LMFDB - Embedded newform 392.2.b.f.197.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(197,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("392.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.b (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:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.1142512.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - x^{4} + 5x^{3} - 2x^{2} - 4x + 8 $ x^6 - x^5 - x^4 + 5x^3 - 2x^2 - 4*x + 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			197.3
Root			$-1.37241 + 0.341295i$ of defining polynomial
Character	$\chi$	$=$	392.197
Dual form			392.2.b.f.197.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.605378 - 1.27809i) q^{2} -0.682591i q^{3} +(-1.26704 - 1.54746i) q^{4} -3.23877i q^{5} +(-0.872413 - 0.413225i) q^{6} +(-2.74483 + 0.682591i) q^{8} +2.53407 q^{9} +(-4.13945 - 1.96068i) q^{10} +2.41232i q^{11} +(-1.05628 + 0.864866i) q^{12} -3.09491i q^{13} -2.21076 q^{15} +(-0.789244 + 3.92136i) q^{16} -3.95558 q^{17} +(1.53407 - 3.23877i) q^{18} +2.70004i q^{19} +(-5.01186 + 4.10364i) q^{20} +(3.08317 + 1.46037i) q^{22} +2.74483 q^{23} +(0.465930 + 1.87359i) q^{24} -5.48965 q^{25} +(-3.95558 - 1.87359i) q^{26} -3.77750i q^{27} +2.01745i q^{29} +(-1.33834 + 2.82555i) q^{30} +2.21076 q^{31} +(4.53407 + 3.38263i) q^{32} +1.64663 q^{33} +(-2.39462 + 5.05560i) q^{34} +(-3.21076 - 3.92136i) q^{36} -4.96851i q^{37} +(3.45090 + 1.63455i) q^{38} -2.11256 q^{39} +(2.21076 + 8.88987i) q^{40} +2.11256 q^{41} -11.5899i q^{43} +(3.73296 - 3.05650i) q^{44} -8.20728i q^{45} +(1.66166 - 3.50814i) q^{46} +6.63227 q^{47} +(2.67669 + 0.538731i) q^{48} +(-3.32331 + 7.01628i) q^{50} +2.70004i q^{51} +(-4.78924 + 3.92136i) q^{52} +2.58650i q^{53} +(-4.82799 - 2.28682i) q^{54} +7.81297 q^{55} +1.84302 q^{57} +(2.57849 + 1.22132i) q^{58} +12.2725i q^{59} +(2.80111 + 3.42105i) q^{60} -8.71569i q^{61} +(1.33834 - 2.82555i) q^{62} +(7.06814 - 3.74718i) q^{64} -10.0237 q^{65} +(0.996833 - 2.10454i) q^{66} +5.79496i q^{67} +(5.01186 + 6.12109i) q^{68} -1.87359i q^{69} +6.64663 q^{71} +(-6.95558 + 1.72973i) q^{72} +9.55779 q^{73} +(-6.35020 - 3.00782i) q^{74} +3.74718i q^{75} +(4.17820 - 3.42105i) q^{76} +(-1.27890 + 2.70004i) q^{78} +1.67669 q^{79} +(12.7004 + 2.55618i) q^{80} +5.02372 q^{81} +(1.27890 - 2.70004i) q^{82} +6.47755i q^{83} +12.8112i q^{85} +(-14.8130 - 7.01628i) q^{86} +1.37709 q^{87} +(-1.64663 - 6.62141i) q^{88} -13.9793 q^{89} +(-10.4897 - 4.96851i) q^{90} +(-3.47779 - 4.24750i) q^{92} -1.50904i q^{93} +(4.01503 - 8.47664i) q^{94} +8.74483 q^{95} +(2.30895 - 3.09491i) q^{96} +1.37709 q^{97} +6.11300i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 4 q^{6} + 2 q^{8} - 8 q^{10} - 2 q^{12} - 10 q^{15} - 8 q^{16} - 2 q^{17} - 6 q^{18} - 4 q^{20} + 6 q^{22} - 2 q^{23} + 18 q^{24} + 4 q^{25} - 2 q^{26} - 14 q^{30} + 10 q^{31} + 12 q^{32}+ \cdots - 20 q^{97}+O(q^{100}) $ 6 * q + 2 * q^2 + 4 * q^6 + 2 * q^8 - 8 * q^10 - 2 * q^12 - 10 * q^15 - 8 * q^16 - 2 * q^17 - 6 * q^18 - 4 * q^20 + 6 * q^22 - 2 * q^23 + 18 * q^24 + 4 * q^25 - 2 * q^26 - 14 * q^30 + 10 * q^31 + 12 * q^32 - 14 * q^33 - 16 * q^34 - 16 * q^36 + 18 * q^38 - 4 * q^39 + 10 * q^40 + 4 * q^41 + 30 * q^44 + 4 * q^46 + 30 * q^47 + 28 * q^48 - 8 * q^50 - 32 * q^52 + 2 * q^54 - 2 * q^55 - 2 * q^57 + 22 * q^58 - 6 * q^60 + 14 * q^62 + 12 * q^64 - 8 * q^65 - 38 * q^66 + 4 * q^68 + 16 * q^71 - 20 * q^72 - 10 * q^73 - 18 * q^74 - 26 * q^76 + 26 * q^78 + 22 * q^79 + 36 * q^80 - 22 * q^81 - 26 * q^82 - 40 * q^86 - 20 * q^87 + 14 * q^88 - 10 * q^89 - 26 * q^90 - 10 * q^92 + 42 * q^94 + 34 * q^95 + 16 * q^96 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	0.605378	−	1.27809i	0.428067	−	0.903747i
$2$	0.605378	−	1.27809i	0.428067	−	0.903747i
$3$		−	0.682591i		−	0.394094i	−0.980394	−	0.197047i	$-0.936865\pi$
$3$		−	0.682591i		−	0.394094i	0.980394	−	0.197047i	$-0.0631351\pi$
$4$	−1.26704	−	1.54746i	−0.633518	−	0.773728i
$5$		−	3.23877i		−	1.44842i	−0.689578	−	0.724212i	$-0.742204\pi$
$5$		−	3.23877i		−	1.44842i	0.689578	−	0.724212i	$-0.257796\pi$
$6$	−0.872413	−	0.413225i	−0.356161	−	0.168698i
$7$		0			0
$7$		0			0
$8$	−2.74483	+	0.682591i	−0.970443	+	0.241332i
$9$	2.53407			0.844690
$10$	−4.13945	−	1.96068i	−1.30901	−	0.620022i
$11$			2.41232i			0.727343i	0.931527	+	0.363671i	$0.118477\pi$
$11$			2.41232i			0.727343i	−0.931527	+	0.363671i	$0.881523\pi$
$12$	−1.05628	+	0.864866i	−0.304922	+	0.249665i
$13$		−	3.09491i		−	0.858375i	−0.903216	−	0.429187i	$-0.858800\pi$
$13$		−	3.09491i		−	0.858375i	0.903216	−	0.429187i	$-0.141200\pi$
$14$		0			0
$15$	−2.21076			−0.570815
$16$	−0.789244	+	3.92136i	−0.197311	+	0.980341i
$17$	−3.95558			−0.959370			−0.479685	−	0.877441i	$-0.659249\pi$
$17$	−3.95558			−0.959370			−0.479685	+	0.877441i	$0.659249\pi$
$18$	1.53407	−	3.23877i	0.361584	−	0.763386i
$19$			2.70004i			0.619432i	0.950829	+	0.309716i	$0.100234\pi$
$19$			2.70004i			0.619432i	−0.950829	+	0.309716i	$0.899766\pi$
$20$	−5.01186	+	4.10364i	−1.12069	+	0.917602i
$21$		0			0
$22$	3.08317	+	1.46037i	0.657334	+	0.311351i
$23$	2.74483			0.572336			0.286168	−	0.958179i	$-0.407618\pi$
$23$	2.74483			0.572336			0.286168	+	0.958179i	$0.407618\pi$
$24$	0.465930	+	1.87359i	0.0951075	+	0.382445i
$25$	−5.48965			−1.09793
$26$	−3.95558	−	1.87359i	−0.775753	−	0.367442i
$27$		−	3.77750i		−	0.726981i
$28$		0			0
$29$			2.01745i			0.374631i	0.982300	+	0.187316i	$0.0599787\pi$
$29$			2.01745i			0.374631i	−0.982300	+	0.187316i	$0.940021\pi$
$30$	−1.33834	+	2.82555i	−0.244347	+	0.515872i
$31$	2.21076			0.397063			0.198532	−	0.980094i	$-0.436383\pi$
$31$	2.21076			0.397063			0.198532	+	0.980094i	$0.436383\pi$
$32$	4.53407	+	3.38263i	0.801518	+	0.597971i
$33$	1.64663			0.286641
$34$	−2.39462	+	5.05560i	−0.410674	+	0.867027i
$35$		0			0
$36$	−3.21076	−	3.92136i	−0.535126	−	0.653561i
$37$		−	4.96851i		−	0.816817i	−0.912799	−	0.408409i	$-0.866084\pi$
$37$		−	4.96851i		−	0.816817i	0.912799	−	0.408409i	$-0.133916\pi$
$38$	3.45090	+	1.63455i	0.559810	+	0.265158i
$39$	−2.11256			−0.338280
$40$	2.21076	+	8.88987i	0.349551	+	1.40561i
$41$	2.11256			0.329926			0.164963	−	0.986300i	$-0.447249\pi$
$41$	2.11256			0.329926			0.164963	+	0.986300i	$0.447249\pi$
$42$		0			0
$43$		−	11.5899i		−	1.76745i	−0.468011	−	0.883723i	$-0.655029\pi$
$43$		−	11.5899i		−	1.76745i	0.468011	−	0.883723i	$-0.344971\pi$
$44$	3.73296	−	3.05650i	0.562766	−	0.460784i
$45$		−	8.20728i		−	1.22347i
$46$	1.66166	−	3.50814i	0.244998	−	0.517247i
$47$	6.63227			0.967416			0.483708	−	0.875230i	$-0.339290\pi$
$47$	6.63227			0.967416			0.483708	+	0.875230i	$0.339290\pi$
$48$	2.67669	+	0.538731i	0.386346	+	0.0777591i
$49$		0			0
$50$	−3.32331	+	7.01628i	−0.469988	+	0.992251i
$51$			2.70004i			0.378082i
$52$	−4.78924	+	3.92136i	−0.664149	+	0.543795i
$53$			2.58650i			0.355283i	0.984095	+	0.177642i	$0.0568468\pi$
$53$			2.58650i			0.355283i	−0.984095	+	0.177642i	$0.943153\pi$
$54$	−4.82799	−	2.28682i	−0.657007	−	0.311196i
$55$	7.81297			1.05350
$56$		0			0
$57$	1.84302			0.244114
$58$	2.57849	+	1.22132i	0.338572	+	0.160367i
$59$			12.2725i			1.59774i	0.601501	+	0.798872i	$0.294569\pi$
$59$			12.2725i			1.59774i	−0.601501	+	0.798872i	$0.705431\pi$
$60$	2.80111	+	3.42105i	0.361621	+	0.441656i
$61$		−	8.71569i		−	1.11593i	−0.829865	−	0.557965i	$-0.811582\pi$
$61$		−	8.71569i		−	1.11593i	0.829865	−	0.557965i	$-0.188418\pi$
$62$	1.33834	−	2.82555i	0.169970	−	0.358845i
$63$		0			0
$64$	7.06814	−	3.74718i	0.883518	−	0.468398i
$65$	−10.0237			−1.24329
$66$	0.996833	−	2.10454i	0.122702	−	0.259051i
