LMFDB - Embedded newform 637.2.x.b.570.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(19,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 5]))

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

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

chi := DirichletCharacter("637.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.x (of order $12$, degree $4$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			570.6
Character	$\chi$	$=$	637.570
Dual form			637.2.x.b.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33353 - 0.357317i) q^{2} +1.07207i q^{3} +(-0.0814361 + 0.0470171i) q^{4} +(-2.77200 - 0.742756i) q^{5} +(0.383068 + 1.42963i) q^{6} +(-2.04421 + 2.04421i) q^{8} +1.85067 q^{9} +O(q^{10})$	\(q+(1.33353 - 0.357317i) q^{2} +1.07207i q^{3} +(-0.0814361 + 0.0470171i) q^{4} +(-2.77200 - 0.742756i) q^{5} +(0.383068 + 1.42963i) q^{6} +(-2.04421 + 2.04421i) q^{8} +1.85067 q^{9} -3.96194 q^{10} +(-1.00979 + 1.00979i) q^{11} +(-0.0504055 - 0.0873049i) q^{12} +(-3.54926 + 0.634621i) q^{13} +(0.796284 - 2.97177i) q^{15} +(-1.90154 + 3.29357i) q^{16} +(-2.09909 - 3.63573i) q^{17} +(2.46792 - 0.661277i) q^{18} +(-4.35974 + 4.35974i) q^{19} +(0.260663 - 0.0698445i) q^{20} +(-0.985770 + 1.70740i) q^{22} +(-6.77658 - 3.91246i) q^{23} +(-2.19153 - 2.19153i) q^{24} +(2.80219 + 1.61784i) q^{25} +(-4.50627 + 2.11449i) q^{26} +5.20025i q^{27} +(0.441485 + 0.764674i) q^{29} -4.24746i q^{30} +(0.237463 + 0.886225i) q^{31} +(0.137560 - 0.513380i) q^{32} +(-1.08257 - 1.08257i) q^{33} +(-4.09830 - 4.09830i) q^{34} +(-0.150711 + 0.0870133i) q^{36} +(1.92747 + 7.19341i) q^{37} +(-4.25601 + 7.37163i) q^{38} +(-0.680356 - 3.80505i) q^{39} +(7.18492 - 4.14822i) q^{40} +(11.4714 + 3.07376i) q^{41} +(0.809734 + 0.467500i) q^{43} +(0.0347561 - 0.129711i) q^{44} +(-5.13007 - 1.37460i) q^{45} +(-10.4347 - 2.79598i) q^{46} +(-0.808679 + 3.01803i) q^{47} +(-3.53093 - 2.03858i) q^{48} +(4.31487 + 1.15617i) q^{50} +(3.89775 - 2.25037i) q^{51} +(0.259200 - 0.218557i) q^{52} +(-1.26243 + 2.18659i) q^{53} +(1.85814 + 6.93466i) q^{54} +(3.54919 - 2.04912i) q^{55} +(-4.67393 - 4.67393i) q^{57} +(0.861962 + 0.861962i) q^{58} +(1.51488 - 5.65360i) q^{59} +(0.0748780 + 0.279449i) q^{60} -0.0854082i q^{61} +(0.633327 + 1.09695i) q^{62} -8.33994i q^{64} +(10.3099 + 0.877064i) q^{65} +(-1.83045 - 1.05681i) q^{66} +(0.728594 + 0.728594i) q^{67} +(0.341884 + 0.197387i) q^{68} +(4.19442 - 7.26495i) q^{69} +(2.79996 - 0.750247i) q^{71} +(-3.78317 + 3.78317i) q^{72} +(2.75156 - 0.737278i) q^{73} +(5.14066 + 8.90388i) q^{74} +(-1.73444 + 3.00414i) q^{75} +(0.150057 - 0.560022i) q^{76} +(-2.26688 - 4.83102i) q^{78} +(-4.71534 - 8.16721i) q^{79} +(7.71741 - 7.71741i) q^{80} -0.0229961 q^{81} +16.3958 q^{82} +(-1.54040 + 1.54040i) q^{83} +(3.11823 + 11.6374i) q^{85} +(1.24685 + 0.334092i) q^{86} +(-0.819782 + 0.473301i) q^{87} -4.12847i q^{88} +(4.75720 - 1.27469i) q^{89} -7.33225 q^{90} +0.735811 q^{92} +(-0.950093 + 0.254577i) q^{93} +4.31358i q^{94} +(15.3234 - 8.84698i) q^{95} +(0.550378 + 0.147473i) q^{96} +(2.37752 + 8.87303i) q^{97} +(-1.86880 + 1.86880i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9	$ 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 8 q^{15} + 12 q^{16} - 64 q^{18} + 4 q^{22} + 12 q^{23} + 4 q^{29} + 64 q^{32} + 4 q^{37} + 36 q^{39} - 48 q^{43} - 84 q^{44} - 108 q^{46} - 44 q^{50} + 12 q^{51} - 36 q^{53} - 92 q^{57} + 44 q^{58} + 28 q^{60} + 28 q^{65} + 64 q^{67} + 84 q^{71} + 4 q^{72} - 24 q^{74} + 148 q^{78} + 40 q^{79} - 56 q^{81} + 36 q^{85} + 108 q^{86} + 24 q^{92} - 24 q^{93} + 84 q^{95} - 60 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 8 * q^15 + 12 * q^16 - 64 * q^18 + 4 * q^22 + 12 * q^23 + 4 * q^29 + 64 * q^32 + 4 * q^37 + 36 * q^39 - 48 * q^43 - 84 * q^44 - 108 * q^46 - 44 * q^50 + 12 * q^51 - 36 * q^53 - 92 * q^57 + 44 * q^58 + 28 * q^60 + 28 * q^65 + 64 * q^67 + 84 * q^71 + 4 * q^72 - 24 * q^74 + 148 * q^78 + 40 * q^79 - 56 * q^81 + 36 * q^85 + 108 * q^86 + 24 * q^92 - 24 * q^93 + 84 * q^95 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.33353	−	0.357317i	0.942945	−	0.252661i	0.245579	−	0.969377i	$-0.421022\pi$
$2$	1.33353	−	0.357317i	0.942945	−	0.252661i	0.697366	+	0.716715i	$0.254355\pi$
$3$			1.07207i			0.618958i	0.950906	+	0.309479i	$0.100155\pi$
$3$			1.07207i			0.618958i	−0.950906	+	0.309479i	$0.899845\pi$
$4$	−0.0814361	+	0.0470171i	−0.0407180	+	0.0235086i
$5$	−2.77200	−	0.742756i	−1.23968	−	0.332171i	−0.421337	−	0.906904i	$-0.638439\pi$
$5$	−2.77200	−	0.742756i	−1.23968	−	0.332171i	−0.818341	+	0.574734i	$0.805106\pi$
$6$	0.383068	+	1.42963i	0.156387	+	0.583644i
$7$		0			0
$7$		0			0
$8$	−2.04421	+	2.04421i	−0.722739	+	0.722739i
$9$	1.85067			0.616891
$10$	−3.96194			−1.25287
$11$	−1.00979	+	1.00979i	−0.304465	+	0.304465i	−0.842758	−	0.538293i	$-0.819069\pi$
$11$	−1.00979	+	1.00979i	−0.304465	+	0.304465i	0.538293	+	0.842758i	$0.319069\pi$
$12$	−0.0504055	−	0.0873049i	−0.0145508	−	0.0252028i
$13$	−3.54926	+	0.634621i	−0.984388	+	0.176012i
$13$	−3.54926	+	0.634621i	−0.984388	+	0.176012i
$14$		0			0
$15$	0.796284	−	2.97177i	0.205600	−	0.767309i
$16$	−1.90154	+	3.29357i	−0.475386	+	0.823393i
$17$	−2.09909	−	3.63573i	−0.509105	−	0.881795i	−0.999944	−	0.0105451i	$-0.996643\pi$
$17$	−2.09909	−	3.63573i	−0.509105	−	0.881795i	0.490840	−	0.871250i	$-0.336690\pi$
$18$	2.46792	−	0.661277i	0.581694	−	0.155864i
$19$	−4.35974	+	4.35974i	−1.00019	+	1.00019i	−0.000191931		1.00000i	$0.500061\pi$
$19$	−4.35974	+	4.35974i	−1.00019	+	1.00019i	−1.00000		0.000191931i	$0.999939\pi$
$20$	0.260663	−	0.0698445i	0.0582861	−	0.0156177i
$21$		0			0
$22$	−0.985770	+	1.70740i	−0.210167	+	0.364020i
$23$	−6.77658	−	3.91246i	−1.41302	−	0.815805i	−0.417344	−	0.908748i	$-0.637039\pi$
$23$	−6.77658	−	3.91246i	−1.41302	−	0.815805i	−0.995671	+	0.0929436i	$0.970372\pi$
$24$	−2.19153	−	2.19153i	−0.447345	−	0.447345i
$25$	2.80219	+	1.61784i	0.560438	+	0.323569i
$26$	−4.50627	+	2.11449i	−0.883752	+	0.414687i
$27$			5.20025i			1.00079i
$28$		0			0
$29$	0.441485	+	0.764674i	0.0819817	+	0.141996i	0.904101	−	0.427319i	$-0.140542\pi$
$29$	0.441485	+	0.764674i	0.0819817	+	0.141996i	−0.822119	+	0.569315i	$0.807208\pi$
$30$		−	4.24746i		−	0.775477i
$31$	0.237463	+	0.886225i	0.0426497	+	0.159171i	0.983966	−	0.178354i	$-0.0570771\pi$
$31$	0.237463	+	0.886225i	0.0426497	+	0.159171i	−0.941317	+	0.337524i	$0.890410\pi$
$32$	0.137560	−	0.513380i	0.0243174	−	0.0907536i
$33$	−1.08257	−	1.08257i	−0.188451	−	0.188451i
$34$	−4.09830	−	4.09830i	−0.702853	−	0.702853i
$35$		0			0
$36$	−0.150711	+	0.0870133i	−0.0251186	+	0.0145022i
$37$	1.92747	+	7.19341i	0.316874	+	1.18259i	0.922232	+	0.386637i	$0.126363\pi$
$37$	1.92747	+	7.19341i	0.316874	+	1.18259i	−0.605358	+	0.795953i	$0.706970\pi$
$38$	−4.25601	+	7.37163i	−0.690416	+	1.19584i
$39$	−0.680356	−	3.80505i	−0.108944	−	0.609295i
$40$	7.18492	−	4.14822i	1.13604	−	0.655890i
$41$	11.4714	+	3.07376i	1.79154	+	0.480041i	0.992606	−	0.121379i	$-0.0387317\pi$
$41$	11.4714	+	3.07376i	1.79154	+	0.480041i	0.798933	+	0.601421i	$0.205398\pi$
$42$		0			0
$43$	0.809734	+	0.467500i	0.123483	+	0.0712931i	0.560469	−	0.828175i	$-0.310621\pi$
$43$	0.809734	+	0.467500i	0.123483	+	0.0712931i	−0.436986	+	0.899468i	$0.643954\pi$
$44$	0.0347561	−	0.129711i	0.00523967	−	0.0195547i
$45$	−5.13007	−	1.37460i	−0.764746	−	0.204913i
$46$	−10.4347	−	2.79598i	−1.53852	−	0.412245i
$47$	−0.808679	+	3.01803i	−0.117958	+	0.440225i	−0.999491	−	0.0318968i	$-0.989845\pi$
$47$	−0.808679	+	3.01803i	−0.117958	+	0.440225i	0.881533	+	0.472122i	$0.156512\pi$
$48$	−3.53093	−	2.03858i	−0.509646	−	0.294244i
$49$		0			0
$50$	4.31487	+	1.15617i	0.610215	+	0.163507i
$51$	3.89775	−	2.25037i	0.545794	−	0.315114i
$52$	0.259200	−	0.218557i	0.0359446	−	0.0303084i
$53$	−1.26243	+	2.18659i	−0.173408	+	0.300351i	−0.939609	−	0.342249i	$-0.888811\pi$
$53$	−1.26243	+	2.18659i	−0.173408	+	0.300351i	0.766201	+	0.642601i	$0.222145\pi$
$54$	1.85814	+	6.93466i	0.252860	+	0.943688i
$55$	3.54919	−	2.04912i	0.478572	−	0.276304i
$56$		0			0
$57$	−4.67393	−	4.67393i	−0.619077	−	0.619077i
$58$	0.861962	+	0.861962i	0.113181	+	0.113181i
$59$	1.51488	−	5.65360i	0.197220	−	0.736035i	−0.794461	−	0.607315i	$-0.792246\pi$
$59$	1.51488	−	5.65360i	0.197220	−	0.736035i	0.991681	−	0.128720i	$-0.0410869\pi$
$60$	0.0748780	+	0.279449i	0.00966671	+	0.0360767i
$61$		−	0.0854082i		−	0.0109354i	−0.999985	−	0.00546770i	$-0.998260\pi$
$61$		−	0.0854082i		−	0.0109354i	0.999985	−	0.00546770i	$-0.00174043\pi$
$62$	0.633327	+	1.09695i	0.0804326	+	0.139313i
$63$		0			0
$64$		−	8.33994i		−	1.04249i
$65$	10.3099	+	0.877064i	1.27879	+	0.108786i
$66$	−1.83045	−	1.05681i	−0.225313	−	0.130085i
