LMFDB - Embedded newform 637.2.x.b.19.5

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			19.5
Character	$\chi$	$=$	637.19
Dual form			637.2.x.b.570.6

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

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	0.697366	−	0.716715i	$-0.254355\pi$
$2$	1.33353	+	0.357317i	0.942945	+	0.252661i	0.245579	+	0.969377i	$0.421022\pi$
$3$		−	1.07207i		−	0.618958i	−0.950906	−	0.309479i	$-0.899845\pi$
$3$		−	1.07207i		−	0.618958i	0.950906	−	0.309479i	$-0.100155\pi$
$4$	−0.0814361	−	0.0470171i	−0.0407180	−	0.0235086i
$5$	−2.77200	+	0.742756i	−1.23968	+	0.332171i	−0.818341	−	0.574734i	$-0.805106\pi$
$5$	−2.77200	+	0.742756i	−1.23968	+	0.332171i	−0.421337	+	0.906904i	$0.638439\pi$
$6$	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	0.538293	−	0.842758i	$-0.319069\pi$
$11$	−1.00979	−	1.00979i	−0.304465	−	0.304465i	−0.842758	+	0.538293i	$0.819069\pi$
$12$	−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	0.490840	+	0.871250i	$0.336690\pi$
$17$	−2.09909	+	3.63573i	−0.509105	+	0.881795i	−0.999944	+	0.0105451i	$0.996643\pi$
$18$	2.46792	+	0.661277i	0.581694	+	0.155864i
$19$	−4.35974	−	4.35974i	−1.00019	−	1.00019i	−1.00000		0.000191931i	$-0.999939\pi$
$19$	−4.35974	−	4.35974i	−1.00019	−	1.00019i	−0.000191931	−	1.00000i	$-0.500061\pi$
$20$	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	−0.995671	−	0.0929436i	$-0.970372\pi$
$23$	−6.77658	+	3.91246i	−1.41302	+	0.815805i	−0.417344	+	0.908748i	$0.637039\pi$
$24$	−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	−0.822119	−	0.569315i	$-0.807208\pi$
$29$	0.441485	−	0.764674i	0.0819817	−	0.141996i	0.904101	+	0.427319i	$0.140542\pi$
$30$			4.24746i			0.775477i
$31$	0.237463	−	0.886225i	0.0426497	−	0.159171i	−0.941317	−	0.337524i	$-0.890410\pi$
$31$	0.237463	−	0.886225i	0.0426497	−	0.159171i	0.983966	+	0.178354i	$0.0570771\pi$
$32$	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	−0.605358	−	0.795953i	$-0.706970\pi$
$37$	1.92747	−	7.19341i	0.316874	−	1.18259i	0.922232	−	0.386637i	$-0.126363\pi$
$38$	−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	0.798933	−	0.601421i	$-0.205398\pi$
$41$	11.4714	−	3.07376i	1.79154	−	0.480041i	0.992606	+	0.121379i	$0.0387317\pi$
$42$		0			0
$43$	0.809734	−	0.467500i	0.123483	−	0.0712931i	−0.436986	−	0.899468i	$-0.643954\pi$
$43$	0.809734	−	0.467500i	0.123483	−	0.0712931i	0.560469	+	0.828175i	$0.310621\pi$
$44$	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	0.881533	−	0.472122i	$-0.156512\pi$
$47$	−0.808679	−	3.01803i	−0.117958	−	0.440225i	−0.999491	+	0.0318968i	$0.989845\pi$
$48$	−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	0.766201	−	0.642601i	$-0.222145\pi$
$53$	−1.26243	−	2.18659i	−0.173408	−	0.300351i	−0.939609	+	0.342249i	$0.888811\pi$
$54$	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	0.991681	+	0.128720i	$0.0410869\pi$
$59$	1.51488	+	5.65360i	0.197220	+	0.736035i	−0.794461	+	0.607315i	$0.792246\pi$
$60$	0.0748780	−	0.279449i	0.00966671	−	0.0360767i
$61$			0.0854082i			0.0109354i	0.999985	+	0.00546770i	$0.00174043\pi$
$61$			0.0854082i			0.0109354i	−0.999985	+	0.00546770i	$0.998260\pi$