$67$			5.79496i			0.707967i	0.935252	+	0.353983i	$0.115173\pi$
$67$			5.79496i			0.707967i	−0.935252	+	0.353983i	$0.884827\pi$
$68$	5.01186	+	6.12109i	0.607777	+	0.742291i
$69$		−	1.87359i		−	0.225554i
$70$		0			0
$71$	6.64663			0.788810			0.394405	−	0.918937i	$-0.370951\pi$
$71$	6.64663			0.788810			0.394405	+	0.918937i	$0.370951\pi$
$72$	−6.95558	+	1.72973i	−0.819723	+	0.203851i
$73$	9.55779			1.11866			0.559328	−	0.828947i	$-0.311059\pi$
$73$	9.55779			1.11866			0.559328	+	0.828947i	$0.311059\pi$
$74$	−6.35020	−	3.00782i	−0.738196	−	0.349652i
$75$			3.74718i			0.432688i
$76$	4.17820	−	3.42105i	0.479272	−	0.392421i
$77$		0			0
$78$	−1.27890	+	2.70004i	−0.144806	+	0.305720i
$79$	1.67669			0.188642			0.0943209	−	0.995542i	$-0.469932\pi$
$79$	1.67669			0.188642			0.0943209	+	0.995542i	$0.469932\pi$
$80$	12.7004	+	2.55618i	1.41995	+	0.285790i
$81$	5.02372			0.558191
$82$	1.27890	−	2.70004i	0.141230	−	0.298170i
$83$			6.47755i			0.711003i	0.934676	+	0.355502i	$0.115690\pi$
$83$			6.47755i			0.711003i	−0.934676	+	0.355502i	$0.884310\pi$
$84$		0			0
$85$			12.8112i			1.38957i
$86$	−14.8130	−	7.01628i	−1.59732	−	0.756585i
$87$	1.37709			0.147640
$88$	−1.64663	−	6.62141i	−0.175531	−	0.705844i
$89$	−13.9793			−1.48180			−0.740902	−	0.671614i	$-0.765602\pi$
$89$	−13.9793			−1.48180			−0.740902	+	0.671614i	$0.765602\pi$
$90$	−10.4897	−	4.96851i	−1.10571	−	0.523726i
$91$		0			0
$92$	−3.47779	−	4.24750i	−0.362585	−	0.442832i
$93$		−	1.50904i		−	0.156480i
$94$	4.01503	−	8.47664i	0.414119	−	0.874299i
$95$	8.74483			0.897200
$96$	2.30895	−	3.09491i	0.235657	−	0.315873i
$97$	1.37709			0.139823			0.0699113	−	0.997553i	$-0.477728\pi$
$97$	1.37709			0.139823			0.0699113	+	0.997553i	$0.477728\pi$
$98$		0			0
$99$			6.11300i			0.614379i
$100$	6.95558	+	8.49500i	0.695558	+	0.849500i
$101$		−	0.796131i		−	0.0792180i	−0.999215	−	0.0396090i	$-0.987389\pi$
$101$		−	0.796131i		−	0.0792180i	0.999215	−	0.0396090i	$-0.0126112\pi$
$102$	3.45090	+	1.63455i	0.341690	+	0.161844i
$103$	2.65599			0.261702			0.130851	−	0.991402i	$-0.458229\pi$
$103$	2.65599			0.261702			0.130851	+	0.991402i	$0.458229\pi$
$104$	2.11256	+	8.49500i	0.207153	+	0.833003i
$105$		0			0
$106$	3.30579	+	1.56581i	0.321086	+	0.152085i
$107$		−	5.43040i		−	0.524977i	−0.964935	−	0.262489i	$-0.915457\pi$
$107$		−	5.43040i		−	0.524977i	0.964935	−	0.262489i	$-0.0845432\pi$
$108$	−5.84552	+	4.78623i	−0.562486	+	0.460555i
$109$		−	13.8119i		−	1.32294i	−0.749973	−	0.661468i	$-0.769934\pi$
$109$		−	13.8119i		−	1.32294i	0.749973	−	0.661468i	$-0.230066\pi$
$110$	4.72980	−	9.98569i	0.450969	−	0.952098i
$111$	−3.39145			−0.321903
$112$		0			0
$113$	4.53407			0.426529			0.213265	−	0.976994i	$-0.431590\pi$
$113$	4.53407			0.426529			0.213265	+	0.976994i	$0.431590\pi$
$114$	1.11573	−	2.35555i	0.104497	−	0.220618i
$115$		−	8.88987i		−	0.828985i
$116$	3.12192	−	2.55618i	0.289863	−	0.237336i
$117$		−	7.84273i		−	0.725060i
$118$	15.6854	+	7.42950i	1.44396	+	0.683941i
$119$		0			0
$120$	6.06814	−	1.50904i	0.553943	−	0.137756i
$121$	5.18070			0.470973
$122$	−11.1394	−	5.27629i	−1.00852	−	0.477693i
$123$		−	1.44201i		−	0.130022i
$124$	−2.80111	−	3.42105i	−0.251547	−	0.307219i
$125$			1.58587i			0.141845i
$126$		0			0
$127$	−15.4897			−1.37448			−0.687242	−	0.726428i	$-0.741179\pi$
$127$	−15.4897			−1.37448			−0.687242	+	0.726428i	$0.741179\pi$
$128$	−0.510348	−	11.3022i	−0.0451088	−	0.998982i
$129$	−7.91116			−0.696539
$130$	−6.06814	+	12.8112i	−0.532211	+	1.12362i
$131$			16.8094i			1.46865i	0.678800	+	0.734323i	$0.262500\pi$
$131$			16.8094i			1.46865i	−0.678800	+	0.734323i	$0.737500\pi$
$132$	−2.08634	−	2.54809i	−0.181592	−	0.221782i
$133$		0			0
$134$	7.40648	+	3.50814i	0.639823	+	0.303057i
$135$	−12.2345			−1.05298
$136$	10.8574	−	2.70004i	0.931013	−	0.231527i
$137$	−0.887442			−0.0758192			−0.0379096	−	0.999281i	$-0.512070\pi$
$137$	−0.887442			−0.0758192			−0.0379096	+	0.999281i	$0.512070\pi$
$138$	−2.39462	−	1.13423i	−0.203844	−	0.0965522i
$139$			2.44264i			0.207182i	0.994620	+	0.103591i	$0.0330333\pi$
$139$			2.44264i			0.207182i	−0.994620	+	0.103591i	$0.966967\pi$
$140$		0			0
$141$		−	4.52712i		−	0.381253i
$142$	4.02372	−	8.49500i	0.337663	−	0.712884i
$143$	7.46593			0.624332
$144$	−2.00000	+	9.93701i	−0.166667	+	0.828084i
$145$	6.53407			0.542625
$146$	5.78608	−	12.2157i	0.478859	−	1.01098i
$147$		0			0
$148$	−7.68855	+	6.29527i	−0.631995	+	0.517468i
$149$			9.42860i			0.772421i	0.922411	+	0.386210i	$0.126216\pi$
$149$			9.42860i			0.772421i	−0.922411	+	0.386210i	$0.873784\pi$
$150$	4.78924	+	2.26846i	0.391040	+	0.185219i
$151$	−7.05378			−0.574028			−0.287014	−	0.957926i	$-0.592663\pi$
$151$	−7.05378			−0.574028			−0.287014	+	0.957926i	$0.592663\pi$
$152$	−1.84302	−	7.41115i	−0.149489	−	0.601123i
$153$	−10.0237			−0.810370
$154$		0			0
$155$		−	7.16014i		−	0.575116i
$156$	2.67669	+	3.26909i	0.214306	+	0.261737i
$157$			8.71569i			0.695588i	0.937571	+	0.347794i	$0.113069\pi$
$157$			8.71569i			0.695588i	−0.937571	+	0.347794i	$0.886931\pi$
$158$	1.01503	−	2.14296i	0.0807513	−	0.170485i
$159$	1.76552			0.140015
$160$	10.9556	−	14.6848i	0.866115	−	1.16094i
$161$		0			0
$162$	3.04125	−	6.42078i	0.238943	−	0.504464i
$163$			19.8275i			1.55301i	0.630111	+	0.776505i	$0.283009\pi$
$163$			19.8275i			1.55301i	−0.630111	+	0.776505i	$0.716991\pi$
$164$	−2.67669	−	3.26909i	−0.209014	−	0.255273i
$165$		−	5.33306i		−	0.415178i
$166$	8.27890	+	3.92136i	0.642567	+	0.304357i
$167$	−22.1600			−1.71479			−0.857396	−	0.514657i	$-0.827919\pi$
$167$	−22.1600			−1.71479			−0.857396	+	0.514657i	$0.827919\pi$
$168$		0			0
$169$	3.42151			0.263193
$170$	16.3739	+	7.75564i	1.25582	+	0.594830i
$171$			6.84210i			0.523228i
$172$	−17.9349	+	14.6848i	−1.36752	+	1.11971i
$173$			21.7314i			1.65221i	0.563517	+	0.826105i	$0.309448\pi$
$173$			21.7314i			1.65221i	−0.563517	+	0.826105i	$0.690552\pi$
$174$	0.833662	−	1.76005i	0.0631998	−	0.133429i
$175$		0			0
$176$	−9.45960	−	1.90391i	−0.713044	−	0.143513i
$177$	8.37709			0.629661
$178$	−8.46276	+	17.8668i	−0.634311	+	1.33918i
$179$		−	3.77750i		−	0.282344i	−0.989985	−	0.141172i	$-0.954913\pi$
$179$		−	3.77750i		−	0.282344i	0.989985	−	0.141172i	$-0.0450870\pi$
$180$	−12.7004	+	10.3989i	−0.946633	+	0.775089i
$181$			14.0326i			1.04303i	0.853242	+	0.521516i	$0.174633\pi$
$181$			14.0326i			1.04303i	−0.853242	+	0.521516i	$0.825367\pi$
$182$		0			0
$183$	−5.94925			−0.439781
$184$	−7.53407	+	1.87359i	−0.555419	+	0.138123i
$185$	−16.0919			−1.18310
$186$	−1.92869	−	0.913540i	−0.141419	−	0.0669840i
$187$		−	9.54214i		−	0.697790i
$188$	−8.40332	−	10.2631i	−0.612875	−	0.748517i
$189$		0			0
$190$	5.29392	−	11.1767i	0.384062	−	0.810842i
$191$	7.27890			0.526682			0.263341	−	0.964703i	$-0.415175\pi$
$191$	7.27890			0.526682			0.263341	+	0.964703i	$0.415175\pi$
$192$	−2.55779	−	4.82465i	−0.184593	−	0.348189i
$193$	9.53407			0.686277			0.343139	−	0.939285i	$-0.388510\pi$
$193$	9.53407			0.686277			0.343139	+	0.939285i	$0.388510\pi$
$194$	0.833662	−	1.76005i	0.0598535	−	0.126364i
$195$			6.84210i			0.489973i
$196$		0			0
$197$		−	11.6667i		−	0.831221i	−0.909543	−	0.415611i	$-0.863568\pi$
$197$		−	11.6667i		−	0.831221i	0.909543	−	0.415611i	$-0.136432\pi$
$198$	7.81297	+	3.70067i	0.555243	+	0.262995i
$199$	−18.9649			−1.34439			−0.672195	−	0.740375i	$-0.734648\pi$
$199$	−18.9649			−1.34439			−0.672195	+	0.740375i	$0.734648\pi$
$200$	15.0681	−	3.74718i	1.06548	−	0.264966i
$201$	3.95558			0.279005
$202$	−1.01753	−	0.481960i	−0.0715930	−	0.0339106i
$203$		0			0