$67$	0.728594	+	0.728594i	0.0890119	+	0.0890119i	0.750211	−	0.661199i	$-0.229952\pi$
$67$	0.728594	+	0.728594i	0.0890119	+	0.0890119i	−0.661199	+	0.750211i	$0.729952\pi$
$68$	0.341884	+	0.197387i	0.0414595	+	0.0239366i
$69$	4.19442	−	7.26495i	0.504949	−	0.874598i
$70$		0			0
$71$	2.79996	−	0.750247i	0.332294	−	0.0890380i	−0.0888143	−	0.996048i	$-0.528308\pi$
$71$	2.79996	−	0.750247i	0.332294	−	0.0890380i	0.421109	+	0.907010i	$0.361641\pi$
$72$	−3.78317	+	3.78317i	−0.445851	+	0.445851i
$73$	2.75156	−	0.737278i	0.322046	−	0.0862919i	−0.0941746	−	0.995556i	$-0.530021\pi$
$73$	2.75156	−	0.737278i	0.322046	−	0.0862919i	0.416220	+	0.909264i	$0.363355\pi$
$74$	5.14066	+	8.90388i	0.597589	+	1.03506i
$75$	−1.73444	+	3.00414i	−0.200276	+	0.346888i
$76$	0.150057	−	0.560022i	0.0172128	−	0.0642389i
$77$		0			0
$78$	−2.26688	−	4.83102i	−0.256674	−	0.547006i
$79$	−4.71534	−	8.16721i	−0.530517	−	0.918883i	−0.999366	−	0.0356045i	$-0.988664\pi$
$79$	−4.71534	−	8.16721i	−0.530517	−	0.918883i	0.468849	−	0.883279i	$-0.344669\pi$
$80$	7.71741	−	7.71741i	0.862832	−	0.862832i
$81$	−0.0229961			−0.00255513
$82$	16.3958			1.81061
$83$	−1.54040	+	1.54040i	−0.169081	+	0.169081i	−0.786575	−	0.617494i	$-0.788148\pi$
$83$	−1.54040	+	1.54040i	−0.169081	+	0.169081i	0.617494	+	0.786575i	$0.288148\pi$
$84$		0			0
$85$	3.11823	+	11.6374i	0.338219	+	1.26225i
$86$	1.24685	+	0.334092i	0.134451	+	0.0360260i
$87$	−0.819782	+	0.473301i	−0.0878898	+	0.0507432i
$88$		−	4.12847i		−	0.440097i
$89$	4.75720	−	1.27469i	0.504262	−	0.135117i	0.00228491	−	0.999997i	$-0.499273\pi$
$89$	4.75720	−	1.27469i	0.504262	−	0.135117i	0.501977	+	0.864881i	$0.332606\pi$
$90$	−7.33225			−0.772887
$91$		0			0
$92$	0.735811			0.0767136
$93$	−0.950093	+	0.254577i	−0.0985201	+	0.0263984i
$94$			4.31358i			0.444912i
$95$	15.3234	−	8.84698i	1.57215	−	0.907681i
$96$	0.550378	+	0.147473i	0.0561727	+	0.0150514i
$97$	2.37752	+	8.87303i	0.241401	+	0.900920i	0.975158	+	0.221509i	$0.0710981\pi$
$97$	2.37752	+	8.87303i	0.241401	+	0.900920i	−0.733758	+	0.679411i	$0.762235\pi$
$98$		0			0
$99$	−1.86880	+	1.86880i	−0.187821	+	0.187821i
$100$	−0.304266			−0.0304266
$101$	6.54977			0.651726			0.325863	−	0.945417i	$-0.394345\pi$
$101$	6.54977			0.651726			0.325863	+	0.945417i	$0.394345\pi$
$102$	4.39366	−	4.39366i	0.435037	−	0.435037i
$103$	−4.92770	−	8.53503i	−0.485541	−	0.840982i	0.514321	−	0.857598i	$-0.328044\pi$
$103$	−4.92770	−	8.53503i	−0.485541	−	0.840982i	−0.999862	+	0.0166161i	$0.994711\pi$
$104$	5.95815	−	8.55275i	0.584245	−	0.838666i
$105$		0			0
$106$	−0.902174	+	3.36696i	−0.0876269	+	0.327028i
$107$	−5.29678	+	9.17430i	−0.512059	+	0.886913i	0.487843	+	0.872931i	$0.337784\pi$
$107$	−5.29678	+	9.17430i	−0.512059	+	0.886913i	−0.999902	+	0.0139814i	$0.995549\pi$
$108$	−0.244501	−	0.423488i	−0.0235271	−	0.0407501i
$109$	−15.9403	+	4.27118i	−1.52680	+	0.409105i	−0.921974	−	0.387252i	$-0.873424\pi$
$109$	−15.9403	+	4.27118i	−1.52680	+	0.409105i	−0.604827	+	0.796357i	$0.706758\pi$
$110$	4.00074	−	4.00074i	0.381456	−	0.381456i
$111$	−7.71182	+	2.06638i	−0.731974	+	0.196132i
$112$		0			0
$113$	−0.322118	+	0.557925i	−0.0303023	+	0.0524851i	−0.880779	−	0.473528i	$-0.842980\pi$
$113$	−0.322118	+	0.557925i	−0.0303023	+	0.0524851i	0.850477	+	0.526013i	$0.176314\pi$
$114$	−7.90288	−	4.56273i	−0.740172	−	0.427339i
$115$	15.8787	+	15.8787i	1.48070	+	1.48070i
$116$	−0.0719056	−	0.0415147i	−0.00667627	−	0.00385454i
$117$	−6.56852	+	1.17448i	−0.607260	+	0.108580i
$118$		−	8.08051i		−	0.743871i
$119$		0			0
$120$	4.44717	+	7.70272i	0.405969	+	0.703159i
$121$			8.96063i			0.814603i
$122$	−0.0305178	−	0.113894i	−0.00276295	−	0.0103115i
$123$	−3.29528	+	12.2982i	−0.297126	+	1.10889i
$124$	−0.0610059	−	0.0610059i	−0.00547849	−	0.00547849i
$125$	3.58022	+	3.58022i	0.320225	+	0.320225i
$126$		0			0
$127$	−14.1284	+	8.15702i	−1.25369	+	0.723819i	−0.971841	−	0.235640i	$-0.924282\pi$
$127$	−14.1284	+	8.15702i	−1.25369	+	0.723819i	−0.281850	+	0.959458i	$0.590948\pi$
$128$	−2.70488	−	10.0948i	−0.239080	−	0.892259i
$129$	−0.501191	+	0.868089i	−0.0441274	+	0.0764310i
$130$	14.0619	−	2.51433i	1.23331	−	0.220521i
$131$	2.03759	−	1.17640i	0.178025	−	0.102783i	−0.408340	−	0.912830i	$-0.633892\pi$
$131$	2.03759	−	1.17640i	0.178025	−	0.102783i	0.586364	+	0.810047i	$0.300559\pi$
$132$	0.139059	+	0.0372608i	0.0121036	+	0.00324314i
$133$		0			0
$134$	1.23194	+	0.711259i	0.106423	+	0.0614435i
$135$	3.86251	−	14.4151i	0.332432	−	1.24065i
$136$	11.7232	+	3.14122i	1.00526	+	0.269358i
$137$	−10.0332	−	2.68838i	−0.857190	−	0.229683i	−0.196650	−	0.980474i	$-0.563006\pi$
$137$	−10.0332	−	2.68838i	−0.857190	−	0.229683i	−0.660541	+	0.750790i	$0.729673\pi$
$138$	2.99748	−	11.1867i	0.255162	−	0.952278i
$139$	−5.33208	−	3.07848i	−0.452261	−	0.261113i	0.256524	−	0.966538i	$-0.417423\pi$
$139$	−5.33208	−	3.07848i	−0.452261	−	0.261113i	−0.708784	+	0.705425i	$0.750756\pi$
$140$		0			0
$141$	−3.23553	−	0.866959i	−0.272481	−	0.0730111i
$142$	3.46574	−	2.00095i	0.290839	−	0.167916i
$143$	2.94319	−	4.22486i	0.246122	−	0.353301i
$144$	−3.51914	+	6.09532i	−0.293261	+	0.507943i
$145$	−0.655831	−	2.44759i	−0.0544638	−	0.203262i
$146$	3.40583	−	1.96636i	0.281869	−	0.162737i
$147$		0			0
$148$	−0.495179	−	0.495179i	−0.0407035	−	0.0407035i
$149$	6.15629	+	6.15629i	0.504343	+	0.504343i	0.912784	−	0.408442i	$-0.133928\pi$
$149$	6.15629	+	6.15629i	0.504343	+	0.504343i	−0.408442	+	0.912784i	$0.633928\pi$
$150$	−1.23949	+	4.62584i	−0.101204	+	0.377698i
$151$	3.49627	+	13.0482i	0.284522	+	1.06185i	0.949188	+	0.314710i	$0.101907\pi$
$151$	3.49627	+	13.0482i	0.284522	+	1.06185i	−0.664665	+	0.747141i	$0.731426\pi$
$152$		−	17.8245i		−	1.44575i
$153$	−3.88473	−	6.72855i	−0.314062	−	0.543971i
$154$		0			0
$155$		−	2.63300i		−	0.211487i
$156$	0.234308	+	0.277880i	0.0187597	+	0.0222482i
$157$	5.87142	+	3.38986i	0.468590	+	0.270541i	0.715649	−	0.698460i	$-0.246131\pi$
$157$	5.87142	+	3.38986i	0.468590	+	0.270541i	−0.247059	+	0.969000i	$0.579464\pi$
$158$	−9.20631	−	9.20631i	−0.732415	−	0.732415i
$159$	−2.34417	−	1.35341i	−0.185905	−	0.107332i
$160$	−0.762632	+	1.32092i	−0.0602914	+	0.104428i
$161$		0			0
$162$	−0.0306659	+	0.00821691i	−0.00240934	+	0.000645582i
$163$	−7.72493	+	7.72493i	−0.605063	+	0.605063i	−0.941652	−	0.336588i	$-0.890727\pi$
$163$	−7.72493	+	7.72493i	−0.605063	+	0.605063i	0.336588	+	0.941652i	$0.390727\pi$
$164$	−1.07871	+	0.289039i	−0.0842330	+	0.0225702i
$165$	2.19680	+	3.80497i	0.171020	+	0.296216i
$166$	−1.50375	+	2.60458i	−0.116714	+	0.202155i
$167$	−4.71387	+	17.5924i	−0.364770	+	1.36134i	0.502962	+	0.864308i	$0.332244\pi$
$167$	−4.71387	+	17.5924i	−0.364770	+	1.36134i	−0.867732	+	0.497032i	$0.834423\pi$
$168$		0			0
$169$	12.1945	−	4.50487i	0.938039	−	0.346529i
$170$	8.31647	+	14.4045i	0.637844	+	1.10478i
$171$	−8.06844	+	8.06844i	−0.617009	+	0.617009i
$172$	−0.0879221			−0.00670400
$173$	−20.1522			−1.53214			−0.766070	−	0.642757i	$-0.777791\pi$
$173$	−20.1522			−1.53214			−0.766070	+	0.642757i	$0.777791\pi$
$174$	−0.924081	+	0.924081i	−0.0700544	+	0.0700544i
$175$		0			0
$176$	−1.40566	−	5.24600i	−0.105956	−	0.395432i
$177$	6.06103	+	1.62405i	0.455575	+	0.122071i
$178$	5.88838	−	3.39966i	0.441353	−	0.254815i
$179$		−	16.5322i		−	1.23567i	−0.786306	−	0.617837i	$-0.788009\pi$
$179$		−	16.5322i		−	1.23567i	0.786306	−	0.617837i	$-0.211991\pi$
$180$	0.482402	−	0.129259i	0.0359562	−	0.00963442i
$181$	−13.6897			−1.01755			−0.508774	−	0.860900i	$-0.669901\pi$
$181$	−13.6897			−1.01755			−0.508774	+	0.860900i	$0.669901\pi$
$182$		0			0
$183$	0.0915633			0.00676855
$184$	21.8507	−	5.85488i	1.61085	−	0.431627i
$185$		−	21.3718i		−	1.57129i
$186$	−1.17601	+	0.678969i	−0.0862292	+	0.0497844i
$187$	5.79100	+	1.55169i	0.423480	+	0.113471i
$188$	−0.0760436	−	0.283799i	−0.00554605	−	0.0206981i
$189$		0			0
$190$	17.2730	−	17.2730i	1.25311	−	1.25311i
$191$	−8.14890			−0.589633			−0.294817	−	0.955554i	$-0.595259\pi$
$191$	−8.14890			−0.589633			−0.294817	+	0.955554i	$0.595259\pi$
$192$	8.94097			0.645259
$193$	18.9414	−	18.9414i	1.36343	−	1.36343i	0.493935	−	0.869499i	$-0.335558\pi$
$193$	18.9414	−	18.9414i	1.36343	−	1.36343i	0.869499	−	0.493935i	$-0.164442\pi$
$194$	6.34097	+	10.9829i	0.455255	+	0.788525i
$195$	−0.940271	+	11.0529i	−0.0673342	+	0.791517i
$196$		0			0
$197$	4.77033	−	17.8031i	0.339872	−	1.26842i	−0.558617	−	0.829426i	$-0.688668\pi$
$197$	4.77033	−	17.8031i	0.339872	−	1.26842i	0.898490	−	0.438995i	$-0.144665\pi$
$198$	−1.82434	+	3.15985i	−0.129650	+	0.224560i
$199$	6.35578	+	11.0085i	0.450550	+	0.780375i	0.998420	−	0.0561884i	$-0.0178947\pi$
$199$	6.35578	+	11.0085i	0.450550	+	0.780375i	−0.547871	+	0.836563i	$0.684561\pi$
