LMFDB - Embedded newform 338.2.e.e.147.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [338,2,Mod(23,338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(338, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("338.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	338.e (of order $6$, degree $2$, not 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:	$2.69894358832$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			147.3
Root			$-0.385418 - 0.222521i$ of defining polynomial
Character	$\chi$	$=$	338.147
Dual form			338.2.e.e.23.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.02446 - 1.77441i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.60388i q^{5} +(-1.77441 + 1.02446i) q^{6} +(0.961216 - 0.554958i) q^{7} -1.00000i q^{8} +(-0.599031 - 1.03755i) q^{9} +(1.80194 - 3.12105i) q^{10} +(2.04113 + 1.17845i) q^{11} +2.04892 q^{12} -1.10992 q^{14} +(6.39477 + 3.69202i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.98039 + 5.16218i) q^{17} +1.19806i q^{18} +(-0.789689 + 0.455927i) q^{19} +(-3.12105 + 1.80194i) q^{20} -2.27413i q^{21} +(-1.17845 - 2.04113i) q^{22} +(1.69202 - 2.93067i) q^{23} +(-1.77441 - 1.02446i) q^{24} -7.98792 q^{25} +3.69202 q^{27} +(0.961216 + 0.554958i) q^{28} +(1.89008 - 3.27372i) q^{29} +(-3.69202 - 6.39477i) q^{30} -8.49396i q^{31} +(0.866025 - 0.500000i) q^{32} +(4.18211 - 2.41454i) q^{33} -5.96077i q^{34} +(2.00000 + 3.46410i) q^{35} +(0.599031 - 1.03755i) q^{36} +(-4.23494 - 2.44504i) q^{37} +0.911854 q^{38} +3.60388 q^{40} +(-6.22324 - 3.59299i) q^{41} +(-1.13706 + 1.96945i) q^{42} +(-0.257865 - 0.446635i) q^{43} +2.35690i q^{44} +(3.73921 - 2.15883i) q^{45} +(-2.93067 + 1.69202i) q^{46} +6.98792i q^{47} +(1.02446 + 1.77441i) q^{48} +(-2.88404 + 4.99531i) q^{49} +(6.91774 + 3.99396i) q^{50} +12.2131 q^{51} -3.38404 q^{53} +(-3.19738 - 1.84601i) q^{54} +(-4.24698 + 7.35598i) q^{55} +(-0.554958 - 0.961216i) q^{56} +1.86831i q^{57} +(-3.27372 + 1.89008i) q^{58} +(8.78735 - 5.07338i) q^{59} +7.38404i q^{60} +(0.219833 + 0.380761i) q^{61} +(-4.24698 + 7.35598i) q^{62} +(-1.15160 - 0.664874i) q^{63} -1.00000 q^{64} -4.82908 q^{66} +(1.85914 + 1.07338i) q^{67} +(-2.98039 + 5.16218i) q^{68} +(-3.46681 - 6.00469i) q^{69} -4.00000i q^{70} +(-0.533434 + 0.307979i) q^{71} +(-1.03755 + 0.599031i) q^{72} +6.32304i q^{73} +(2.44504 + 4.23494i) q^{74} +(-8.18329 + 14.1739i) q^{75} +(-0.789689 - 0.455927i) q^{76} +2.61596 q^{77} -15.4819 q^{79} +(-3.12105 - 1.80194i) q^{80} +(5.57942 - 9.66383i) q^{81} +(3.59299 + 6.22324i) q^{82} +0.911854i q^{83} +(1.96945 - 1.13706i) q^{84} +(-18.6039 + 10.7409i) q^{85} +0.515729i q^{86} +(-3.87263 - 6.70758i) q^{87} +(1.17845 - 2.04113i) q^{88} +(-3.24814 - 1.87531i) q^{89} -4.31767 q^{90} +3.38404 q^{92} +(-15.0718 - 8.70171i) q^{93} +(3.49396 - 6.05171i) q^{94} +(-1.64310 - 2.84594i) q^{95} -2.04892i q^{96} +(12.7085 - 7.33728i) q^{97} +(4.99531 - 2.88404i) q^{98} -2.82371i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 6 q^{4} - 16 q^{9} + 4 q^{10} - 12 q^{12} - 16 q^{14} - 6 q^{16} + 10 q^{17} - 6 q^{22} - 20 q^{25} + 24 q^{27} + 20 q^{29} - 24 q^{30} + 24 q^{35} + 16 q^{36} - 4 q^{38} + 8 q^{40} + 8 q^{42}+ \cdots - 36 q^{95}+O(q^{100}) $ 12 * q - 6 * q^3 + 6 * q^4 - 16 * q^9 + 4 * q^10 - 12 * q^12 - 16 * q^14 - 6 * q^16 + 10 * q^17 - 6 * q^22 - 20 * q^25 + 24 * q^27 + 20 * q^29 - 24 * q^30 + 24 * q^35 + 16 * q^36 - 4 * q^38 + 8 * q^40 + 8 * q^42 + 22 * q^43 - 6 * q^48 + 6 * q^49 + 64 * q^51 - 32 * q^55 - 8 * q^56 + 8 * q^61 - 32 * q^62 - 12 * q^64 - 16 * q^66 - 10 * q^68 - 28 * q^69 + 28 * q^74 - 46 * q^75 + 72 * q^77 - 72 * q^79 + 50 * q^81 + 14 * q^82 + 20 * q^87 + 6 * q^88 + 16 * q^90 + 4 * q^94 - 36 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.02446	−	1.77441i	0.591471	−	1.02446i	−0.402563	−	0.915392i	$-0.631881\pi$
$3$	1.02446	−	1.77441i	0.591471	−	1.02446i	0.994034	−	0.109066i	$-0.0347861\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$			3.60388i			1.61170i	0.592118	+	0.805851i	$0.298292\pi$
$5$			3.60388i			1.61170i	−0.592118	+	0.805851i	$0.701708\pi$
$6$	−1.77441	+	1.02446i	−0.724402	+	0.418234i
$7$	0.961216	−	0.554958i	0.363305	−	0.209754i	−0.307224	−	0.951637i	$-0.599400\pi$
$7$	0.961216	−	0.554958i	0.363305	−	0.209754i	0.670530	+	0.741883i	$0.266067\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.599031	−	1.03755i	−0.199677	−	0.345851i
$10$	1.80194	−	3.12105i	0.569823	−	0.986962i
$11$	2.04113	+	1.17845i	0.615424	+	0.355315i	0.775085	−	0.631856i	$-0.217707\pi$
$11$	2.04113	+	1.17845i	0.615424	+	0.355315i	−0.159661	+	0.987172i	$0.551040\pi$
$12$	2.04892			0.591471
$13$		0			0
$13$		0			0
$14$	−1.10992			−0.296638
$15$	6.39477	+	3.69202i	1.65112	+	0.953276i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.98039	+	5.16218i	0.722850	+	1.25201i	0.959853	+	0.280504i	$0.0905015\pi$
$17$	2.98039	+	5.16218i	0.722850	+	1.25201i	−0.237003	+	0.971509i	$0.576165\pi$
$18$			1.19806i			0.282386i
$19$	−0.789689	+	0.455927i	−0.181167	+	0.104597i	−0.587841	−	0.808977i	$-0.700022\pi$
$19$	−0.789689	+	0.455927i	−0.181167	+	0.104597i	0.406674	+	0.913573i	$0.366689\pi$
$20$	−3.12105	+	1.80194i	−0.697887	+	0.402926i
$21$		−	2.27413i		−	0.496255i
$22$	−1.17845	−	2.04113i	−0.251246	−	0.435171i
$23$	1.69202	−	2.93067i	0.352811	−	0.611086i	−0.633930	−	0.773391i	$-0.718559\pi$
$23$	1.69202	−	2.93067i	0.352811	−	0.611086i	0.986741	+	0.162304i	$0.0518926\pi$
$24$	−1.77441	−	1.02446i	−0.362201	−	0.209117i
$25$	−7.98792			−1.59758
$26$		0			0
$27$	3.69202			0.710530
$28$	0.961216	+	0.554958i	0.181653	+	0.104877i
$29$	1.89008	−	3.27372i	0.350980	−	0.607915i	−0.635442	−	0.772149i	$-0.719182\pi$
$29$	1.89008	−	3.27372i	0.350980	−	0.607915i	0.986421	+	0.164234i	$0.0525153\pi$
$30$	−3.69202	−	6.39477i	−0.674068	−	1.16752i
$31$		−	8.49396i		−	1.52556i	−0.646658	−	0.762780i	$-0.723834\pi$
$31$		−	8.49396i		−	1.52556i	0.646658	−	0.762780i	$-0.276166\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	4.18211	−	2.41454i	0.728012	−	0.420318i
$34$		−	5.96077i		−	1.02226i
$35$	2.00000	+	3.46410i	0.338062	+	0.585540i
$36$	0.599031	−	1.03755i	0.0998385	−	0.172925i
$37$	−4.23494	−	2.44504i	−0.696219	−	0.401962i	0.109718	−	0.993963i	$-0.465005\pi$
$37$	−4.23494	−	2.44504i	−0.696219	−	0.401962i	−0.805938	+	0.592000i	$0.798338\pi$
$38$	0.911854			0.147922
$39$		0			0
$40$	3.60388			0.569823
$41$	−6.22324	−	3.59299i	−0.971907	−	0.561131i	−0.0720900	−	0.997398i	$-0.522967\pi$
$41$	−6.22324	−	3.59299i	−0.971907	−	0.561131i	−0.899817	+	0.436267i	$0.856300\pi$
$42$	−1.13706	+	1.96945i	−0.175453	+	0.303893i
$43$	−0.257865	−	0.446635i	−0.0393240	−	0.0681112i	0.845694	−	0.533669i	$-0.179187\pi$
$43$	−0.257865	−	0.446635i	−0.0393240	−	0.0681112i	−0.885018	+	0.465558i	$0.845854\pi$
$44$			2.35690i			0.355315i
$45$	3.73921	−	2.15883i	0.557408	−	0.321820i
$46$	−2.93067	+	1.69202i	−0.432103	+	0.249475i
$47$			6.98792i			1.01929i	0.860384	+	0.509646i	$0.170224\pi$
$47$			6.98792i			1.01929i	−0.860384	+	0.509646i	$0.829776\pi$
$48$	1.02446	+	1.77441i	0.147868	+	0.256115i
$49$	−2.88404	+	4.99531i	−0.412006	+	0.713616i
$50$	6.91774	+	3.99396i	0.978316	+	0.564831i
$51$	12.2131			1.71018
$52$		0			0
$53$	−3.38404			−0.464834			−0.232417	−	0.972616i	$-0.574663\pi$
$53$	−3.38404			−0.464834			−0.232417	+	0.972616i	$0.574663\pi$
$54$	−3.19738	−	1.84601i	−0.435109	−	0.251210i
$55$	−4.24698	+	7.35598i	−0.572663	+	0.991881i
$56$	−0.554958	−	0.961216i	−0.0741594	−	0.128448i
$57$			1.86831i			0.247464i
$58$	−3.27372	+	1.89008i	−0.429861	+	0.248180i
$59$	8.78735	−	5.07338i	1.14401	−	0.660497i	0.196593	−	0.980485i	$-0.437012\pi$
$59$	8.78735	−	5.07338i	1.14401	−	0.660497i	0.947422	+	0.319988i	$0.103679\pi$
$60$			7.38404i			0.953276i
$61$	0.219833	+	0.380761i	0.0281467	+	0.0487515i	0.879756	−	0.475426i	$-0.157706\pi$
$61$	0.219833	+	0.380761i	0.0281467	+	0.0487515i	−0.851609	+	0.524178i	$0.824373\pi$
$62$	−4.24698	+	7.35598i	−0.539367	+	0.934211i
$63$	−1.15160	−	0.664874i	−0.145087	−	0.0837663i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−4.82908			−0.594419
$67$	1.85914	+	1.07338i	0.227130	+	0.131134i	0.609248	−	0.792980i	$-0.291472\pi$
$67$	1.85914	+	1.07338i	0.227130	+	0.131134i	−0.382117	+	0.924114i	$0.624805\pi$
$68$	−2.98039	+	5.16218i	−0.361425	+	0.626006i
$69$	−3.46681	−	6.00469i	−0.417355	−	0.722880i
$70$		−	4.00000i		−	0.478091i