$204$	4.17820	−	3.42105i	0.292532	−	0.239521i
$205$		−	6.84210i		−	0.477873i
$206$	1.60788	−	3.39460i	0.112026	−	0.236513i
$207$	6.95558			0.483446
$208$	12.1363	+	2.44264i	0.841500	+	0.169367i
$209$	−6.51337			−0.450540
$210$		0			0
$211$			16.1268i			1.11022i	0.831778	+	0.555109i	$0.187323\pi$
$211$			16.1268i			1.11022i	−0.831778	+	0.555109i	$0.812677\pi$
$212$	4.00250	−	3.27719i	0.274893	−	0.225078i
$213$		−	4.53693i		−	0.310865i
$214$	−6.94055	−	3.28745i	−0.474446	−	0.224725i
$215$	−37.5371			−2.56001
$216$	2.57849	+	10.3686i	0.175444	+	0.705493i
$217$		0			0
$218$	−17.6528	−	8.36140i	−1.19560	−	0.566305i
$219$		−	6.52406i		−	0.440855i
$220$	−9.89930	−	12.0902i	−0.667411	−	0.815123i
$221$			12.2422i			0.823498i
$222$	−2.05311	+	4.33459i	−0.137796	+	0.290919i
$223$	7.71477			0.516619			0.258310	−	0.966062i	$-0.416835\pi$
$223$	7.71477			0.516619			0.258310	+	0.966062i	$0.416835\pi$
$224$		0			0
$225$	−13.9112			−0.927411
$226$	2.74483	−	5.79496i	0.182583	−	0.385475i
$227$			2.12460i			0.141015i	0.997511	+	0.0705074i	$0.0224618\pi$
$227$			2.12460i			0.141015i	−0.997511	+	0.0705074i	$0.977538\pi$
$228$	−2.33518	−	2.85200i	−0.154651	−	0.188878i
$229$			9.36796i			0.619052i	0.950891	+	0.309526i	$0.100170\pi$
$229$			9.36796i			0.619052i	−0.950891	+	0.309526i	$0.899830\pi$
$230$	−11.3621	−	5.38173i	−0.749192	−	0.354861i
$231$		0			0
$232$	−1.37709	−	5.53756i	−0.0904106	−	0.363558i
$233$	−8.82733			−0.578297			−0.289149	−	0.957284i	$-0.593372\pi$
$233$	−8.82733			−0.578297			−0.289149	+	0.957284i	$0.593372\pi$
$234$	−10.0237	−	4.74781i	−0.655271	−	0.310374i
$235$		−	21.4804i		−	1.40123i
$236$	18.9912	−	15.5497i	1.23622	−	1.01220i
$237$		−	1.14449i		−	0.0743426i
$238$		0			0
$239$	5.93489			0.383896			0.191948	−	0.981405i	$-0.438520\pi$
$239$	5.93489			0.383896			0.191948	+	0.981405i	$0.438520\pi$
$240$	1.74483	−	8.66918i	0.112628	−	0.559593i
$241$	10.6860			0.688349			0.344174	−	0.938906i	$-0.388159\pi$
$241$	10.6860			0.688349			0.344174	+	0.938906i	$0.388159\pi$
$242$	3.13628	−	6.62141i	0.201608	−	0.425640i
$243$		−	14.7617i		−	0.946961i
$244$	−13.4872	+	11.0431i	−0.863426	+	0.706961i
$245$		0			0
$246$	−1.84302	−	0.872962i	−0.117507	−	0.0556581i
$247$	8.35640			0.531705
$248$	−6.06814	+	1.50904i	−0.385327	+	0.0958242i
$249$	4.42151			0.280202
$250$	2.02689	+	0.960052i	0.128192	+	0.0607190i
$251$			3.82402i			0.241370i	0.992691	+	0.120685i	$0.0385091\pi$
$251$			3.82402i			0.241370i	−0.992691	+	0.120685i	$0.961491\pi$
$252$		0			0
$253$			6.62141i			0.416284i
$254$	−9.37709	+	19.7972i	−0.588371	+	1.24219i
$255$	8.74483			0.547622
$256$	−14.7542	−	6.18983i	−0.922137	−	0.386864i
$257$	−12.4058			−0.773854			−0.386927	−	0.922110i	$-0.626463\pi$
$257$	−12.4058			−0.773854			−0.386927	+	0.922110i	$0.626463\pi$
$258$	−4.78924	+	10.1112i	−0.298165	+	0.629495i
$259$		0			0
$260$	12.7004	+	15.5113i	0.787646	+	0.961968i
$261$			5.11237i			0.316447i
$262$	21.4840	+	10.1761i	1.32729	+	0.628679i
$263$	−1.34401			−0.0828752			−0.0414376	−	0.999141i	$-0.513194\pi$
$263$	−1.34401			−0.0828752			−0.0414376	+	0.999141i	$0.513194\pi$
$264$	−4.51971	+	1.12397i	−0.278169	+	0.0691758i
$265$	8.37709			0.514601
$266$		0			0
$267$			9.54214i			0.583970i
$268$	8.96744	−	7.34241i	0.547774	−	0.448509i
$269$			1.95042i			0.118919i	0.998231	+	0.0594597i	$0.0189378\pi$
$269$			1.95042i			0.118919i	−0.998231	+	0.0594597i	$0.981062\pi$
$270$	−7.40648	+	15.6368i	−0.450744	+	0.951624i
$271$	26.0381			1.58170			0.790850	−	0.612009i	$-0.209639\pi$
$271$	26.0381			1.58170			0.790850	+	0.612009i	$0.209639\pi$
$272$	3.12192	−	15.5113i	0.189294	−	0.940509i
$273$		0			0
$274$	−0.537238	+	1.13423i	−0.0324557	+	0.0685214i
$275$		−	13.2428i		−	0.798572i
$276$	−2.89930	+	2.37391i	−0.174518	+	0.142892i
$277$			16.1170i			0.968379i	0.874963	+	0.484189i	$0.160885\pi$
$277$			16.1170i			0.968379i	−0.874963	+	0.484189i	$0.839115\pi$
$278$	3.12192	+	1.47872i	0.187240	+	0.0886878i
$279$	5.60221			0.335396
$280$		0			0
$281$	−16.1313			−0.962312			−0.481156	−	0.876635i	$-0.659783\pi$
$281$	−16.1313			−0.962312			−0.481156	+	0.876635i	$0.659783\pi$
$282$	−5.78608	−	2.74062i	−0.344556	−	0.163202i
$283$		−	26.3212i		−	1.56464i	−0.622879	−	0.782318i	$-0.714037\pi$
$283$		−	26.3212i		−	1.56464i	0.622879	−	0.782318i	$-0.285963\pi$
$284$	−8.42151	−	10.2854i	−0.499725	−	0.610324i
$285$		−	5.96914i		−	0.353581i
$286$	4.51971	−	9.54214i	0.267256	−	0.564239i
$287$		0			0
$288$	11.4897	+	8.57183i	0.677034	+	0.505100i
$289$	−1.35337			−0.0796101
$290$	3.95558	−	8.35114i	0.232280	−	0.490396i
$291$		−	0.939991i		−	0.0551033i
$292$	−12.1101	−	14.7903i	−0.708688	−	0.865535i
$293$		−	9.64929i		−	0.563718i	−0.959456	−	0.281859i	$-0.909049\pi$
$293$		−	9.64929i		−	0.563718i	0.959456	−	0.281859i	$-0.0909510\pi$
$294$		0			0
$295$	39.7479			2.31421
$296$	3.39145	+	13.6377i	0.197124	+	0.792674i
$297$	9.11256			0.528764
$298$	12.0506	+	5.70787i	0.698073	+	0.330648i
$299$		−	8.49500i		−	0.491278i
$300$	5.79861	−	4.74781i	0.334783	−	0.274115i
$301$		0			0
$302$	−4.27020	+	9.01537i	−0.245723	+	0.518777i
$303$	−0.543432			−0.0312193
$304$	−10.5878	−	2.13099i	−0.607255	−	0.122221i
$305$	−28.2281			−1.61634
$306$	−6.06814	+	12.8112i	−0.346892	+	0.732369i
$307$		−	25.2741i		−	1.44247i	−0.692691	−	0.721235i	$-0.743575\pi$
$307$		−	25.2741i		−	1.44247i	0.692691	−	0.721235i	$-0.256425\pi$
$308$		0			0
$309$		−	1.81295i		−	0.103135i
$310$	−9.15131	−	4.33459i	−0.519759	−	0.246188i
$311$	−22.5484			−1.27860			−0.639302	−	0.768956i	$-0.720777\pi$
$311$	−22.5484			−1.27860			−0.639302	+	0.768956i	$0.720777\pi$
$312$	5.79861	−	1.44201i	0.328281	−	0.0816379i
$313$	25.3801			1.43457			0.717285	−	0.696780i	$-0.245385\pi$
$313$	25.3801			1.43457			0.717285	+	0.696780i	$0.245385\pi$
$314$	11.1394	+	5.27629i	0.628635	+	0.297758i
$315$		0			0
$316$	−2.12442	−	2.59460i	−0.119508	−	0.145958i
$317$			17.1339i			0.962333i	0.876629	+	0.481167i	$0.159787\pi$
$317$			17.1339i			0.962333i	−0.876629	+	0.481167i	$0.840213\pi$
$318$	1.06881	−	2.25650i	0.0599358	−	0.126538i
$319$	−4.86675			−0.272485
$320$	−12.1363	−	22.8921i	−0.678439	−	1.27971i
$321$	−3.70674			−0.206890
$322$		0			0
$323$		−	10.6802i		−	0.594264i
$324$	−6.36523	−	7.77399i	−0.353624	−	0.431888i
$325$			16.9900i			0.942435i
$326$	25.3414	+	12.0031i	1.40353	+	0.664792i
$327$	−9.42785			−0.521361
$328$	−5.79861	+	1.44201i	−0.320174	+	0.0796218i
$329$		0			0
$330$	−6.81613	−	3.22851i	−0.375216	−	0.177724i
$331$		−	8.58596i		−	0.471927i	−0.971762	−	0.235963i	$-0.924175\pi$
$331$		−	8.58596i		−	0.471927i	0.971762	−	0.235963i	$-0.0758246\pi$
$332$	10.0237	−	8.20728i	0.550123	−	0.450433i
$333$		−	12.5905i		−	0.689957i
$334$	−13.4152	+	28.3225i	−0.734046	+	1.54974i
$335$	18.7685			1.02544
$336$		0			0
$337$	−3.18070			−0.173264			−0.0866319	−	0.996240i	$-0.527610\pi$
$337$	−3.18070			−0.173264			−0.0866319	+	0.996240i	$0.527610\pi$
$338$	2.07131	−	4.37300i	0.112664	−	0.237860i
$339$		−	3.09491i		−	0.168093i
$340$	19.8248	−	16.2323i	1.07515	−	0.880319i
$341$			5.33306i			0.288801i
$342$	8.74483	+	4.14206i	0.472866	+	0.223977i
$343$		0			0
$344$	7.91116	+	31.8123i	0.426541	+	1.71520i
$345$	−6.06814			−0.326698
$346$	27.7747	+	13.1557i	1.49318	+	0.707256i
$347$			21.9824i			1.18008i	0.807374	+	0.590039i	$0.200888\pi$
$347$			21.9824i			1.18008i	−0.807374	+	0.590039i	$0.799112\pi$
$348$	−1.74483	−	2.13099i	−0.0935325	−	0.114233i
$349$			15.5480i			0.832265i	0.909304	+	0.416132i	$0.136615\pi$
$349$			15.5480i			0.832265i	−0.909304	+	0.416132i	$0.863385\pi$
$350$		0			0
$351$	−11.6910			−0.624022