$200$	−9.03550	+	2.42105i	−0.638906	+	0.171194i
$201$	−0.781101	+	0.781101i	−0.0550947	+	0.0550947i
$202$	8.73428	−	2.34034i	0.614542	−	0.164666i
$203$		0			0
$204$	−0.211612	+	0.366522i	−0.0148158	+	0.0256617i
$205$	−29.5158	−	17.0410i	−2.06147	−	1.19019i
$206$	−9.62093	−	9.62093i	−0.670322	−	0.670322i
$207$	−12.5412	−	7.24069i	−0.871676	−	0.503262i
$208$	4.65891	−	12.8965i	0.323037	−	0.894212i
$209$		−	8.80488i		−	0.609046i
$210$		0			0
$211$	−2.26459	−	3.92239i	−0.155901	−	0.270028i	0.777486	−	0.628900i	$-0.216495\pi$
$211$	−2.26459	−	3.92239i	−0.155901	−	0.270028i	−0.933387	+	0.358872i	$0.883161\pi$
$212$		−	0.237423i		−	0.0163063i
$213$	0.804316	+	3.00175i	0.0551108	+	0.205676i
$214$	−3.78526	+	14.1268i	−0.258755	+	0.965688i
$215$	−1.89735	−	1.89735i	−0.129398	−	0.129398i
$216$	−10.6304	−	10.6304i	−0.723308	−	0.723308i
$217$		0			0
$218$	−19.7306	+	11.3915i	−1.33632	+	0.771527i
$219$	0.790412	+	2.94986i	0.0534111	+	0.199333i
$220$	−0.192688	+	0.333745i	−0.0129910	+	0.0225011i
$221$	9.75754	+	11.5720i	0.656363	+	0.778420i
$222$	−9.54556	+	5.51113i	−0.640656	+	0.369883i
$223$	−22.4788	−	6.02318i	−1.50529	−	0.403342i	−0.590423	−	0.807094i	$-0.701039\pi$
$223$	−22.4788	−	6.02318i	−1.50529	−	0.403342i	−0.914868	+	0.403752i	$0.867706\pi$
$224$		0			0
$225$	5.18593	+	2.99410i	0.345729	+	0.199607i
$226$	−0.230197	+	0.859105i	−0.0153124	+	0.0571468i
$227$	10.0685	+	2.69786i	0.668273	+	0.179063i	0.576977	−	0.816761i	$-0.304232\pi$
$227$	10.0685	+	2.69786i	0.668273	+	0.179063i	0.0912961	+	0.995824i	$0.470899\pi$
$228$	0.600381	+	0.160872i	0.0397612	+	0.0106540i
$229$	−0.499191	+	1.86301i	−0.0329875	+	0.123111i	−0.980456	−	0.196738i	$-0.936965\pi$
$229$	−0.499191	+	1.86301i	−0.0329875	+	0.123111i	0.947469	+	0.319848i	$0.103632\pi$
$230$	26.8484	+	15.5009i	1.77033	+	1.02210i
$231$		0			0
$232$	−2.46565	−	0.660668i	−0.161878	−	0.0433750i
$233$	7.44377	−	4.29766i	0.487657	−	0.281549i	−0.235945	−	0.971766i	$-0.575818\pi$
$233$	7.44377	−	4.29766i	0.487657	−	0.281549i	0.723602	+	0.690217i	$0.242485\pi$
$234$	−8.33963	+	3.91324i	−0.545179	+	0.255816i
$235$	4.48332	−	7.76535i	0.292460	−	0.506555i
$236$	0.142450	+	0.531632i	0.00927273	+	0.0346063i
$237$	8.75580	−	5.05516i	0.568750	−	0.328368i
$238$		0			0
$239$	−6.45158	−	6.45158i	−0.417318	−	0.417318i	0.466960	−	0.884278i	$-0.345349\pi$
$239$	−6.45158	−	6.45158i	−0.417318	−	0.417318i	−0.884278	+	0.466960i	$0.845349\pi$
$240$	8.27358	+	8.27358i	0.534057	+	0.534057i
$241$	−1.12940	+	4.21497i	−0.0727509	+	0.271510i	−0.992714	−	0.120495i	$-0.961552\pi$
$241$	−1.12940	+	4.21497i	−0.0727509	+	0.271510i	0.919963	+	0.392005i	$0.128218\pi$
$242$	3.20179	+	11.9492i	0.205819	+	0.768125i
$243$			15.5761i			0.999206i
$244$	0.00401565	+	0.00695531i	0.000257076	+	0.000445268i
$245$		0			0
$246$			17.5774i			1.12069i
$247$	12.7071	−	18.2406i	0.808531	−	1.16062i
$248$	−2.29706	−	1.32621i	−0.145863	−	0.0842143i
$249$	−1.65142	−	1.65142i	−0.104654	−	0.104654i
$250$	6.05359	+	3.49504i	0.382863	+	0.221046i
$251$	−2.27953	+	3.94826i	−0.143883	+	0.249212i	−0.928956	−	0.370191i	$-0.879292\pi$
$251$	−2.27953	+	3.94826i	−0.143883	+	0.249212i	0.785073	+	0.619403i	$0.212625\pi$
$252$		0			0
$253$	10.7937	−	2.89218i	0.678597	−	0.181830i
$254$	−15.9259	+	15.9259i	−0.999280	+	0.999280i
$255$	−12.4761	+	3.34295i	−0.781281	+	0.209344i
$256$	1.12588	+	1.95008i	0.0703674	+	0.121880i
$257$	4.31666	−	7.47667i	0.269266	−	0.466382i	−0.699407	−	0.714724i	$-0.746552\pi$
$257$	4.31666	−	7.47667i	0.269266	−	0.466382i	0.968672	+	0.248342i	$0.0798857\pi$
$258$	−0.358169	+	1.33670i	−0.0222986	+	0.0832195i
$259$		0			0
$260$	−0.880838	+	0.413319i	−0.0546272	+	0.0256330i
$261$	0.817044	+	1.41516i	0.0505737	+	0.0875963i
$262$	2.29683	−	2.29683i	0.141898	−	0.141898i
$263$	−13.0629			−0.805491			−0.402745	−	0.915312i	$-0.631944\pi$
$263$	−13.0629			−0.805491			−0.402745	+	0.915312i	$0.631944\pi$
$264$	4.42600			0.272402
$265$	5.12356	−	5.12356i	0.314738	−	0.314738i
$266$		0			0
$267$	1.36655	+	5.10004i	0.0836316	+	0.312117i
$268$	−0.0935902	−	0.0250774i	−0.00571693	−	0.00153185i
$269$	−10.8756	+	6.27901i	−0.663095	+	0.382838i	−0.793455	−	0.608629i	$-0.791720\pi$
$269$	−10.8756	+	6.27901i	−0.663095	+	0.382838i	0.130360	+	0.991467i	$0.458387\pi$
$270$		−	20.6030i		−	1.25386i
$271$	4.45677	−	1.19419i	0.270730	−	0.0725418i	−0.120900	−	0.992665i	$-0.538578\pi$
$271$	4.45677	−	1.19419i	0.270730	−	0.0725418i	0.391630	+	0.920123i	$0.371911\pi$
$272$	15.9661			0.968085
$273$		0			0
$274$	−14.3401			−0.866315
$275$	−4.46333	+	1.19595i	−0.269149	+	0.0721182i
$276$			0.788839i			0.0474825i
$277$	1.44840	−	0.836232i	0.0870257	−	0.0502443i	−0.455856	−	0.890054i	$-0.650667\pi$
$277$	1.44840	−	0.836232i	0.0870257	−	0.0502443i	0.542881	+	0.839809i	$0.317333\pi$
$278$	−8.21045	−	2.19998i	−0.492430	−	0.131946i
$279$	0.439467	+	1.64011i	0.0263102	+	0.0981910i
$280$		0			0
$281$	−13.9259	+	13.9259i	−0.830749	+	0.830749i	−0.987619	−	0.156870i	$-0.949860\pi$
$281$	−13.9259	+	13.9259i	−0.830749	+	0.830749i	0.156870	+	0.987619i	$0.449860\pi$
$282$	−4.62445			−0.275382
$283$	−32.9939			−1.96128			−0.980642	−	0.195810i	$-0.937266\pi$
$283$	−32.9939			−1.96128			−0.980642	+	0.195810i	$0.937266\pi$
$284$	−0.192743	+	0.192743i	−0.0114372	+	0.0114372i
$285$	9.48456	+	16.4277i	0.561817	+	0.973095i
$286$	2.41520	−	6.68561i	0.142814	−	0.395329i
$287$		0			0
$288$	0.254578	−	0.950098i	0.0150012	−	0.0559851i
$289$	−0.312374	+	0.541047i	−0.0183749	+	0.0318263i
$290$	−1.74913	−	3.02959i	−0.102713	−	0.177904i
$291$	−9.51249	+	2.54886i	−0.557632	+	0.149417i
$292$	−0.189412	+	0.189412i	−0.0110845	+	0.0110845i
$293$	21.2120	−	5.68375i	1.23922	−	0.332048i	0.421057	−	0.907034i	$-0.361659\pi$
$293$	21.2120	−	5.68375i	1.23922	−	0.332048i	0.818163	+	0.574986i	$0.194993\pi$
$294$		0			0
$295$	−8.39849	+	14.5466i	−0.488979	+	0.846936i
$296$	−18.6450	−	10.7647i	−1.08372	−	0.625686i
$297$	−5.25118	−	5.25118i	−0.304704	−	0.304704i
$298$	10.4093	+	6.00982i	0.602996	+	0.348140i
$299$	26.5348	+	9.58579i	1.53455	+	0.554361i
$300$		−	0.326193i		−	0.0188328i
$301$		0			0
$302$	9.32472	+	16.1509i	0.536578	+	0.929380i
$303$			7.02179i			0.403391i
$304$	−6.06887	−	22.6493i	−0.348074	−	1.29903i
$305$	−0.0634374	+	0.236752i	−0.00363242	+	0.0135564i
$306$	−7.58461	−	7.58461i	−0.433584	−	0.433584i
$307$	13.7833	+	13.7833i	0.786656	+	0.786656i	0.980944	−	0.194289i	$-0.0622399\pi$
$307$	13.7833	+	13.7833i	0.786656	+	0.786656i	−0.194289	+	0.980944i	$0.562240\pi$
$308$		0			0
$309$	9.15013	−	5.28283i	0.520533	−	0.300530i
$310$	−0.940815	−	3.51117i	−0.0534347	−	0.199421i
$311$	12.9133	−	22.3666i	0.732248	−	1.26829i	−0.223672	−	0.974664i	$-0.571804\pi$
$311$	12.9133	−	22.3666i	0.732248	−	1.26829i	0.955920	−	0.293627i	$-0.0948622\pi$
$312$	9.16912	+	6.38753i	0.519099	+	0.361623i
$313$	−24.8257	+	14.3331i	−1.40323	+	0.810155i	−0.994723	−	0.102600i	$-0.967284\pi$
$313$	−24.8257	+	14.3331i	−1.40323	+	0.810155i	−0.408507	+	0.912755i	$0.633950\pi$
$314$	9.04094	+	2.42251i	0.510210	+	0.136710i
$315$		0			0
$316$	0.767998	+	0.443404i	0.0432033	+	0.0249434i
$317$	3.22651	−	12.0415i	0.181219	−	0.676317i	−0.814190	−	0.580599i	$-0.802819\pi$
$317$	3.22651	−	12.0415i	0.181219	−	0.676317i	0.995408	−	0.0957183i	$-0.0305148\pi$
$318$	−3.60961	−	0.967191i	−0.202417	−	0.0542374i
$319$	−1.21797	−	0.326355i	−0.0681934	−	0.0182724i
$320$	−6.19454	+	23.1183i	−0.346285	+	1.29235i
$321$	−9.83546	−	5.67851i	−0.548962	−	0.316943i
$322$		0			0
$323$	25.0023	+	6.69935i	1.39117	+	0.372762i
$324$	0.00187272	−	0.00108121i	0.000104040	−	6.00674e-5i
$325$	−10.9724	−	3.96383i	−0.608640	−	0.219873i
$326$	−7.54114	+	13.0616i	−0.417665	+	0.723418i
$327$	−4.57899	−	17.0890i	−0.253219	−	0.945026i
$328$	−29.7335	+	17.1667i	−1.64176	+	0.947870i
$329$		0			0
$330$	4.28907	+	4.28907i	0.236105	+	0.236105i
$331$	21.1797	+	21.1797i	1.16414	+	1.16414i	0.983561	+	0.180578i	$0.0577970\pi$
$331$	21.1797	+	21.1797i	1.16414	+	1.16414i	0.180578	+	0.983561i	$0.442203\pi$
$332$	0.0530190	−	0.197870i	0.00290980	−	0.0108595i
$333$	3.56711	+	13.3126i	0.195477	+	0.729529i
$334$			25.1443i			1.37583i
$335$	−1.47850	−	2.56083i	−0.0807789	−	0.139913i
$336$		0			0
$337$		−	13.4402i		−	0.732137i	−0.930588	−	0.366068i	$-0.880704\pi$
$337$		−	13.4402i		−	0.732137i	0.930588	−	0.366068i	$-0.119296\pi$
$338$	14.6520	−	10.3647i	0.796965	−	0.563764i
$339$	−0.598133	−	0.345332i	−0.0324861	−	0.0187559i
$340$	−0.801093	−	0.801093i	−0.0434453	−	0.0434453i
$341$	−1.13470	−	0.655117i	−0.0614472	−	0.0354766i
$342$	−7.87648	+	13.6425i	−0.425911	+	0.737700i
$343$		0			0
$344$	−2.61094	+	0.699599i	−0.140772	+	0.0377199i
$345$	−17.0230	+	17.0230i	−0.916490	+	0.916490i