$71$	−0.533434	+	0.307979i	−0.0633070	+	0.0365503i	−0.531319	−	0.847172i	$-0.678304\pi$
$71$	−0.533434	+	0.307979i	−0.0633070	+	0.0365503i	0.468012	+	0.883722i	$0.344970\pi$
$72$	−1.03755	+	0.599031i	−0.122277	+	0.0705965i
$73$			6.32304i			0.740056i	0.929021	+	0.370028i	$0.120652\pi$
$73$			6.32304i			0.740056i	−0.929021	+	0.370028i	$0.879348\pi$
$74$	2.44504	+	4.23494i	0.284230	+	0.492301i
$75$	−8.18329	+	14.1739i	−0.944925	+	1.63666i
$76$	−0.789689	−	0.455927i	−0.0905835	−	0.0522984i
$77$	2.61596			0.298116
$78$		0			0
$79$	−15.4819			−1.74185			−0.870924	−	0.491418i	$-0.836479\pi$
$79$	−15.4819			−1.74185			−0.870924	+	0.491418i	$0.836479\pi$
$80$	−3.12105	−	1.80194i	−0.348944	−	0.201463i
$81$	5.57942	−	9.66383i	0.619935	−	1.07376i
$82$	3.59299	+	6.22324i	0.396779	+	0.687242i
$83$			0.911854i			0.100089i	0.998747	+	0.0500445i	$0.0159363\pi$
$83$			0.911854i			0.100089i	−0.998747	+	0.0500445i	$0.984064\pi$
$84$	1.96945	−	1.13706i	0.214885	−	0.124064i
$85$	−18.6039	+	10.7409i	−2.01787	+	1.16502i
$86$			0.515729i			0.0556125i
$87$	−3.87263	−	6.70758i	−0.415189	−	0.719128i
$88$	1.17845	−	2.04113i	0.125623	−	0.217585i
$89$	−3.24814	−	1.87531i	−0.344302	−	0.198783i	0.317871	−	0.948134i	$-0.397032\pi$
$89$	−3.24814	−	1.87531i	−0.344302	−	0.198783i	−0.662173	+	0.749351i	$0.730366\pi$
$90$	−4.31767			−0.455122
$91$		0			0
$92$	3.38404			0.352811
$93$	−15.0718	−	8.70171i	−1.56287	−	0.902325i
$94$	3.49396	−	6.05171i	0.360374	−	0.624187i
$95$	−1.64310	−	2.84594i	−0.168579	−	0.291987i
$96$		−	2.04892i		−	0.209117i
$97$	12.7085	−	7.33728i	1.29036	−	0.744988i	0.311640	−	0.950200i	$-0.399122\pi$
$97$	12.7085	−	7.33728i	1.29036	−	0.744988i	0.978717	+	0.205212i	$0.0657885\pi$
$98$	4.99531	−	2.88404i	0.504602	−	0.291332i
$99$		−	2.82371i		−	0.283793i
$100$	−3.99396	−	6.91774i	−0.399396	−	0.691774i
$101$	4.38404	−	7.59339i	0.436229	−	0.755570i	−0.561166	−	0.827703i	$-0.689647\pi$
$101$	4.38404	−	7.59339i	0.436229	−	0.755570i	0.997395	+	0.0721329i	$0.0229806\pi$
$102$	−10.5769	−	6.10656i	−1.04727	−	0.604640i
$103$	−18.8116			−1.85356			−0.926782	−	0.375599i	$-0.877437\pi$
$103$	−18.8116			−1.85356			−0.926782	+	0.375599i	$0.877437\pi$
$104$		0			0
$105$	8.19567			0.799815
$106$	2.93067	+	1.69202i	0.284652	+	0.164344i
$107$	−9.02595	+	15.6334i	−0.872572	+	1.51134i	−0.0132443	+	0.999912i	$0.504216\pi$
$107$	−9.02595	+	15.6334i	−0.872572	+	1.51134i	−0.859327	+	0.511426i	$0.829117\pi$
$108$	1.84601	+	3.19738i	0.177632	+	0.307668i
$109$		−	6.09783i		−	0.584067i	−0.956408	−	0.292033i	$-0.905668\pi$
$109$		−	6.09783i		−	0.584067i	0.956408	−	0.292033i	$-0.0943318\pi$
$110$	7.35598	−	4.24698i	0.701366	−	0.404934i
$111$	−8.67704	+	5.00969i	−0.823588	+	0.475499i
$112$			1.10992i			0.104877i
$113$	6.10052	+	10.5664i	0.573889	+	0.994005i	0.996161	+	0.0875358i	$0.0278992\pi$
$113$	6.10052	+	10.5664i	0.573889	+	0.994005i	−0.422272	+	0.906469i	$0.638767\pi$
$114$	0.934157	−	1.61801i	0.0874918	−	0.151540i
$115$	10.5618	+	6.09783i	0.984889	+	0.568626i
$116$	3.78017			0.350980
$117$		0			0
$118$	−10.1468			−0.934084
$119$	5.72959	+	3.30798i	0.525230	+	0.303242i
$120$	3.69202	−	6.39477i	0.337034	−	0.583760i
$121$	−2.72252	−	4.71554i	−0.247502	−	0.428686i
$122$		−	0.439665i		−	0.0398054i
$123$	−12.7509	+	7.36174i	−1.14971	+	0.663786i
$124$	7.35598	−	4.24698i	0.660587	−	0.381390i
$125$		−	10.7681i		−	0.963127i
$126$	0.664874	+	1.15160i	0.0592317	+	0.102592i
$127$	5.71379	−	9.89658i	0.507017	−	0.878179i	−0.492950	−	0.870058i	$-0.664081\pi$
$127$	5.71379	−	9.89658i	0.507017	−	0.878179i	0.999967	−	0.00812161i	$-0.00258522\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−1.05669			−0.0930361
$130$		0			0
$131$	2.29590			0.200593			0.100297	−	0.994958i	$-0.468021\pi$
$131$	2.29590			0.200593			0.100297	+	0.994958i	$0.468021\pi$
$132$	4.18211	+	2.41454i	0.364006	+	0.210159i
$133$	−0.506041	+	0.876488i	−0.0438793	+	0.0760012i
$134$	−1.07338	−	1.85914i	−0.0927256	−	0.160605i
$135$			13.3056i			1.14516i
$136$	5.16218	−	2.98039i	0.442653	−	0.255566i
$137$	7.86384	−	4.54019i	0.671853	−	0.387894i	−0.124925	−	0.992166i	$-0.539869\pi$
$137$	7.86384	−	4.54019i	0.671853	−	0.387894i	0.796778	+	0.604272i	$0.206536\pi$
$138$			6.93362i			0.590229i
$139$	−9.45257	−	16.3723i	−0.801757	−	1.38868i	−0.918459	−	0.395517i	$-0.870566\pi$
$139$	−9.45257	−	16.3723i	−0.801757	−	1.38868i	0.116702	−	0.993167i	$-0.462768\pi$
$140$	−2.00000	+	3.46410i	−0.169031	+	0.292770i
$141$	12.3995	+	7.15883i	1.04422	+	0.602883i
$142$	0.615957			0.0516900
$143$		0			0
$144$	1.19806			0.0998385
$145$	11.7981	+	6.81163i	0.979777	+	0.565675i
$146$	3.16152	−	5.47592i	0.261649	−	0.453190i
$147$	5.90917	+	10.2350i	0.487380	+	0.844167i
$148$		−	4.89008i		−	0.401962i
$149$	−16.1857	+	9.34481i	−1.32598	+	0.765557i	−0.984676	−	0.174395i	$-0.944203\pi$
$149$	−16.1857	+	9.34481i	−1.32598	+	0.765557i	−0.341308	+	0.939952i	$0.610870\pi$
$150$	14.1739	−	8.18329i	1.15729	−	0.668163i
$151$		−	0.317667i		−	0.0258514i	−0.999916	−	0.0129257i	$-0.995886\pi$
$151$		−	0.317667i		−	0.0258514i	0.999916	−	0.0129257i	$-0.00411449\pi$
$152$	0.455927	+	0.789689i	0.0369806	+	0.0640522i
$153$	3.57069	−	6.18461i	0.288673	−	0.499996i
$154$	−2.26549	−	1.30798i	−0.182558	−	0.105400i
$155$	30.6112			2.45875
$156$		0			0
$157$	18.8901			1.50759			0.753796	−	0.657108i	$-0.228220\pi$
$157$	18.8901			1.50759			0.753796	+	0.657108i	$0.228220\pi$
$158$	13.4077	+	7.74094i	1.06666	+	0.615836i
$159$	−3.46681	+	6.00469i	−0.274936	+	0.476203i
$160$	1.80194	+	3.12105i	0.142456	+	0.246740i
$161$		−	3.75600i		−	0.296015i
$162$	−9.66383	+	5.57942i	−0.759262	+	0.438360i
$163$	−3.75226	+	2.16637i	−0.293899	+	0.169683i	−0.639699	−	0.768625i	$-0.720941\pi$
$163$	−3.75226	+	2.16637i	−0.293899	+	0.169683i	0.345800	+	0.938308i	$0.387608\pi$
$164$		−	7.18598i		−	0.561131i
$165$	8.70171	+	15.0718i	0.677427	+	1.17334i
$166$	0.455927	−	0.789689i	0.0353868	−	0.0612917i
$167$	−12.1244	−	7.00000i	−0.938211	−	0.541676i	−0.0488118	−	0.998808i	$-0.515543\pi$
$167$	−12.1244	−	7.00000i	−0.938211	−	0.541676i	−0.889399	+	0.457132i	$0.848877\pi$
$168$	−2.27413			−0.175453
$169$		0			0
$170$	21.4819			1.64758
$171$	0.946096	+	0.546229i	0.0723498	+	0.0417712i
$172$	0.257865	−	0.446635i	0.0196620	−	0.0340556i
$173$	−5.49396	−	9.51582i	−0.417698	−	0.723474i	0.578010	−	0.816030i	$-0.303830\pi$
$173$	−5.49396	−	9.51582i	−0.417698	−	0.723474i	−0.995707	+	0.0925559i	$0.970496\pi$
$174$			7.74525i			0.587166i
$175$	−7.67811	+	4.43296i	−0.580411	+	0.335100i
$176$	−2.04113	+	1.17845i	−0.153856	+	0.0888289i
$177$		−	20.7899i		−	1.56266i
$178$	1.87531	+	3.24814i	0.140561	+	0.243458i
$179$	2.32759	−	4.03151i	0.173972	−	0.301329i	−0.765833	−	0.643040i	$-0.777673\pi$
$179$	2.32759	−	4.03151i	0.173972	−	0.301329i	0.939805	+	0.341711i	$0.111006\pi$
$180$	3.73921	+	2.15883i	0.278704	+	0.160910i
$181$	1.06638			0.0792631			0.0396315	−	0.999214i	$-0.487382\pi$
$181$	1.06638			0.0792631			0.0396315	+	0.999214i	$0.487382\pi$
$182$		0			0
$183$	0.900837			0.0665918
$184$	−2.93067	−	1.69202i	−0.216052	−	0.124737i
$185$	8.81163	−	15.2622i	0.647844	−	1.12210i
$186$	8.70171	+	15.0718i	0.638040	+	1.10512i
$187$			14.0489i			1.02736i
$188$	−6.05171	+	3.49396i	−0.441367	+	0.254823i
$189$	3.54883	−	2.04892i	0.258139	−	0.149037i
$190$			3.28621i			0.238407i
$191$	−0.445042	−	0.770835i	−0.0322021	−	0.0557757i	0.849475	−	0.527629i	$-0.176919\pi$
$191$	−0.445042	−	0.770835i	−0.0322021	−	0.0557757i	−0.881677	+	0.471853i	$0.843585\pi$
$192$	−1.02446	+	1.77441i	−0.0739339	+	0.128057i
$193$	−14.0447	−	8.10872i	−1.01096	−	0.583678i	−0.0994879	−	0.995039i	$-0.531720\pi$
$193$	−14.0447	−	8.10872i	−1.01096	−	0.583678i	−0.911473	+	0.411360i	$0.865054\pi$
$194$	−14.6746			−1.05357
$195$		0			0
$196$	−5.76809			−0.412006
$197$	−9.93428	−	5.73556i	−0.707788	−	0.408642i	0.102453	−	0.994738i	$-0.467331\pi$
$197$	−9.93428	−	5.73556i	−0.707788	−	0.408642i	−0.810242	+	0.586096i	$0.800664\pi$
$198$	−1.41185	+	2.44540i	−0.100336	+	0.173787i
$199$	−1.89977	−	3.29050i	−0.134671	−	0.233258i	0.790801	−	0.612074i	$-0.209665\pi$
$199$	−1.89977	−	3.29050i	−0.134671	−	0.233258i	−0.925472	+	0.378816i	$0.876331\pi$
$200$			7.98792i			0.564831i
$201$	3.80923	−	2.19926i	0.268682	−	0.155124i
$202$	−7.59339	+	4.38404i	−0.534269	+	0.308460i
$203$		−	4.19567i		−	0.294478i
$204$	6.10656	+	10.5769i	0.427545	+	0.740530i
$205$	12.9487	−	22.4278i	0.904376	−	1.56642i