$352$	−8.16000	+	10.9376i	−0.434930	+	0.582978i
$353$	26.5608			1.41369			0.706845	−	0.707369i	$-0.250118\pi$
$353$	26.5608			1.41369			0.706845	+	0.707369i	$0.250118\pi$
$354$	5.07131	−	10.7067i	0.269537	−	0.569054i
$355$		−	21.5269i		−	1.14253i
$356$	17.7123	+	21.6324i	0.938748	+	1.14651i
$357$		0			0
$358$	−4.82799	−	2.28682i	−0.255167	−	0.120862i
$359$	−31.0124			−1.63677			−0.818386	−	0.574669i	$-0.805131\pi$
$359$	−31.0124			−1.63677			−0.818386	+	0.574669i	$0.805131\pi$
$360$	5.60221	+	22.5276i	0.295262	+	1.18731i
$361$	11.7098			0.616304
$362$	17.9349	+	8.49500i	0.942637	+	0.446487i
$363$		−	3.53630i		−	0.185607i
$364$		0			0
$365$		−	30.9555i		−	1.62029i
$366$	−3.60154	+	7.60368i	−0.188256	+	0.397451i
$367$	12.7735			0.666774			0.333387	−	0.942790i	$-0.391808\pi$
$367$	12.7735			0.666774			0.333387	+	0.942790i	$0.391808\pi$
$368$	−2.16634	+	10.7635i	−0.112928	+	0.561084i
$369$	5.35337			0.278685
$370$	−9.74166	+	20.5669i	−0.506445	+	1.06922i
$371$		0			0
$372$	−2.33518	+	1.91201i	−0.121073	+	0.0991330i
$373$		−	6.62141i		−	0.342843i	−0.985198	−	0.171422i	$-0.945164\pi$
$373$		−	6.62141i		−	0.342843i	0.985198	−	0.171422i	$-0.0548361\pi$
$374$	−12.1957	−	5.77660i	−0.630626	−	0.298701i
$375$	1.08250			0.0559001
$376$	−18.2044	+	4.52712i	−0.938821	+	0.233469i
$377$	6.24384			0.321574
$378$		0			0
$379$			18.7804i			0.964683i	0.875983	+	0.482341i	$0.160214\pi$
$379$			18.7804i			0.964683i	−0.875983	+	0.482341i	$0.839786\pi$
$380$	−11.0800	−	13.5322i	−0.568392	−	0.694189i
$381$			10.5731i			0.541676i
$382$	4.40648	−	9.30309i	0.225455	−	0.475988i
$383$	20.4359			1.04422			0.522112	−	0.852877i	$-0.325144\pi$
$383$	20.4359			1.04422			0.522112	+	0.852877i	$0.325144\pi$
$384$	−7.71477	+	0.348359i	−0.393693	+	0.0177771i
$385$		0			0
$386$	5.77172	−	12.1854i	0.293773	−	0.620221i
$387$		−	29.3697i		−	1.49294i
$388$	−1.74483	−	2.13099i	−0.0885801	−	0.108185i
$389$			2.37561i			0.120448i	0.998185	+	0.0602242i	$0.0191816\pi$
$389$			2.37561i			0.120448i	−0.998185	+	0.0602242i	$0.980818\pi$
$390$	8.74483	+	4.14206i	0.442811	+	0.209741i
$391$	−10.8574			−0.549082
$392$		0			0
$393$	11.4740			0.578785
$394$	−14.9112	−	7.06279i	−0.751214	−	0.355818i
$395$		−	5.43040i		−	0.273233i
$396$	9.45960	−	7.74538i	0.475363	−	0.389220i
$397$			22.1694i			1.11265i	0.830965	+	0.556325i	$0.187789\pi$
$397$			22.1694i			1.11265i	−0.830965	+	0.556325i	$0.812211\pi$
$398$	−11.4810	+	24.2389i	−0.575488	+	1.21499i
$399$		0			0
$400$	4.33268	−	21.5269i	0.216634	−	1.07635i
$401$	26.3170			1.31421			0.657104	−	0.753800i	$-0.271781\pi$
$401$	26.3170			1.31421			0.657104	+	0.753800i	$0.271781\pi$
$402$	2.39462	−	5.05560i	0.119433	−	0.252150i
$403$		−	6.84210i		−	0.340829i
$404$	−1.23198	+	1.00873i	−0.0612932	+	0.0501860i
$405$		−	16.2707i		−	0.808497i
$406$		0			0
$407$	11.9856			0.594106
$408$	−1.84302	−	7.41115i	−0.0912433	−	0.366906i
$409$	0.662325			0.0327498			0.0163749	−	0.999866i	$-0.494787\pi$
$409$	0.662325			0.0327498			0.0163749	+	0.999866i	$0.494787\pi$
$410$	−8.74483	−	4.14206i	−0.431876	−	0.204562i
$411$			0.605759i			0.0298799i
$412$	−3.36523	−	4.11003i	−0.165793	−	0.202487i
$413$		0			0
$414$	4.21076	−	8.88987i	0.206947	−	0.436913i
$415$	20.9793			1.02983
$416$	10.4690	−	14.0326i	0.513283	−	0.688003i
$417$	1.66732			0.0816492
$418$	−3.94305	+	8.32469i	−0.192861	+	0.407174i
$419$		−	7.55501i		−	0.369086i	−0.982824	−	0.184543i	$-0.940919\pi$
$419$		−	7.55501i		−	0.369086i	0.982824	−	0.184543i	$-0.0590805\pi$
$420$		0			0
$421$		−	12.5905i		−	0.613625i	−0.951770	−	0.306813i	$-0.900737\pi$
$421$		−	12.5905i		−	0.613625i	0.951770	−	0.306813i	$-0.0992625\pi$
$422$	20.6116	+	9.76283i	1.00336	+	0.475247i
$423$	16.8066			0.817166
$424$	−1.76552	−	7.09950i	−0.0857413	−	0.344782i
$425$	21.7148			1.05332
$426$	−5.79861	−	2.74655i	−0.280943	−	0.133071i
$427$		0			0
$428$	−8.40332	+	6.88051i	−0.406190	+	0.332582i
$429$		−	5.09617i		−	0.246046i
$430$	−22.7241	+	47.9758i	−1.09585	+	2.31360i
$431$	−12.9048			−0.621604			−0.310802	−	0.950475i	$-0.600598\pi$
$431$	−12.9048			−0.621604			−0.310802	+	0.950475i	$0.600598\pi$
$432$	14.8130	+	2.98137i	0.712689	+	0.143441i
$433$	40.5815			1.95022			0.975112	−	0.221715i	$-0.0711654\pi$
$433$	40.5815			1.95022			0.975112	+	0.221715i	$0.0711654\pi$
$434$		0			0
$435$		−	4.46009i		−	0.213845i
$436$	−21.3733	+	17.5001i	−1.02359	+	0.838104i
$437$			7.41115i			0.354523i
$438$	−8.33834	−	3.94952i	−0.398421	−	0.188715i
$439$	−36.4546			−1.73988			−0.869941	−	0.493155i	$-0.835844\pi$
$439$	−36.4546			−1.73988			−0.869941	+	0.493155i	$0.835844\pi$
$440$	−21.4452	+	5.33306i	−1.02236	+	0.254244i
$441$		0			0
$442$	15.6466	+	7.41115i	0.744234	+	0.352512i
$443$			32.4787i			1.54311i	0.636163	+	0.771555i	$0.280521\pi$
$443$			32.4787i			1.54311i	−0.636163	+	0.771555i	$0.719479\pi$
$444$	4.29709	+	5.24813i	0.203931	+	0.249065i
$445$			45.2758i			2.14628i
$446$	4.67035	−	9.86018i	0.221148	−	0.466893i
$447$	6.43587			0.304406
$448$		0			0
$449$	25.9823			1.22618			0.613091	−	0.790012i	$-0.289926\pi$
$449$	25.9823			1.22618			0.613091	+	0.790012i	$0.289926\pi$
$450$	−8.42151	+	17.7797i	−0.396994	+	0.838145i
$451$			5.09617i			0.239969i
$452$	−5.74483	−	7.01628i	−0.270214	−	0.330018i
$453$			4.81484i			0.226221i
$454$	2.71544	+	1.28619i	0.127442	+	0.0603638i
$455$		0			0
$456$	−5.05878	+	1.25803i	−0.236899	+	0.0589127i
$457$	−11.4690			−0.536495			−0.268248	−	0.963350i	$-0.586445\pi$
$457$	−11.4690			−0.536495			−0.268248	+	0.963350i	$0.586445\pi$
$458$	11.9731	+	5.67116i	0.559467	+	0.264996i
$459$			14.9422i			0.697443i
$460$	−13.7567	+	11.2638i	−0.641409	+	0.525176i
$461$		−	25.1973i		−	1.17355i	−0.809749	−	0.586777i	$-0.800396\pi$
$461$		−	25.1973i		−	1.17355i	0.809749	−	0.586777i	$-0.199604\pi$
$462$		0			0
$463$	−31.8223			−1.47891			−0.739454	−	0.673207i	$-0.764916\pi$
$463$	−31.8223			−1.47891			−0.739454	+	0.673207i	$0.764916\pi$
$464$	−7.91116	−	1.59226i	−0.367267	−	0.0739189i
$465$	−4.88744			−0.226650
$466$	−5.34387	+	11.2821i	−0.247550	+	0.522635i
$467$		−	14.2131i		−	0.657705i	−0.944381	−	0.328852i	$-0.893338\pi$
$467$		−	14.2131i		−	0.657705i	0.944381	−	0.328852i	$-0.106662\pi$
$468$	−12.1363	+	9.93701i	−0.561000	+	0.459338i
$469$		0			0
$470$	−27.4539	−	13.0038i	−1.26636	−	0.599819i
$471$	5.94925			0.274127
$472$	−8.37709	−	33.6859i	−0.385587	−	1.55052i
$473$	27.9586			1.28554
$474$	−1.46276	−	0.692849i	−0.0671869	−	0.0318236i
$475$		−	14.8223i		−	0.680094i
$476$		0			0
$477$			6.55438i			0.300104i
$478$	3.59285	−	7.58533i	0.164333	−	0.346945i
$479$	11.5404			0.527295			0.263647	−	0.964619i	$-0.415075\pi$
$479$	11.5404			0.527295			0.263647	+	0.964619i	$0.415075\pi$
$480$	−10.0237	−	7.47818i	−0.457518	−	0.341330i
$481$	−15.3771			−0.701135
$482$	6.46910	−	13.6577i	0.294659	−	0.622093i
$483$		0			0
$484$	−6.56413	−	8.01691i	−0.298369	−	0.364405i
$485$		−	4.46009i		−	0.202522i
$486$	−18.8667	−	8.93638i	−0.855813	−	0.405362i
$487$	−17.6166			−0.798283			−0.399142	−	0.916889i	$-0.630692\pi$
$487$	−17.6166			−0.798283			−0.399142	+	0.916889i	$0.630692\pi$
$488$	5.94925	+	23.9231i	0.269310	+	1.08295i
$489$	13.5341			0.612032
$490$		0			0
$491$			26.8502i			1.21173i	0.795567	+	0.605866i	$0.207173\pi$
$491$			26.8502i			1.21173i	−0.795567	+	0.605866i	$0.792827\pi$
$492$	−2.23145	+	1.82708i	−0.100602	+	0.0823711i
$493$		−	7.98020i		−	0.359410i
$494$	5.05878	−	10.6802i	0.227605	−	0.480527i
$495$	19.7986			0.889881
$496$	−1.74483	+	8.66918i	−0.0783450	+	0.389258i
$497$		0			0
$498$	2.67669	−	5.65110i	0.119945	−	0.253232i