$346$	−26.8734	+	7.20071i	−1.44472	+	0.387113i
$347$	7.24936	+	12.5563i	0.389166	+	0.674055i	0.992338	−	0.123556i	$-0.0394299\pi$
$347$	7.24936	+	12.5563i	0.389166	+	0.674055i	−0.603172	+	0.797611i	$0.706097\pi$
$348$	0.0445066	−	0.0770876i	0.00238580	−	0.00413233i
$349$	5.68220	−	21.2063i	0.304161	−	1.13515i	−0.629504	−	0.776998i	$-0.716742\pi$
$349$	5.68220	−	21.2063i	0.304161	−	1.13515i	0.933665	−	0.358148i	$-0.116592\pi$
$350$		0			0
$351$	−3.30019	−	18.4570i	−0.176151	−	0.985163i
$352$	0.379501	+	0.657316i	0.0202275	+	0.0350351i
$353$	−8.16512	+	8.16512i	−0.434585	+	0.434585i	−0.890185	−	0.455600i	$-0.849425\pi$
$353$	−8.16512	+	8.16512i	−0.434585	+	0.434585i	0.455600	+	0.890185i	$0.349425\pi$
$354$	8.66284			0.460425
$355$	−8.31875			−0.441514
$356$	−0.327476	+	0.327476i	−0.0173562	+	0.0173562i
$357$		0			0
$358$	−5.90723	−	22.0461i	−0.312207	−	1.16517i
$359$	0.861987	+	0.230969i	0.0454939	+	0.0121901i	0.281494	−	0.959563i	$-0.409170\pi$
$359$	0.861987	+	0.230969i	0.0454939	+	0.0121901i	−0.236000	+	0.971753i	$0.575837\pi$
$360$	13.2969	−	7.67699i	0.700810	−	0.404613i
$361$		−	19.0146i		−	1.00077i
$362$	−18.2556	+	4.89156i	−0.959491	+	0.257095i
$363$	−9.60639			−0.504205
$364$		0			0
$365$	−8.17495			−0.427897
$366$	0.122102	−	0.0327171i	0.00638237	−	0.00171015i
$367$			14.4731i			0.755489i	0.925910	+	0.377744i	$0.123300\pi$
$367$			14.4731i			0.755489i	−0.925910	+	0.377744i	$0.876700\pi$
$368$	25.7720	−	14.8794i	1.34346	−	0.775645i
$369$	21.2299	+	5.68853i	1.10518	+	0.296133i
$370$	−7.63651	−	28.4998i	−0.397003	−	1.48164i
$371$		0			0
$372$	0.0654024	−	0.0654024i	0.00339096	−	0.00339096i
$373$	20.9269			1.08356			0.541778	−	0.840522i	$-0.317751\pi$
$373$	20.9269			1.08356			0.541778	+	0.840522i	$0.317751\pi$
$374$	8.27689			0.427988
$375$	−3.83824	+	3.83824i	−0.198206	+	0.198206i
$376$	−4.51639	−	7.82262i	−0.232915	−	0.403421i
$377$	−2.05222	−	2.43385i	−0.105695	−	0.125350i
$378$		0			0
$379$	−5.53128	+	20.6430i	−0.284123	+	1.06036i	0.665355	+	0.746527i	$0.268280\pi$
$379$	−5.53128	+	20.6430i	−0.284123	+	1.06036i	−0.949478	+	0.313834i	$0.898387\pi$
$380$	−0.831920	+	1.44093i	−0.0426766	+	0.0739180i
$381$	−8.74488	−	15.1466i	−0.448014	−	0.775982i
$382$	−10.8668	+	2.91174i	−0.555992	+	0.148978i
$383$	12.6750	−	12.6750i	0.647662	−	0.647662i	−0.304765	−	0.952427i	$-0.598578\pi$
$383$	12.6750	−	12.6750i	0.647662	−	0.647662i	0.952427	+	0.304765i	$0.0985781\pi$
$384$	10.8223	−	2.89981i	0.552271	−	0.147981i
$385$		0			0
$386$	18.4908	−	32.0270i	0.941156	−	1.63013i
$387$	1.49855	+	0.865189i	0.0761757	+	0.0439800i
$388$	−0.610801	−	0.610801i	−0.0310087	−	0.0310087i
$389$	4.21022	+	2.43077i	0.213467	+	0.123245i	0.602921	−	0.797801i	$-0.294003\pi$
$389$	4.21022	+	2.43077i	0.213467	+	0.123245i	−0.389455	+	0.921046i	$0.627337\pi$
$390$	2.69553	+	15.0754i	0.136493	+	0.763370i
$391$			32.8505i			1.66132i
$392$		0			0
$393$	1.26118	+	2.18443i	0.0636182	+	0.110190i
$394$		−	25.4454i		−	1.28192i
$395$	7.00470	+	26.1419i	0.352445	+	1.31534i
$396$	0.0643221	−	0.240053i	0.00323231	−	0.0120631i
$397$	13.8333	+	13.8333i	0.694275	+	0.694275i	0.963170	−	0.268895i	$-0.0866584\pi$
$397$	13.8333	+	13.8333i	0.694275	+	0.694275i	−0.268895	+	0.963170i	$0.586658\pi$
$398$	12.4091	+	12.4091i	0.622014	+	0.622014i
$399$		0			0
$400$	−10.6570	+	6.15281i	−0.532849	+	0.307640i
$401$	−1.11204	−	4.15019i	−0.0555327	−	0.207251i	0.932585	−	0.360951i	$-0.117548\pi$
$401$	−1.11204	−	4.15019i	−0.0555327	−	0.207251i	−0.988118	+	0.153700i	$0.950881\pi$
$402$	−0.762518	+	1.32072i	−0.0380309	+	0.0658715i
$403$	−1.40524	−	2.99475i	−0.0699998	−	0.149179i
$404$	−0.533387	+	0.307951i	−0.0265370	+	0.0153212i
$405$	0.0637454	+	0.0170805i	0.00316753	+	0.000848738i
$406$		0			0
$407$	−9.21022	−	5.31752i	−0.456534	−	0.263580i
$408$	−3.36760	+	12.5681i	−0.166721	+	0.622212i
$409$	−29.2989	−	7.85062i	−1.44874	−	0.388188i	−0.553154	−	0.833079i	$-0.686576\pi$
$409$	−29.2989	−	7.85062i	−1.44874	−	0.388188i	−0.895585	+	0.444891i	$0.853242\pi$
$410$	−45.4491	−	12.1781i	−2.24457	−	0.601432i
$411$	2.88212	−	10.7562i	0.142164	−	0.530565i
$412$	0.802586	+	0.463373i	0.0395406	+	0.0228288i
$413$		0			0
$414$	−19.3113	−	5.17444i	−0.949098	−	0.254310i
$415$	5.41415	−	3.12586i	0.265770	−	0.153442i
$416$	−0.162434	+	1.90942i	−0.00796397	+	0.0936170i
$417$	3.30033	−	5.71634i	0.161618	−	0.279930i
$418$	−3.14613	−	11.7415i	−0.153882	−	0.574297i
$419$	6.87240	−	3.96778i	0.335739	−	0.193839i	−0.322647	−	0.946519i	$-0.604573\pi$
$419$	6.87240	−	3.96778i	0.335739	−	0.193839i	0.658386	+	0.752680i	$0.271239\pi$
$420$		0			0
$421$	−5.98090	−	5.98090i	−0.291491	−	0.291491i	0.546178	−	0.837669i	$-0.316082\pi$
$421$	−5.98090	−	5.98090i	−0.291491	−	0.291491i	−0.837669	+	0.546178i	$0.816082\pi$
$422$	−4.42143	−	4.42143i	−0.215232	−	0.215232i
$423$	−1.49660	+	5.58539i	−0.0727672	+	0.271571i
$424$	−1.88918	−	7.05053i	−0.0917469	−	0.342404i
$425$		−	13.5840i		−	0.658922i
$426$	2.14515	+	3.71551i	0.103933	+	0.180017i
$427$		0			0
$428$		−	0.996159i		−	0.0481511i
$429$	4.52934	+	3.15530i	0.218678	+	0.152339i
$430$	−3.20811	−	1.85221i	−0.154709	−	0.0893213i
$431$	0.409100	+	0.409100i	0.0197057	+	0.0197057i	0.716891	−	0.697185i	$-0.245565\pi$
$431$	0.409100	+	0.409100i	0.0197057	+	0.0197057i	−0.697185	+	0.716891i	$0.745565\pi$
$432$	−17.1274	−	9.88850i	−0.824042	−	0.475761i
$433$	−4.11334	+	7.12452i	−0.197675	+	0.342382i	−0.947774	−	0.318943i	$-0.896672\pi$
$433$	−4.11334	+	7.12452i	−0.197675	+	0.342382i	0.750099	+	0.661325i	$0.230006\pi$
$434$		0			0
$435$	2.62399	−	0.703095i	0.125810	−	0.0337108i
$436$	1.09729	−	1.09729i	0.0525509	−	0.0525509i
$437$	46.6014	−	12.4868i	2.22925	−	0.597325i
$438$	2.10807	+	3.65128i	0.100727	+	0.174465i
$439$	−6.36168	+	11.0188i	−0.303626	+	0.525896i	−0.976955	−	0.213447i	$-0.931531\pi$
$439$	−6.36168	+	11.0188i	−0.303626	+	0.525896i	0.673328	+	0.739344i	$0.264864\pi$
$440$	−3.06645	+	11.4441i	−0.146187	+	0.545578i
$441$		0			0
$442$	17.1468	+	11.9451i	0.815591	+	0.568169i
$443$	1.11534	+	1.93182i	0.0529912	+	0.0917834i	0.891304	−	0.453406i	$-0.149791\pi$
$443$	1.11534	+	1.93182i	0.0529912	+	0.0917834i	−0.838313	+	0.545189i	$0.816458\pi$
$444$	0.530865	−	0.530865i	0.0251938	−	0.0251938i
$445$	−14.1338			−0.670005
$446$	−32.1282			−1.52132
$447$	−6.59996	+	6.59996i	−0.312167	+	0.312167i
$448$		0			0
$449$	10.0883	+	37.6500i	0.476096	+	1.77682i	0.617184	+	0.786819i	$0.288273\pi$
$449$	10.0883	+	37.6500i	0.476096	+	1.77682i	−0.141088	+	0.989997i	$0.545060\pi$
$450$	7.98542	+	2.13969i	0.376436	+	0.100866i
$451$	−14.6877	+	8.47994i	−0.691616	+	0.399305i
$452$		−	0.0605803i		−	0.00284946i
$453$	−13.9886	+	3.74823i	−0.657242	+	0.176107i
$454$	14.3906			0.675387
$455$		0			0
$456$	19.1090			0.894862
$457$	−22.2431	+	5.96003i	−1.04049	+	0.278798i	−0.738316	−	0.674455i	$-0.764379\pi$
$457$	−22.2431	+	5.96003i	−1.04049	+	0.278798i	−0.302174	+	0.953253i	$0.597712\pi$
$458$			2.66273i			0.124421i
$459$	18.9067	−	10.9158i	0.882490	−	0.509506i
$460$	−2.03967	−	0.546528i	−0.0951002	−	0.0254820i
$461$	−7.81461	−	29.1645i	−0.363962	−	1.35833i	−0.868822	−	0.495125i	$-0.835122\pi$
$461$	−7.81461	−	29.1645i	−0.363962	−	1.35833i	0.504859	−	0.863202i	$-0.331544\pi$
$462$		0			0
$463$	2.19856	−	2.19856i	0.102176	−	0.102176i	−0.654171	−	0.756347i	$-0.726982\pi$
$463$	2.19856	−	2.19856i	0.102176	−	0.102176i	0.756347	+	0.654171i	$0.226982\pi$
$464$	−3.35801			−0.155892
$465$	2.82275			0.130902
$466$	8.39083	−	8.39083i	0.388698	−	0.388698i
$467$	−10.5856	−	18.3348i	−0.489844	−	0.848434i	0.510088	−	0.860122i	$-0.329613\pi$
$467$	−10.5856	−	18.3348i	−0.489844	−	0.848434i	−0.999932	+	0.0116879i	$0.996280\pi$
$468$	0.479694	−	0.404478i	0.0221739	−	0.0186970i
$469$		0			0
$470$	3.20394	−	11.9573i	0.147787	−	0.551547i
$471$	−3.63416	+	6.29455i	−0.167453	+	0.290038i
$472$	8.46043	+	14.6539i	0.389423	+	0.674500i
$473$	−1.28974	+	0.345586i	−0.0593025	+	0.0158901i
$474$	9.86978	−	9.86978i	0.453334	−	0.453334i
$475$	−19.2702	+	5.16343i	−0.884176	+	0.236914i
$476$		0			0
$477$	−2.33634	+	4.04666i	−0.106974	+	0.185284i
$478$	−10.9086	−	6.29809i	−0.498948	−	0.288068i
$479$	−16.9808	−	16.9808i	−0.775871	−	0.775871i	0.203255	−	0.979126i	$-0.434848\pi$
$479$	−16.9808	−	16.9808i	−0.775871	−	0.775871i	−0.979126	+	0.203255i	$0.934848\pi$
$480$	−1.41611	−	0.817593i	−0.0646364	−	0.0373179i
$481$	−11.4062	−	24.3081i	−0.520077	−	1.10835i
$482$			6.02432i			0.274400i
$483$		0			0
$484$	−0.421303	−	0.729719i	−0.0191501	−	0.0331690i
$485$		−	26.3620i		−	1.19704i
$486$	5.56560	+	20.7711i	0.252461	+	0.942196i
$487$	−8.81975	+	32.9158i	−0.399661	+	1.49156i	0.414032	+	0.910262i	$0.364120\pi$
$487$	−8.81975	+	32.9158i	−0.399661	+	1.49156i	−0.813694	+	0.581294i	$0.802547\pi$