$62$	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	−0.661199	−	0.750211i	$-0.729952\pi$
$67$	0.728594	−	0.728594i	0.0890119	−	0.0890119i	0.750211	+	0.661199i	$0.229952\pi$
$68$	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	0.421109	−	0.907010i	$-0.361641\pi$
$71$	2.79996	+	0.750247i	0.332294	+	0.0890380i	−0.0888143	+	0.996048i	$0.528308\pi$
$72$	−3.78317	−	3.78317i	−0.445851	−	0.445851i
$73$	2.75156	+	0.737278i	0.322046	+	0.0862919i	0.416220	−	0.909264i	$-0.363355\pi$
$73$	2.75156	+	0.737278i	0.322046	+	0.0862919i	−0.0941746	+	0.995556i	$0.530021\pi$
$74$	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	0.468849	+	0.883279i	$0.344669\pi$
$79$	−4.71534	+	8.16721i	−0.530517	+	0.918883i	−0.999366	+	0.0356045i	$0.988664\pi$
$80$	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	0.617494	−	0.786575i	$-0.288148\pi$
$83$	−1.54040	−	1.54040i	−0.169081	−	0.169081i	−0.786575	+	0.617494i	$0.788148\pi$
$84$		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	0.501977	−	0.864881i	$-0.332606\pi$
$89$	4.75720	+	1.27469i	0.504262	+	0.135117i	0.00228491	+	0.999997i	$0.499273\pi$
$90$	−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	−0.733758	−	0.679411i	$-0.762235\pi$
$97$	2.37752	−	8.87303i	0.241401	−	0.900920i	0.975158	−	0.221509i	$-0.0710981\pi$
$98$		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	−0.999862	−	0.0166161i	$-0.994711\pi$
$103$	−4.92770	+	8.53503i	−0.485541	+	0.840982i	0.514321	+	0.857598i	$0.328044\pi$
$104$	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	−0.999902	−	0.0139814i	$-0.995549\pi$
$107$	−5.29678	−	9.17430i	−0.512059	−	0.886913i	0.487843	−	0.872931i	$-0.337784\pi$
$108$	−0.244501	+	0.423488i	−0.0235271	+	0.0407501i
$109$	−15.9403	−	4.27118i	−1.52680	−	0.409105i	−0.604827	−	0.796357i	$-0.706758\pi$
$109$	−15.9403	−	4.27118i	−1.52680	−	0.409105i	−0.921974	+	0.387252i	$0.873424\pi$
$110$	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	0.850477	−	0.526013i	$-0.176314\pi$
$113$	−0.322118	−	0.557925i	−0.0303023	−	0.0524851i	−0.880779	+	0.473528i	$0.842980\pi$
$114$	−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	−0.281850	−	0.959458i	$-0.590948\pi$
$127$	−14.1284	−	8.15702i	−1.25369	−	0.723819i	−0.971841	+	0.235640i	$0.924282\pi$
$128$	−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	0.586364	−	0.810047i	$-0.300559\pi$
$131$	2.03759	+	1.17640i	0.178025	+	0.102783i	−0.408340	+	0.912830i	$0.633892\pi$
$132$	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	−0.660541	−	0.750790i	$-0.729673\pi$
$137$	−10.0332	+	2.68838i	−0.857190	+	0.229683i	−0.196650	+	0.980474i	$0.563006\pi$
$138$	2.99748	+	11.1867i	0.255162	+	0.952278i
$139$	−5.33208	+	3.07848i	−0.452261	+	0.261113i	−0.708784	−	0.705425i	$-0.750756\pi$
$139$	−5.33208	+	3.07848i	−0.452261	+	0.261113i	0.256524	+	0.966538i	$0.417423\pi$
$140$		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	−0.408442	−	0.912784i	$-0.633928\pi$
$149$	6.15629	−	6.15629i	0.504343	−	0.504343i	0.912784	+	0.408442i	$0.133928\pi$
$150$	−1.23949	−	4.62584i	−0.101204	−	0.377698i
$151$	3.49627	−	13.0482i	0.284522	−	1.06185i	−0.664665	−	0.747141i	$-0.731426\pi$