$206$	16.2913	+	9.40581i	1.13507	+	0.655334i
$207$	−4.05429			−0.281793
$208$		0			0
$209$	−2.14914			−0.148659
$210$	−7.09766	−	4.09783i	−0.489785	−	0.282777i
$211$	12.5233	−	21.6909i	0.862137	−	1.49326i	−0.00772527	−	0.999970i	$-0.502459\pi$
$211$	12.5233	−	21.6909i	0.862137	−	1.49326i	0.869862	−	0.493295i	$-0.164208\pi$
$212$	−1.69202	−	2.93067i	−0.116209	−	0.201279i
$213$			1.26205i			0.0864739i
$214$	15.6334	−	9.02595i	1.06868	−	0.617001i
$215$	1.60962	−	0.929312i	0.109775	−	0.0633786i
$216$		−	3.69202i		−	0.251210i
$217$	−4.71379	−	8.16453i	−0.319993	−	0.554244i
$218$	−3.04892	+	5.28088i	−0.206499	+	0.357666i
$219$	11.2197	+	6.47770i	0.758157	+	0.437722i
$220$	−8.49396			−0.572663
$221$		0			0
$222$	10.0194			0.672457
$223$	11.2479	+	6.49396i	0.753213	+	0.434868i	0.826854	−	0.562417i	$-0.190128\pi$
$223$	11.2479	+	6.49396i	0.753213	+	0.434868i	−0.0736407	+	0.997285i	$0.523462\pi$
$224$	0.554958	−	0.961216i	0.0370797	−	0.0642239i
$225$	4.78501	+	8.28788i	0.319001	+	0.552526i
$226$		−	12.2010i		−	0.811602i
$227$	11.9554	−	6.90246i	0.793509	−	0.458132i	−0.0476877	−	0.998862i	$-0.515185\pi$
$227$	11.9554	−	6.90246i	0.793509	−	0.458132i	0.841196	+	0.540730i	$0.181852\pi$
$228$	−1.61801	+	0.934157i	−0.107155	+	0.0618660i
$229$		−	11.5603i		−	0.763928i	−0.924177	−	0.381964i	$-0.875248\pi$
$229$		−	11.5603i		−	0.763928i	0.924177	−	0.381964i	$-0.124752\pi$
$230$	−6.09783	−	10.5618i	−0.402079	−	0.696422i
$231$	2.67994	−	4.64179i	0.176327	−	0.305407i
$232$	−3.27372	−	1.89008i	−0.214930	−	0.124090i
$233$	−9.77479			−0.640368			−0.320184	−	0.947355i	$-0.603745\pi$
$233$	−9.77479			−0.640368			−0.320184	+	0.947355i	$0.603745\pi$
$234$		0			0
$235$	−25.1836			−1.64280
$236$	8.78735	+	5.07338i	0.572007	+	0.330249i
$237$	−15.8605	+	27.4713i	−1.03025	+	1.78445i
$238$	−3.30798	−	5.72959i	−0.214424	−	0.371394i
$239$			0.944378i			0.0610867i	0.999533	+	0.0305434i	$0.00972377\pi$
$239$			0.944378i			0.0610867i	−0.999533	+	0.0305434i	$0.990276\pi$
$240$	−6.39477	+	3.69202i	−0.412781	+	0.238319i
$241$	−0.190381	+	0.109916i	−0.0122635	+	0.00708033i	−0.506119	−	0.862464i	$-0.668920\pi$
$241$	−0.190381	+	0.109916i	−0.0122635	+	0.00708033i	0.493856	+	0.869544i	$0.335587\pi$
$242$			5.44504i			0.350021i
$243$	−5.89373	−	10.2082i	−0.378083	−	0.654859i
$244$	−0.219833	+	0.380761i	−0.0140733	+	0.0243757i
$245$	−18.0025	−	10.3937i	−1.15014	−	0.664031i
$246$	14.7235			0.938735
$247$		0			0
$248$	−8.49396			−0.539367
$249$	1.61801	+	0.934157i	0.102537	+	0.0591998i
$250$	−5.38404	+	9.32544i	−0.340517	+	0.589792i
$251$	8.12714	+	14.0766i	0.512980	+	0.888508i	0.999887	+	0.0150539i	$0.00479198\pi$
$251$	8.12714	+	14.0766i	0.512980	+	0.888508i	−0.486906	+	0.873454i	$0.661875\pi$
$252$		−	1.32975i		−	0.0837663i
$253$	6.90728	−	3.98792i	0.434257	−	0.250718i
$254$	−9.89658	+	5.71379i	−0.620967	+	0.358515i
$255$			44.0146i			2.75630i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−11.2186	+	19.4312i	−0.699799	+	1.21209i	0.268737	+	0.963214i	$0.413394\pi$
$257$	−11.2186	+	19.4312i	−0.699799	+	1.21209i	−0.968536	+	0.248874i	$0.919939\pi$
$258$	0.915118	+	0.528344i	0.0569727	+	0.0328932i
$259$	−5.42758			−0.337254
$260$		0			0
$261$	−4.52888			−0.280330
$262$	−1.98831	−	1.14795i	−0.122838	−	0.0709205i
$263$	5.24698	−	9.08804i	0.323543	−	0.560392i	−0.657674	−	0.753303i	$-0.728459\pi$
$263$	5.24698	−	9.08804i	0.323543	−	0.560392i	0.981216	+	0.192911i	$0.0617928\pi$
$264$	−2.41454	−	4.18211i	−0.148605	−	0.257391i
$265$		−	12.1957i		−	0.749174i
$266$	0.876488	−	0.506041i	0.0537409	−	0.0310274i
$267$	−6.65517	+	3.84236i	−0.407290	+	0.235149i
$268$			2.14675i			0.131134i
$269$	−13.2078	−	22.8765i	−0.805291	−	1.39480i	−0.916095	−	0.400962i	$-0.868676\pi$
$269$	−13.2078	−	22.8765i	−0.805291	−	1.39480i	0.110804	−	0.993842i	$-0.464657\pi$
$270$	6.65279	−	11.5230i	0.404876	−	0.701266i
$271$	19.0787	+	11.0151i	1.15895	+	0.669118i	0.951051	−	0.309034i	$-0.100006\pi$
$271$	19.0787	+	11.0151i	1.15895	+	0.669118i	0.207895	+	0.978151i	$0.433339\pi$
$272$	−5.96077			−0.361425
$273$		0			0
$274$	−9.08038			−0.548566
$275$	−16.3044	−	9.41335i	−0.983192	−	0.567646i
$276$	3.46681	−	6.00469i	0.208678	−	0.361440i
$277$	1.08815	+	1.88472i	0.0653804	+	0.113242i	0.896863	−	0.442309i	$-0.145841\pi$
$277$	1.08815	+	1.88472i	0.0653804	+	0.113242i	−0.831482	+	0.555551i	$0.812507\pi$
$278$			18.9051i			1.13386i
$279$	−8.81293	+	5.08815i	−0.527616	+	0.304619i
$280$	3.46410	−	2.00000i	0.207020	−	0.119523i
$281$			25.0030i			1.49155i	0.666196	+	0.745776i	$0.267921\pi$
$281$			25.0030i			1.49155i	−0.666196	+	0.745776i	$0.732079\pi$
$282$	−7.15883	−	12.3995i	−0.426302	−	0.738377i
$283$	−8.15764	+	14.1294i	−0.484921	+	0.839908i	−0.999850	−	0.0173249i	$-0.994485\pi$
$283$	−8.15764	+	14.1294i	−0.484921	+	0.839908i	0.514929	+	0.857233i	$0.327818\pi$
$284$	−0.533434	−	0.307979i	−0.0316535	−	0.0182752i
$285$	−6.73317			−0.398839
$286$		0			0
$287$	−7.97584			−0.470799
$288$	−1.03755	−	0.599031i	−0.0611384	−	0.0352982i
$289$	−9.26540	+	16.0481i	−0.545023	+	0.944008i
$290$	−6.81163	−	11.7981i	−0.399992	−	0.692807i
$291$		−	30.0670i		−	1.76256i
$292$	−5.47592	+	3.16152i	−0.320454	+	0.185014i
$293$	−1.62640	+	0.939001i	−0.0950152	+	0.0548570i	−0.546755	−	0.837293i	$-0.684137\pi$
$293$	−1.62640	+	0.939001i	−0.0950152	+	0.0548570i	0.451740	+	0.892150i	$0.350804\pi$
$294$		−	11.8183i		−	0.689259i
$295$	18.2838	+	31.6685i	1.06452	+	1.84381i
$296$	−2.44504	+	4.23494i	−0.142115	+	0.246151i
$297$	7.53590	+	4.35086i	0.437277	+	0.252462i
$298$	18.6896			1.08266
$299$		0			0
$300$	−16.3666			−0.944925
$301$	−0.495727	−	0.286208i	−0.0285732	−	0.0164968i
$302$	−0.158834	+	0.275108i	−0.00913985	+	0.0158307i
$303$	−8.98254	−	15.5582i	−0.516034	−	0.893796i
$304$		−	0.911854i		−	0.0522984i
$305$	−1.37222	+	0.792249i	−0.0785728	+	0.0453640i
$306$	−6.18461	+	3.57069i	−0.353551	+	0.204123i
$307$		−	23.9801i		−	1.36862i	−0.729192	−	0.684310i	$-0.760104\pi$
$307$		−	23.9801i		−	1.36862i	0.729192	−	0.684310i	$-0.239896\pi$
$308$	1.30798	+	2.26549i	0.0745290	+	0.129088i
$309$	−19.2717	+	33.3796i	−1.09633	+	1.89890i
$310$	−26.5101	−	15.3056i	−1.50567	−	0.869299i
$311$	5.38404			0.305301			0.152651	−	0.988280i	$-0.451219\pi$
$311$	5.38404			0.305301			0.152651	+	0.988280i	$0.451219\pi$
$312$		0			0
$313$	18.9487			1.07104			0.535522	−	0.844522i	$-0.320115\pi$
$313$	18.9487			1.07104			0.535522	+	0.844522i	$0.320115\pi$
$314$	−16.3593	−	9.44504i	−0.923208	−	0.533015i
$315$	2.39612	−	4.15021i	0.135006	−	0.233838i
$316$	−7.74094	−	13.4077i	−0.435462	−	0.754242i
$317$			11.5013i			0.645975i	0.946403	+	0.322987i	$0.104687\pi$
$317$			11.5013i			0.645975i	−0.946403	+	0.322987i	$0.895313\pi$
$318$	6.00469	−	3.46681i	0.336727	−	0.194409i
$319$	7.71582	−	4.45473i	0.432003	−	0.249417i
$320$		−	3.60388i		−	0.201463i
$321$	18.4934	+	32.0316i	1.03220	+	1.78783i
$322$	−1.87800	+	3.25280i	−0.104657	+	0.181271i
$323$	−4.70715	−	2.71768i	−0.261913	−	0.151216i
$324$	11.1588			0.619935
$325$		0			0
$326$	4.33273			0.239968
$327$	−10.8201	−	6.24698i	−0.598352	−	0.345459i
$328$	−3.59299	+	6.22324i	−0.198390	+	0.343621i
$329$	3.87800	+	6.71690i	0.213801	+	0.370315i
$330$		−	17.4034i		−	0.958027i
$331$	29.9742	−	17.3056i	1.64753	−	0.951201i	0.669478	−	0.742832i	$-0.266518\pi$
$331$	29.9742	−	17.3056i	1.64753	−	0.951201i	0.978050	−	0.208369i	$-0.0668156\pi$
$332$	−0.789689	+	0.455927i	−0.0433398	+	0.0250222i
$333$			5.85862i			0.321051i
$334$	7.00000	+	12.1244i	0.383023	+	0.663415i
$335$	−3.86831	+	6.70012i	−0.211349	+	0.366066i
$336$	1.96945	+	1.13706i	0.107442	+	0.0620319i
$337$	−1.95407			−0.106445			−0.0532224	−	0.998583i	$-0.516949\pi$
$337$	−1.95407			−0.106445			−0.0532224	+	0.998583i	$0.516949\pi$
$338$		0			0
$339$	24.9989			1.35776
$340$	−18.6039	−	10.7409i	−1.00894	−	0.582509i
$341$	10.0097	−	17.3373i	0.542055	−	0.938867i
$342$	−0.546229	−	0.946096i	−0.0295367	−	0.0511590i
$343$			14.1715i			0.765189i
$344$	−0.446635	+	0.257865i	−0.0240809	+	0.0139031i
$345$	21.6402	−	12.4940i	1.16507	−	0.672652i
$346$			10.9879i			0.590714i
$347$	3.20775	+	5.55599i	0.172201	+	0.298261i	0.939189	−	0.343400i	$-0.111579\pi$
$347$	3.20775	+	5.55599i	0.172201	+	0.298261i	−0.766988	+	0.641661i	$0.778245\pi$
$348$	3.87263	−	6.70758i	0.207595	−	0.359564i
$349$	0.940290	+	0.542877i	0.0503326	+	0.0290595i	0.524955	−	0.851130i	$-0.324082\pi$