$488$	0.174593	+	0.174593i	0.00790344	+	0.00790344i
$489$	−8.28165	−	8.28165i	−0.374509	−	0.374509i
$490$		0			0
$491$	12.2688	−	7.08337i	0.553681	−	0.319668i	−0.196924	−	0.980419i	$-0.563095\pi$
$491$	12.2688	−	7.08337i	0.553681	−	0.319668i	0.750605	+	0.660751i	$0.229762\pi$
$492$	−0.309869	−	1.15645i	−0.0139700	−	0.0521367i
$493$	1.85343	−	3.21024i	0.0834745	−	0.144582i
$494$	10.4275	−	28.8648i	0.469156	−	1.29869i
$495$	6.56838	−	3.79226i	0.295227	−	0.170449i
$496$	−3.37039	−	0.903094i	−0.151335	−	0.0405501i
$497$		0			0
$498$	−2.79228	−	1.61213i	−0.125125	−	0.0722411i
$499$	−7.71779	+	28.8032i	−0.345496	+	1.28941i	0.546536	+	0.837436i	$0.315946\pi$
$499$	−7.71779	+	28.8032i	−0.345496	+	1.28941i	−0.892032	+	0.451972i	$0.850721\pi$
$500$	−0.459891	−	0.123227i	−0.0205670	−	0.00551090i
$501$	−18.8602	−	5.05358i	−0.842613	−	0.225777i
$502$	−1.62903	+	6.07962i	−0.0727072	+	0.271347i
$503$	−11.8147	−	6.82122i	−0.526791	−	0.304143i	0.212918	−	0.977070i	$-0.431703\pi$
$503$	−11.8147	−	6.82122i	−0.526791	−	0.304143i	−0.739709	+	0.672927i	$0.765037\pi$
$504$		0			0
$505$	−18.1560	−	4.86488i	−0.807930	−	0.216484i
$506$	13.3603	−	7.71358i	0.593938	−	0.342910i
$507$	4.82952	+	13.0733i	0.214487	+	0.580607i
$508$	0.767040	−	1.32855i	0.0340319	−	0.0589450i
$509$	0.690957	+	2.57869i	0.0306261	+	0.114298i	0.979547	−	0.201216i	$-0.0644895\pi$
$509$	0.690957	+	2.57869i	0.0306261	+	0.114298i	−0.948921	+	0.315515i	$0.897823\pi$
$510$	−15.4426	+	8.91581i	−0.683812	+	0.394799i
$511$		0			0
$512$	16.9779	+	16.9779i	0.750326	+	0.750326i
$513$	−22.6717	−	22.6717i	−1.00098	−	1.00098i
$514$	3.08483	−	11.5127i	0.136066	−	0.507806i
$515$	7.32016	+	27.3192i	0.322565	+	1.20383i
$516$		−	0.0942584i		−	0.00414949i
$517$	−2.23099	−	3.86419i	−0.0981190	−	0.169947i
$518$		0			0
$519$		−	21.6045i		−	0.948331i
$520$	−22.8686	+	19.2828i	−1.00286	+	0.845607i
$521$	13.4638	+	7.77333i	0.589860	+	0.340556i	0.765042	−	0.643980i	$-0.222718\pi$
$521$	13.4638	+	7.77333i	0.589860	+	0.340556i	−0.175182	+	0.984536i	$0.556052\pi$
$522$	1.59521	+	1.59521i	0.0698204	+	0.0698204i
$523$	−0.102601	−	0.0592367i	−0.00448643	−	0.00259024i	0.497755	−	0.867318i	$-0.334158\pi$
$523$	−0.102601	−	0.0592367i	−0.00448643	−	0.00259024i	−0.502242	+	0.864727i	$0.667491\pi$
$524$	−0.110622	+	0.191603i	−0.00483255	+	0.00837022i
$525$		0			0
$526$	−17.4197	+	4.66758i	−0.759533	+	0.203516i
$527$	2.72362	−	2.72362i	0.118643	−	0.118643i
$528$	5.62407	−	1.50696i	0.244756	−	0.0655822i
$529$	19.1147	+	33.1077i	0.831075	+	1.43946i
$530$	5.00166	−	8.66313i	0.217258	−	0.376302i
$531$	2.80354	−	10.4630i	0.121663	−	0.454053i
$532$		0			0
$533$	−42.6658	−	3.62957i	−1.84806	−	0.157214i
$534$	3.64466	+	6.31274i	0.157720	+	0.273179i
$535$	21.4970	−	21.4970i	0.929395	−	0.929395i
$536$	−2.97880			−0.128665
$537$	17.7236			0.764830
$538$	−12.2592	+	12.2592i	−0.528534	+	0.528534i
$539$		0			0
$540$	0.363209	+	1.35551i	0.0156300	+	0.0583320i
$541$	4.47060	+	1.19789i	0.192206	+	0.0515014i	0.353638	−	0.935382i	$-0.384945\pi$
$541$	4.47060	+	1.19789i	0.192206	+	0.0515014i	−0.161432	+	0.986884i	$0.551611\pi$
$542$	5.51652	−	3.18496i	0.236955	−	0.136806i
$543$		−	14.6763i		−	0.629819i
$544$	−2.15526	+	0.577501i	−0.0924062	+	0.0247602i
$545$	47.3589			2.02863
$546$		0			0
$547$	29.4860			1.26073			0.630365	−	0.776299i	$-0.282905\pi$
$547$	29.4860			1.26073			0.630365	+	0.776299i	$0.282905\pi$
$548$	0.943461	−	0.252800i	0.0403026	−	0.0107991i
$549$		−	0.158063i		−	0.00674594i
$550$	−5.52463	+	3.18965i	−0.235571	+	0.136007i
$551$	−5.25853	−	1.40902i	−0.224021	−	0.0600263i
$552$	6.27682	+	23.4254i	0.267159	+	0.997052i
$553$		0			0
$554$	1.63267	−	1.63267i	0.0693657	−	0.0693657i
$555$	22.9120			0.972561
$556$	0.578964			0.0245536
$557$	0.959258	−	0.959258i	0.0406451	−	0.0406451i	−0.686492	−	0.727137i	$-0.740850\pi$
$557$	0.959258	−	0.959258i	0.0406451	−	0.0406451i	0.727137	+	0.686492i	$0.240850\pi$
$558$	1.17208	+	2.03010i	0.0496181	+	0.0859411i
$559$	−3.17064	−	1.14541i	−0.134104	−	0.0484455i
$560$		0			0
$561$	−1.66352	+	6.20834i	−0.0702338	+	0.262116i
$562$	−13.5946	+	23.5465i	−0.573453	+	0.993249i
$563$	16.4050	+	28.4143i	0.691388	+	1.19752i	0.971383	+	0.237517i	$0.0763337\pi$
$563$	16.4050	+	28.4143i	0.691388	+	1.19752i	−0.279995	+	0.960001i	$0.590333\pi$
$564$	0.304251	−	0.0815238i	0.0128113	−	0.00343277i
$565$	1.30731	−	1.30731i	0.0549991	−	0.0549991i
$566$	−43.9982	+	11.7893i	−1.84938	+	0.495541i
$567$		0			0
$568$	−4.19005	+	7.25739i	−0.175811	+	0.304513i
$569$	25.8745	+	14.9387i	1.08472	+	0.626261i	0.932165	−	0.362034i	$-0.117918\pi$
$569$	25.8745	+	14.9387i	1.08472	+	0.626261i	0.152552	+	0.988296i	$0.451251\pi$
$570$	18.5178	+	18.5178i	0.775626	+	0.775626i
$571$	−0.640877	−	0.370010i	−0.0268198	−	0.0154844i	0.486530	−	0.873664i	$-0.338262\pi$
$571$	−0.640877	−	0.370010i	−0.0268198	−	0.0154844i	−0.513350	+	0.858179i	$0.671596\pi$
$572$	−0.0410408	+	0.482437i	−0.00171600	+	0.0201717i
$573$		−	8.73616i		−	0.364958i
$574$		0			0
$575$	−12.6595	−	21.9269i	−0.527938	−	0.914416i
$576$		−	15.4345i		−	0.643104i
$577$	−8.82812	−	32.9470i	−0.367519	−	1.37160i	−0.863973	−	0.503538i	$-0.832031\pi$
$577$	−8.82812	−	32.9470i	−0.367519	−	1.37160i	0.496454	−	0.868063i	$-0.334635\pi$
$578$	−0.223233	+	0.833116i	−0.00928526	+	0.0346531i
$579$	20.3065	+	20.3065i	0.843909	+	0.843909i
$580$	0.168487	+	0.168487i	0.00699605	+	0.00699605i
$581$		0			0
$582$	−11.7744	+	6.79795i	−0.488064	+	0.281784i
$583$	−0.933213	−	3.48280i	−0.0386498	−	0.144243i
$584$	−4.11762	+	7.13193i	−0.170388	+	0.295121i
$585$	19.0803	+	1.62316i	0.788874	+	0.0671093i
$586$	26.2559	−	15.1588i	1.08462	−	0.626206i
$587$	−11.9740	−	3.20842i	−0.494219	−	0.132426i	0.00309648	−	0.999995i	$-0.499014\pi$
$587$	−11.9740	−	3.20842i	−0.494219	−	0.132426i	−0.497316	+	0.867569i	$0.665681\pi$
$588$		0			0
$589$	−4.89899	−	2.82843i	−0.201859	−	0.116543i
$590$	−6.00184	+	22.3992i	−0.247092	+	0.922160i
$591$	19.0861	+	5.11412i	0.785099	+	0.210367i
$592$	−27.3572	−	7.33034i	−1.12437	−	0.301275i
$593$	5.91611	−	22.0792i	0.242945	−	0.906685i	−0.731460	−	0.681885i	$-0.761161\pi$
$593$	5.91611	−	22.0792i	0.242945	−	0.906685i	0.974405	−	0.224800i	$-0.0721728\pi$
$594$	−8.87892	−	5.12625i	−0.364307	−	0.210333i
$595$		0			0
$596$	−0.790795	−	0.211893i	−0.0323922	−	0.00867948i
$597$	−11.8019	+	6.81383i	−0.483019	+	0.278871i
$598$	38.8100	+	3.30156i	1.58706	+	0.135011i
$599$	−1.24701	+	2.15989i	−0.0509516	+	0.0882508i	−0.890376	−	0.455225i	$-0.849559\pi$
$599$	−1.24701	+	2.15989i	−0.0509516	+	0.0882508i	0.839425	+	0.543476i	$0.182892\pi$
$600$	−2.59553	−	9.68666i	−0.105962	−	0.395456i
$601$	18.5873	−	10.7314i	0.758193	−	0.437743i	−0.0704537	−	0.997515i	$-0.522445\pi$
$601$	18.5873	−	10.7314i	0.758193	−	0.437743i	0.828647	+	0.559772i	$0.189111\pi$
$602$		0			0
$603$	1.34839	+	1.34839i	0.0549106	+	0.0549106i
$604$	−0.898214	−	0.898214i	−0.0365478	−	0.0365478i
$605$	6.65556	−	24.8389i	0.270587	−	1.00984i
$606$	2.50901	+	9.36374i	0.101921	+	0.380376i
$607$			16.0396i			0.651028i	0.945537	+	0.325514i	$0.105537\pi$
$607$			16.0396i			0.651028i	−0.945537	+	0.325514i	$0.894463\pi$
$608$	1.63848	+	2.83793i	0.0664490	+	0.115093i
$609$		0			0
$610$			0.338382i			0.0137007i
$611$	0.954908	−	11.2250i	0.0386314	−	0.454115i
$612$	0.632715	+	0.365298i	0.0255760	+	0.0147663i
$613$	−4.88837	−	4.88837i	−0.197440	−	0.197440i	0.601462	−	0.798901i	$-0.294585\pi$
$613$	−4.88837	−	4.88837i	−0.197440	−	0.197440i	−0.798901	+	0.601462i	$0.794585\pi$
$614$	23.3054	+	13.4554i	0.940530	+	0.543015i
$615$	18.2691	−	31.6429i	0.736680	−	1.27597i
$616$		0			0
$617$	26.9254	−	7.21463i	1.08397	−	0.290450i	0.327751	−	0.944764i	$-0.393709\pi$
$617$	26.9254	−	7.21463i	1.08397	−	0.290450i	0.756223	+	0.654314i	$0.227043\pi$
$618$	10.3143	−	10.3143i	0.414901	−	0.414901i
$619$	13.3912	−	3.58815i	0.538237	−	0.144220i	0.0205475	−	0.999789i	$-0.493459\pi$
$619$	13.3912	−	3.58815i	0.538237	−	0.144220i	0.517689	+	0.855569i	$0.326792\pi$
$620$	0.123796	+	0.214421i	0.00497177	+	0.00861136i
$621$	20.3458	−	35.2399i	0.816448	−	1.41413i
$622$	9.22831	−	34.4405i	0.370022	−	1.38094i
$623$		0			0
$624$	13.8259	+	4.99466i	0.553480	+	0.199947i
$625$	−15.3544	−	26.5946i	−0.614175	−	1.06378i
$626$	−27.9842	+	27.9842i	−1.11847	+	1.11847i
$627$	9.43942			0.376974
$628$	−0.637527			−0.0254401
$629$	22.1074	−	22.1074i	0.881480	−	0.881480i
$630$		0			0
$631$	6.69536	+	24.9874i	0.266538	+	0.994733i	0.961302	+	0.275496i	$0.0888419\pi$
$631$	6.69536	+	24.9874i	0.266538	+	0.994733i	−0.694764	+	0.719237i	$0.744491\pi$
$632$	26.3347	+	7.05636i	1.04754	+	0.280687i
$633$	4.20506	−	2.42779i	0.167136	−	0.0964961i
