.0178546	−	0.246455i
$671$	55.9737			2.16084
$672$	13.6105	−	6.22527i	0.525037	−	0.240145i
$673$	34.4184			1.32673			0.663365	−	0.748296i	$-0.269127\pi$
$673$	34.4184			1.32673			0.663365	+	0.748296i	$0.269127\pi$
$674$	0.615904	+	8.50160i	0.0237237	+	0.327469i
$675$	−1.00000			−0.0384900
$676$	14.8013	−	2.15590i	0.569281	−	0.0829191i
$677$			37.6392i			1.44659i	0.690538	+	0.723296i	$0.257374\pi$
$677$			37.6392i			1.44659i	−0.690538	+	0.723296i	$0.742626\pi$
$678$	0.701606	+	9.68458i	0.0269450	+	0.371934i
$679$	−27.7725	+	1.87423i	−1.06581	+	0.0719264i
$680$	4.08023	+	18.5105i	0.156470	+	0.709846i
$681$	−1.76552			−0.0676550
$682$	−19.2282	+	1.39300i	−0.736288	+	0.0533409i
$683$		−	25.5973i		−	0.979454i	−0.871876	−	0.489727i	$-0.837096\pi$
$683$		−	25.5973i		−	0.979454i	0.871876	−	0.489727i	$-0.162904\pi$
$684$	5.58072	−	0.812865i	0.213384	−	0.0310807i
$685$			5.47214i			0.209080i
$686$	−25.2112	+	7.09884i	−0.962570	+	0.271035i
$687$			8.94803i			0.341389i
$688$	8.46699	+	28.4484i	0.322801	+	1.08459i
$689$			16.7122i			0.636682i
$690$	−0.0877385	−	1.21109i	−0.00334015	−	0.0461056i
$691$	20.4140			0.776585			0.388293	−	0.921536i	$-0.373065\pi$
$691$	20.4140			0.776585			0.388293	+	0.921536i	$0.373065\pi$
$692$	−2.71927	−	18.6691i	−0.103371	−	0.709693i
$693$	−13.8020	+	0.931432i	−0.524297	+	0.0353822i
$694$	13.5000	−	0.978013i	0.512451	−	0.0371249i
$695$			2.83943i			0.107706i
$696$	3.94127	+	17.8801i	0.149393	+	0.677744i
$697$	−58.4025			−2.21215
$698$	−18.2579	+	1.32271i	−0.691073	+	0.0500653i
$699$	−21.8087			−0.824881
$700$	1.11353	+	5.17301i	0.0420873	+	0.195521i
$701$	−7.73141			−0.292011			−0.146006	−	0.989284i	$-0.546642\pi$
$701$	−7.73141			−0.292011			−0.146006	+	0.989284i	$0.546642\pi$
$702$	6.38308	−	0.462426i	0.240914	−	0.0174532i
$703$	−6.03370			−0.227565
$704$	−17.5858	−	37.9520i	−0.662790	−	1.43037i
$705$			9.82671i			0.370095i
$706$	16.3915	−	1.18750i	0.616903	−	0.0446920i
$707$	10.5019	−	0.708718i	0.394963	−	0.0266541i
$708$	8.46986	−	1.23368i	0.318317	−	0.0463647i
$709$	29.7793			1.11839			0.559193	−	0.829038i	$-0.311111\pi$
$709$	29.7793			1.11839			0.559193	+	0.829038i	$0.311111\pi$
$710$	0.739328	+	10.2053i	0.0277465	+	0.382997i
$711$		−	2.68314i		−	0.100626i
$712$	23.5751	−	5.19661i	0.883515	−	0.194751i
$713$			2.23862i			0.0838369i
$714$	−3.49164	−	24.8306i	−0.130671	−	0.929264i
$715$		−	23.6610i		−	0.884871i
$716$	6.18677	+	42.4753i	0.231211	+	1.58738i
$717$		−	14.7558i		−	0.551064i
$718$	7.65182	−	0.554341i	0.285563	−	0.0206878i
$719$	−18.4203			−0.686963			−0.343481	−	0.939160i	$-0.611606\pi$
$719$	−18.4203			−0.686963			−0.343481	+	0.939160i	$0.611606\pi$
$720$	1.14104	+	3.83380i	0.0425240	+	0.142877i
$721$	−0.675047	−	10.0029i	−0.0251401	−	0.372528i
$722$	1.12902	+	15.5844i	0.0420178	+	0.579990i
$723$		−	15.3302i		−	0.570135i
$724$	−6.96851	−	47.8423i	−0.258983	−	1.77804i