$349$	0.940290	+	0.542877i	0.0503326	+	0.0290595i	−0.474623	+	0.880189i	$0.657415\pi$
$350$	8.86592			0.473903
$351$		0			0
$352$	2.35690			0.125623
$353$	−3.71455	−	2.14460i	−0.197706	−	0.114145i	0.397879	−	0.917438i	$-0.369746\pi$
$353$	−3.71455	−	2.14460i	−0.197706	−	0.114145i	−0.595585	+	0.803292i	$0.703080\pi$
$354$	−10.3949	+	18.0045i	−0.552484	+	0.956931i
$355$	−1.10992	−	1.92243i	−0.0589082	−	0.102032i
$356$		−	3.75063i		−	0.198783i
$357$	11.7394	−	6.77777i	0.621318	−	0.358718i
$358$	−4.03151	+	2.32759i	−0.213072	+	0.123017i
$359$			15.5060i			0.818378i	0.912450	+	0.409189i	$0.134188\pi$
$359$			15.5060i			0.818378i	−0.912450	+	0.409189i	$0.865812\pi$
$360$	−2.15883	−	3.73921i	−0.113781	−	0.197074i
$361$	−9.08426	+	15.7344i	−0.478119	+	0.828126i
$362$	−0.923508	−	0.533188i	−0.0485385	−	0.0280237i
$363$	−11.1564			−0.585561
$364$		0			0
$365$	−22.7875			−1.19275
$366$	−0.780148	−	0.450419i	−0.0407790	−	0.0235438i
$367$	−8.71379	+	15.0927i	−0.454856	+	0.787834i	−0.998680	−	0.0513654i	$-0.983643\pi$
$367$	−8.71379	+	15.0927i	−0.454856	+	0.787834i	0.543824	+	0.839199i	$0.316976\pi$
$368$	1.69202	+	2.93067i	0.0882027	+	0.152772i
$369$			8.60925i			0.448180i
$370$	−15.2622	+	8.81163i	−0.793443	+	0.458095i
$371$	−3.25280	+	1.87800i	−0.168877	+	0.0975010i
$372$		−	17.4034i		−	0.902325i
$373$	−4.09783	−	7.09766i	−0.212178	−	0.367503i	0.740218	−	0.672367i	$-0.234722\pi$
$373$	−4.09783	−	7.09766i	−0.212178	−	0.367503i	−0.952396	+	0.304864i	$0.901389\pi$
$374$	7.02446	−	12.1667i	0.363226	−	0.629126i
$375$	−19.1070	−	11.0315i	−0.986684	−	0.569662i
$376$	6.98792			0.360374
$377$		0			0
$378$	−4.09783			−0.210770
$379$	13.0316	+	7.52379i	0.669388	+	0.386471i	0.795845	−	0.605501i	$-0.207027\pi$
$379$	13.0316	+	7.52379i	0.669388	+	0.386471i	−0.126457	+	0.991972i	$0.540360\pi$
$380$	1.64310	−	2.84594i	0.0842895	−	0.145994i
$381$	−11.7071	−	20.2773i	−0.599772	−	1.03884i
$382$			0.890084i			0.0455406i
$383$	−9.63078	+	5.56033i	−0.492110	+	0.284120i	−0.725449	−	0.688276i	$-0.758368\pi$
$383$	−9.63078	+	5.56033i	−0.492110	+	0.284120i	0.233339	+	0.972395i	$0.425035\pi$
$384$	1.77441	−	1.02446i	0.0905502	−	0.0522792i
$385$			9.42758i			0.480474i
$386$	8.10872	+	14.0447i	0.412723	+	0.714857i
$387$	−0.308938	+	0.535096i	−0.0157042	+	0.0272005i
$388$	12.7085	+	7.33728i	0.645179	+	0.372494i
$389$	8.04354			0.407824			0.203912	−	0.978989i	$-0.434634\pi$
$389$	8.04354			0.407824			0.203912	+	0.978989i	$0.434634\pi$
$390$		0			0
$391$	20.1715			1.02012
$392$	4.99531	+	2.88404i	0.252301	+	0.145666i
$393$	2.35205	−	4.07387i	0.118645	−	0.205500i
$394$	5.73556	+	9.93428i	0.288953	+	0.500482i
$395$		−	55.7948i		−	2.80734i
$396$	2.44540	−	1.41185i	0.122886	−	0.0709483i
$397$	18.9730	−	10.9541i	0.952228	−	0.549769i	0.0584554	−	0.998290i	$-0.481382\pi$
$397$	18.9730	−	10.9541i	0.952228	−	0.549769i	0.893772	+	0.448521i	$0.148049\pi$
$398$			3.79954i			0.190454i
$399$	1.03684	+	1.79585i	0.0519067	+	0.0899051i
$400$	3.99396	−	6.91774i	0.199698	−	0.345887i
$401$	15.1058	+	8.72132i	0.754347	+	0.435522i	0.827262	−	0.561816i	$-0.189897\pi$
$401$	15.1058	+	8.72132i	0.754347	+	0.435522i	−0.0729157	+	0.997338i	$0.523230\pi$
$402$	−4.39852			−0.219378
$403$		0			0
$404$	8.76809			0.436229
$405$	34.8273	+	20.1075i	1.73058	+	0.999151i
$406$	−2.09783	+	3.63356i	−0.104114	+	0.180330i
$407$	−5.76271	−	9.98130i	−0.285647	−	0.494755i
$408$		−	12.2131i		−	0.604640i
$409$	−15.0974	+	8.71648i	−0.746518	+	0.431002i	−0.824434	−	0.565958i	$-0.808507\pi$
$409$	−15.0974	+	8.71648i	−0.746518	+	0.431002i	0.0779166	+	0.996960i	$0.475173\pi$
$410$	−22.4278	+	12.9487i	−1.10763	+	0.639490i
$411$		−	18.6049i		−	0.917714i
$412$	−9.40581	−	16.2913i	−0.463391	−	0.802617i
$413$	5.63102	−	9.75322i	0.277085	−	0.479924i
$414$	3.51112	+	2.02715i	0.172562	+	0.0996288i
$415$	−3.28621			−0.161314
$416$		0			0
$417$	−38.7351			−1.89687
$418$	1.86121	+	1.07457i	0.0910350	+	0.0525591i
$419$	−4.98792	+	8.63933i	−0.243676	+	0.422059i	−0.961758	−	0.273899i	$-0.911687\pi$
$419$	−4.98792	+	8.63933i	−0.243676	+	0.422059i	0.718083	+	0.695958i	$0.245020\pi$
$420$	4.09783	+	7.09766i	0.199954	+	0.346330i
$421$			0.615957i			0.0300199i	0.999887	+	0.0150100i	$0.00477800\pi$
$421$			0.615957i			0.0300199i	−0.999887	+	0.0150100i	$0.995222\pi$
$422$	−21.6909	+	12.5233i	−1.05590	+	0.609623i
$423$	7.25033	−	4.18598i	0.352523	−	0.203529i
$424$			3.38404i			0.164344i
$425$	−23.8071	−	41.2351i	−1.15481	−	2.00019i
$426$	0.631023	−	1.09296i	0.0305731	−	0.0529542i
$427$	0.422613	+	0.243996i	0.0204517	+	0.0118078i
$428$	−18.0519			−0.872572
$429$		0			0
$430$	−1.85862			−0.0896308
$431$	12.8105	+	7.39612i	0.617058	+	0.356259i	0.775723	−	0.631074i	$-0.217385\pi$
$431$	12.8105	+	7.39612i	0.617058	+	0.356259i	−0.158665	+	0.987333i	$0.550719\pi$
$432$	−1.84601	+	3.19738i	−0.0888162	+	0.153834i
$433$	8.26606	+	14.3172i	0.397242	+	0.688043i	0.993384	−	0.114836i	$-0.0366342\pi$
$433$	8.26606	+	14.3172i	0.397242	+	0.688043i	−0.596143	+	0.802878i	$0.703301\pi$
$434$			9.42758i			0.452538i
$435$	24.1733	−	13.9565i	1.15902	−	0.669161i
$436$	5.28088	−	3.04892i	0.252908	−	0.146017i
$437$			3.08575i			0.147612i
$438$	−6.47770	−	11.2197i	−0.309516	−	0.536098i
$439$	1.75063	−	3.03218i	0.0835529	−	0.144718i	−0.821221	−	0.570611i	$-0.806707\pi$
$439$	1.75063	−	3.03218i	0.0835529	−	0.144718i	0.904774	+	0.425893i	$0.140040\pi$
$440$	7.35598	+	4.24698i	0.350683	+	0.202467i
$441$	6.91053			0.329073
$442$		0			0
$443$	17.4077			0.827066			0.413533	−	0.910489i	$-0.364295\pi$
$443$	17.4077			0.827066			0.413533	+	0.910489i	$0.364295\pi$
$444$	−8.67704	−	5.00969i	−0.411794	−	0.237749i
$445$	6.75840	−	11.7059i	0.320379	−	0.554912i
$446$	−6.49396	−	11.2479i	−0.307498	−	0.532602i
$447$			38.2935i			1.81122i
$448$	−0.961216	+	0.554958i	−0.0454132	+	0.0262193i
$449$	−29.5745	+	17.0749i	−1.39571	+	0.805813i	−0.993940	−	0.109928i	$-0.964938\pi$
$449$	−29.5745	+	17.0749i	−1.39571	+	0.805813i	−0.401769	+	0.915741i	$0.631605\pi$
$450$		−	9.57002i		−	0.451135i
$451$	−8.46830	−	14.6675i	−0.398757	−	0.690667i
$452$	−6.10052	+	10.5664i	−0.286944	+	0.497002i
$453$	−0.563673	−	0.325437i	−0.0264837	−	0.0152904i
$454$	−13.8049			−0.647897
$455$		0			0
$456$	1.86831			0.0874918
$457$	−8.14360	−	4.70171i	−0.380942	−	0.219937i	0.297286	−	0.954788i	$-0.403918\pi$
$457$	−8.14360	−	4.70171i	−0.380942	−	0.219937i	−0.678228	+	0.734852i	$0.737252\pi$
$458$	−5.78017	+	10.0115i	−0.270089	+	0.467809i
$459$	11.0036	+	19.0589i	0.513606	+	0.889592i
$460$			12.1957i			0.568626i
$461$	−0.634943	+	0.366585i	−0.0295722	+	0.0170735i	−0.514713	−	0.857362i	$-0.672102\pi$
$461$	−0.634943	+	0.366585i	−0.0295722	+	0.0170735i	0.485141	+	0.874436i	$0.338768\pi$
$462$	−4.64179	+	2.67994i	−0.215956	+	0.124682i
$463$		−	7.24267i		−	0.336595i	−0.985736	−	0.168298i	$-0.946173\pi$
$463$		−	7.24267i		−	0.336595i	0.985736	−	0.168298i	$-0.0538270\pi$
$464$	1.89008	+	3.27372i	0.0877449	+	0.151979i
$465$	31.3599	−	54.3169i	1.45428	−	2.51889i
$466$	8.46522	+	4.88740i	0.392144	+	0.226404i
$467$	−30.2446			−1.39955			−0.699776	−	0.714362i	$-0.746717\pi$
$467$	−30.2446			−1.39955			−0.699776	+	0.714362i	$0.746717\pi$
$468$		0			0
$469$	2.38271			0.110024
$470$	21.8096	+	12.5918i	1.00600	+	0.580816i
$471$	19.3521	−	33.5188i	0.891698	−	1.54447i
$472$	−5.07338	−	8.78735i	−0.233521	−	0.404470i
$473$		−	1.21552i		−	0.0558897i
$474$	27.4713	−	15.8605i	1.26180	−	0.728499i
$475$	6.30797	−	3.64191i	0.289429	−	0.167102i
$476$			6.61596i			0.303242i
$477$	2.02715	+	3.51112i	0.0928167	+	0.160763i
$478$	0.472189	−	0.817855i	0.0215974	−	0.0374078i
$479$	−31.8002	−	18.3599i	−1.45299	−	0.838884i	−0.454340	−	0.890828i	$-0.650125\pi$
$479$	−31.8002	−	18.3599i	−1.45299	−	0.838884i	−0.998650	+	0.0519439i	$0.983458\pi$
$480$	7.38404			0.337034
$481$		0			0
$482$	0.219833			0.0100131
$483$	−6.66471	−	3.84787i	−0.303255	−	0.175084i
$484$	2.72252	−	4.71554i	0.123751	−	0.214343i
$485$	26.4426	+	45.8000i	1.20070	+	2.07967i
$486$			11.7875i			0.534690i
$487$	−24.8157	+	14.3274i	−1.12451	+	0.649234i	−0.942548	−	0.334072i	$-0.891577\pi$
$487$	−24.8157	+	14.3274i	−1.12451	+	0.649234i	−0.181959	+	0.983306i	$0.558244\pi$
$488$	0.380761	−	0.219833i	0.0172362	−	0.00995135i
$489$			8.87741i			0.401450i
$490$	10.3937	+	18.0025i	0.469541	+	0.813269i
$491$	15.2148	−	26.3527i	0.686632	−	1.18928i	−0.286289	−	0.958143i	$-0.592422\pi$