$634$		−	17.2105i		−	0.683517i
$635$	45.2226	−	12.1174i	1.79460	−	0.480863i
$636$	0.254533			0.0100929
$637$		0			0
$638$	−1.74081			−0.0689193
$639$	5.18181	−	1.38846i	0.204989	−	0.0549267i
$640$			29.9918i			1.18553i
$641$	10.8902	−	6.28745i	0.430136	−	0.248339i	−0.269269	−	0.963065i	$-0.586782\pi$
$641$	10.8902	−	6.28745i	0.430136	−	0.248339i	0.699405	+	0.714726i	$0.253449\pi$
$642$	−15.1449	−	4.05806i	−0.597720	−	0.160159i
$643$	6.40174	+	23.8916i	0.252460	+	0.942193i	0.969486	+	0.245147i	$0.0788361\pi$
$643$	6.40174	+	23.8916i	0.252460	+	0.942193i	−0.717026	+	0.697046i	$0.754497\pi$
$644$		0			0
$645$	2.03408	−	2.03408i	0.0800919	−	0.0800919i
$646$	35.7350			1.40598
$647$	34.6235			1.36119			0.680595	−	0.732660i	$-0.261721\pi$
$647$	34.6235			1.36119			0.680595	+	0.732660i	$0.261721\pi$
$648$	0.0470090	−	0.0470090i	0.00184669	−	0.00184669i
$649$	4.17926	+	7.23869i	0.164050	+	0.284143i
$650$	−16.0483	−	1.36523i	−0.629468	−	0.0535487i
$651$		0			0
$652$	0.265884	−	0.992293i	0.0104128	−	0.0388612i
$653$	13.7001	−	23.7293i	0.536127	−	0.928600i	−0.462980	−	0.886368i	$-0.653220\pi$
$653$	13.7001	−	23.7293i	0.536127	−	0.928600i	0.999108	−	0.0422314i	$-0.0134467\pi$
$654$	−12.2124	−	21.1525i	−0.477543	−	0.827129i
$655$	−6.52198	+	1.74756i	−0.254835	+	0.0682828i
$656$	−31.9371	+	31.9371i	−1.24694	+	1.24694i
$657$	5.09224	−	1.36446i	0.198667	−	0.0532327i
$658$		0			0
$659$	2.14617	−	3.71728i	0.0836031	−	0.144805i	−0.821192	−	0.570652i	$-0.806691\pi$
$659$	2.14617	−	3.71728i	0.0836031	−	0.144805i	0.904795	+	0.425847i	$0.140024\pi$
$660$	−0.357797	−	0.206574i	−0.0139272	−	0.00804090i
$661$	10.7570	+	10.7570i	0.418399	+	0.418399i	0.884652	−	0.466252i	$-0.154396\pi$
$661$	10.7570	+	10.7570i	0.418399	+	0.418399i	−0.466252	+	0.884652i	$0.654396\pi$
$662$	35.8115	+	20.6758i	1.39185	+	0.803586i
$663$	−12.4060	+	10.4607i	−0.481809	+	0.406261i
$664$		−	6.29783i		−	0.244403i
$665$		0			0
$666$	9.51367	+	16.4782i	0.368647	+	0.638516i
$667$		−	6.90917i		−	0.267524i
$668$	−0.443265	−	1.65429i	−0.0171504	−	0.0640063i
$669$	6.45725	−	24.0988i	0.249652	−	0.931713i
$670$	−2.88664	−	2.88664i	−0.111521	−	0.111521i
$671$	0.0862447	+	0.0862447i	0.00332944	+	0.00332944i
$672$		0			0
$673$	26.3013	−	15.1851i	1.01384	−	0.585341i	0.101526	−	0.994833i	$-0.467627\pi$
$673$	26.3013	−	15.1851i	1.01384	−	0.585341i	0.912314	+	0.409492i	$0.134294\pi$
$674$	−4.80243	−	17.9229i	−0.184983	−	0.690365i
$675$	−8.41319	+	14.5721i	−0.323824	+	0.560879i
$676$	−0.781267	+	0.940210i	−0.0300487	+	0.0361619i
$677$	31.7593	−	18.3363i	1.22061	−	0.704720i	0.255562	−	0.966793i	$-0.417739\pi$
$677$	31.7593	−	18.3363i	1.22061	−	0.704720i	0.965048	+	0.262073i	$0.0844060\pi$
$678$	−0.921018	−	0.246786i	−0.0353715	−	0.00947776i
$679$		0			0
$680$	−30.1636	−	17.4150i	−1.15672	−	0.667834i
$681$	−2.89228	+	10.7942i	−0.110833	+	0.413633i
$682$	−1.74723	−	0.468169i	−0.0669049	−	0.0179271i
$683$	−15.4630	−	4.14330i	−0.591676	−	0.158539i	−0.0494567	−	0.998776i	$-0.515749\pi$
$683$	−15.4630	−	4.14330i	−0.591676	−	0.158539i	−0.542219	+	0.840237i	$0.682416\pi$
$684$	0.277707	−	1.03642i	0.0106184	−	0.0396284i
$685$	25.8151	+	14.9044i	0.986346	+	0.569467i
$686$		0			0
$687$	−1.99727	−	0.535166i	−0.0762005	−	0.0204179i
$688$	−3.07949	+	1.77794i	−0.117404	+	0.0677835i
$689$	3.09303	−	8.56194i	0.117835	−	0.326184i
$690$	−16.6180	+	28.7833i	−0.632638	+	1.09576i
$691$	4.67596	+	17.4509i	0.177882	+	0.663864i	0.996043	+	0.0888748i	$0.0283271\pi$
$691$	4.67596	+	17.4509i	0.177882	+	0.663864i	−0.818161	+	0.574989i	$0.805006\pi$
$692$	1.64111	−	0.947497i	0.0623858	−	0.0360184i
$693$		0			0
$694$	14.1538	+	14.1538i	0.537270	+	0.537270i
$695$	12.4940	+	12.4940i	0.473923	+	0.473923i
$696$	0.708280	−	2.64334i	0.0268473	−	0.100195i
$697$	−12.9042	−	48.1592i	−0.488783	−	1.82416i
$698$		−	30.3094i		−	1.14723i
$699$	4.60738	+	7.98022i	0.174267	+	0.301840i
$700$		0			0
$701$			37.6363i			1.42150i	0.703444	+	0.710751i	$0.251645\pi$
$701$			37.6363i			1.42150i	−0.703444	+	0.710751i	$0.748355\pi$
$702$	−10.9959	−	23.4337i	−0.415013	−	0.884448i
$703$	−39.7646	−	22.9581i	−1.49975	−	0.865882i
$704$	8.42163	+	8.42163i	0.317402	+	0.317402i
$705$	8.32497	+	4.80642i	0.313537	+	0.181020i
$706$	−7.97086	+	13.8059i	−0.299987	+	0.519593i
$707$		0			0
$708$	−0.569945	+	0.152716i	−0.0214198	+	0.00573943i
$709$	−8.15239	+	8.15239i	−0.306169	+	0.306169i	−0.843422	−	0.537252i	$-0.819462\pi$
$709$	−8.15239	+	8.15239i	−0.306169	+	0.306169i	0.537252	+	0.843422i	$0.319462\pi$
$710$	−11.0933	+	2.97243i	−0.416323	+	0.111553i
$711$	−8.72655	−	15.1148i	−0.327271	−	0.566850i
$712$	−7.11900	+	12.3305i	−0.266796	+	0.462104i
$713$	1.85813	−	6.93465i	0.0695876	−	0.259705i
$714$		0			0
$715$	−11.2966	+	9.52526i	−0.422468	+	0.356225i
$716$	0.777296	+	1.34632i	0.0290489	+	0.0503142i
$717$	6.91652	−	6.91652i	0.258302	−	0.258302i
$718$	1.23201			0.0459782
$719$	46.1930			1.72271			0.861355	−	0.508004i	$-0.169616\pi$
$719$	46.1930			1.72271			0.861355	+	0.508004i	$0.169616\pi$
$720$	14.2824	−	14.2824i	0.532273	−	0.532273i
$721$		0			0
$722$	−6.79424	−	25.3564i	−0.252855	−	0.943669i
$723$	−4.51873	−	1.21079i	−0.168053	−	0.0450298i
$724$	1.11484	−	0.643651i	0.0414325	−	0.0239211i
$725$			2.85702i			0.106107i
$726$	−12.8104	+	3.43253i	−0.475438	+	0.127393i
$727$	−3.27502			−0.121464			−0.0607318	−	0.998154i	$-0.519343\pi$
$727$	−3.27502			−0.121464			−0.0607318	+	0.998154i	$0.519343\pi$
$728$		0			0
$729$	−16.7676			−0.621022
$730$	−10.9015	+	2.92105i	−0.403483	+	0.108113i
$731$		−	3.92530i		−	0.145183i
$732$	−0.00745656	+	0.00430505i	−0.000275602	+	0.000159119i
$733$	−32.5986	−	8.73478i	−1.20406	−	0.322626i	−0.399630	−	0.916676i	$-0.630861\pi$
$733$	−32.5986	−	8.73478i	−1.20406	−	0.322626i	−0.804428	+	0.594050i	$0.797528\pi$
$734$	5.17148	+	19.3002i	0.190883	+	0.712384i
$735$		0			0
$736$	−2.94077	+	2.94077i	−0.108398	+	0.108398i
$737$	−1.47146			−0.0542020
$738$	30.3432			1.11695
$739$	−1.49619	+	1.49619i	−0.0550382	+	0.0550382i	−0.734090	−	0.679052i	$-0.762391\pi$
$739$	−1.49619	+	1.49619i	−0.0550382	+	0.0550382i	0.679052	+	0.734090i	$0.262391\pi$
$740$	1.00484	+	1.74044i	0.0369387	+	0.0639797i
$741$	19.5552	+	13.6228i	0.718377	+	0.500447i
$742$		0			0
$743$	−7.14174	+	26.6533i	−0.262005	+	0.977816i	0.702053	+	0.712125i	$0.252267\pi$
$743$	−7.14174	+	26.6533i	−0.262005	+	0.977816i	−0.964058	+	0.265692i	$0.914400\pi$
$744$	1.42178	−	2.46260i	0.0521251	−	0.0902834i
$745$	−12.4926	−	21.6379i	−0.457695	−	0.792751i
$746$	27.9066	−	7.47755i	1.02173	−	0.273773i
$747$	−2.85078	+	2.85078i	−0.104305	+	0.104305i
$748$	−0.544552	+	0.145912i	−0.0199108	+	0.00533508i
$749$		0			0
$750$	−3.74692	+	6.48986i	−0.136818	+	0.236976i
$751$	6.52544	+	3.76747i	0.238117	+	0.137477i	0.614311	−	0.789064i	$-0.289434\pi$
$751$	6.52544	+	3.76747i	0.238117	+	0.137477i	−0.376194	+	0.926541i	$0.622767\pi$
$752$	−8.40237	−	8.40237i	−0.306403	−	0.306403i
$753$	−4.23280	−	2.44381i	−0.154252	−	0.0890574i
$754$	−3.60635	−	2.51231i	−0.131335	−	0.0914929i
$755$		−	38.7667i		−	1.41086i
$756$		0			0
$757$	−21.0971	−	36.5412i	−0.766786	−	1.32811i	−0.939297	−	0.343104i	$-0.888522\pi$
$757$	−21.0971	−	36.5412i	−0.766786	−	1.32811i	0.172512	−	0.985007i	$-0.444812\pi$
$758$			29.5044i			1.07165i
$759$	3.10061	+	11.5716i	0.112545	+	0.420023i
$760$	−13.2392	+	49.4095i	−0.480237	+	1.79227i
$761$	1.20610	+	1.20610i	0.0437212	+	0.0437212i	0.728629	−	0.684908i	$-0.240158\pi$
$761$	1.20610	+	1.20610i	0.0437212	+	0.0437212i	−0.684908	+	0.728629i	$0.740158\pi$
$762$	−17.0736	−	17.0736i	−0.618513	−	0.618513i
$763$		0			0
$764$	0.663614	−	0.383138i	0.0240087	−	0.0138614i
$765$	5.77082	+	21.5370i	0.208644	+	0.778671i
$766$	12.3734	−	21.4314i	0.447070	−	0.774349i
$767$	−1.78880	+	21.0275i	−0.0645899	+	0.759258i
$768$	−2.09061	+	1.20702i	−0.0754385	+	0.0435545i
$769$	−3.49612	−	0.936782i	−0.126073	−	0.0337812i	0.195231	−	0.980757i	$-0.437454\pi$
$769$	−3.49612	−	0.936782i	−0.126073	−	0.0337812i	−0.321304	+	0.946976i	$0.604121\pi$
$770$		0			0
$771$	8.01550	+	4.62775i	0.288671	+	0.166664i
$772$	−0.651944	+	2.43309i	−0.0234640	+	0.0875688i
$773$	−25.8153	−	6.91718i	−0.928510	−	0.248794i	−0.237291	−	0.971439i	$-0.576259\pi$
$773$	−25.8153	−	6.91718i	−0.928510	−	0.248794i	−0.691219	+	0.722645i	$0.742926\pi$
$774$	2.30750	+	0.618294i	0.0829415	+	0.0222241i
$775$	−0.768358	+	2.86755i	−0.0276002	+	0.103005i
$776$	−22.9985	−	13.2782i	−0.825600	−	0.476660i
$777$		0			0
$778$	6.48299	+	1.73711i	0.232426	+	0.0622785i
$779$	−63.4133	+	36.6117i	−2.27202	+	1.31175i
$780$	−0.443106	−	0.944317i	−0.0158657	−	0.0338120i
$781$	−2.06979	+	3.58498i	−0.0740629	+	0.128281i
$782$	11.7380	+	43.8069i	0.419751	+	1.56653i