$725$	−6.47333			−0.240414
$726$	1.66949	+	23.0447i	0.0619604	+	0.855267i
$727$	−30.7292			−1.13968			−0.569842	−	0.821754i	$-0.692996\pi$
$727$	−30.7292			−1.13968			−0.569842	+	0.821754i	$0.692996\pi$
$728$	−9.49986	−	32.5048i	−0.352088	−	1.20471i
$729$	1.00000			0.0370370
$730$	0.944910	+	13.0430i	0.0349727	+	0.482743i
$731$	49.7284			1.83927
$732$	3.08604	+	21.1872i	0.114063	+	0.783102i
$733$			5.09061i			0.188026i	0.995571	+	0.0940130i	$0.0299695\pi$
$733$			5.09061i			0.188026i	−0.995571	+	0.0940130i	$0.970030\pi$
$734$	2.90415	+	40.0873i	0.107194	+	1.47965i
$735$	−0.940508	−	6.93653i	−0.0346911	−	0.255858i
$736$	−4.54298	+	1.71828i	−0.167456	+	0.0633365i
$737$	23.6471			0.871052
$738$	−12.2923	+	0.890525i	−0.452486	+	0.0327807i
$739$			15.1154i			0.556030i	0.960577	+	0.278015i	$0.0896765\pi$
$739$			15.1154i			0.556030i	−0.960577	+	0.278015i	$0.910323\pi$
$740$	−0.616827	−	4.23483i	−0.0226750	−	0.155675i
$741$		−	12.7606i		−	0.468772i
$742$	13.6834	−	1.92413i	0.502332	−	0.0706370i
$743$		−	42.0496i		−	1.54265i	−0.636440	−	0.771326i	$-0.719594\pi$
$743$		−	42.0496i		−	1.54265i	0.636440	−	0.771326i	$-0.280406\pi$
$744$	−1.58741	−	7.20149i	−0.0581972	−	0.264020i
$745$			1.72856i			0.0633295i
$746$	−2.35971	−	32.5721i	−0.0863951	−	1.19255i
$747$	16.2812			0.595699
$748$	−69.3471	+	10.1008i	−2.53558	+	0.369322i
$749$	6.30551	−	0.425527i	0.230398	−	0.0155484i
$750$	−1.41052	+	0.102186i	−0.0515048	+	0.00373130i
$751$		−	24.8965i		−	0.908487i	−0.890877	−	0.454244i	$-0.849910\pi$
$751$		−	24.8965i		−	0.908487i	0.890877	−	0.454244i	$-0.150090\pi$
$752$	37.6736	−	11.2127i	1.37382	−	0.408884i
$753$	−15.4063			−0.561436
$754$	41.3198	−	2.99344i	1.50478	−	0.109015i
$755$	14.9532			0.544202
$756$	−1.11353	−	5.17301i	−0.0404985	−	0.188141i
$757$	−39.7946			−1.44636			−0.723179	−	0.690661i	$-0.757320\pi$
$757$	−39.7946			−1.44636			−0.723179	+	0.690661i	$0.757320\pi$
$758$	−17.0396	+	1.23444i	−0.618905	+	0.0448370i
$759$	4.48932			0.162952
$760$	7.78864	−	1.71683i	0.282524	−	0.0622760i
$761$		−	27.5663i		−	0.999279i	−0.866234	−	0.499639i	$-0.833466\pi$
$761$		−	27.5663i		−	0.999279i	0.866234	−	0.499639i	$-0.166534\pi$
$762$	14.7870	−	1.07125i	0.535676	−	0.0388074i
$763$	1.03278	+	15.3039i	0.0373893	+	0.554038i
$764$	5.47199	+	37.5680i	0.197970	+	1.35916i
$765$	6.70156			0.242295
$766$	0.414468	+	5.72108i	0.0149753	+	0.206711i
$767$		−	19.3667i		−	0.699292i
$768$	13.3961	−	8.74903i	0.483389	−	0.315703i
$769$			5.38100i			0.194044i	0.995282	+	0.0970219i	$0.0309317\pi$
$769$			5.38100i			0.194044i	−0.995282	+	0.0970219i	$0.969068\pi$
$770$	−19.3728	+	2.72418i	−0.698149	+	0.0981725i
$771$		−	11.6114i		−	0.418174i
$772$	−52.6155	+	7.66376i	−1.89367	+	0.275825i
$773$			18.8696i			0.678693i	0.940661	+	0.339347i	$0.110206\pi$
$773$			18.8696i			0.678693i	−0.940661	+	0.339347i	$0.889794\pi$
$774$	10.4666	−	0.758262i	0.376215	−	0.0272552i