$151$	3.49627	−	13.0482i	0.284522	−	1.06185i	0.949188	−	0.314710i	$-0.101907\pi$
$152$			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	−0.247059	−	0.969000i	$-0.579464\pi$
$157$	5.87142	−	3.38986i	0.468590	−	0.270541i	0.715649	+	0.698460i	$0.246131\pi$
$158$	−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	0.336588	−	0.941652i	$-0.390727\pi$
$163$	−7.72493	−	7.72493i	−0.605063	−	0.605063i	−0.941652	+	0.336588i	$0.890727\pi$
$164$	−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	−0.867732	−	0.497032i	$-0.834423\pi$
$167$	−4.71387	−	17.5924i	−0.364770	−	1.36134i	0.502962	−	0.864308i	$-0.332244\pi$
$168$		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	$0.211991\pi$
$179$			16.5322i			1.23567i	−0.786306	+	0.617837i	$0.788009\pi$
$180$	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	0.869499	+	0.493935i	$0.164442\pi$
$193$	18.9414	+	18.9414i	1.36343	+	1.36343i	0.493935	+	0.869499i	$0.335558\pi$
$194$	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	0.898490	+	0.438995i	$0.144665\pi$
$197$	4.77033	+	17.8031i	0.339872	+	1.26842i	−0.558617	+	0.829426i	$0.688668\pi$
$198$	−1.82434	−	3.15985i	−0.129650	−	0.224560i
$199$	6.35578	−	11.0085i	0.450550	−	0.780375i	−0.547871	−	0.836563i	$-0.684561\pi$
$199$	6.35578	−	11.0085i	0.450550	−	0.780375i	0.998420	+	0.0561884i	$0.0178947\pi$
$200$	−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	−0.933387	−	0.358872i	$-0.883161\pi$
$211$	−2.26459	+	3.92239i	−0.155901	+	0.270028i	0.777486	+	0.628900i	$0.216495\pi$
$212$			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	−0.914868	−	0.403752i	$-0.867706\pi$
$223$	−22.4788	+	6.02318i	−1.50529	+	0.403342i	−0.590423	+	0.807094i	$0.701039\pi$
$224$		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	0.0912961	−	0.995824i	$-0.470899\pi$
$227$	10.0685	−	2.69786i	0.668273	−	0.179063i	0.576977	+	0.816761i	$0.304232\pi$
$228$	0.600381	−	0.160872i	0.0397612	−	0.0106540i
$229$	−0.499191	−	1.86301i	−0.0329875	−	0.123111i	0.947469	−	0.319848i	$-0.103632\pi$
$229$	−0.499191	−	1.86301i	−0.0329875	−	0.123111i	−0.980456	+	0.196738i	$0.936965\pi$
$230$	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	0.723602	−	0.690217i	$-0.242485\pi$
$233$	7.44377	+	4.29766i	0.487657	+	0.281549i	−0.235945	+	0.971766i	$0.575818\pi$
$234$	−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	−0.884278	−	0.466960i	$-0.845349\pi$
$239$	−6.45158	+	6.45158i	−0.417318	+	0.417318i	0.466960	+	0.884278i	$0.345349\pi$
$240$	8.27358	−	8.27358i	0.534057	−	0.534057i
$241$	−1.12940	−	4.21497i	−0.0727509	−	0.271510i	0.919963	−	0.392005i	$-0.128218\pi$
$241$	−1.12940	−	4.21497i	−0.0727509	−	0.271510i	−0.992714	+	0.120495i	$0.961552\pi$
$242$	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	0.785073	−	0.619403i	$-0.212625\pi$
$251$	−2.27953	−	3.94826i	−0.143883	−	0.249212i	−0.928956	+	0.370191i	$0.879292\pi$
$252$		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	0.968672	−	0.248342i	$-0.0798857\pi$
$257$	4.31666	+	7.47667i	0.269266	+	0.466382i	−0.699407	+	0.714724i	$0.746552\pi$
$258$	−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	0.130360	−	0.991467i	$-0.458387\pi$