$783$	−3.97649	+	2.29583i	−0.142108	+	0.0820463i
$784$		0			0
$785$	−13.7577	−	13.7577i	−0.491035	−	0.491035i
$786$	2.46235	+	2.46235i	0.0878292	+	0.0878292i
$787$	−11.3925	+	42.5173i	−0.406098	+	1.51558i	0.395923	+	0.918284i	$0.370425\pi$
$787$	−11.3925	+	42.5173i	−0.406098	+	1.51558i	−0.802021	+	0.597296i	$0.796242\pi$
$788$	0.448575	+	1.67410i	0.0159798	+	0.0596375i
$789$		−	14.0043i		−	0.498565i
$790$	18.6819	+	32.3580i	0.664672	+	1.15124i
$791$		0			0
$792$		−	7.64045i		−	0.271492i
$793$	0.0542018	+	0.303136i	0.00192476	+	0.0107647i
$794$	23.3900	+	13.5042i	0.830079	+	0.479246i
$795$	5.49280	+	5.49280i	0.194809	+	0.194809i
$796$	−1.03518	−	0.597662i	−0.0366910	−	0.0211836i
$797$	−6.94770	+	12.0338i	−0.246100	+	0.426258i	−0.962440	−	0.271493i	$-0.912483\pi$
$797$	−6.94770	+	12.0338i	−0.246100	+	0.426258i	0.716340	+	0.697751i	$0.245816\pi$
$798$		0			0
$799$	12.6703	−	3.39499i	0.448241	−	0.120106i
$800$	1.21604	−	1.21604i	0.0429934	−	0.0429934i
$801$	8.80402	−	2.35903i	0.311075	−	0.0833522i
$802$	−2.96587	−	5.13704i	−0.104728	−	0.181395i
$803$	−2.03401	+	3.52301i	−0.0717787	+	0.124324i
$804$	0.0268847	−	0.100335i	0.000948150	−	0.00353854i
$805$		0			0
$806$	−2.94399	−	3.49146i	−0.103698	−	0.122981i
$807$	−6.73152	−	11.6593i	−0.236961	−	0.410428i
$808$	−13.3891	+	13.3891i	−0.471028	+	0.471028i
$809$	−44.4045			−1.56118			−0.780589	−	0.625045i	$-0.785081\pi$
$809$	−44.4045			−1.56118			−0.780589	+	0.625045i	$0.785081\pi$
$810$	0.0911092			0.00320125
$811$	9.49597	−	9.49597i	0.333449	−	0.333449i	−0.520446	−	0.853895i	$-0.674234\pi$
$811$	9.49597	−	9.49597i	0.333449	−	0.333449i	0.853895	+	0.520446i	$0.174234\pi$
$812$		0			0
$813$	1.28025	+	4.77796i	0.0449004	+	0.167570i
$814$	−14.1821	−	3.80008i	−0.497083	−	0.133193i
$815$	27.1513	−	15.6758i	0.951068	−	0.549099i
$816$			17.1167i			0.599204i
$817$	−5.56840	+	1.49205i	−0.194814	+	0.0522002i
$818$	−41.8760			−1.46416
$819$		0			0
$820$	3.20487			0.111919
$821$	−49.6560	+	13.3053i	−1.73301	+	0.464358i	−0.980873	−	0.194651i	$-0.937643\pi$
$821$	−49.6560	+	13.3053i	−1.73301	+	0.464358i	−0.752135	+	0.659009i	$0.770976\pi$
$822$		−	15.3735i		−	0.536213i
$823$	−22.4979	+	12.9892i	−0.784227	+	0.452774i	−0.837926	−	0.545783i	$-0.816232\pi$
$823$	−22.4979	+	12.9892i	−0.784227	+	0.452774i	0.0536991	+	0.998557i	$0.482899\pi$
$824$	27.5207	+	7.37415i	0.958729	+	0.256891i
$825$	−1.28213	−	4.78499i	−0.0446382	−	0.166592i
$826$		0			0
$827$	−1.05853	+	1.05853i	−0.0368089	+	0.0368089i	−0.725272	−	0.688463i	$-0.758286\pi$
$827$	−1.05853	+	1.05853i	−0.0368089	+	0.0368089i	0.688463	+	0.725272i	$0.258286\pi$
$828$	1.36175			0.0473239
$829$	−14.6896			−0.510192			−0.255096	−	0.966916i	$-0.582107\pi$
$829$	−14.6896			−0.510192			−0.255096	+	0.966916i	$0.582107\pi$
$830$	6.10298	−	6.10298i	0.211837	−	0.211837i
$831$	0.896497	+	1.55278i	0.0310991	+	0.0538653i
$832$	5.29270	+	29.6006i	0.183491	+	1.02622i
$833$		0			0
$834$	2.35853	−	8.80215i	0.0816692	−	0.304794i
$835$	26.1337	−	45.2649i	0.904395	−	1.56646i
$836$	0.413980	+	0.717035i	0.0143178	+	0.0247992i
$837$	−4.60859	+	1.23487i	−0.159296	+	0.0426833i
$838$	7.74676	−	7.74676i	0.267607	−	0.267607i
$839$	−18.7042	+	5.01177i	−0.645740	+	0.173025i	−0.566802	−	0.823854i	$-0.691820\pi$
$839$	−18.7042	+	5.01177i	−0.645740	+	0.173025i	−0.0789379	+	0.996880i	$0.525153\pi$
$840$		0			0
$841$	14.1102	−	24.4396i	0.486558	−	0.842743i
$842$	−10.1128	−	5.83860i	−0.348509	−	0.201211i
$843$	−14.9295	−	14.9295i	−0.514199	−	0.514199i
$844$	0.368839	+	0.212949i	0.0126960	+	0.00733001i
$845$	−37.1493	+	3.42997i	−1.27797	+	0.117995i
$846$			7.98302i			0.274462i
$847$		0			0
$848$	−4.80113	−	8.31579i	−0.164871	−	0.285566i
$849$		−	35.3717i		−	1.21395i
$850$	−4.85380	−	18.1146i	−0.166484	−	0.621327i
$851$	15.0823	−	56.2879i	0.517015	−	1.92953i
$852$	−0.206634	−	0.206634i	−0.00707916	−	0.00707916i
$853$	−16.7852	−	16.7852i	−0.574713	−	0.574713i	0.358728	−	0.933442i	$-0.383210\pi$
$853$	−16.7852	−	16.7852i	−0.574713	−	0.574713i	−0.933442	+	0.358728i	$0.883210\pi$
$854$		0			0
$855$	28.3586	−	16.3729i	0.969845	−	0.559940i
$856$	−7.92647	−	29.5820i	−0.270921	−	1.01109i
$857$	−25.5716	+	44.2913i	−0.873508	+	1.51296i	−0.0151651	+	0.999885i	$0.504827\pi$
$857$	−25.5716	+	44.2913i	−0.873508	+	1.51296i	−0.858343	+	0.513076i	$0.828506\pi$
$858$	7.16743	+	2.58926i	0.244692	+	0.0883958i
$859$	−13.0666	+	7.54398i	−0.445825	+	0.257397i	−0.706065	−	0.708147i	$-0.749532\pi$
$859$	−13.0666	+	7.54398i	−0.445825	+	0.257397i	0.260240	+	0.965544i	$0.416198\pi$
$860$	0.243720	+	0.0653047i	0.00831079	+	0.00222687i
$861$		0			0
$862$	0.691725	+	0.399367i	0.0235602	+	0.0136025i
$863$	−3.41659	+	12.7509i	−0.116302	+	0.434045i	−0.999381	−	0.0351791i	$-0.988800\pi$
$863$	−3.41659	+	12.7509i	−0.116302	+	0.434045i	0.883079	+	0.469225i	$0.155467\pi$
$864$	2.66970	+	0.715345i	0.0908251	+	0.0243365i
$865$	55.8619	+	14.9681i	1.89936	+	0.508932i
$866$	−2.93953	+	10.9705i	−0.0998895	+	0.372793i
$867$	−0.580039	−	0.334885i	−0.0196991	−	0.0113733i
$868$		0			0
$869$	13.0087	+	3.48568i	0.441291	+	0.118244i
$870$	3.24792	−	1.87519i	0.110115	−	0.0635749i
$871$	−3.04835	−	2.12359i	−0.103289	−	0.0719551i
$872$	23.8541	−	41.3165i	0.807802	−	1.39915i
$873$	4.40001	+	16.4211i	0.148918	+	0.555769i
$874$	57.6824	−	33.3030i	1.95114	−	1.12649i
$875$		0			0
$876$	−0.203062	−	0.203062i	−0.00686083	−	0.00686083i
$877$	27.5566	+	27.5566i	0.930519	+	0.930519i	0.997738	−	0.0672193i	$-0.0214127\pi$
$877$	27.5566	+	27.5566i	0.930519	+	0.930519i	−0.0672193	+	0.997738i	$0.521413\pi$
$878$	−4.54627	+	16.9669i	−0.153429	+	0.572606i
$879$	6.09336	+	22.7407i	0.205524	+	0.767025i
$880$			15.5860i			0.525404i
$881$	14.6029	+	25.2929i	0.491983	+	0.852140i	0.999957	−	0.00923231i	$-0.00293878\pi$
$881$	14.6029	+	25.2929i	0.491983	+	0.852140i	−0.507974	+	0.861372i	$0.669605\pi$
$882$		0			0
$883$		−	2.58799i		−	0.0870929i	−0.999051	−	0.0435464i	$-0.986134\pi$
$883$		−	2.58799i		−	0.0870929i	0.999051	−	0.0435464i	$-0.0138656\pi$
$884$	−1.33870	−	0.483610i	−0.0450254	−	0.0162656i
$885$	−15.5949	−	9.00374i	−0.524218	−	0.302657i
$886$	2.17760	+	2.17760i	0.0731579	+	0.0731579i
$887$	−32.6723	−	18.8634i	−1.09703	−	0.633370i	−0.161590	−	0.986858i	$-0.551662\pi$
$887$	−32.6723	−	18.8634i	−1.09703	−	0.633370i	−0.935439	+	0.353488i	$0.884996\pi$
$888$	11.5405	−	19.9887i	0.387274	−	0.670778i
$889$		0			0
$890$	−18.8477	+	5.05023i	−0.631777	+	0.169284i
$891$	0.0232214	−	0.0232214i	0.000777946	−	0.000777946i
$892$	2.11378	−	0.566385i	0.0707745	−	0.0189640i
$893$	−9.63220	−	16.6835i	−0.322329	−	0.558291i
$894$	−6.44293	+	11.1595i	−0.215484	+	0.373229i
$895$	−12.2794	+	45.8273i	−0.410454	+	1.53184i
$896$		0			0
$897$	−10.2766	+	28.4471i	−0.343126	+	0.949821i
$898$	26.9060	+	46.6026i	0.897865	+	1.55515i
$899$	−0.572837	+	0.572837i	−0.0191052	+	0.0191052i
$900$	−0.563096			−0.0187699
$901$	10.5998			0.353131
$902$	−16.5564	+	16.5564i	−0.551267	+	0.551267i
$903$		0			0
$904$	−0.482039	−	1.79900i	−0.0160324	−	0.0598337i
$905$	37.9479	+	10.1681i	1.26143	+	0.337999i
$906$	−17.3148	+	9.99673i	−0.575247	+	0.332119i
$907$		−	51.9116i		−	1.72369i	−0.507168	−	0.861847i	$-0.669308\pi$
$907$		−	51.9116i		−	1.72369i	0.507168	−	0.861847i	$-0.330692\pi$
$908$	−0.946788	+	0.253691i	−0.0314203	+	0.00841904i
$909$	12.1215			0.402044
$910$		0			0
$911$	15.0311			0.498003			0.249002	−	0.968503i	$-0.419898\pi$
$911$	15.0311			0.498003			0.249002	+	0.968503i	$0.419898\pi$
$912$	24.2816	−	6.50624i	0.804044	−	0.215443i
$913$		−	3.11098i		−	0.102958i
$914$	−27.5322	+	15.8957i	−0.910683	+	0.525783i
$915$	−0.253814	−	0.0680092i	−0.00839082	−	0.00224831i
$916$	−0.0469410	−	0.175186i	−0.00155098	−	0.00578832i
$917$		0			0
$918$	21.3122	−	21.3122i	0.703407	−	0.703407i
$919$	3.25134			0.107252			0.0536259	−	0.998561i	$-0.482922\pi$
$919$	3.25134			0.107252			0.0536259	+	0.998561i	$0.482922\pi$
$920$	−64.9190			−2.14031
$921$	−14.7766	+	14.7766i	−0.486907	+	0.486907i
$922$	−20.8420	−	36.0993i	−0.686393	−	1.18887i
$923$	−9.46167	+	4.43974i	−0.311435	+	0.146136i
$924$		0			0
$925$	−6.23669	+	23.2757i	−0.205061	+	0.765299i
$926$	2.14626	−	3.71742i	0.0705303	−	0.122162i
$927$	−9.11956	−	15.7955i	−0.299526	−	0.518794i
$928$	0.453299	−	0.121461i	0.0148803	−	0.00398716i
$929$	−30.2470	+	30.2470i	−0.992373	+	0.992373i	−0.999971	−	0.00759811i	$-0.997581\pi$
$929$	−30.2470	+	30.2470i	−0.992373	+	0.992373i	0.00759811	+	0.999971i	$0.497581\pi$
$930$	3.76421	−	1.00862i	0.123433	−	0.0330738i
$931$		0			0
$932$	−0.404128	+	0.699969i	−0.0132376	+	0.0229283i
$933$	23.9785	+	13.8440i	0.785019	+	0.453231i
$934$	−20.6675	−	20.6675i	−0.676262	−	0.676262i
$935$	−14.9001	−	8.60260i	−0.487287	−	0.281335i