$775$	2.60723			0.0936546
$776$	−29.0600	+	6.40563i	−1.04319	+	0.229949i
$777$	0.381184	+	5.64842i	0.0136749	+	0.202636i
$778$	−0.540363	−	7.45887i	−0.0193730	−	0.267413i
$779$			24.5739i			0.880453i
$780$	8.95618	−	1.30452i	0.320683	−	0.0467093i
$781$	−37.8292			−1.35364
$782$	0.587985	+	8.11622i	0.0210263	+	0.290235i
$783$	6.47333			0.231338
$784$	−25.5201	+	11.5206i	−0.911433	+	0.411449i
$785$	11.0383			0.393974
$786$	1.95109	+	26.9318i	0.0695932	+	0.960626i
$787$	−36.8177			−1.31241			−0.656204	−	0.754583i	$-0.727839\pi$
$787$	−36.8177			−1.31241			−0.656204	+	0.754583i	$0.727839\pi$
$788$	−45.9171	+	6.68809i	−1.63573	+	0.238253i
$789$			14.4160i			0.513222i
$790$	−0.274179	−	3.78461i	−0.00975485	−	0.134651i
$791$	−1.22313	−	18.1244i	−0.0434895	−	0.644431i
$792$	−14.4419	+	3.18339i	−0.513170	+	0.113117i
$793$	48.4456			1.72035
$794$	21.1660	−	1.53338i	0.751153	−	0.0544178i
$795$			3.69301i			0.130978i
$796$	−39.3581	+	5.73274i	−1.39501	+	0.203191i
$797$			26.2324i			0.929200i	0.885521	+	0.464600i	$0.153802\pi$
$797$			26.2324i			0.929200i	−0.885521	+	0.464600i	$0.846198\pi$
$798$	−10.4480	+	1.46917i	−0.369854	+	0.0520082i
$799$		−	65.8543i		−	2.32976i
$800$	2.00121	+	5.29104i	0.0707536	+	0.187067i
$801$		−	8.53516i		−	0.301575i
$802$	−1.97862	−	27.3118i	−0.0698676	−	0.964414i
$803$	−48.3482			−1.70617
$804$	1.30375	+	8.95093i	0.0459799	+	0.315675i
$805$	0.152957	+	2.26653i	0.00539103	+	0.0798848i
$806$	−16.6422	+	1.20565i	−0.586196	+	0.0424673i
$807$			10.8482i			0.381874i
$808$	10.9887	−	2.42221i	0.386581	−	0.0852131i
$809$	−38.8484			−1.36584			−0.682919	−	0.730494i	$-0.739290\pi$
$809$	−38.8484			−1.36584			−0.682919	+	0.730494i	$0.739290\pi$
$810$	1.41052	−	0.102186i	0.0495605	−	0.00359045i
$811$	5.18833			0.182187			0.0910935	−	0.995842i	$-0.470964\pi$
$811$	5.18833			0.182187			0.0910935	+	0.995842i	$0.470964\pi$
$812$	−7.20823	−	33.4866i	−0.252959	−	1.17515i
$813$	−18.9758			−0.665510
$814$	15.7806	−	1.14324i	0.553110	−	0.0400705i
$815$	18.7969			0.658427
$816$	−7.64674	−	25.6924i	−0.267689	−	0.899416i
$817$		−	20.9242i		−	0.732043i
$818$	0.610013	−	0.0441928i	0.0213286	−	0.00154516i
$819$	−11.9458	+	0.806161i	−0.417419	+	0.0281695i
$820$	−17.2475	+	2.51220i	−0.602310	+	0.0877299i
$821$	19.2600			0.672178			0.336089	−	0.941830i	$-0.390896\pi$
$821$	19.2600			0.672178			0.336089	+	0.941830i	$0.390896\pi$
$822$	−0.559175	−	7.71854i	−0.0195035	−	0.269215i
$823$		−	7.22802i		−	0.251953i	−0.992033	−	0.125976i	$-0.959794\pi$
$823$		−	7.22802i		−	0.251953i	0.992033	−	0.125976i	$-0.0402064\pi$
$824$	−2.30713	−	10.4666i	−0.0803727	−	0.364622i
$825$		−	5.22855i		−	0.182035i
$826$	−15.8569	+	2.22976i	−0.551730	+	0.0775834i
$827$		−	48.2236i		−	1.67690i	−0.544979	−	0.838449i	$-0.683463\pi$
$827$		−	48.2236i		−	1.67690i	0.544979	−	0.838449i	$-0.316537\pi$
$828$	0.247513	+	1.69930i	0.00860169	+	0.0590549i