$499$			2.56257i			0.114717i	0.998354	+	0.0573583i	$0.0182677\pi$
$499$			2.56257i			0.114717i	−0.998354	+	0.0573583i	$0.981732\pi$
$500$	2.45407	−	2.00936i	0.109749	−	0.0898611i
$501$			15.1262i			0.675789i
$502$	4.88744	+	2.31497i	0.218137	+	0.103322i
$503$	14.6941			0.655176			0.327588	−	0.944821i	$-0.393764\pi$
$503$	14.6941			0.655176			0.327588	+	0.944821i	$0.393764\pi$
$504$		0			0
$505$	−2.57849			−0.114741
$506$	8.46276	+	4.00845i	0.376216	+	0.178197i
$507$		−	2.33549i		−	0.103723i
$508$	19.6259	+	23.9696i	0.870760	+	1.06348i
$509$		−	12.7344i		−	0.564442i	−0.959349	−	0.282221i	$-0.908929\pi$
$509$		−	12.7344i		−	0.564442i	0.959349	−	0.282221i	$-0.0910712\pi$
$510$	5.29392	−	11.1767i	0.234419	−	0.494912i
$511$		0			0
$512$	−16.8430	+	15.1100i	−0.744364	+	0.667775i
$513$	10.1994			0.450315
$514$	−7.51021	+	15.8558i	−0.331261	+	0.699368i
$515$		−	8.60215i		−	0.379056i
$516$	10.0237	+	12.2422i	0.441270	+	0.538932i
$517$			15.9992i			0.703643i
$518$		0			0
$519$	14.8337			0.651126
$520$	27.5134	−	6.84210i	1.20654	−	0.300046i
$521$	−34.0267			−1.49074			−0.745369	−	0.666652i	$-0.767727\pi$
$521$	−34.0267			−1.49074			−0.745369	+	0.666652i	$0.767727\pi$
$522$	6.53407	+	3.09491i	0.285988	+	0.135461i
$523$		−	6.79559i		−	0.297150i	−0.988901	−	0.148575i	$-0.952531\pi$
$523$		−	6.79559i		−	0.297150i	0.988901	−	0.148575i	$-0.0474687\pi$
$524$	26.0119	−	21.2981i	1.13633	−	0.930413i
$525$		0			0
$526$	−0.813634	+	1.71777i	−0.0354761	+	0.0748982i
$527$	−8.74483			−0.380931
$528$	−1.29959	+	6.45703i	−0.0565575	+	0.281006i
$529$	−15.4659			−0.672432
$530$	5.07131	−	10.7067i	0.220284	−	0.465069i
$531$			31.0994i			1.34960i
$532$		0			0
$533$		−	6.53819i		−	0.283200i
$534$	12.1957	+	5.77660i	0.527761	+	0.249978i
$535$	−17.5878			−0.760389
$536$	−3.95558	−	15.9061i	−0.170855	−	0.687041i
$537$	−2.57849			−0.111270
$538$	2.49282	+	1.18074i	0.107473	+	0.0509055i
$539$		0			0
$540$	15.5015	+	18.9323i	0.667079	+	0.814718i
$541$		−	24.7051i		−	1.06215i	−0.847324	−	0.531077i	$-0.821788\pi$
$541$		−	24.7051i		−	1.06215i	0.847324	−	0.531077i	$-0.178212\pi$
$542$	15.7629	−	33.2790i	0.677074	−	1.42946i
$543$	9.57849			0.411052
$544$	−17.9349	−	13.3803i	−0.768952	−	0.573675i
$545$	−44.7335			−1.91617
$546$		0			0
$547$		−	27.5793i		−	1.17920i	−0.807694	−	0.589602i	$-0.799284\pi$
$547$		−	27.5793i		−	1.17920i	0.807694	−	0.589602i	$-0.200716\pi$
$548$	1.12442	+	1.37328i	0.0480328	+	0.0586635i
$549$		−	22.0862i		−	0.942615i
$550$	−16.9255	−	8.01691i	−0.721707	−	0.341842i
$551$	−5.44721			−0.232059
$552$	1.27890	+	5.14268i	0.0544334	+	0.218887i
$553$		0			0
$554$	20.5990	+	9.75690i	0.875169	+	0.414531i
$555$			10.9842i			0.466251i
$556$	3.77988	−	3.09491i	0.160303	−	0.131254i
$557$		−	45.2152i		−	1.91583i	−0.287056	−	0.957914i	$-0.592677\pi$
$557$		−	45.2152i		−	1.91583i	0.287056	−	0.957914i	$-0.407323\pi$
$558$	3.39145	−	7.16014i	0.143572	−	0.303113i
$559$	−35.8698			−1.51713
$560$		0			0
$561$	−6.51337			−0.274995
$562$	−9.76552	+	20.6173i	−0.411934	+	0.869686i
$563$			15.2299i			0.641866i	0.947102	+	0.320933i	$0.103996\pi$
$563$			15.2299i			0.641866i	−0.947102	+	0.320933i	$0.896004\pi$
$564$	−7.00553	+	5.73602i	−0.294986	+	0.241530i
$565$		−	14.6848i		−	0.617795i
$566$	−33.6410	−	15.9343i	−1.41404	−	0.669769i
$567$		0			0
$568$	−18.2438	+	4.53693i	−0.765495	+	0.190365i
$569$	14.0869			0.590552			0.295276	−	0.955412i	$-0.404588\pi$
$569$	14.0869			0.590552			0.295276	+	0.955412i	$0.404588\pi$
$570$	−7.62910	−	3.61358i	−0.319548	−	0.151356i
$571$		−	22.2257i		−	0.930117i	−0.885280	−	0.465058i	$-0.846033\pi$
$571$		−	22.2257i		−	0.930117i	0.885280	−	0.465058i	$-0.153967\pi$
$572$	−9.45960	−	11.5532i	−0.395526	−	0.483064i
$573$		−	4.96851i		−	0.207562i
$574$		0			0
$575$	−15.0681			−0.628385
$576$	17.9112	−	9.49563i	0.746298	−	0.395651i
$577$	−9.36140			−0.389720			−0.194860	−	0.980831i	$-0.562425\pi$
$577$	−9.36140			−0.389720			−0.194860	+	0.980831i	$0.562425\pi$
$578$	−0.819301	+	1.72973i	−0.0340784	+	0.0719474i
$579$		−	6.50787i		−	0.270458i
$580$	−8.27890	−	10.1112i	−0.343762	−	0.419844i
$581$		0			0
$582$	−1.20139	−	0.569050i	−0.0497994	−	0.0235879i
$583$	−6.23948			−0.258413
$584$	−26.2345	+	6.52406i	−1.08559	+	0.269967i
$585$	−25.4008			−1.05019
$586$	−12.3327	−	5.84147i	−0.509458	−	0.241309i
$587$			13.0157i			0.537217i	0.963249	+	0.268608i	$0.0865637\pi$
$587$			13.0157i			0.537217i	−0.963249	+	0.268608i	$0.913436\pi$
$588$		0			0
$589$			5.96914i			0.245954i
$590$	24.0625	−	50.8014i	0.990636	−	2.09146i
$591$	−7.96361			−0.327579
$592$	19.4833	+	3.92136i	0.800759	+	0.161167i
$593$	1.39779			0.0574003			0.0287002	−	0.999588i	$-0.490863\pi$
$593$	1.39779			0.0574003			0.0287002	+	0.999588i	$0.490863\pi$
$594$	5.51654	−	11.6467i	0.226346	−	0.477869i
$595$		0			0
$596$	14.5903	−	11.9464i	0.597644	−	0.489342i
$597$			12.9453i			0.529815i
$598$	−10.8574	−	5.14268i	−0.443991	−	0.210300i
$599$	−31.8604			−1.30178			−0.650891	−	0.759172i	$-0.725604\pi$
$599$	−31.8604			−1.30178			−0.650891	+	0.759172i	$0.725604\pi$
$600$	−2.55779	−	10.2854i	−0.104421	−	0.419898i
$601$	−34.4927			−1.40699			−0.703493	−	0.710702i	$-0.748377\pi$
$601$	−34.4927			−1.40699			−0.703493	+	0.710702i	$0.748377\pi$
$602$		0			0
$603$			14.6848i			0.598012i
$604$	8.93739	+	10.9154i	0.363657	+	0.444142i
$605$		−	16.7791i		−	0.682168i
$606$	−0.328981	+	0.694555i	−0.0133640	+	0.0282144i
$607$	9.23145			0.374693			0.187347	−	0.982294i	$-0.440011\pi$
$607$	9.23145			0.374693			0.187347	+	0.982294i	$0.440011\pi$
$608$	−9.13325	+	12.2422i	−0.370402	+	0.496486i
$609$		0			0
$610$	−17.0887	+	36.0781i	−0.691901	+	1.46076i
$611$		−	20.5263i		−	0.830405i
$612$	12.7004	+	15.5113i	0.513384	+	0.627006i
$613$		−	32.3813i		−	1.30787i	−0.756551	−	0.653935i	$-0.773117\pi$
$613$		−	32.3813i		−	1.30787i	0.756551	−	0.653935i	$-0.226883\pi$
$614$	−32.3026	−	15.3004i	−1.30363	−	0.617473i
$615$	−4.67035			−0.188327
$616$		0			0
$617$	−10.1600			−0.409026			−0.204513	−	0.978864i	$-0.565561\pi$
$617$	−10.1600			−0.409026			−0.204513	+	0.978864i	$0.565561\pi$
$618$	−2.31712	−	1.09752i	−0.0932082	−	0.0441488i
$619$		−	37.1659i		−	1.49382i	−0.664924	−	0.746911i	$-0.731536\pi$
$619$		−	37.1659i		−	1.49382i	0.664924	−	0.746911i	$-0.268464\pi$
$620$	−11.0800	+	9.07214i	−0.444984	+	0.364346i
$621$		−	10.3686i		−	0.416077i
$622$	−13.6503	+	28.8190i	−0.547328	+	1.15553i
$623$		0			0
$624$	1.66732	−	8.28411i	0.0667464	−	0.331630i
$625$	−22.3120			−0.892479
$626$	15.3646	−	32.4381i	0.614092	−	1.29649i
$627$			4.44597i			0.177555i
$628$	13.4872	−	11.0431i	0.538196	−	0.440667i
$629$			19.6533i			0.783630i
$630$		0			0
$631$	−7.31198			−0.291085			−0.145543	−	0.989352i	$-0.546493\pi$
$631$	−7.31198			−0.291085			−0.145543	+	0.989352i	$0.546493\pi$
$632$	−4.60221	+	1.14449i	−0.183066	+	0.0455254i
$633$	11.0080			0.437530
$634$	21.8986	+	10.3725i	0.869706	+	0.411943i
$635$			50.1675i			1.99084i
$636$	−2.23698	−	2.73207i	−0.0887019	−	0.108334i
$637$		0			0
$638$	−2.94622	+	6.22015i	−0.116642	+	0.246258i
$639$	16.8430			0.666300
$640$	−36.6052	+	1.65290i	−1.44695	+	0.0653366i
$641$	13.7067			0.541384			0.270692	−	0.962666i	$-0.412748\pi$
$641$	13.7067			0.541384			0.270692	+	0.962666i	$0.412748\pi$
$642$	−2.24398	+	4.73756i	−0.0885628	+	0.186976i
$643$		−	30.5812i		−	1.20600i	−0.797740	−	0.603002i	$-0.793971\pi$
$643$		−	30.5812i		−	1.20600i	0.797740	−	0.603002i	$-0.206029\pi$
$644$		0			0
$645$			25.6225i			1.00888i
$646$	−13.6503	−	6.46558i	−0.537065	−	0.254385i
$647$	−42.5959			−1.67462			−0.837308	−	0.546731i	$-0.815872\pi$