$491$	15.2148	−	26.3527i	0.686632	−	1.18928i	0.972921	−	0.231138i	$-0.0742450\pi$
$492$	−12.7509	−	7.36174i	−0.574855	−	0.331893i
$493$	22.5327			1.01482
$494$		0			0
$495$	10.1763			0.457390
$496$	7.35598	+	4.24698i	0.330293	+	0.190695i
$497$	−0.341830	+	0.592068i	−0.0153332	+	0.0265579i
$498$	−0.934157	−	1.61801i	−0.0418606	−	0.0725046i
$499$			15.9715i			0.714984i	0.933916	+	0.357492i	$0.116368\pi$
$499$			15.9715i			0.714984i	−0.933916	+	0.357492i	$0.883632\pi$
$500$	9.32544	−	5.38404i	0.417046	−	0.240782i
$501$	−24.8418	+	14.3424i	−1.10985	+	0.640772i
$502$		−	16.2543i		−	0.725464i
$503$	20.9855	+	36.3480i	0.935698	+	1.62068i	0.773384	+	0.633938i	$0.218563\pi$
$503$	20.9855	+	36.3480i	0.935698	+	1.62068i	0.162314	+	0.986739i	$0.448104\pi$
$504$	−0.664874	+	1.15160i	−0.0296159	+	0.0512962i
$505$	27.3656	+	15.7995i	1.21775	+	0.703071i
$506$	−7.97584			−0.354569
$507$		0			0
$508$	11.4276			0.507017
$509$	−0.791761	−	0.457123i	−0.0350942	−	0.0202616i	0.482350	−	0.875978i	$-0.339783\pi$
$509$	−0.791761	−	0.457123i	−0.0350942	−	0.0202616i	−0.517444	+	0.855717i	$0.673117\pi$
$510$	22.0073	−	38.1178i	0.974499	−	1.68788i
$511$	3.50902	+	6.07781i	0.155230	+	0.268866i
$512$			1.00000i			0.0441942i
$513$	−2.91555	+	1.68329i	−0.128725	+	0.0743192i
$514$	19.4312	−	11.2186i	0.857076	−	0.494833i
$515$		−	67.7948i		−	2.98739i
$516$	−0.528344	−	0.915118i	−0.0232590	−	0.0402858i
$517$	−8.23490	+	14.2633i	−0.362170	+	0.627298i
$518$	4.70043	+	2.71379i	0.206525	+	0.119237i
$519$	−22.5133			−0.988226
$520$		0			0
$521$	−3.31096			−0.145056			−0.0725279	−	0.997366i	$-0.523107\pi$
$521$	−3.31096			−0.145056			−0.0725279	+	0.997366i	$0.523107\pi$
$522$	3.92212	+	2.26444i	0.171667	+	0.0991118i
$523$	0.425428	−	0.736862i	0.0186026	−	0.0322207i	−0.856574	−	0.516024i	$-0.827412\pi$
$523$	0.425428	−	0.736862i	0.0186026	−	0.0322207i	0.875177	+	0.483803i	$0.160745\pi$
$524$	1.14795	+	1.98831i	0.0501484	+	0.0868595i
$525$			18.1655i			0.792809i
$526$	−9.08804	+	5.24698i	−0.396257	+	0.228779i
$527$	43.8473	−	25.3153i	1.91002	−	1.10275i
$528$			4.82908i			0.210159i
$529$	5.77413	+	10.0011i	0.251049	+	0.434830i
$530$	−6.09783	+	10.5618i	−0.264873	+	0.458774i
$531$	−10.5278	−	6.07822i	−0.456867	−	0.263772i
$532$	−1.01208			−0.0438793
$533$		0			0
$534$	7.68473			0.332551
$535$	−56.3408	−	32.5284i	−2.43583	−	1.40633i
$536$	1.07338	−	1.85914i	0.0463628	−	0.0803027i
$537$	−4.76905	−	8.26023i	−0.205799	−	0.356455i
$538$			26.4155i			1.13885i
$539$	−11.7734	+	6.79739i	−0.507117	+	0.292784i
$540$	−11.5230	+	6.65279i	−0.495870	+	0.286291i
$541$			40.8853i			1.75780i	0.477010	+	0.878898i	$0.341721\pi$
$541$			40.8853i			1.75780i	−0.477010	+	0.878898i	$0.658279\pi$
$542$	−11.0151	−	19.0787i	−0.473138	−	0.819498i
$543$	1.09246	−	1.89219i	0.0468819	−	0.0812018i
$544$	5.16218	+	2.98039i	0.221327	+	0.127783i
$545$	21.9758			0.941341
$546$		0			0
$547$	−2.39075			−0.102221			−0.0511105	−	0.998693i	$-0.516276\pi$
$547$	−2.39075			−0.102221			−0.0511105	+	0.998693i	$0.516276\pi$
$548$	7.86384	+	4.54019i	0.335926	+	0.193947i
$549$	0.263373	−	0.456176i	0.0112405	−	0.0194691i
$550$	9.41335	+	16.3044i	0.401386	+	0.695222i
$551$			3.44696i			0.146845i
$552$	−6.00469	+	3.46681i	−0.255577	+	0.147557i
$553$	−14.8814	+	8.59179i	−0.632822	+	0.365360i
$554$		−	2.17629i		−	0.0924618i
$555$	−18.0543	−	31.2710i	−0.766362	−	1.32738i
$556$	9.45257	−	16.3723i	0.400878	−	0.694342i
$557$	23.5133	+	13.5754i	0.996290	+	0.575208i	0.907148	−	0.420811i	$-0.138254\pi$
$557$	23.5133	+	13.5754i	0.996290	+	0.575208i	0.0891414	+	0.996019i	$0.471588\pi$
$558$	10.1763			0.430797
$559$		0			0
$560$	−4.00000			−0.169031
$561$	24.9286	+	14.3925i	1.05249	+	0.607653i
$562$	12.5015	−	21.6532i	0.527344	−	0.913386i
$563$	−3.26205	−	5.65003i	−0.137479	−	0.238120i	0.789063	−	0.614312i	$-0.210567\pi$
$563$	−3.26205	−	5.65003i	−0.137479	−	0.238120i	−0.926542	+	0.376192i	$0.877233\pi$
$564$			14.3177i			0.602883i
$565$	−38.0800	+	21.9855i	−1.60204	+	0.924938i
$566$	14.1294	−	8.15764i	0.593905	−	0.342891i
$567$		−	12.3854i		−	0.520137i
$568$	0.307979	+	0.533434i	0.0129225	+	0.0223824i
$569$	3.65010	−	6.32217i	0.153020	−	0.265039i	−0.779316	−	0.626631i	$-0.784433\pi$
$569$	3.65010	−	6.32217i	0.153020	−	0.265039i	0.932336	+	0.361592i	$0.117767\pi$
$570$	5.83110	+	3.36658i	0.244238	+	0.141011i
$571$	43.6722			1.82762			0.913812	−	0.406138i	$-0.133125\pi$
$571$	43.6722			1.82762			0.913812	+	0.406138i	$0.133125\pi$
$572$		0			0
$573$	−1.82371			−0.0761865
$574$	6.90728	+	3.98792i	0.288304	+	0.166452i
$575$	−13.5157	+	23.4099i	−0.563645	+	0.976262i
$576$	0.599031	+	1.03755i	0.0249596	+	0.0432313i
$577$			16.8528i			0.701590i	0.936452	+	0.350795i	$0.114089\pi$
$577$			16.8528i			0.701590i	−0.936452	+	0.350795i	$0.885911\pi$
$578$	16.0481	−	9.26540i	0.667515	−	0.385390i
$579$	−28.7765	+	16.6141i	−1.19591	+	0.690458i
$580$			13.6233i			0.565675i
$581$	0.506041	+	0.876488i	0.0209941	+	0.0363629i
$582$	−15.0335	+	26.0388i	−0.623158	+	1.07934i
$583$	−6.90728	−	3.98792i	−0.286070	−	0.165163i
$584$	6.32304			0.261649
$585$		0			0
$586$	1.87800			0.0775796
$587$	19.2106	+	11.0913i	0.792907	+	0.457785i	0.840985	−	0.541058i	$-0.181976\pi$
$587$	19.2106	+	11.0913i	0.792907	+	0.457785i	−0.0480776	+	0.998844i	$0.515309\pi$
$588$	−5.90917	+	10.2350i	−0.243690	+	0.422083i
$589$	3.87263	+	6.70758i	0.159569	+	0.276381i
$590$		−	36.5676i		−	1.50547i
$591$	−20.3545	+	11.7517i	−0.837273	+	0.483400i
$592$	4.23494	−	2.44504i	0.174055	−	0.100491i
$593$		−	3.98493i		−	0.163642i	−0.996647	−	0.0818208i	$-0.973926\pi$
$593$		−	3.98493i		−	0.163642i	0.996647	−	0.0818208i	$-0.0260735\pi$
$594$	−4.35086	−	7.53590i	−0.178518	−	0.309202i
$595$	−11.9215	+	20.6487i	−0.488736	+	0.846515i
$596$	−16.1857	−	9.34481i	−0.662992	−	0.382779i
$597$	−7.78495			−0.318617
$598$		0			0
$599$	33.2379			1.35806			0.679032	−	0.734109i	$-0.262400\pi$
$599$	33.2379			1.35806			0.679032	+	0.734109i	$0.262400\pi$
$600$	14.1739	+	8.18329i	0.578646	+	0.334082i
$601$	−4.89858	+	8.48458i	−0.199817	+	0.346093i	−0.948469	−	0.316870i	$-0.897368\pi$
$601$	−4.89858	+	8.48458i	−0.199817	+	0.346093i	0.748652	+	0.662963i	$0.230701\pi$
$602$	0.286208	+	0.495727i	0.0116650	+	0.0202043i
$603$		−	2.57194i		−	0.104738i
$604$	0.275108	−	0.158834i	0.0111940	−	0.00646285i
$605$	16.9942	−	9.81163i	0.690914	−	0.398899i
$606$			17.9651i			0.729782i
$607$	12.1129	+	20.9802i	0.491647	+	0.851558i	0.999954	−	0.00961799i	$-0.00306155\pi$
$607$	12.1129	+	20.9802i	0.491647	+	0.851558i	−0.508306	+	0.861176i	$0.669728\pi$
$608$	−0.455927	+	0.789689i	−0.0184903	+	0.0320261i
$609$	−7.44486	−	4.29829i	−0.301681	−	0.174175i
$610$	1.58450			0.0641545
$611$		0			0
$612$	7.14138			0.288673
$613$	13.0386	+	7.52781i	0.526622	+	0.304045i	0.739640	−	0.673003i	$-0.234996\pi$
$613$	13.0386	+	7.52781i	0.526622	+	0.304045i	−0.213018	+	0.977048i	$0.568329\pi$
$614$	−11.9901	+	20.7674i	−0.483880	+	0.838105i
$615$	−26.5308	−	45.9527i	−1.06982	−	1.85299i
$616$		−	2.61596i		−	0.105400i
$617$	−1.74832	+	1.00939i	−0.0703847	+	0.0406366i	−0.534779	−	0.844992i	$-0.679605\pi$
$617$	−1.74832	+	1.00939i	−0.0703847	+	0.0406366i	0.464395	+	0.885628i	$0.346272\pi$
$618$	33.3796	−	19.2717i	1.34273	−	0.775223i
$619$			7.84309i			0.315240i	0.987500	+	0.157620i	$0.0503821\pi$
$619$			7.84309i			0.315240i	−0.987500	+	0.157620i	$0.949618\pi$
$620$	15.3056	+	26.5101i	0.614687	+	1.06467i
$621$	6.24698	−	10.8201i	0.250683	−	0.434195i
$622$	−4.66272	−	2.69202i	−0.186958	−	0.107940i
$623$	−4.16288			−0.166782
$624$		0			0
$625$	−1.13275			−0.0453101
$626$	−16.4100	−	9.47434i	−0.655877	−	0.378671i
$627$	−2.20171	+	3.81347i	−0.0879278	+	0.152295i
$628$	9.44504	+	16.3593i	0.376898	+	0.652807i
$629$		−	29.1487i		−	1.16223i
$630$	−4.15021	+	2.39612i	−0.165348	+	0.0954639i
$631$	−21.2460	+	12.2664i	−0.845788	+	0.488316i	−0.859227	−	0.511594i	$-0.829055\pi$
$631$	−21.2460	+	12.2664i	−0.845788	+	0.488316i	0.0134394	+	0.999910i	$0.495722\pi$
$632$			15.4819i			0.615836i
$633$	−25.6591	−	44.4429i	−1.01986	−	1.76645i
$634$	5.75063	−	9.96038i	0.228387	−	0.395577i
$635$	35.6660	+	20.5918i	1.41536	+	0.817160i
$636$	−6.93362			−0.274936
$637$		0			0
$638$	−8.90946			−0.352729
$639$	0.639088	+	0.368977i	0.0252819	+	0.0145965i
$640$	−1.80194	+	3.12105i	−0.0712278	+	0.123370i
$641$	−20.8007	−	36.0279i	−0.821580	−	1.42302i	−0.904505	−	0.426462i	$-0.859760\pi$