$829$			38.5326i			1.33829i	0.743130	+	0.669147i	$0.233340\pi$
$829$			38.5326i			1.33829i	−0.743130	+	0.669147i	$0.766660\pi$
$830$	22.9649	−	1.66371i	0.797125	−	0.0577483i
$831$	11.0960			0.384915
$832$	−15.2206	−	32.8477i	−0.527680	−	1.13879i
$833$	6.30287	+	46.4856i	0.218381	+	1.61063i
$834$	−0.290150	−	4.00507i	−0.0100471	−	0.138684i
$835$			1.89315i			0.0655151i
$836$	4.25011	+	29.1791i	0.146993	+	1.00918i
$837$	−2.60723			−0.0901192
$838$	−0.568374	−	7.84552i	−0.0196342	−	0.271019i
$839$	36.5920			1.26330			0.631649	−	0.775255i	$-0.282378\pi$
$839$	36.5920			1.26330			0.631649	+	0.775255i	$0.282378\pi$
$840$	−2.09926	−	7.18284i	−0.0724312	−	0.247831i
$841$	12.9040			0.444967
$842$	0.202199	+	2.79105i	0.00696825	+	0.0961858i
$843$	−26.1397			−0.900300
$844$	0.724474	+	4.97387i	0.0249374	+	0.171208i
$845$		−	7.47874i		−	0.257277i
$846$	−1.00415	−	13.8607i	−0.0345234	−	0.476542i
$847$	−2.91046	−	43.1275i	−0.100005	−	1.48188i
$848$	14.1583	−	4.21387i	0.486197	−	0.144705i
$849$	15.0023			0.514877
$850$	9.45266	−	0.684805i	0.324224	−	0.0234886i
$851$		−	1.83723i		−	0.0629795i
$852$	−2.08567	−	14.3192i	−0.0714539	−	0.490566i
$853$		−	11.8256i		−	0.404901i	−0.979292	−	0.202451i	$-0.935109\pi$
$853$		−	11.8256i		−	0.404901i	0.979292	−	0.202451i	$-0.0648906\pi$
$854$	−5.57772	−	39.6657i	−0.190865	−	1.35733i
$855$		−	2.81981i		−	0.0964354i
$856$	6.59781	−	1.45434i	0.225509	−	0.0497083i
$857$		−	44.9795i		−	1.53647i	−0.640167	−	0.768235i	$-0.721135\pi$
$857$		−	44.9795i		−	1.53647i	0.640167	−	0.768235i	$-0.278865\pi$
$858$	2.41782	+	33.3742i	0.0825430	+	1.13938i
$859$	54.7905			1.86943			0.934713	−	0.355402i	$-0.115656\pi$
$859$	54.7905			1.86943			0.934713	+	0.355402i	$0.115656\pi$
$860$	14.6859	−	2.13908i	0.500784	−	0.0729421i
$861$	23.0048	−	1.55248i	0.784000	−	0.0529083i
$862$	19.8846	−	1.44056i	0.677273	−	0.0490655i
$863$		−	12.9172i		−	0.439708i	−0.975533	−	0.219854i	$-0.929442\pi$
$863$		−	12.9172i		−	0.439708i	0.975533	−	0.219854i	$-0.0705580\pi$
$864$	−2.00121	−	5.29104i	−0.0680827	−	0.180005i
$865$	−9.43306			−0.320734
$866$	−25.8824	+	1.87507i	−0.879521	+	0.0637175i
$867$	−27.9109			−0.947904
$868$	2.90322	+	13.4873i	0.0985418	+	0.457787i
$869$	14.0289			0.475899
$870$	9.13075	−	0.661483i	0.309561	−	0.0224264i
$871$	20.4667			0.693489
$872$	3.52978	+	16.0133i	0.119533	+	0.542280i
$873$			10.5209i			0.356079i
$874$	3.41505	−	0.247406i	0.115516	−	0.00836862i
$875$	2.63975	−	0.178143i	0.0892397	−	0.00602235i
$876$	−2.66562	−	18.3008i	−0.0900630	−	0.618328i
$877$	−1.64568			−0.0555706			−0.0277853	−	0.999614i	$-0.508845\pi$
$877$	−1.64568			−0.0555706			−0.0277853	+	0.999614i	$0.508845\pi$
$878$	−0.854777	−	11.7989i	−0.0288473	−	0.398192i
$879$		−	30.1766i		−	1.01783i
$880$	−20.0452	+	5.96598i	−0.675724	+	0.201113i
$881$		−	38.0777i		−	1.28287i	−0.767177	−	0.641435i	$-0.778339\pi$