$647$	−42.5959			−1.67462			−0.837308	+	0.546731i	$0.815872\pi$
$648$	−13.7892	+	3.42915i	−0.541693	+	0.134710i
$649$	−29.6052			−1.16211
$650$	21.7148	+	10.2854i	0.851723	+	0.403425i
$651$		0			0
$652$	30.6822	−	25.1222i	1.20161	−	0.983859i
$653$			31.0930i			1.21676i	0.793645	+	0.608381i	$0.208181\pi$
$653$			31.0930i			1.21676i	−0.793645	+	0.608381i	$0.791819\pi$
$654$	−5.70741	+	12.0496i	−0.223177	+	0.471179i
$655$	54.4419			2.12722
$656$	−1.66732	+	8.28411i	−0.0650981	+	0.323440i
$657$	24.2201			0.944917
$658$		0			0
$659$		−	35.8472i		−	1.39641i	−0.715899	−	0.698204i	$-0.753983\pi$
$659$		−	35.8472i		−	1.39641i	0.715899	−	0.698204i	$-0.246017\pi$
$660$	−8.25267	+	6.75717i	−0.321235	+	0.263022i
$661$			27.2852i			1.06127i	0.847600	+	0.530635i	$0.178047\pi$
$661$			27.2852i			1.06127i	−0.847600	+	0.530635i	$0.821953\pi$
$662$	−10.9736	−	5.19775i	−0.426503	−	0.202016i
$663$	8.35640			0.324536
$664$	−4.42151	−	17.7797i	−0.171588	−	0.689988i
$665$		0			0
$666$	−16.0919	−	7.62204i	−0.623547	−	0.295348i
$667$			5.53756i			0.214415i
$668$	28.0775	+	34.2916i	1.08635	+	1.32678i
$669$		−	5.26603i		−	0.203596i
$670$	11.3621	−	23.9879i	0.438955	−	0.926734i
$671$	21.0251			0.811663
$672$		0			0
$673$	−32.2963			−1.24493			−0.622465	−	0.782648i	$-0.713869\pi$
$673$	−32.2963			−1.24493			−0.622465	+	0.782648i	$0.713869\pi$
$674$	−1.92552	+	4.06522i	−0.0741684	+	0.156587i
$675$			20.7372i			0.798175i
$676$	−4.33518	−	5.29464i	−0.166738	−	0.203640i
$677$			15.6791i			0.602595i	0.953530	+	0.301298i	$0.0974198\pi$
$677$			15.6791i			0.602595i	−0.953530	+	0.301298i	$0.902580\pi$
$678$	−3.95558	−	1.87359i	−0.151913	−	0.0719549i
$679$		0			0
$680$	−8.74483	−	35.1646i	−0.335349	−	1.34850i
$681$	1.45023			0.0555731
$682$	6.81613	+	3.22851i	0.261003	+	0.123626i
$683$			19.0540i			0.729080i	0.931188	+	0.364540i	$0.118774\pi$
$683$			19.0540i			0.729080i	−0.931188	+	0.364540i	$0.881226\pi$
$684$	10.5878	−	8.66918i	0.404837	−	0.331474i
$685$			2.87422i			0.109818i
$686$		0			0
$687$	6.39448			0.243965
$688$	45.4483	+	9.14727i	1.73270	+	0.348736i
$689$	8.00500			0.304966
$690$	−3.67352	+	7.75564i	−0.139848	+	0.295252i
$691$			31.0691i			1.18192i	0.806700	+	0.590961i	$0.201251\pi$
$691$			31.0691i			1.18192i	−0.806700	+	0.590961i	$0.798749\pi$
$692$	33.6284	−	27.5345i	1.27836	−	1.04670i
$693$		0			0
$694$	28.0956	+	13.3077i	1.06649	+	0.505153i
$695$	7.91116			0.300088
$696$	−3.77988	+	0.939991i	−0.143276	+	0.0356303i
$697$	−8.35640			−0.316521
$698$	19.8717	+	9.41241i	0.752157	+	0.356265i
$699$			6.02545i			0.227903i
$700$		0			0
$701$			33.5258i			1.26625i	0.774048	+	0.633127i	$0.218229\pi$
$701$			33.5258i			1.26625i	−0.774048	+	0.633127i	$0.781771\pi$
$702$	−7.07750	+	14.9422i	−0.267123	+	0.563958i
$703$	13.4152			0.505963
$704$	9.03942	+	17.0506i	0.340686	+	0.642620i
$705$	−14.6623			−0.552215
$706$	16.0793	−	33.9472i	0.605154	−	1.27762i
$707$		0			0
$708$	−10.6141	−	12.9632i	−0.398901	−	0.487186i
$709$		−	8.27431i		−	0.310748i	−0.987856	−	0.155374i	$-0.950342\pi$
$709$		−	8.27431i		−	0.310748i	0.987856	−	0.155374i	$-0.0496583\pi$
$710$	−27.5134	−	13.0319i	−1.03256	−	0.489079i
$711$	4.24884			0.159344
$712$	38.3708	−	9.54214i	1.43800	−	0.357607i
$713$	6.06814			0.227254
$714$		0			0
$715$		−	24.1805i		−	0.904298i
$716$	−5.84552	+	4.78623i	−0.218457	+	0.178870i
$717$		−	4.05110i		−	0.151291i
$718$	−18.7742	+	39.6367i	−0.700648	+	1.47923i
$719$	3.62924			0.135348			0.0676739	−	0.997707i	$-0.478442\pi$
$719$	3.62924			0.135348			0.0676739	+	0.997707i	$0.478442\pi$
$720$	32.1837	+	6.47755i	1.19942	+	0.241404i
$721$		0			0
$722$	7.08884	−	14.9662i	0.263819	−	0.556983i
$723$		−	7.29419i		−	0.271274i
$724$	21.7148	−	17.7797i	0.807023	−	0.660779i
$725$		−	11.0751i		−	0.411319i
$726$	−4.51971	−	2.14080i	−0.167742	−	0.0794524i
$727$	−28.1550			−1.04421			−0.522106	−	0.852881i	$-0.674853\pi$
$727$	−28.1550			−1.04421			−0.522106	+	0.852881i	$0.674853\pi$
$728$		0			0
$729$	4.99500			0.185000
$730$	−39.5640	−	18.7398i	−1.46433	−	0.693591i
$731$			45.8448i			1.69563i
$732$	7.53791	+	9.20620i	0.278609	+	0.340271i
$733$		−	29.3598i		−	1.08443i	−0.840240	−	0.542215i	$-0.817586\pi$
$733$		−	29.3598i		−	1.08443i	0.840240	−	0.542215i	$-0.182414\pi$
$734$	7.73282	−	16.3258i	0.285424	−	0.602595i
$735$		0			0
$736$	12.4452	+	9.28474i	0.458737	+	0.342240i
$737$	−13.9793			−0.514934
$738$	3.24081	−	6.84210i	0.119296	−	0.251861i
$739$			12.9854i			0.477676i	0.971059	+	0.238838i	$0.0767665\pi$
$739$			12.9854i			0.477676i	−0.971059	+	0.238838i	$0.923233\pi$
$740$	20.3890	+	24.9015i	0.749513	+	0.915396i
$741$		−	5.70400i		−	0.209542i
$742$		0			0
$743$	21.8510			0.801637			0.400819	−	0.916157i	$-0.368726\pi$
$743$	21.8510			0.801637			0.400819	+	0.916157i	$0.368726\pi$
$744$	1.03006	+	4.14206i	0.0377637	+	0.151855i
$745$	30.5371			1.11879
$746$	−8.46276	−	4.00845i	−0.309844	−	0.146760i
$747$			16.4146i			0.600577i
$748$	−14.7660	+	12.0902i	−0.539900	+	0.442062i
$749$		0			0
$750$	0.655322	−	1.38354i	0.0239290	−	0.0505196i
$751$	12.0745			0.440604			0.220302	−	0.975432i	$-0.429296\pi$
$751$	12.0745			0.440604			0.220302	+	0.975432i	$0.429296\pi$
$752$	−5.23448	+	26.0075i	−0.190882	+	0.948397i
$753$	2.61024			0.0951223
$754$	3.77988	−	7.98020i	0.137655	−	0.290622i
$755$			22.8456i			0.831436i
$756$		0			0
$757$			27.2309i			0.989725i	0.868971	+	0.494862i	$0.164782\pi$
$757$			27.2309i			0.989725i	−0.868971	+	0.494862i	$0.835218\pi$
$758$	24.0030	+	11.3692i	0.871829	+	0.412949i
$759$	4.51971			0.164055
$760$	−24.0030	+	5.96914i	−0.870681	+	0.216523i
$761$	−30.4847			−1.10507			−0.552534	−	0.833490i	$-0.686339\pi$
$761$	−30.4847			−1.10507			−0.552534	+	0.833490i	$0.686339\pi$
$762$	13.5134	+	6.40072i	0.489538	+	0.231873i
$763$		0			0
$764$	−9.22262	−	11.2638i	−0.333663	−	0.407509i
$765$			32.4646i			1.17376i
$766$	12.3714	−	26.1189i	0.446998	−	0.943715i
$767$	37.9823			1.37146
$768$	−4.22512	+	10.0711i	−0.152461	+	0.363408i
$769$	−36.6991			−1.32340			−0.661701	−	0.749768i	$-0.730165\pi$
$769$	−36.6991			−1.32340			−0.661701	+	0.749768i	$0.730165\pi$
$770$		0			0
$771$			8.46809i			0.304971i
$772$	−12.0800	−	14.7536i	−0.434769	−	0.530992i
$773$		−	33.0498i		−	1.18872i	−0.804200	−	0.594359i	$-0.797406\pi$
$773$		−	33.0498i		−	1.18872i	0.804200	−	0.594359i	$-0.202594\pi$
$774$	−37.5371	−	17.7797i	−1.34924	−	0.639080i
$775$	−12.1363			−0.435948
$776$	−3.77988	+	0.939991i	−0.135690	+	0.0337437i
$777$		0			0
$778$	3.03625	+	1.43814i	0.108855	+	0.0515600i
$779$			5.70400i			0.204367i
$780$	10.5878	−	8.66918i	0.379106	−	0.310406i
$781$			16.0338i			0.573735i
$782$	−6.57282	+	13.8767i	−0.235044	+	0.496231i
$783$	7.62093			0.272350
$784$		0			0
$785$	28.2281			1.00751
$786$	6.94608	−	14.6648i	0.247758	−	0.523075i
$787$			17.3114i			0.617087i	0.951210	+	0.308543i	$0.0998415\pi$
$787$			17.3114i			0.617087i	−0.951210	+	0.308543i	$0.900159\pi$
$788$	−18.0538	+	14.7822i	−0.643139	+	0.526593i
$789$			0.917408i			0.0326606i
$790$	−6.94055	−	3.28745i	−0.246934	−	0.116962i
$791$		0			0
$792$	−4.17267	−	16.7791i	−0.148269	−	0.596220i
$793$	−26.9743			−0.957886
$794$	28.3345	+	13.4209i	1.00555	+	0.476289i
$795$		−	5.71812i		−	0.202801i
$796$	24.0292	+	29.3474i	0.851694	+	1.04019i
$797$			41.7331i			1.47826i	0.673561	+	0.739131i	$0.264764\pi$
$797$			41.7331i			1.47826i	−0.673561	+	0.739131i	$0.735236\pi$
$798$		0			0
$799$	−26.2345			−0.928109
$800$	−24.8905	−	18.5695i	−0.880011	−	0.656530i
$801$	−35.4245			−1.25166
$802$	15.9317	−	33.6355i	0.562569	−	1.18771i