$641$	−20.8007	−	36.0279i	−0.821580	−	1.42302i	0.0829254	−	0.996556i	$-0.473574\pi$
$642$		−	36.9869i		−	1.45975i
$643$	39.3278	−	22.7059i	1.55094	−	0.895433i	0.552869	−	0.833268i	$-0.313533\pi$
$643$	39.3278	−	22.7059i	1.55094	−	0.895433i	0.998066	−	0.0621650i	$-0.0198005\pi$
$644$	3.25280	−	1.87800i	0.128178	−	0.0740037i
$645$		−	3.80817i		−	0.149946i
$646$	2.71768	+	4.70715i	0.106926	+	0.185200i
$647$	17.9172	−	31.0336i	0.704399	−	1.22005i	−0.262509	−	0.964930i	$-0.584550\pi$
$647$	17.9172	−	31.0336i	0.704399	−	1.22005i	0.966908	−	0.255125i	$-0.0821167\pi$
$648$	−9.66383	−	5.57942i	−0.379631	−	0.219180i
$649$	23.9148			0.938740
$650$		0			0
$651$	−19.3163			−0.757067
$652$	−3.75226	−	2.16637i	−0.146950	−	0.0848415i
$653$	−9.27950	+	16.0726i	−0.363135	+	0.628968i	−0.988475	−	0.151384i	$-0.951627\pi$
$653$	−9.27950	+	16.0726i	−0.363135	+	0.628968i	0.625340	+	0.780352i	$0.284960\pi$
$654$	6.24698	+	10.8201i	0.244276	+	0.423099i
$655$			8.27413i			0.323297i
$656$	6.22324	−	3.59299i	0.242977	−	0.140283i
$657$	6.56049	−	3.78770i	0.255949	−	0.147772i
$658$		−	7.75600i		−	0.302361i
$659$	1.98762	+	3.44266i	0.0774268	+	0.134107i	0.902139	−	0.431445i	$-0.141996\pi$
$659$	1.98762	+	3.44266i	0.0774268	+	0.134107i	−0.824712	+	0.565553i	$0.808663\pi$
$660$	−8.70171	+	15.0718i	−0.338714	+	0.586669i
$661$	1.06687	+	0.615957i	0.0414964	+	0.0239580i	0.520605	−	0.853798i	$-0.325707\pi$
$661$	1.06687	+	0.615957i	0.0414964	+	0.0239580i	−0.479108	+	0.877756i	$0.659040\pi$
$662$	−34.6112			−1.34520
$663$		0			0
$664$	0.911854			0.0353868
$665$	−3.15875	−	1.82371i	−0.122491	−	0.0707204i
$666$	2.92931	−	5.07372i	0.113509	−	0.196603i
$667$	−6.39612	−	11.0784i	−0.247659	−	0.428958i
$668$		−	14.0000i		−	0.541676i
$669$	23.0460	−	13.3056i	0.891008	−	0.514424i
$670$	6.70012	−	3.86831i	0.258848	−	0.149446i
$671$			1.03624i			0.0400038i
$672$	−1.13706	−	1.96945i	−0.0438632	−	0.0759732i
$673$	−18.4128	+	31.8919i	−0.709762	+	1.22934i	0.255184	+	0.966893i	$0.417864\pi$
$673$	−18.4128	+	31.8919i	−0.709762	+	1.22934i	−0.964945	+	0.262451i	$0.915469\pi$
$674$	1.69227	+	0.977033i	0.0651839	+	0.0376339i
$675$	−29.4916			−1.13513
$676$		0			0
$677$	−25.9215			−0.996246			−0.498123	−	0.867106i	$-0.665977\pi$
$677$	−25.9215			−0.996246			−0.498123	+	0.867106i	$0.665977\pi$
$678$	−21.6497	−	12.4995i	−0.831452	−	0.480039i
$679$	8.14377	−	14.1054i	0.312529	−	0.541316i
$680$	10.7409	+	18.6039i	0.411896	+	0.713425i
$681$		−	28.2851i		−	1.08389i
$682$	−17.3373	+	10.0097i	−0.663879	+	0.383291i
$683$	−32.5168	+	18.7736i	−1.24422	+	0.718352i	−0.969951	−	0.243301i	$-0.921770\pi$
$683$	−32.5168	+	18.7736i	−1.24422	+	0.718352i	−0.274271	+	0.961653i	$0.588436\pi$
$684$			1.09246i			0.0417712i
$685$	16.3623	+	28.3403i	0.625170	+	1.08283i
$686$	7.08575	−	12.2729i	0.270535	−	0.468581i
$687$	−20.5128	−	11.8431i	−0.782613	−	0.451842i
$688$	0.515729			0.0196620
$689$		0			0
$690$	−24.9879			−0.951274
$691$	−39.1919	−	22.6274i	−1.49093	−	0.860788i	−0.490983	−	0.871169i	$-0.663362\pi$
$691$	−39.1919	−	22.6274i	−1.49093	−	0.860788i	−0.999946	+	0.0103812i	$0.996695\pi$
$692$	5.49396	−	9.51582i	0.208849	−	0.361737i
$693$	−1.56704	−	2.71419i	−0.0595269	−	0.103104i
$694$		−	6.41550i		−	0.243529i
$695$	59.0039	−	34.0659i	2.23814	−	1.29219i
$696$	−6.70758	+	3.87263i	−0.254250	+	0.146791i
$697$		−	42.8340i		−	1.62245i
$698$	−0.542877	−	0.940290i	−0.0205482	−	0.0355905i
$699$	−10.0139	+	17.3445i	−0.378759	+	0.656030i
$700$	−7.67811	−	4.43296i	−0.290205	−	0.167550i
$701$	−36.0823			−1.36281			−0.681405	−	0.731907i	$-0.738631\pi$
$701$	−36.0823			−1.36281			−0.681405	+	0.731907i	$0.738631\pi$
$702$		0			0
$703$	4.45904			0.168176
$704$	−2.04113	−	1.17845i	−0.0769280	−	0.0444144i
$705$	−25.7995	+	44.6861i	−0.971667	+	1.68298i
$706$	2.14460	+	3.71455i	0.0807129	+	0.139799i
$707$		−	9.73184i		−	0.366004i
$708$	18.0045	−	10.3949i	0.676652	−	0.390665i
$709$	16.5120	−	9.53319i	0.620120	−	0.358026i	−0.156796	−	0.987631i	$-0.550116\pi$
$709$	16.5120	−	9.53319i	0.620120	−	0.358026i	0.776916	+	0.629605i	$0.216783\pi$
$710$			2.21983i			0.0833088i
$711$	9.27413	+	16.0633i	0.347807	+	0.602419i
$712$	−1.87531	+	3.24814i	−0.0702804	+	0.121729i
$713$	−24.8930	−	14.3720i	−0.932249	−	0.538234i
$714$	−13.5555			−0.507304
$715$		0			0
$716$	4.65519			0.173972
$717$	1.67572	+	0.967476i	0.0625808	+	0.0361311i
$718$	7.75302	−	13.4286i	0.289340	−	0.501152i
$719$	−7.65279	−	13.2550i	−0.285401	−	0.494329i	0.687305	−	0.726369i	$-0.258793\pi$
$719$	−7.65279	−	13.2550i	−0.285401	−	0.494329i	−0.972706	+	0.232040i	$0.925460\pi$
$720$			4.31767i			0.160910i
$721$	−18.0820	+	10.4397i	−0.673410	+	0.388793i
$722$	15.7344	−	9.08426i	0.585574	−	0.338081i
$723$			0.450419i			0.0167513i
$724$	0.533188	+	0.923508i	0.0198158	+	0.0343219i
$725$	−15.0978	+	26.1502i	−0.560720	+	0.971195i
$726$	9.66176	+	5.57822i	0.358582	+	0.207027i
$727$	−3.46250			−0.128417			−0.0642085	−	0.997937i	$-0.520452\pi$
$727$	−3.46250			−0.128417			−0.0642085	+	0.997937i	$0.520452\pi$
$728$		0			0
$729$	9.32496			0.345369
$730$	19.7345	+	11.3937i	0.730407	+	0.421701i
$731$	1.53707	−	2.66229i	0.0568507	−	0.0984683i
$732$	0.450419	+	0.780148i	0.0166480	+	0.0288351i
$733$		−	26.0930i		−	0.963769i	−0.876235	−	0.481884i	$-0.839953\pi$
$733$		−	26.0930i		−	0.963769i	0.876235	−	0.481884i	$-0.160047\pi$
$734$	15.0927	−	8.71379i	0.557083	−	0.321632i
$735$	−36.8856	+	21.2959i	−1.36054	+	0.785511i
$736$		−	3.38404i		−	0.124737i
$737$	2.52984	+	4.38180i	0.0931877	+	0.161406i
$738$	4.30463	−	7.45583i	0.158455	−	0.274453i
$739$	−22.9491	−	13.2497i	−0.844196	−	0.487397i	0.0144922	−	0.999895i	$-0.495387\pi$
$739$	−22.9491	−	13.2497i	−0.844196	−	0.487397i	−0.858688	+	0.512498i	$0.828720\pi$
$740$	17.6233			0.647844
$741$		0			0
$742$	3.75600			0.137887
$743$	0.359835	+	0.207751i	0.0132011	+	0.00762164i	0.506586	−	0.862189i	$-0.330907\pi$
$743$	0.359835	+	0.207751i	0.0132011	+	0.00762164i	−0.493385	+	0.869811i	$0.664241\pi$
$744$	−8.70171	+	15.0718i	−0.319020	+	0.552559i
$745$	−33.6775	−	58.3312i	−1.23385	−	2.13709i
$746$			8.19567i			0.300065i
$747$	0.946096	−	0.546229i	0.0346159	−	0.0199855i
$748$	−12.1667	+	7.02446i	−0.444859	+	0.256840i
$749$			20.0361i			0.732103i
$750$	11.0315	+	19.1070i	0.402812	+	0.697691i
$751$	1.45473	−	2.51967i	0.0530839	−	0.0919440i	−0.838262	−	0.545267i	$-0.816428\pi$
$751$	1.45473	−	2.51967i	0.0530839	−	0.0919440i	0.891346	+	0.453323i	$0.149762\pi$
$752$	−6.05171	−	3.49396i	−0.220683	−	0.127412i
$753$	33.3037			1.21365
$754$		0			0
$755$	1.14483			0.0416647
$756$	3.54883	+	2.04892i	0.129070	+	0.0745184i
$757$	−6.18598	+	10.7144i	−0.224833	+	0.389423i	−0.956269	−	0.292487i	$-0.905517\pi$
$757$	−6.18598	+	10.7144i	−0.224833	+	0.389423i	0.731436	+	0.681910i	$0.238850\pi$
$758$	−7.52379	−	13.0316i	−0.273277	−	0.473329i
$759$		−	16.3418i		−	0.593171i
$760$	−2.84594	+	1.64310i	−0.103233	+	0.0596017i
$761$	−36.7459	+	21.2153i	−1.33204	+	0.769053i	−0.985612	−	0.169023i	$-0.945939\pi$
$761$	−36.7459	+	21.2153i	−1.33204	+	0.769053i	−0.346428	+	0.938077i	$0.612605\pi$
$762$			23.4142i			0.848206i
$763$	−3.38404	−	5.86133i	−0.122511	−	0.212195i
$764$	0.445042	−	0.770835i	0.0161010	−	0.0278878i
$765$	22.2886	+	12.8683i	0.805845	+	0.465255i
$766$	11.1207			0.401806
$767$		0			0
$768$	−2.04892			−0.0739339
$769$	−11.5476	−	6.66703i	−0.416418	−	0.240419i	0.277125	−	0.960834i	$-0.410618\pi$
$769$	−11.5476	−	6.66703i	−0.416418	−	0.240419i	−0.693544	+	0.720415i	$0.743952\pi$
$770$	4.71379	−	8.16453i	0.169873	−	0.294229i
$771$	22.9861	+	39.8130i	0.827823	+	1.43383i
$772$		−	16.2174i		−	0.583678i
$773$	−5.06957	+	2.92692i	−0.182340	+	0.105274i	−0.588392	−	0.808576i	$-0.700239\pi$
$773$	−5.06957	+	2.92692i	−0.182340	+	0.105274i	0.406052	+	0.913850i	$0.366905\pi$
$774$	0.535096	−	0.308938i	0.0192336	−	0.0111045i
$775$			67.8491i			2.43721i
$776$	−7.33728	−	12.7085i	−0.263393	−	0.456210i
$777$	−5.56033	+	9.63078i	−0.199476	+	0.345502i
$778$	−6.96591	−	4.02177i	−0.249740	−	0.144187i
$779$	6.55257			0.234770
$780$		0			0
$781$	−1.45175			−0.0519476
$782$	−17.4690	−	10.0858i	−0.624691	−	0.360666i
$783$	6.97823	−	12.0866i	0.249382	−	0.431942i
$784$	−2.88404	−	4.99531i	−0.103002	−	0.178404i
$785$			68.0775i			2.42979i
$786$	−4.07387	+	2.35205i	−0.145310	+	0.0838949i
$787$	20.1754	−	11.6482i	0.719174	−	0.415215i	−0.0952749	−	0.995451i	$-0.530373\pi$