$881$		−	38.0777i		−	1.28287i	0.767177	−	0.641435i	$-0.221661\pi$
$882$	2.03542	+	9.68799i	0.0685361	+	0.326211i
$883$			7.08731i			0.238507i	0.992864	+	0.119253i	$0.0380501\pi$
$883$			7.08731i			0.238507i	−0.992864	+	0.119253i	$0.961950\pi$
$884$	−60.0204	+	8.74232i	−2.01870	+	0.294036i
$885$		−	4.27962i		−	0.143858i
$886$	2.08034	−	0.150712i	0.0698905	−	0.00506327i
$887$	−14.6383			−0.491506			−0.245753	−	0.969333i	$-0.579035\pi$
$887$	−14.6383			−0.491506			−0.245753	+	0.969333i	$0.579035\pi$
$888$	1.30278	+	5.91026i	0.0437186	+	0.198335i
$889$	−27.6735	+	1.86755i	−0.928139	+	0.0626355i
$890$	−0.872173	−	12.0390i	−0.0292353	−	0.403548i
$891$			5.22855i			0.175163i
$892$	−2.44553	+	0.356205i	−0.0818823	+	0.0119266i
$893$	−27.7094			−0.927260
$894$	−0.176634	−	2.43816i	−0.00590753	−	0.0815443i
$895$	21.4618			0.717387
$896$	−25.1422	+	16.2440i	−0.839943	+	0.542675i
$897$	3.88554			0.129734
$898$	1.65410	+	22.8322i	0.0551979	+	0.761921i
$899$	−16.8775			−0.562896
$900$	1.97912	−	0.288270i	0.0659705	−	0.00960899i
$901$		−	24.7489i		−	0.824507i
$902$	−4.65616	−	64.2710i	−0.155033	−	2.13999i
$903$	−19.5880	+	1.32190i	−0.651849	+	0.0439901i
$904$	−4.18033	−	18.9646i	−0.139036	−	0.630755i
$905$	−24.1736			−0.803556
$906$	−21.0917	+	1.52800i	−0.700725	+	0.0507645i
$907$			32.1062i			1.06607i	0.846094	+	0.533034i	$0.178948\pi$
$907$			32.1062i			1.06607i	−0.846094	+	0.533034i	$0.821052\pi$
$908$	3.49417	−	0.508947i	0.115958	−	0.0168900i
$909$		−	3.97836i		−	0.131954i
$910$	−16.7673	+	2.35779i	−0.555831	+	0.0781600i
$911$		−	1.73881i		−	0.0576092i	−0.999585	−	0.0288046i	$-0.990830\pi$
$911$		−	1.73881i		−	0.0576092i	0.999585	−	0.0288046i	$-0.00917006\pi$
$912$	−10.8106	+	3.21751i	−0.357974	+	0.106542i
$913$			85.1272i			2.81730i
$914$	2.72377	+	37.5974i	0.0900943	+	1.24361i
$915$	10.7054			0.353909
$916$	−2.57945	−	17.7092i	−0.0852273	−	0.585128i
$917$	−3.40139	−	50.4022i	−0.112324	−	1.66443i
$918$	−9.45266	+	0.684805i	−0.311984	+	0.0226019i
$919$		−	40.8342i		−	1.34700i	−0.739189	−	0.673498i	$-0.764791\pi$
$919$		−	40.8342i		−	1.34700i	0.739189	−	0.673498i	$-0.235209\pi$
$920$	0.522767	+	2.37160i	0.0172351	+	0.0781894i
$921$	−6.17458			−0.203459
$922$	48.4242	−	3.50812i	1.59477	−	0.115534i
$923$	−32.7415			−1.07770
$924$	27.0474	−	5.82213i	0.889793	−	0.191534i
$925$	−2.13976			−0.0703548
$926$	23.8077	−	1.72477i	0.782371	−	0.0566794i
$927$	−3.78934			−0.124458
$928$	−12.9545	−	34.2507i	−0.425253	−	1.12433i
$929$			0.604846i			0.0198444i	0.999951	+	0.00992218i	$0.00315838\pi$
$929$			0.604846i			0.0198444i	−0.999951	+	0.00992218i	$0.996842\pi$
$930$	−3.67755	+	0.266423i	−0.120592	+	0.00873634i
$931$	19.5597	−	2.65205i	0.641042	−	0.0869174i
$932$	43.1620	−	6.28679i	1.41382	−	0.205931i
$933$	3.80564			0.124591
$934$	3.42204	+	47.2359i	0.111973	+	1.54561i
$935$			35.0394i			1.14591i
$936$	−12.4995	+	2.75524i	−0.408560	+	0.0900579i