$803$			23.0565i			0.813646i
$804$	−5.01186	−	6.12109i	−0.176755	−	0.215874i
$805$		0			0
$806$	−8.74483	−	4.14206i	−0.308023	−	0.145898i
$807$	1.33134			0.0468654
$808$	0.543432	+	2.18524i	0.0191179	+	0.0768765i
$809$	−9.72547			−0.341929			−0.170965	−	0.985277i	$-0.554688\pi$
$809$	−9.72547			−0.341929			−0.170965	+	0.985277i	$0.554688\pi$
$810$	−20.7954	−	9.84992i	−0.730677	−	0.346091i
$811$			55.3405i			1.94327i	0.236492	+	0.971633i	$0.424002\pi$
$811$			55.3405i			1.94327i	−0.236492	+	0.971633i	$0.575998\pi$
$812$		0			0
$813$		−	17.7733i		−	0.623339i
$814$	7.25584	−	15.3187i	0.254317	−	0.536922i
$815$	64.2168			2.24942
$816$	−10.5878	−	2.13099i	−0.370649	−	0.0745997i
$817$	31.2933			1.09481
$818$	0.400957	−	0.846511i	0.0140191	−	0.0295976i
$819$		0			0
$820$	−10.5878	+	8.66918i	−0.369744	+	0.302741i
$821$		−	42.1647i		−	1.47156i	−0.677222	−	0.735779i	$-0.736816\pi$
$821$		−	42.1647i		−	1.47156i	0.677222	−	0.735779i	$-0.263184\pi$
$822$	0.774216	+	0.366713i	0.0270039	+	0.0127906i
$823$	15.2138			0.530319			0.265160	−	0.964205i	$-0.414575\pi$
$823$	15.2138			0.530319			0.265160	+	0.964205i	$0.414575\pi$
$824$	−7.29023	+	1.81295i	−0.253967	+	0.0631572i
$825$	−9.03942			−0.314712
$826$		0			0
$827$		−	1.24390i		−	0.0432548i	−0.999766	−	0.0216274i	$-0.993115\pi$
$827$		−	1.24390i		−	0.0432548i	0.999766	−	0.0216274i	$-0.00688475\pi$
$828$	−8.81297	−	10.7635i	−0.306272	−	0.374056i
$829$			21.3062i			0.739996i	0.929033	+	0.369998i	$0.120642\pi$
$829$			21.3062i			0.739996i	−0.929033	+	0.369998i	$0.879358\pi$
$830$	12.7004	−	26.8135i	0.440838	−	0.930709i
$831$	11.0013			0.381632
$832$	−11.5972	−	21.8753i	−0.402061	−	0.758389i
$833$		0			0
$834$	1.00936	−	2.13099i	0.0349513	−	0.0737902i
$835$			71.7712i			2.48375i
$836$	8.25267	+	10.0792i	0.285425	+	0.348595i
$837$		−	8.35114i		−	0.288658i
$838$	−9.65599	−	4.57363i	−0.333561	−	0.157994i
$839$	20.9379			0.722857			0.361429	−	0.932400i	$-0.382289\pi$
$839$	20.9379			0.722857			0.361429	+	0.932400i	$0.382289\pi$
$840$		0			0
$841$	24.9299			0.859651
$842$	−16.0919	−	7.62204i	−0.554562	−	0.262673i
$843$			11.0111i			0.379241i
$844$	24.9556	−	20.4333i	0.859007	−	0.703342i
$845$		−	11.0815i		−	0.381215i
$846$	10.1744	−	21.4804i	0.349802	−	0.738512i
$847$		0			0
$848$	−10.1426	−	2.04138i	−0.348299	−	0.0701013i
$849$	−17.9666			−0.616613
$850$	13.1456	−	27.7535i	0.450892	−	0.951936i
$851$		−	13.6377i		−	0.467494i
$852$	−7.02070	+	5.74844i	−0.240525	+	0.196938i
$853$		−	17.4758i		−	0.598361i	−0.954197	−	0.299180i	$-0.903287\pi$
$853$		−	17.4758i		−	0.598361i	0.954197	−	0.299180i	$-0.0967133\pi$
$854$		0			0
$855$	22.1600			0.757856
$856$	3.70674	+	14.9055i	0.126694	+	0.509460i
$857$	−3.51035			−0.119911			−0.0599556	−	0.998201i	$-0.519096\pi$
$857$	−3.51035			−0.119911			−0.0599556	+	0.998201i	$0.519096\pi$
$858$	−6.51337	−	3.08511i	−0.222363	−	0.105324i
$859$		−	5.14268i		−	0.175466i	−0.996144	−	0.0877331i	$-0.972038\pi$
$859$		−	5.14268i		−	0.175466i	0.996144	−	0.0877331i	$-0.0279623\pi$
$860$	47.5608	+	58.0870i	1.62181	+	1.98075i
$861$		0			0
$862$	−7.81230	+	16.4936i	−0.266088	+	0.561773i
$863$	−40.2819			−1.37121			−0.685606	−	0.727973i	$-0.740463\pi$
$863$	−40.2819			−1.37121			−0.685606	+	0.727973i	$0.740463\pi$
$864$	12.7779	−	17.1275i	0.434713	−	0.582688i
$865$	70.3831			2.39310
$866$	24.5672	−	51.8669i	0.834826	−	1.76251i
$867$			0.923798i			0.0313738i
$868$		0			0
$869$			4.04471i			0.137207i
$870$	−5.70041	−	2.70004i	−0.193262	−	0.0915400i
$871$	17.9349			0.607700
$872$	9.42785	+	37.9112i	0.319267	+	1.28383i
$873$	3.48965			0.118107
$874$	9.47212	+	4.48655i	0.320399	+	0.151760i
$875$		0			0
$876$	−10.0957	+	8.26621i	−0.341102	+	0.279289i
$877$		−	41.9700i		−	1.41723i	−0.705597	−	0.708613i	$-0.749321\pi$
$877$		−	41.9700i		−	1.41723i	0.705597	−	0.708613i	$-0.250679\pi$
$878$	−22.0688	+	46.5923i	−0.744786	+	1.57241i
$879$	−6.58651			−0.222158
$880$	−6.16634	+	30.6375i	−0.207867	+	1.03279i
$881$	16.5992			0.559241			0.279620	−	0.960111i	$-0.409791\pi$
$881$	16.5992			0.559241			0.279620	+	0.960111i	$0.409791\pi$
$882$		0			0
$883$		−	12.8210i		−	0.431462i	−0.976453	−	0.215731i	$-0.930787\pi$
$883$		−	12.8210i		−	0.431462i	0.976453	−	0.215731i	$-0.0692135\pi$
$884$	18.9442	−	15.5113i	0.637164	−	0.521701i
$885$		−	27.1315i		−	0.912016i
$886$	41.5107	+	19.6619i	1.39458	+	0.660554i
$887$	−8.29959			−0.278673			−0.139337	−	0.990245i	$-0.544497\pi$
$887$	−8.29959			−0.278673			−0.139337	+	0.990245i	$0.544497\pi$
$888$	9.30895	−	2.31497i	0.312388	−	0.0776855i
$889$		0			0
$890$	57.8666	+	27.4090i	1.93969	+	0.918751i
$891$			12.1188i			0.405996i
$892$	−9.77488	−	11.9383i	−0.327287	−	0.399723i
$893$			17.9074i			0.599248i
$894$	3.89614	−	8.22563i	0.130306	−	0.275106i
$895$	−12.2345			−0.408954
$896$		0			0
$897$	−5.79861			−0.193610
$898$	15.7291	−	33.2078i	0.524888	−	1.10816i
$899$			4.46009i			0.148752i
$900$	17.6259	+	21.5269i	0.587531	+	0.717564i
$901$		−	10.2311i		−	0.340848i
$902$	6.51337	+	3.08511i	0.216872	+	0.102723i
$903$		0			0
$904$	−12.4452	+	3.09491i	−0.413922	+	0.102935i
$905$	45.4483			1.51075
$906$	6.15381	+	2.91480i	0.204447	+	0.0968377i
$907$		−	16.4287i		−	0.545506i	−0.962084	−	0.272753i	$-0.912066\pi$
$907$		−	16.4287i		−	0.545506i	0.962084	−	0.272753i	$-0.0879341\pi$
$908$	3.28773	−	2.69195i	0.109107	−	0.0893354i
$909$		−	2.01745i		−	0.0669147i
$910$		0			0
$911$	−37.1630			−1.23127			−0.615633	−	0.788033i	$-0.711100\pi$
$911$	−37.1630			−1.23127			−0.615633	+	0.788033i	$0.711100\pi$
$912$	−1.45460	+	7.22717i	−0.0481665	+	0.239315i
$913$	−15.6259			−0.517143
$914$	−6.94305	+	14.6584i	−0.229656	+	0.484856i
$915$			19.2683i			0.636989i
$916$	14.4965	−	11.8695i	0.478978	−	0.392180i
$917$		0			0
$918$	19.0975	+	9.04569i	0.630312	+	0.298552i
$919$	−36.3056			−1.19761			−0.598806	−	0.800894i	$-0.704358\pi$
$919$	−36.3056			−1.19761			−0.598806	+	0.800894i	$0.704358\pi$
$920$	6.06814	+	24.4011i	0.200061	+	0.804482i
$921$	−17.2519			−0.568468
$922$	−32.2044	−	15.2539i	−1.06060	−	0.502360i
$923$		−	20.5707i		−	0.677094i
$924$		0			0
$925$			27.2754i			0.896809i
$926$	−19.2645	+	40.6718i	−0.633072	+	1.33656i
$927$	6.73047			0.221057
$928$	−6.82430	+	9.14727i	−0.224019	+	0.300274i
$929$	21.6527			0.710401			0.355201	−	0.934790i	$-0.384413\pi$
$929$	21.6527			0.710401			0.355201	+	0.934790i	$0.384413\pi$
$930$	−2.95875	+	6.24660i	−0.0970212	+	0.204834i
$931$		0			0
$932$	11.1845	+	13.6599i	0.366362	+	0.447445i
$933$			15.3913i			0.503890i
$934$	−18.1657	−	8.60431i	−0.594399	−	0.281542i
$935$	−30.9048			−1.01070
$936$	5.35337	+	21.5269i	0.174980	+	0.703629i
$937$	15.8637			0.518245			0.259123	−	0.965844i	$-0.416567\pi$
$937$	15.8637			0.518245			0.259123	+	0.965844i	$0.416567\pi$
$938$		0			0
$939$		−	17.3242i		−	0.565355i
$940$	−33.2400	+	27.2164i	−1.08417	+	0.887702i
$941$		−	14.6912i		−	0.478920i	−0.970906	−	0.239460i	$-0.923030\pi$
$941$		−	14.6912i		−	0.478920i	0.970906	−	0.239460i	$-0.0769704\pi$
$942$	3.60154	−	7.60368i	0.117345	−	0.247741i
$943$	5.79861			0.188829
$944$	−48.1249	−	9.68600i	−1.56633	−	0.315252i
$945$		0			0
$946$	16.9255	−	35.7337i	0.550296	−	1.16180i
$947$		−	13.9254i		−	0.452515i	−0.974068	−	0.226257i	$-0.927351\pi$
$947$		−	13.9254i		−	0.452515i	0.974068	−	0.226257i	$-0.0726491\pi$
$948$	−1.77105	+	1.45011i	−0.0575210	+	0.0470973i
$949$		−	29.5805i		−	0.960225i
$950$	−18.9442	−	8.97309i	−0.614633	−	0.291126i
$951$	11.6954			0.379250
$952$		0			0
$953$	11.2883			0.365663			0.182831	−	0.983144i	$-0.441474\pi$