$787$	20.1754	−	11.6482i	0.719174	−	0.415215i	0.814448	+	0.580236i	$0.197040\pi$
$788$		−	11.4711i		−	0.408642i
$789$	−10.7506	−	18.6206i	−0.382732	−	0.662912i
$790$	−27.8974	+	48.3197i	−0.992544	+	1.71914i
$791$	11.7278	+	6.77107i	0.416994	+	0.240752i
$792$	−2.82371			−0.100336
$793$		0			0
$794$	−21.9081			−0.777491
$795$	−21.6402	−	12.4940i	−0.767498	−	0.443115i
$796$	1.89977	−	3.29050i	0.0673356	−	0.116629i
$797$	17.9051	+	31.0126i	0.634233	+	1.09852i	0.986677	+	0.162691i	$0.0520173\pi$
$797$	17.9051	+	31.0126i	0.634233	+	1.09852i	−0.352444	+	0.935833i	$0.614649\pi$
$798$		−	2.07367i		−	0.0734072i
$799$	−36.0729	+	20.8267i	−1.27617	+	0.736795i
$800$	−6.91774	+	3.99396i	−0.244579	+	0.141208i
$801$			4.49349i			0.158769i
$802$	−8.72132	−	15.1058i	−0.307961	−	0.533404i
$803$	−7.45138	+	12.9062i	−0.262953	+	0.455449i
$804$	3.80923	+	2.19926i	0.134341	+	0.0775619i
$805$	13.5362			0.477087
$806$		0			0
$807$	−54.1232			−1.90523
$808$	−7.59339	−	4.38404i	−0.267134	−	0.154230i
$809$	−14.1872	+	24.5729i	−0.498795	+	0.863938i	−0.999999	−	0.00139133i	$-0.999557\pi$
$809$	−14.1872	+	24.5729i	−0.498795	+	0.863938i	0.501204	+	0.865329i	$0.332890\pi$
$810$	−20.1075	−	34.8273i	−0.706506	−	1.22370i
$811$			5.20344i			0.182717i	0.995818	+	0.0913587i	$0.0291210\pi$
$811$			5.20344i			0.182717i	−0.995818	+	0.0913587i	$0.970879\pi$
$812$	3.63356	−	2.09783i	0.127513	−	0.0736196i
$813$	39.0906	−	22.5690i	1.37097	−	0.791528i
$814$			11.5254i			0.403966i
$815$	−7.80731	−	13.5227i	−0.273478	−	0.473678i
$816$	−6.10656	+	10.5769i	−0.213772	+	0.370265i
$817$	0.407266	+	0.235135i	0.0142484	+	0.00822633i
$818$	17.4330			0.609529
$819$		0			0
$820$	25.8974			0.904376
$821$	4.89597	+	2.82669i	0.170871	+	0.0986522i	0.582996	−	0.812475i	$-0.301880\pi$
$821$	4.89597	+	2.82669i	0.170871	+	0.0986522i	−0.412126	+	0.911127i	$0.635214\pi$
$822$	−9.30247	+	16.1124i	−0.324461	+	0.561983i
$823$	19.5308	+	33.8283i	0.680801	+	1.17918i	0.974737	+	0.223356i	$0.0717014\pi$
$823$	19.5308	+	33.8283i	0.680801	+	1.17918i	−0.293936	+	0.955825i	$0.594965\pi$
$824$			18.8116i			0.655334i
$825$	−33.4064	+	19.2872i	−1.16306	+	0.671493i
$826$	−9.75322	+	5.63102i	−0.339358	+	0.195928i
$827$			5.40283i			0.187875i	0.995578	+	0.0939374i	$0.0299454\pi$
$827$			5.40283i			0.187875i	−0.995578	+	0.0939374i	$0.970055\pi$
$828$	−2.02715	−	3.51112i	−0.0704482	−	0.122020i
$829$	−4.19269	+	7.26194i	−0.145618	+	0.252218i	−0.929603	−	0.368562i	$-0.879850\pi$
$829$	−4.19269	+	7.26194i	−0.145618	+	0.252218i	0.783985	+	0.620779i	$0.213184\pi$
$830$	2.84594	+	1.64310i	0.0987840	+	0.0570330i
$831$	4.45904			0.154682
$832$		0			0
$833$	−34.3822			−1.19127
$834$	33.5456	+	19.3675i	1.16159	+	0.670643i
$835$	25.2271	−	43.6947i	0.873021	−	1.51212i
$836$	−1.07457	−	1.86121i	−0.0371649	−	0.0643714i
$837$		−	31.3599i		−	1.08396i
$838$	8.63933	−	4.98792i	0.298441	−	0.172305i
$839$	3.44732	−	1.99031i	0.119015	−	0.0687132i	−0.439311	−	0.898335i	$-0.644777\pi$
$839$	3.44732	−	1.99031i	0.119015	−	0.0687132i	0.558326	+	0.829622i	$0.311444\pi$
$840$		−	8.19567i		−	0.282777i
$841$	7.35517	+	12.7395i	0.253626	+	0.439294i
$842$	0.307979	−	0.533434i	0.0106136	−	0.0183834i
$843$	44.3657	+	25.6145i	1.52803	+	0.882211i
$844$	25.0465			0.862137
$845$		0			0
$846$	−8.37196			−0.287834
$847$	−5.23386	−	3.02177i	−0.179838	−	0.103829i
$848$	1.69202	−	2.93067i	0.0581043	−	0.100640i
$849$	16.7143	+	28.9501i	0.573634	+	0.993563i
$850$			47.6142i			1.63315i
$851$	−14.3312	+	8.27413i	−0.491267	+	0.283633i
$852$	−1.09296	+	0.631023i	−0.0374443	+	0.0216185i
$853$		−	6.29350i		−	0.215485i	−0.994179	−	0.107743i	$-0.965638\pi$
$853$		−	6.29350i		−	0.215485i	0.994179	−	0.107743i	$-0.0343623\pi$
$854$	−0.243996	−	0.422613i	−0.00834936	−	0.0144615i
$855$	−1.96854	+	3.40961i	−0.0673227	+	0.116606i
$856$	15.6334	+	9.02595i	0.534339	+	0.308501i
$857$	−4.37627			−0.149491			−0.0747453	−	0.997203i	$-0.523814\pi$
$857$	−4.37627			−0.149491			−0.0747453	+	0.997203i	$0.523814\pi$
$858$		0			0
$859$	15.0261			0.512683			0.256342	−	0.966586i	$-0.417483\pi$
$859$	15.0261			0.512683			0.256342	+	0.966586i	$0.417483\pi$
$860$	1.60962	+	0.929312i	0.0548875	+	0.0316893i
$861$	−8.17092	+	14.1524i	−0.278464	+	0.482314i
$862$	−7.39612	−	12.8105i	−0.251913	−	0.436326i
$863$			6.21121i			0.211432i	0.994396	+	0.105716i	$0.0337134\pi$
$863$			6.21121i			0.211432i	−0.994396	+	0.105716i	$0.966287\pi$
$864$	3.19738	−	1.84601i	0.108777	−	0.0628026i
$865$	34.2938	−	19.7995i	1.16602	−	0.673205i
$866$		−	16.5321i		−	0.561784i
$867$	18.9840	+	32.8813i	0.644732	+	1.11671i
$868$	4.71379	−	8.16453i	0.159997	−	0.277122i
$869$	−31.6006	−	18.2446i	−1.07198	−	0.618905i
$870$	−27.9129			−0.946337
$871$		0			0
$872$	−6.09783			−0.206499
$873$	−15.2256	−	8.79052i	−0.515309	−	0.297514i
$874$	1.54288	−	2.67234i	0.0521886	−	0.0903933i
$875$	−5.97584	−	10.3505i	−0.202020	−	0.349909i
$876$			12.9554i			0.437722i
$877$	33.0993	−	19.1099i	1.11769	−	0.645296i	0.176876	−	0.984233i	$-0.443401\pi$
$877$	33.0993	−	19.1099i	1.11769	−	0.645296i	0.940809	+	0.338937i	$0.110067\pi$
$878$	−3.03218	+	1.75063i	−0.102331	+	0.0590808i
$879$			3.84787i			0.129785i
$880$	−4.24698	−	7.35598i	−0.143166	−	0.247970i
$881$	13.3916	−	23.1949i	0.451174	−	0.781456i	−0.547286	−	0.836946i	$-0.684339\pi$
$881$	13.3916	−	23.1949i	0.451174	−	0.781456i	0.998459	+	0.0554902i	$0.0176722\pi$
$882$	−5.98469	−	3.45526i	−0.201515	−	0.116345i
$883$	34.4956			1.16087			0.580435	−	0.814307i	$-0.302883\pi$
$883$	34.4956			1.16087			0.580435	+	0.814307i	$0.302883\pi$
$884$		0			0
$885$	74.9241			2.51854
$886$	−15.0755	−	8.70387i	−0.506473	−	0.292412i
$887$	11.9933	−	20.7730i	0.402695	−	0.697489i	−0.591355	−	0.806411i	$-0.701407\pi$
$887$	11.9933	−	20.7730i	0.402695	−	0.697489i	0.994050	+	0.108923i	$0.0347400\pi$
$888$	5.00969	+	8.67704i	0.168114	+	0.291182i
$889$		−	12.6837i		−	0.425396i
$890$	−11.7059	+	6.75840i	−0.392382	+	0.226542i
$891$	22.7766	−	13.1501i	0.763046	−	0.440545i
$892$			12.9879i			0.434868i
$893$	−3.18598	−	5.51828i	−0.106615	−	0.184662i
$894$	19.1468	−	33.1631i	0.640363	−	1.10914i
$895$	14.5291	+	8.38835i	0.485653	+	0.280392i
$896$	1.10992			0.0370797
$897$		0			0
$898$	34.1497			1.13959
$899$	−27.8069	−	16.0543i	−0.927410	−	0.535441i
$900$	−4.78501	+	8.28788i	−0.159500	+	0.276263i
$901$	−10.0858	−	17.4690i	−0.336005	−	0.581978i
$902$			16.9366i			0.563927i
$903$	−1.01570	+	0.586417i	−0.0338005	+	0.0195147i
$904$	10.5664	−	6.10052i	0.351434	−	0.202900i
$905$			3.84309i			0.127748i
$906$	0.325437	+	0.563673i	0.0108119	+	0.0187268i
$907$	11.9635	−	20.7213i	0.397240	−	0.688040i	−0.596144	−	0.802877i	$-0.703301\pi$
$907$	11.9635	−	20.7213i	0.397240	−	0.688040i	0.993384	+	0.114837i	$0.0366347\pi$
$908$	11.9554	+	6.90246i	0.396754	+	0.229066i
$909$	−10.5047			−0.348419
$910$		0			0
$911$	−35.8866			−1.18898			−0.594488	−	0.804104i	$-0.702645\pi$
$911$	−35.8866			−1.18898			−0.594488	+	0.804104i	$0.702645\pi$
$912$	−1.61801	−	0.934157i	−0.0535776	−	0.0309330i
$913$	−1.07457	+	1.86121i	−0.0355632	+	0.0615972i
$914$	4.70171	+	8.14360i	0.155519	+	0.269366i
$915$			3.24651i			0.107326i
$916$	10.0115	−	5.78017i	0.330791	−	0.190982i
$917$	2.20685	−	1.27413i	0.0728767	−	0.0420754i
$918$		−	22.0073i		−	0.726349i
$919$	−16.6233	−	28.7923i	−0.548351	−	0.949771i	−0.998388	−	0.0567612i	$-0.981923\pi$
$919$	−16.6233	−	28.7923i	−0.548351	−	0.949771i	0.450037	−	0.893010i	$-0.351411\pi$
$920$	6.09783	−	10.5618i	0.201040	−	0.348211i
$921$	−42.5507	−	24.5667i	−1.40209	−	0.809499i
$922$	0.733169			0.0241456
$923$		0			0
$924$	5.35988			0.176327
$925$	33.8283	+	19.5308i	1.11227	+	0.642169i
$926$	−3.62133	+	6.27233i	−0.119004	+	0.206122i
$927$	11.2687	+	19.5180i	0.370114	+	0.641057i
$928$		−	3.78017i		−	0.124090i
$929$	46.9891	−	27.1292i	1.54166	−	0.890079i	0.542928	−	0.839779i	$-0.317316\pi$
$929$	46.9891	−	27.1292i	1.54166	−	0.890079i	0.998734	−	0.0502995i	$-0.0160176\pi$
$930$	−54.3169	+	31.3599i	−1.78112	+	1.02833i
$931$		−	5.25965i		−	0.172378i
$932$	−4.88740	−	8.46522i	−0.160092	−	0.277287i
$933$	5.51573	−	9.55352i	0.180577	−	0.312768i
$934$	26.1926	+	15.1223i	0.857047	+	0.494817i
$935$	−50.6305			−1.65580
$936$		0			0
$937$	16.5265			0.539897			0.269948	−	0.962875i	$-0.412993\pi$
$937$	16.5265			0.539897			0.269948	+	0.962875i	$0.412993\pi$
$938$	−2.06349	−	1.19136i	−0.0673754	−	0.0388992i