$937$			21.4792i			0.701694i	0.936433	+	0.350847i	$0.114106\pi$
$937$			21.4792i			0.701694i	−0.936433	+	0.350847i	$0.885894\pi$
$938$	−2.35641	−	16.7575i	−0.0769394	−	0.547151i
$939$			16.5774i			0.540984i
$940$	−2.83274	−	19.4482i	−0.0923939	−	0.634330i
$941$		−	20.4286i		−	0.665953i	−0.942935	−	0.332976i	$-0.891947\pi$
$941$		−	20.4286i		−	0.665953i	0.942935	−	0.332976i	$-0.108053\pi$
$942$	−15.5697	+	1.12796i	−0.507289	+	0.0367509i
$943$	−7.48264			−0.243668
$944$	−16.4072	+	4.88321i	−0.534009	+	0.158935i
$945$	−2.63975	+	0.178143i	−0.0858710	+	0.00579501i
$946$	3.96461	+	54.7253i	0.128901	+	1.77927i
$947$			2.74440i			0.0891810i	0.999005	+	0.0445905i	$0.0141983\pi$
$947$			2.74440i			0.0891810i	−0.999005	+	0.0445905i	$0.985802\pi$
$948$	0.773468	+	5.31025i	0.0251211	+	0.172469i
$949$	−41.8457			−1.35837
$950$	−0.288144	−	3.97738i	−0.00934864	−	0.129043i
$951$	−11.1118			−0.360323
$952$	14.0683	+	48.1362i	0.455956	+	1.56010i
$953$	−17.4001			−0.563644			−0.281822	−	0.959467i	$-0.590939\pi$
$953$	−17.4001			−0.563644			−0.281822	+	0.959467i	$0.590939\pi$
$954$	−0.377374	−	5.20906i	−0.0122179	−	0.168649i
$955$	18.9822			0.614249
$956$	4.25364	+	29.2034i	0.137573	+	0.944504i
$957$			33.8461i			1.09409i
$958$	2.15961	+	29.8101i	0.0697739	+	0.963120i
$959$	0.974826	+	14.4451i	0.0314788	+	0.466455i
$960$	−3.36342	−	7.25861i	−0.108554	−	0.234271i
$961$	−24.2023			−0.780720
$962$	13.6582	−	0.989480i	0.440359	−	0.0319021i
$963$		−	2.38868i		−	0.0769741i
$964$	4.41922	+	30.3402i	0.142334	+	0.977191i
$965$			26.5854i			0.855813i
$966$	−0.447356	−	3.18135i	−0.0143934	−	0.102358i
$967$			29.1327i			0.936845i	0.883505	+	0.468422i	$0.155177\pi$
$967$			29.1327i			0.936845i	−0.883505	+	0.468422i	$0.844823\pi$
$968$	−9.94718	−	45.1268i	−0.319715	−	1.45043i
$969$			18.8971i			0.607062i
$970$	1.07509	+	14.8399i	0.0345190	+	0.476481i
$971$	−42.2191			−1.35487			−0.677437	−	0.735581i	$-0.736909\pi$
$971$	−42.2191			−1.35487			−0.677437	+	0.735581i	$0.736909\pi$
$972$	−1.97912	+	0.288270i	−0.0634802	+	0.00924626i
$973$	0.505827	+	7.49539i	0.0162161	+	0.240291i
$974$	18.8445	−	1.36520i	0.603816	−	0.0437439i
$975$		−	4.52534i		−	0.144927i
$976$	−12.2153	−	41.0423i	−0.391001	−	1.31373i
$977$	44.1167			1.41142			0.705710	−	0.708501i	$-0.250628\pi$
$977$	44.1167			1.41142			0.705710	+	0.708501i	$0.250628\pi$
$978$	−26.5133	+	1.92078i	−0.847803	+	0.0614197i
$979$	44.6265			1.42627
$980$	3.86097	+	13.4571i	0.123334	+	0.429871i
$981$	5.79748			0.185099
$982$	−14.9623	+	1.08395i	−0.477466	+	0.0345904i
$983$	34.2931			1.09378			0.546890	−	0.837204i	$-0.315811\pi$
$983$	34.2931			1.09378			0.546890	+	0.837204i	$0.315811\pi$
$984$	24.0712	−	5.30596i	0.767362	−	0.169148i
$985$			23.2008i			0.739239i
$986$	−61.1902	+	4.43297i	−1.94869	+	0.141175i
$987$	1.75056	+	25.9400i	0.0557211	+	0.825680i
$988$	3.67849	+	25.2547i	0.117029	+	0.803459i
$989$	6.37130			0.202596