$953$	11.2883			0.365663			0.182831	+	0.983144i	$0.441474\pi$
$954$	8.37709	+	3.96788i	0.271218	+	0.128465i
$955$		−	23.5747i		−	0.762859i
$956$	−7.51971	−	9.18398i	−0.243205	−	0.297031i
$957$			3.32199i			0.107385i
$958$	6.98631	−	14.7497i	0.225717	−	0.476541i
$959$		0			0
$960$	−15.6259	+	8.28411i	−0.504325	+	0.267369i
$961$	−26.1126			−0.842341
$962$	−9.30895	+	19.6533i	−0.300133	+	0.633649i
$963$		−	13.7610i		−	0.443443i
$964$	−13.5396	−	16.5362i	−0.436081	−	0.532595i
$965$		−	30.8787i		−	0.994020i
$966$		0			0
$967$	−36.4276			−1.17143			−0.585716	−	0.810517i	$-0.699187\pi$
$967$	−36.4276			−1.17143			−0.585716	+	0.810517i	$0.699187\pi$
$968$	−14.2201	+	3.53630i	−0.457052	+	0.113661i
$969$	−7.29023			−0.234196
$970$	−5.70041	−	2.70004i	−0.183029	−	0.0866931i
$971$		−	6.64534i		−	0.213259i	−0.994299	−	0.106629i	$-0.965994\pi$
$971$		−	6.64534i		−	0.213259i	0.994299	−	0.106629i	$-0.0340059\pi$
$972$	−22.8430	+	18.7035i	−0.732690	+	0.599916i
$973$		0			0
$974$	−10.6647	+	22.5156i	−0.341719	+	0.721446i
$975$	11.5972			0.371408
$976$	34.1774	+	6.87881i	1.09399	+	0.220185i
$977$	−45.4452			−1.45392			−0.726961	−	0.686679i	$-0.759068\pi$
$977$	−45.4452			−1.45392			−0.726961	+	0.686679i	$0.759068\pi$
$978$	8.19323	−	17.2978i	0.261991	−	0.553122i
$979$		−	33.7226i		−	1.07778i
$980$		0			0
$981$		−	35.0002i		−	1.11747i
$982$	34.3170	+	16.2545i	1.09510	+	0.518702i
$983$	18.5308			0.591040			0.295520	−	0.955337i	$-0.404507\pi$
$983$	18.5308			0.591040			0.295520	+	0.955337i	$0.404507\pi$
$984$	0.984304	+	3.95807i	0.0313785	+	0.126179i
$985$	−37.7859			−1.20396
$986$	−10.1994	−	4.83104i	−0.324816	−	0.153852i
$987$		0			0
$988$	−10.5878	−	12.9312i	−0.336844	−	0.411395i
$989$		−	31.8123i		−	1.01157i
$990$	11.9856	−	25.3044i	0.380929	−	0.804227i
$991$	−36.4783			−1.15877			−0.579386	−	0.815053i	$-0.696708\pi$
$991$	−36.4783			−1.15877			−0.579386	+	0.815053i	$0.696708\pi$
$992$	10.0237	+	7.47818i	0.318254	+	0.237432i
$993$	−5.86069			−0.185983
$994$		0			0
$995$			61.4232i			1.94724i
$996$	−5.60221	−	6.84210i	−0.177513	−	0.216800i
$997$			15.3273i			0.485420i	0.970099	+	0.242710i	$0.0780364\pi$
$997$			15.3273i			0.485420i	−0.970099	+	0.242710i	$0.921964\pi$
$998$	3.27520	+	1.55132i	0.103675	+	0.0491063i
$999$	−18.7685			−0.593811

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.b.f.197.3		6
4.3	odd	2		1568.2.b.e.785.4		6
7.2	even	3		392.2.p.g.165.1		12
7.3	odd	6		56.2.p.a.37.5	yes	12
7.4	even	3		392.2.p.g.373.5		12
7.5	odd	6		56.2.p.a.53.1	yes	12
7.6	odd	2		392.2.b.e.197.3		6
8.3	odd	2		1568.2.b.e.785.3		6
8.5	even	2	inner	392.2.b.f.197.4		6
21.5	even	6		504.2.cj.c.109.6		12
21.17	even	6		504.2.cj.c.37.2		12
28.3	even	6		224.2.t.a.177.3		12
28.11	odd	6		1568.2.t.g.177.4		12
28.19	even	6		224.2.t.a.81.4		12
28.23	odd	6		1568.2.t.g.753.3		12
28.27	even	2		1568.2.b.f.785.3		6
56.3	even	6		224.2.t.a.177.4		12
56.5	odd	6		56.2.p.a.53.5	yes	12
56.11	odd	6		1568.2.t.g.177.3		12
56.13	odd	2		392.2.b.e.197.4		6
56.19	even	6		224.2.t.a.81.3		12
56.27	even	2		1568.2.b.f.785.4		6
56.37	even	6		392.2.p.g.165.5		12
56.45	odd	6		56.2.p.a.37.1	✓	12
56.51	odd	6		1568.2.t.g.753.4		12
56.53	even	6		392.2.p.g.373.1		12
84.47	odd	6		2016.2.cr.c.1873.1		12
84.59	odd	6		2016.2.cr.c.1297.6		12
168.5	even	6		504.2.cj.c.109.2		12
168.59	odd	6		2016.2.cr.c.1297.1		12
168.101	even	6		504.2.cj.c.37.6		12
168.131	odd	6		2016.2.cr.c.1873.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.1	✓	12	56.45	odd	6
56.2.p.a.37.5	yes	12	7.3	odd	6
56.2.p.a.53.1	yes	12	7.5	odd	6
56.2.p.a.53.5	yes	12	56.5	odd	6
224.2.t.a.81.3		12	56.19	even	6
224.2.t.a.81.4		12	28.19	even	6
224.2.t.a.177.3		12	28.3	even	6
224.2.t.a.177.4		12	56.3	even	6
392.2.b.e.197.3		6	7.6	odd	2
392.2.b.e.197.4		6	56.13	odd	2
392.2.b.f.197.3		6	1.1	even	1	trivial
392.2.b.f.197.4		6	8.5	even	2	inner
392.2.p.g.165.1		12	7.2	even	3
392.2.p.g.165.5		12	56.37	even	6
392.2.p.g.373.1		12	56.53	even	6
392.2.p.g.373.5		12	7.4	even	3
504.2.cj.c.37.2		12	21.17	even	6
504.2.cj.c.37.6		12	168.101	even	6
504.2.cj.c.109.2		12	168.5	even	6
504.2.cj.c.109.6		12	21.5	even	6
1568.2.b.e.785.3		6	8.3	odd	2
1568.2.b.e.785.4		6	4.3	odd	2
1568.2.b.f.785.3		6	28.27	even	2
1568.2.b.f.785.4		6	56.27	even	2
1568.2.t.g.177.3		12	56.11	odd	6
1568.2.t.g.177.4		12	28.11	odd	6
1568.2.t.g.753.3		12	28.23	odd	6
1568.2.t.g.753.4		12	56.51	odd	6
2016.2.cr.c.1297.1		12	168.59	odd	6
2016.2.cr.c.1297.6		12	84.59	odd	6
2016.2.cr.c.1873.1		12	84.47	odd	6
2016.2.cr.c.1873.6		12	168.131	odd	6

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.605378 - 1.27809i) q^{2} -0.682591i q^{3} +(-1.26704 - 1.54746i) q^{4} -3.23877i q^{5} +(-0.872413 - 0.413225i) q^{6} +(-2.74483 + 0.682591i) q^{8} +2.53407 q^{9} +(-4.13945 - 1.96068i) q^{10} +2.41232i q^{11} +(-1.05628 + 0.864866i) q^{12} -3.09491i q^{13} -2.21076 q^{15} +(-0.789244 + 3.92136i) q^{16} -3.95558 q^{17} +(1.53407 - 3.23877i) q^{18} +2.70004i q^{19} +(-5.01186 + 4.10364i) q^{20} +(3.08317 + 1.46037i) q^{22} +2.74483 q^{23} +(0.465930 + 1.87359i) q^{24} -5.48965 q^{25} +(-3.95558 - 1.87359i) q^{26} -3.77750i q^{27} +2.01745i q^{29} +(-1.33834 + 2.82555i) q^{30} +2.21076 q^{31} +(4.53407 + 3.38263i) q^{32} +1.64663 q^{33} +(-2.39462 + 5.05560i) q^{34} +(-3.21076 - 3.92136i) q^{36} -4.96851i q^{37} +(3.45090 + 1.63455i) q^{38} -2.11256 q^{39} +(2.21076 + 8.88987i) q^{40} +2.11256 q^{41} -11.5899i q^{43} +(3.73296 - 3.05650i) q^{44} -8.20728i q^{45} +(1.66166 - 3.50814i) q^{46} +6.63227 q^{47} +(2.67669 + 0.538731i) q^{48} +(-3.32331 + 7.01628i) q^{50} +2.70004i q^{51} +(-4.78924 + 3.92136i) q^{52} +2.58650i q^{53} +(-4.82799 - 2.28682i) q^{54} +7.81297 q^{55} +1.84302 q^{57} +(2.57849 + 1.22132i) q^{58} +12.2725i q^{59} +(2.80111 + 3.42105i) q^{60} -8.71569i q^{61} +(1.33834 - 2.82555i) q^{62} +(7.06814 - 3.74718i) q^{64} -10.0237 q^{65} +(0.996833 - 2.10454i) q^{66} +5.79496i q^{67} +(5.01186 + 6.12109i) q^{68} -1.87359i q^{69} +6.64663 q^{71} +(-6.95558 + 1.72973i) q^{72} +9.55779 q^{73} +(-6.35020 - 3.00782i) q^{74} +3.74718i q^{75} +(4.17820 - 3.42105i) q^{76} +(-1.27890 + 2.70004i) q^{78} +1.67669 q^{79} +(12.7004 + 2.55618i) q^{80} +5.02372 q^{81} +(1.27890 - 2.70004i) q^{82} +6.47755i q^{83} +12.8112i q^{85} +(-14.8130 - 7.01628i) q^{86} +1.37709 q^{87} +(-1.64663 - 6.62141i) q^{88} -13.9793 q^{89} +(-10.4897 - 4.96851i) q^{90} +(-3.47779 - 4.24750i) q^{92} -1.50904i q^{93} +(4.01503 - 8.47664i) q^{94} +8.74483 q^{95} +(2.30895 - 3.09491i) q^{96} +1.37709 q^{97} +6.11300i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 4 q^{6} + 2 q^{8} - 8 q^{10} - 2 q^{12} - 10 q^{15} - 8 q^{16} - 2 q^{17} - 6 q^{18} - 4 q^{20} + 6 q^{22} - 2 q^{23} + 18 q^{24} + 4 q^{25} - 2 q^{26} - 14 q^{30} + 10 q^{31} + 12 q^{32}+ \cdots - 20 q^{97}+O(q^{100}) \) 6 * q + 2 * q^2 + 4 * q^6 + 2 * q^8 - 8 * q^10 - 2 * q^12 - 10 * q^15 - 8 * q^16 - 2 * q^17 - 6 * q^18 - 4 * q^20 + 6 * q^22 - 2 * q^23 + 18 * q^24 + 4 * q^25 - 2 * q^26 - 14 * q^30 + 10 * q^31 + 12 * q^32 - 14 * q^33 - 16 * q^34 - 16 * q^36 + 18 * q^38 - 4 * q^39 + 10 * q^40 + 4 * q^41 + 30 * q^44 + 4 * q^46 + 30 * q^47 + 28 * q^48 - 8 * q^50 - 32 * q^52 + 2 * q^54 - 2 * q^55 - 2 * q^57 + 22 * q^58 - 6 * q^60 + 14 * q^62 + 12 * q^64 - 8 * q^65 - 38 * q^66 + 4 * q^68 + 16 * q^71 - 20 * q^72 - 10 * q^73 - 18 * q^74 - 26 * q^76 + 26 * q^78 + 22 * q^79 + 36 * q^80 - 22 * q^81 - 26 * q^82 - 40 * q^86 - 20 * q^87 + 14 * q^88 - 10 * q^89 - 26 * q^90 - 10 * q^92 + 42 * q^94 + 34 * q^95 + 16 * q^96 - 20 * q^97

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