$939$	19.4121	−	33.6228i	0.633492	−	1.09724i
$940$	−12.5918	−	21.8096i	−0.410699	−	0.711352i
$941$			41.7017i			1.35944i	0.733473	+	0.679718i	$0.237898\pi$
$941$			41.7017i			1.35944i	−0.733473	+	0.679718i	$0.762102\pi$
$942$	−33.5188	+	19.3521i	−1.09210	+	0.630526i
$943$	−21.0597	+	12.1588i	−0.685799	+	0.395946i
$944$			10.1468i			0.330249i
$945$	7.38404	+	12.7895i	0.240203	+	0.416044i
$946$	−0.607760	+	1.05267i	−0.0197600	+	0.0342253i
$947$	−2.59900	−	1.50053i	−0.0844561	−	0.0487608i	0.457177	−	0.889376i	$-0.348861\pi$
$947$	−2.59900	−	1.50053i	−0.0844561	−	0.0487608i	−0.541633	+	0.840615i	$0.682194\pi$
$948$	−31.7211			−1.03025
$949$		0			0
$950$	−7.28382			−0.236318
$951$	20.4080	+	11.7826i	0.661775	+	0.382076i
$952$	3.30798	−	5.72959i	0.107212	−	0.185697i
$953$	19.0725	+	33.0345i	0.617818	+	1.07009i	0.989883	+	0.141886i	$0.0453165\pi$
$953$	19.0725	+	33.0345i	0.617818	+	1.07009i	−0.372065	+	0.928207i	$0.621350\pi$
$954$		−	4.05429i		−	0.131263i
$955$	2.77799	−	1.60388i	0.0898938	−	0.0519002i
$956$	−0.817855	+	0.472189i	−0.0264513	+	0.0152717i
$957$		−	18.2547i		−	0.590092i
$958$	18.3599	+	31.8002i	0.593181	+	1.02742i
$959$	5.03923	−	8.72820i	0.162725	−	0.281848i
$960$	−6.39477	−	3.69202i	−0.206390	−	0.119159i
$961$	−41.1473			−1.32733
$962$		0			0
$963$	21.6273			0.696930
$964$	−0.190381	−	0.109916i	−0.00613174	−	0.00354016i
$965$	29.2228	−	50.6154i	0.940716	−	1.62937i
$966$	3.84787	+	6.66471i	0.123803	+	0.214433i
$967$			26.8793i			0.864381i	0.901782	+	0.432190i	$0.142259\pi$
$967$			26.8793i			0.864381i	−0.901782	+	0.432190i	$0.857741\pi$
$968$	−4.71554	+	2.72252i	−0.151563	+	0.0875051i
$969$	−9.64457	+	5.56829i	−0.309828	+	0.178879i
$970$		−	52.8853i		−	1.69804i
$971$	−1.56824	−	2.71626i	−0.0503271	−	0.0871691i	0.839764	−	0.542951i	$-0.182693\pi$
$971$	−1.56824	−	2.71626i	−0.0503271	−	0.0871691i	−0.890092	+	0.455782i	$0.849360\pi$
$972$	5.89373	−	10.2082i	0.189042	−	0.327430i
$973$	−18.1719	−	10.4916i	−0.582565	−	0.336344i
$974$	28.6547			0.918156
$975$		0			0
$976$	−0.439665			−0.0140733
$977$	31.0785	+	17.9432i	0.994289	+	0.574053i	0.906554	−	0.422091i	$-0.138704\pi$
$977$	31.0785	+	17.9432i	0.994289	+	0.574053i	0.0877357	+	0.996144i	$0.472037\pi$
$978$	4.43871	−	7.68806i	0.141934	−	0.245837i
$979$	−4.41992	−	7.65552i	−0.141261	−	0.244672i
$980$		−	20.7875i		−	0.664031i
$981$	−6.32682	+	3.65279i	−0.202000	+	0.116625i
$982$	−26.3527	+	15.2148i	−0.840949	+	0.485522i
$983$		−	30.4370i		−	0.970790i	−0.874295	−	0.485395i	$-0.838676\pi$
$983$		−	30.4370i		−	0.970790i	0.874295	−	0.485395i	$-0.161324\pi$
$984$	7.36174	+	12.7509i	0.234684	+	0.406484i
$985$	20.6703	−	35.8019i	0.658609	−	1.14074i
$986$	−19.5139	−	11.2664i	−0.621449	−	0.358794i
$987$	15.8914			0.505829
$988$		0			0
$989$	−1.74525			−0.0554957
$990$	−8.81293	−	5.08815i	−0.280093	−	0.161712i
$991$	−15.7235	+	27.2339i	−0.499473	+	0.865112i	−1.00000		0.000608632i	$-0.999806\pi$
$991$	−15.7235	+	27.2339i	−0.499473	+	0.865112i	0.500527	+	0.865721i	$0.333140\pi$
$992$	−4.24698	−	7.35598i	−0.134842	−	0.233553i
$993$		−	70.9154i		−	2.25043i
$994$	0.592068	−	0.341830i	0.0187792	−	0.0108422i
$995$	11.8586	−	6.84654i	0.375942	−	0.217050i
$996$			1.86831i			0.0591998i
$997$	−9.55496	−	16.5497i	−0.302609	−	0.524133i	0.674117	−	0.738624i	$-0.264524\pi$
$997$	−9.55496	−	16.5497i	−0.302609	−	0.524133i	−0.976726	+	0.214491i	$0.931191\pi$
$998$	7.98576	−	13.8317i	0.252785	−	0.437836i
$999$	−15.6355	−	9.02715i	−0.494685	−	0.285606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.2.e.e.147.3		12
13.2	odd	12		338.2.c.h.315.3		6
13.3	even	3	inner	338.2.e.e.23.6		12
13.4	even	6		338.2.b.d.337.1		6
13.5	odd	4		338.2.c.h.191.3		6
13.6	odd	12		338.2.a.h.1.1	yes	3
13.7	odd	12		338.2.a.g.1.1	✓	3
13.8	odd	4		338.2.c.i.191.3		6
13.9	even	3		338.2.b.d.337.4		6
13.10	even	6	inner	338.2.e.e.23.3		12
13.11	odd	12		338.2.c.i.315.3		6
13.12	even	2	inner	338.2.e.e.147.6		12
39.17	odd	6		3042.2.b.n.1351.6		6
39.20	even	12		3042.2.a.bi.1.3		3
39.32	even	12		3042.2.a.z.1.1		3
39.35	odd	6		3042.2.b.n.1351.1		6
52.7	even	12		2704.2.a.v.1.3		3
52.19	even	12		2704.2.a.w.1.3		3
52.35	odd	6		2704.2.f.m.337.6		6
52.43	odd	6		2704.2.f.m.337.5		6
65.19	odd	12		8450.2.a.bn.1.3		3
65.59	odd	12		8450.2.a.bx.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
338.2.a.g.1.1	✓	3	13.7	odd	12
338.2.a.h.1.1	yes	3	13.6	odd	12
338.2.b.d.337.1		6	13.4	even	6
338.2.b.d.337.4		6	13.9	even	3
338.2.c.h.191.3		6	13.5	odd	4
338.2.c.h.315.3		6	13.2	odd	12
338.2.c.i.191.3		6	13.8	odd	4
338.2.c.i.315.3		6	13.11	odd	12
338.2.e.e.23.3		12	13.10	even	6	inner
338.2.e.e.23.6		12	13.3	even	3	inner
338.2.e.e.147.3		12	1.1	even	1	trivial
338.2.e.e.147.6		12	13.12	even	2	inner
2704.2.a.v.1.3		3	52.7	even	12
2704.2.a.w.1.3		3	52.19	even	12
2704.2.f.m.337.5		6	52.43	odd	6
2704.2.f.m.337.6		6	52.35	odd	6
3042.2.a.z.1.1		3	39.32	even	12
3042.2.a.bi.1.3		3	39.20	even	12
3042.2.b.n.1351.1		6	39.35	odd	6
3042.2.b.n.1351.6		6	39.17	odd	6
8450.2.a.bn.1.3		3	65.19	odd	12
8450.2.a.bx.1.3		3	65.59	odd	12

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:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	338.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.02446 - 1.77441i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.60388i q^{5} +(-1.77441 + 1.02446i) q^{6} +(0.961216 - 0.554958i) q^{7} -1.00000i q^{8} +(-0.599031 - 1.03755i) q^{9} +(1.80194 - 3.12105i) q^{10} +(2.04113 + 1.17845i) q^{11} +2.04892 q^{12} -1.10992 q^{14} +(6.39477 + 3.69202i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.98039 + 5.16218i) q^{17} +1.19806i q^{18} +(-0.789689 + 0.455927i) q^{19} +(-3.12105 + 1.80194i) q^{20} -2.27413i q^{21} +(-1.17845 - 2.04113i) q^{22} +(1.69202 - 2.93067i) q^{23} +(-1.77441 - 1.02446i) q^{24} -7.98792 q^{25} +3.69202 q^{27} +(0.961216 + 0.554958i) q^{28} +(1.89008 - 3.27372i) q^{29} +(-3.69202 - 6.39477i) q^{30} -8.49396i q^{31} +(0.866025 - 0.500000i) q^{32} +(4.18211 - 2.41454i) q^{33} -5.96077i q^{34} +(2.00000 + 3.46410i) q^{35} +(0.599031 - 1.03755i) q^{36} +(-4.23494 - 2.44504i) q^{37} +0.911854 q^{38} +3.60388 q^{40} +(-6.22324 - 3.59299i) q^{41} +(-1.13706 + 1.96945i) q^{42} +(-0.257865 - 0.446635i) q^{43} +2.35690i q^{44} +(3.73921 - 2.15883i) q^{45} +(-2.93067 + 1.69202i) q^{46} +6.98792i q^{47} +(1.02446 + 1.77441i) q^{48} +(-2.88404 + 4.99531i) q^{49} +(6.91774 + 3.99396i) q^{50} +12.2131 q^{51} -3.38404 q^{53} +(-3.19738 - 1.84601i) q^{54} +(-4.24698 + 7.35598i) q^{55} +(-0.554958 - 0.961216i) q^{56} +1.86831i q^{57} +(-3.27372 + 1.89008i) q^{58} +(8.78735 - 5.07338i) q^{59} +7.38404i q^{60} +(0.219833 + 0.380761i) q^{61} +(-4.24698 + 7.35598i) q^{62} +(-1.15160 - 0.664874i) q^{63} -1.00000 q^{64} -4.82908 q^{66} +(1.85914 + 1.07338i) q^{67} +(-2.98039 + 5.16218i) q^{68} +(-3.46681 - 6.00469i) q^{69} -4.00000i q^{70} +(-0.533434 + 0.307979i) q^{71} +(-1.03755 + 0.599031i) q^{72} +6.32304i q^{73} +(2.44504 + 4.23494i) q^{74} +(-8.18329 + 14.1739i) q^{75} +(-0.789689 - 0.455927i) q^{76} +2.61596 q^{77} -15.4819 q^{79} +(-3.12105 - 1.80194i) q^{80} +(5.57942 - 9.66383i) q^{81} +(3.59299 + 6.22324i) q^{82} +0.911854i q^{83} +(1.96945 - 1.13706i) q^{84} +(-18.6039 + 10.7409i) q^{85} +0.515729i q^{86} +(-3.87263 - 6.70758i) q^{87} +(1.17845 - 2.04113i) q^{88} +(-3.24814 - 1.87531i) q^{89} -4.31767 q^{90} +3.38404 q^{92} +(-15.0718 - 8.70171i) q^{93} +(3.49396 - 6.05171i) q^{94} +(-1.64310 - 2.84594i) q^{95} -2.04892i q^{96} +(12.7085 - 7.33728i) q^{97} +(4.99531 - 2.88404i) q^{98} -2.82371i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 6 q^{4} - 16 q^{9} + 4 q^{10} - 12 q^{12} - 16 q^{14} - 6 q^{16} + 10 q^{17} - 6 q^{22} - 20 q^{25} + 24 q^{27} + 20 q^{29} - 24 q^{30} + 24 q^{35} + 16 q^{36} - 4 q^{38} + 8 q^{40} + 8 q^{42}+ \cdots - 36 q^{95}+O(q^{100}) \) 12 * q - 6 * q^3 + 6 * q^4 - 16 * q^9 + 4 * q^10 - 12 * q^12 - 16 * q^14 - 6 * q^16 + 10 * q^17 - 6 * q^22 - 20 * q^25 + 24 * q^27 + 20 * q^29 - 24 * q^30 + 24 * q^35 + 16 * q^36 - 4 * q^38 + 8 * q^40 + 8 * q^42 + 22 * q^43 - 6 * q^48 + 6 * q^49 + 64 * q^51 - 32 * q^55 - 8 * q^56 + 8 * q^61 - 32 * q^62 - 12 * q^64 - 16 * q^66 - 10 * q^68 - 28 * q^69 + 28 * q^74 - 46 * q^75 + 72 * q^77 - 72 * q^79 + 50 * q^81 + 14 * q^82 + 20 * q^87 + 6 * q^88 + 16 * q^90 + 4 * q^94 - 36 * q^95

Introduction

L-functions

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