$990$	0.534284	+	7.37496i	0.0169807	+	0.234392i
$991$			34.2121i			1.08678i	0.839479	+	0.543392i	$0.182860\pi$
$991$			34.2121i			1.08678i	−0.839479	+	0.543392i	$0.817140\pi$
$992$	5.21764	+	13.7950i	0.165660	+	0.437991i
$993$			22.4709i			0.713093i
$994$	3.76964	+	26.8076i	0.119566	+	0.850287i
$995$			19.8867i			0.630451i
$996$	−32.2224	+	4.69339i	−1.02101	+	0.148716i
$997$		−	30.2000i		−	0.956443i	−0.878239	−	0.478221i	$-0.841282\pi$
$997$		−	30.2000i		−	0.956443i	0.878239	−	0.478221i	$-0.158718\pi$
$998$	32.3192	−	2.34139i	1.02305	−	0.0741154i
$999$	2.13976			0.0676989

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.c.b.391.7	yes	16
3.2	odd	2		1260.2.c.e.811.10		16
4.3	odd	2		420.2.c.a.391.8	yes	16
7.6	odd	2		420.2.c.a.391.7	✓	16
12.11	even	2		1260.2.c.d.811.9		16
21.20	even	2		1260.2.c.d.811.10		16
28.27	even	2	inner	420.2.c.b.391.8	yes	16
84.83	odd	2		1260.2.c.e.811.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.c.a.391.7	✓	16	7.6	odd	2
420.2.c.a.391.8	yes	16	4.3	odd	2
420.2.c.b.391.7	yes	16	1.1	even	1	trivial
420.2.c.b.391.8	yes	16	28.27	even	2	inner
1260.2.c.d.811.9		16	12.11	even	2
1260.2.c.d.811.10		16	21.20	even	2
1260.2.c.e.811.9		16	84.83	odd	2
1260.2.c.e.811.10		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.102186 - 1.41052i) q^{2} +1.00000 q^{3} +(-1.97912 + 0.288270i) q^{4} +1.00000i q^{5} +(-0.102186 - 1.41052i) q^{6} +(0.178143 + 2.63975i) q^{7} +(0.608847 + 2.76212i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.102186 - 1.41052i) q^{2} +1.00000 q^{3} +(-1.97912 + 0.288270i) q^{4} +1.00000i q^{5} +(-0.102186 - 1.41052i) q^{6} +(0.178143 + 2.63975i) q^{7} +(0.608847 + 2.76212i) q^{8} +1.00000 q^{9} +(1.41052 - 0.102186i) q^{10} +5.22855i q^{11} +(-1.97912 + 0.288270i) q^{12} +4.52534i q^{13} +(3.70520 - 0.521019i) q^{14} +1.00000i q^{15} +(3.83380 - 1.14104i) q^{16} -6.70156i q^{17} +(-0.102186 - 1.41052i) q^{18} -2.81981 q^{19} +(-0.288270 - 1.97912i) q^{20} +(0.178143 + 2.63975i) q^{21} +(7.37496 - 0.534284i) q^{22} -0.858617i q^{23} +(0.608847 + 2.76212i) q^{24} -1.00000 q^{25} +(6.38308 - 0.462426i) q^{26} +1.00000 q^{27} +(-1.11353 - 5.17301i) q^{28} +6.47333 q^{29} +(1.41052 - 0.102186i) q^{30} -2.60723 q^{31} +(-2.00121 - 5.29104i) q^{32} +5.22855i q^{33} +(-9.45266 + 0.684805i) q^{34} +(-2.63975 + 0.178143i) q^{35} +(-1.97912 + 0.288270i) q^{36} +2.13976 q^{37} +(0.288144 + 3.97738i) q^{38} +4.52534i q^{39} +(-2.76212 + 0.608847i) q^{40} -8.71476i q^{41} +(3.70520 - 0.521019i) q^{42} +7.42042i q^{43} +(-1.50723 - 10.3479i) q^{44} +1.00000i q^{45} +(-1.21109 + 0.0877385i) q^{46} +9.82671 q^{47} +(3.83380 - 1.14104i) q^{48} +(-6.93653 + 0.940508i) q^{49} +(0.102186 + 1.41052i) q^{50} -6.70156i q^{51} +(-1.30452 - 8.95618i) q^{52} +3.69301 q^{53} +(-0.102186 - 1.41052i) q^{54} -5.22855 q^{55} +(-7.18284 + 2.09926i) q^{56} -2.81981 q^{57} +(-0.661483 - 