$936$	11.0266	−	15.8283i	0.360415	−	0.517365i
$937$		−	14.9401i		−	0.488071i	−0.969766	−	0.244035i	$-0.921529\pi$
$937$		−	14.9401i		−	0.488071i	0.969766	−	0.244035i	$-0.0784713\pi$
$938$		0			0
$939$	−15.3661	−	26.6148i	−0.501452	−	0.868541i
$940$			0.843173i			0.0275013i
$941$	−2.94635	−	10.9959i	−0.0960482	−	0.358457i	0.901128	−	0.433553i	$-0.142740\pi$
$941$	−2.94635	−	10.9959i	−0.0960482	−	0.358457i	−0.997176	+	0.0750961i	$0.976074\pi$
$942$	−2.59710	+	9.69249i	−0.0846180	+	0.315799i
$943$	−65.7112	−	65.7112i	−2.13985	−	2.13985i
$944$	15.7399	+	15.7399i	0.512291	+	0.512291i
$945$		0			0
$946$	−1.59642	+	0.921695i	−0.0519042	+	0.0299669i
$947$	−8.32128	−	31.0554i	−0.270405	−	1.00917i	−0.958858	−	0.283885i	$-0.908377\pi$
$947$	−8.32128	−	31.0554i	−0.270405	−	1.00917i	0.688453	−	0.725281i	$-0.258290\pi$
$948$	−0.475359	+	0.823345i	−0.0154389	+	0.0267410i
$949$	−9.29811	+	4.36299i	−0.301830	+	0.141629i
$950$	−23.8523	+	13.7711i	−0.773871	+	0.446794i
$951$	12.9093	+	3.45903i	0.418612	+	0.112167i
$952$		0			0
$953$	32.4604	+	18.7410i	1.05150	+	0.607081i	0.923068	−	0.384638i	$-0.125674\pi$
$953$	32.4604	+	18.7410i	1.05150	+	0.607081i	0.128428	+	0.991719i	$0.459007\pi$
$954$	−1.66963	+	6.23114i	−0.0540562	+	0.201741i
$955$	22.5888	+	6.05264i	0.730955	+	0.195859i
$956$	0.828726	+	0.222056i	0.0268029	+	0.00718182i
$957$	0.349874	−	1.30575i	0.0113098	−	0.0422089i
$958$	−28.7118	−	16.5768i	−0.927636	−	0.535571i
$959$		0			0
$960$	−24.7844	−	6.64096i	−0.799913	−	0.214336i
$961$	26.1178	−	15.0791i	0.842509	−	0.486423i
$962$	−23.8961	−	28.3398i	−0.770442	−	0.913713i
$963$	−9.80261	+	16.9786i	−0.315885	+	0.547128i
$964$	−0.106202	−	0.396352i	−0.00342054	−	0.0127656i
$965$	−66.5746	+	38.4368i	−2.14311	+	1.23733i
$966$		0			0
$967$	10.9130	+	10.9130i	0.350939	+	0.350939i	0.860459	−	0.509520i	$-0.170177\pi$
$967$	10.9130	+	10.9130i	0.350939	+	0.350939i	−0.509520	+	0.860459i	$0.670177\pi$
$968$	−18.3174	−	18.3174i	−0.588745	−	0.588745i
$969$	−7.18216	+	26.8042i	−0.230724	+	0.861074i
$970$	−9.41959	−	35.1544i	−0.302445	−	1.12874i
$971$			1.78526i			0.0572916i	0.999590	+	0.0286458i	$0.00911949\pi$
$971$			1.78526i			0.0572916i	−0.999590	+	0.0286458i	$0.990881\pi$
$972$	−0.732343	−	1.26846i	−0.0234899	−	0.0406857i
$973$		0			0
$974$			47.0455i			1.50743i
$975$	4.24949	−	11.7632i	0.136093	−	0.376723i
$976$	0.281298	+	0.162407i	0.00900413	+	0.00519854i
$977$	−1.60581	−	1.60581i	−0.0513743	−	0.0513743i	0.680953	−	0.732327i	$-0.261566\pi$
$977$	−1.60581	−	1.60581i	−0.0513743	−	0.0513743i	−0.732327	+	0.680953i	$0.761566\pi$
$978$	−14.0030	−	8.08461i	−0.447765	−	0.258517i
$979$	−3.51662	+	6.09097i	−0.112392	+	0.194668i
$980$		0			0
$981$	−29.5002	+	7.90456i	−0.941869	+	0.252373i
$982$	13.8297	−	13.8297i	0.441323	−	0.441323i
$983$	−41.3763	+	11.0868i	−1.31970	+	0.353613i	−0.848865	−	0.528609i	$-0.822714\pi$
$983$	−41.3763	+	11.0868i	−1.31970	+	0.353613i	−0.470835	+	0.882221i	$0.656047\pi$
$984$	−18.4038	−	31.8763i	−0.586692	−	1.01618i
$985$	−26.4468	+	45.8071i	−0.842664	+	1.45954i
$986$	1.32453	−	4.94320i	0.0421815	−	0.157424i
$987$		0			0
$988$	−0.177191	+	2.08289i	−0.00563721	+	0.0662657i
$989$	−3.65815	−	6.33611i	−0.116323	−	0.201477i
$990$	7.40406	−	7.40406i	0.235317	−	0.235317i
$991$	53.3601			1.69504			0.847519	−	0.530765i	$-0.178095\pi$
$991$	53.3601			1.69504			0.847519	+	0.530765i	$0.178095\pi$
$992$	0.487636			0.0154825
$993$	−22.7060	+	22.7060i	−0.720553	+	0.720553i
$994$		0			0
$995$	−9.44159	−	35.2365i	−0.299319	−	1.11707i
$996$	0.212130	+	0.0568400i	0.00672158	+	0.00180104i
$997$	−40.7247	+	23.5124i	−1.28976	+	0.744645i	−0.978612	−	0.205715i	$-0.934048\pi$
$997$	−40.7247	+	23.5124i	−1.28976	+	0.744645i	−0.311152	+	0.950360i	$0.600715\pi$
$998$			41.1675i			1.30313i
$999$	−37.4075	+	10.0233i	−1.18352	+	0.317124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.x.b.570.6		32
7.2	even	3		637.2.bb.b.362.3		32
7.3	odd	6		91.2.bc.a.76.3	yes	32
7.4	even	3		91.2.bc.a.76.4	yes	32
7.5	odd	6		637.2.bb.b.362.4		32
7.6	odd	2	inner	637.2.x.b.570.5		32
13.6	odd	12		637.2.bb.b.227.4		32
21.11	odd	6		819.2.fm.g.622.5		32
21.17	even	6		819.2.fm.g.622.6		32
91.6	even	12		637.2.bb.b.227.3		32
91.19	even	12	inner	637.2.x.b.19.5		32
91.32	odd	12		91.2.bc.a.6.3	✓	32
91.45	even	12		91.2.bc.a.6.4	yes	32
91.58	odd	12	inner	637.2.x.b.19.6		32
273.32	even	12		819.2.fm.g.370.6		32
273.227	odd	12		819.2.fm.g.370.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.6.3	✓	32	91.32	odd	12
91.2.bc.a.6.4	yes	32	91.45	even	12
91.2.bc.a.76.3	yes	32	7.3	odd	6
91.2.bc.a.76.4	yes	32	7.4	even	3
637.2.x.b.19.5		32	91.19	even	12	inner
637.2.x.b.19.6		32	91.58	odd	12	inner
637.2.x.b.570.5		32	7.6	odd	2	inner
637.2.x.b.570.6		32	1.1	even	1	trivial
637.2.bb.b.227.3		32	91.6	even	12
637.2.bb.b.227.4		32	13.6	odd	12
637.2.bb.b.362.3		32	7.2	even	3
637.2.bb.b.362.4		32	7.5	odd	6
819.2.fm.g.370.5		32	273.227	odd	12
819.2.fm.g.370.6		32	273.32	even	12
819.2.fm.g.622.5		32	21.11	odd	6
819.2.fm.g.622.6		32	21.17	even	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.33353 - 0.357317i) q^{2} +1.07207i q^{3} +(-0.0814361 + 0.0470171i) q^{4} +(-2.77200 - 0.742756i) q^{5} +(0.383068 + 1.42963i) q^{6} +(-2.04421 + 2.04421i) q^{8} +1.85067 q^{9} +O(q^{10})\)	\(q+(1.33353 - 0.357317i) q^{2} +1.07207i q^{3} +(-0.0814361 + 0.0470171i) q^{4} +(-2.77200 - 0.742756i) q^{5} +(0.383068 + 1.42963i) q^{6} +(-2.04421 + 2.04421i) q^{8} +1.85067 q^{9} -3.96194 q^{10} +(-1.00979 + 1.00979i) q^{11} +(-0.0504055 - 0.0873049i) q^{12} +(-3.54926 + 0.634621i) q^{13} +(0.796284 - 2.97177i) q^{15} +(-1.90154 + 3.29357i) q^{16} +(-2.09909 - 3.63573i) q^{17} +(2.46792 - 0.661277i) q^{18} +(-4.35974 + 4.35974i) q^{19} +(0.260663 - 0.0698445i) q^{20} +(-0.985770 + 1.70740i) q^{22} +(-6.77658 - 3.91246i) q^{23} +(-2.19153 - 2.19153i) q^{24} +(2.80219 + 1.61784i) q^{25} +(-4.50627 + 2.11449i) q^{26} +5.20025i q^{27} +(0.441485 + 0.764674i) q^{29} -4.24746i q^{30} +(0.237463 + 0.886225i) q^{31} +(0.137560 - 0.513380i) q^{32} +(-1.08257 - 1.08257i) q^{33} +(-4.09830 - 4.09830i) q^{34} +(-0.150711 + 0.0870133i) q^{36} +(1.92747 + 7.19341i) q^{37} +(-4.25601 + 7.37163i) q^{38} +(-0.680356 - 3.80505i) q^{39} +(7.18492 - 4.14822i) q^{40} +(11.4714 + 3.07376i) q^{41} +(0.809734 + 0.467500i) q^{43} +(0.0347561 - 0.129711i) q^{44} +(-5.13007 - 1.37460i) q^{45} +(-10.4347 - 2.79598i) q^{46} +(-0.808679 + 3.01803i) q^{47} +(-3.53093 - 2.03858i) q^{48} +(4.31487 + 1.15617i) q^{50} +(3.89775 - 2.25037i) q^{51} +(0.259200 - 0.218557i) q^{52} +(-1.26243 + 2.18659i) q^{53} +(1.85814 + 6.93466i) q^{54} +(3.54919 - 2.04912i) q^{55} +(-4.67393 - 4.67393i) q^{57} +(0.861962 + 0.861962i) q^{58} +(1.51488 - 5.65360i) q^{59} +(0.0748780 + 0.279449i) q^{60} -0.0854082i q^{61} +(0.633327 + 1.09695i) q^{62} -8.33994i q^{64} +(10.3099 + 0.877064i) q^{65} +(-1.83045 - 1.05681i) q^{66} +(0.728594 + 0.728594i) q^{67} +(0.341884 + 0.197387i) q^{68} +(4.19442 - 7.26495i) q^{69} +(2.79996 - 0.750247i) q^{71} +(-3.78317 + 3.78317i) q^{72} +(2.75156 - 0.737278i) q^{73} +(5.14066 + 8.90388i) q^{74} +(-1.73444 + 3.00414i) q^{75} +(0.150057 - 0.560022i) q^{76} +(-2.26688 - 4.83102i) q^{78} +(-4.71534 - 8.16721i) q^{79} +(7.71741 - 7.71741i) q^{80} -0.0229961 q^{81} +16.3958 q^{82} +(-1.54040 + 1.54040i) q^{83} +(3.11823 + 11.6374i) q^{85} +(1.24685 + 0.334092i) q^{86} +(-0.819782 + 0.473301i) q^{87} -4.12847i q^{88} +(4.75720 - 1.27469i) q^{89} -7.33225 q^{90} +0.735811 q^{92} +(-0.950093 + 0.254577i) q^{93} +4.31358i q^{94} +(15.3234 - 8.84698i) q^{95} +(0.550378 + 0.147473i) q^{96} +(2.37752 + 8.87303i) q^{97} +(-1.86880 + 1.86880i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9	\( 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 8 q^{15} + 12 q^{16} - 64 q^{18} + 4 q^{22} + 12 q^{23} + 4 q^{29} + 64 q^{32} + 4 q^{37} + 36 q^{39} - 48 q^{43} - 84 q^{44} - 108 q^{46} - 44 q^{50} + 12 q^{51} - 36 q^{53} - 92 q^{57} + 44 q^{58} + 28 q^{60} + 28 q^{65} + 64 q^{67} + 84 q^{71} + 4 q^{72} - 24 q^{74} + 148 q^{78} + 40 q^{79} - 56 q^{81} + 36 q^{85} + 108 q^{86} + 24 q^{92} - 24 q^{93} + 84 q^{95} - 60 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 8 * q^15 + 12 * q^16 - 64 * q^18 + 4 * q^22 + 12 * q^23 + 4 * q^29 + 64 * q^32 + 4 * q^37 + 36 * q^39 - 48 * q^43 - 84 * q^44 - 108 * q^46 - 44 * q^50 + 12 * q^51 - 36 * q^53 - 92 * q^57 + 44 * q^58 + 28 * q^60 + 28 * q^65 + 64 * q^67 + 84 * q^71 + 4 * q^72 - 24 * q^74 + 148 * q^78 + 40 * q^79 - 56 * q^81 + 36 * q^85 + 108 * q^86 + 24 * q^92 - 24 * q^93 + 84 * q^95 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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