9.13075i) q^{58} -4.27962 q^{59} +(-0.288270 - 1.97912i) q^{60} -10.7054i q^{61} +(0.266423 + 3.67755i) q^{62} +(0.178143 + 2.63975i) q^{63} +(-7.25861 + 3.36342i) q^{64} -4.52534 q^{65} +(7.37496 - 0.534284i) q^{66} -4.52269i q^{67} +(1.93186 + 13.2632i) q^{68} -0.858617i q^{69} +(0.521019 + 3.70520i) q^{70} +7.23513i q^{71} +(0.608847 + 2.76212i) q^{72} +9.24697i q^{73} +(-0.218653 - 3.01816i) q^{74} -1.00000 q^{75} +(5.58072 - 0.812865i) q^{76} +(-13.8020 + 0.931432i) q^{77} +(6.38308 - 0.462426i) q^{78} -2.68314i q^{79} +(1.14104 + 3.83380i) q^{80} +1.00000 q^{81} +(-12.2923 + 0.890525i) q^{82} +16.2812 q^{83} +(-1.11353 - 5.17301i) q^{84} +6.70156 q^{85} +(10.4666 - 0.758262i) q^{86} +6.47333 q^{87} +(-14.4419 + 3.18339i) q^{88} -8.53516i q^{89} +(1.41052 - 0.102186i) q^{90} +(-11.9458 + 0.806161i) q^{91} +(0.247513 + 1.69930i) q^{92} -2.60723 q^{93} +(-1.00415 - 13.8607i) q^{94} -2.81981i q^{95} +(-2.00121 - 5.29104i) q^{96} +10.5209i q^{97} +(2.03542 + 9.68799i) q^{98} +5.22855i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 16 q^{3} - 2 q^{4} + 2 q^{6} + 4 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 + 16 * q^3 - 2 * q^4 + 2 * q^6 + 4 * q^7 + 2 * q^8 + 16 * q^9	\( 16 q + 2 q^{2} + 16 q^{3} - 2 q^{4} + 2 q^{6} + 4 q^{7} + 2 q^{8} + 16 q^{9} - 2 q^{12} + 10 q^{14} + 6 q^{16} + 2 q^{18} + 24 q^{19} + 4 q^{21} - 12 q^{22} + 2 q^{24} - 16 q^{25} + 12 q^{26} + 16 q^{27} - 22 q^{28} + 16 q^{29} - 8 q^{31} - 18 q^{32} - 24 q^{34} - 2 q^{36} + 24 q^{37} - 28 q^{38} - 12 q^{40} + 10 q^{42} - 8 q^{44} - 20 q^{46} - 16 q^{47} + 6 q^{48} - 16 q^{49} - 2 q^{50} + 20 q^{52} - 32 q^{53} + 2 q^{54} - 2 q^{56} + 24 q^{57} - 32 q^{58} - 8 q^{59} - 16 q^{62} + 4 q^{63} - 2 q^{64} - 8 q^{65} - 12 q^{66} - 4 q^{68} - 20 q^{70} + 2 q^{72} - 4 q^{74} - 16 q^{75} - 16 q^{76} - 8 q^{77} + 12 q^{78} + 16 q^{80} + 16 q^{81} + 4 q^{82} - 8 q^{83} - 22 q^{84} + 64 q^{86} + 16 q^{87} - 52 q^{88} - 16 q^{91} + 64 q^{92} - 8 q^{93} - 16 q^{94} - 18 q^{96} + 2 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 + 16 * q^3 - 2 * q^4 + 2 * q^6 + 4 * q^7 + 2 * q^8 + 16 * q^9 - 2 * q^12 + 10 * q^14 + 6 * q^16 + 2 * q^18 + 24 * q^19 + 4 * q^21 - 12 * q^22 + 2 * q^24 - 16 * q^25 + 12 * q^26 + 16 * q^27 - 22 * q^28 + 16 * q^29 - 8 * q^31 - 18 * q^32 - 24 * q^34 - 2 * q^36 + 24 * q^37 - 28 * q^38 - 12 * q^40 + 10 * q^42 - 8 * q^44 - 20 * q^46 - 16 * q^47 + 6 * q^48 - 16 * q^49 - 2 * q^50 + 20 * q^52 - 32 * q^53 + 2 * q^54 - 2 * q^56 + 24 * q^57 - 32 * q^58 - 8 * q^59 - 16 * q^62 + 4 * q^63 - 2 * q^64 - 8 * q^65 - 12 * q^66 - 4 * q^68 - 20 * q^70 + 2 * q^72 - 4 * q^74 - 16 * q^75 - 16 * q^76 - 8 * q^77 + 12 * q^78 + 16 * q^80 + 16 * q^81 + 4 * q^82 - 8 * q^83 - 22 * q^84 + 64 * q^86 + 16 * q^87 - 52 * q^88 - 16 * q^91 + 64 * q^92 - 8 * q^93 - 16 * q^94 - 18 * q^96 + 2 * q^98

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