$269$	−10.8756	−	6.27901i	−0.663095	−	0.382838i	−0.793455	+	0.608629i	$0.791720\pi$
$270$			20.6030i			1.25386i
$271$	4.45677	+	1.19419i	0.270730	+	0.0725418i	0.391630	−	0.920123i	$-0.371911\pi$
$271$	4.45677	+	1.19419i	0.270730	+	0.0725418i	−0.120900	+	0.992665i	$0.538578\pi$
$272$	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	0.542881	−	0.839809i	$-0.317333\pi$
$277$	1.44840	+	0.836232i	0.0870257	+	0.0502443i	−0.455856	+	0.890054i	$0.650667\pi$
$278$	−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	0.156870	−	0.987619i	$-0.449860\pi$
$281$	−13.9259	−	13.9259i	−0.830749	−	0.830749i	−0.987619	+	0.156870i	$0.949860\pi$
$282$	−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	0.818163	−	0.574986i	$-0.194993\pi$
$293$	21.2120	+	5.68375i	1.23922	+	0.332048i	0.421057	+	0.907034i	$0.361659\pi$
$294$		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	−0.194289	−	0.980944i	$-0.562240\pi$
$307$	13.7833	−	13.7833i	0.786656	−	0.786656i	0.980944	+	0.194289i	$0.0622399\pi$
$308$		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	0.955920	+	0.293627i	$0.0948622\pi$
$311$	12.9133	+	22.3666i	0.732248	+	1.26829i	−0.223672	+	0.974664i	$0.571804\pi$
$312$	9.16912	−	6.38753i	0.519099	−	0.361623i
$313$	−24.8257	−	14.3331i	−1.40323	−	0.810155i	−0.408507	−	0.912755i	$-0.633950\pi$
$313$	−24.8257	−	14.3331i	−1.40323	−	0.810155i	−0.994723	+	0.102600i	$0.967284\pi$
$314$	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	0.995408	+	0.0957183i	$0.0305148\pi$
$317$	3.22651	+	12.0415i	0.181219	+	0.676317i	−0.814190	+	0.580599i	$0.802819\pi$
$318$	−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	0.180578	−	0.983561i	$-0.442203\pi$
$331$	21.1797	−	21.1797i	1.16414	−	1.16414i	0.983561	−	0.180578i	$-0.0577970\pi$
$332$	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	$0.119296\pi$
$337$			13.4402i			0.732137i	−0.930588	+	0.366068i	$0.880704\pi$
$338$	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	−0.603172	−	0.797611i	$-0.706097\pi$
$347$	7.24936	−	12.5563i	0.389166	−	0.674055i	0.992338	+	0.123556i	$0.0394299\pi$
$348$	0.0445066	+	0.0770876i	0.00238580	+	0.00413233i
$349$	5.68220	+	21.2063i	0.304161	+	1.13515i	0.933665	+	0.358148i	$0.116592\pi$
$349$	5.68220	+	21.2063i	0.304161	+	1.13515i	−0.629504	+	0.776998i	$0.716742\pi$
$350$		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	0.455600	−	0.890185i	$-0.349425\pi$
$353$	−8.16512	−	8.16512i	−0.434585	−	0.434585i	−0.890185	+	0.455600i	$0.849425\pi$
$354$	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	−0.236000	−	0.971753i	$-0.575837\pi$
$359$	0.861987	−	0.230969i	0.0454939	−	0.0121901i	0.281494	+	0.959563i	$0.409170\pi$
$360$	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	$-0.876700\pi$
$367$		−	14.4731i		−	0.755489i	0.925910	−	0.377744i	$-0.123300\pi$
$368$	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	−0.949478	−	0.313834i	$-0.898387\pi$
$379$	−5.53128	−	20.6430i	−0.284123	−	1.06036i	0.665355	−	0.746527i	$-0.268280\pi$
$380$	−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	0.952427	−	0.304765i	$-0.0985781\pi$
$383$	12.6750	+	12.6750i	0.647662	+	0.647662i	−0.304765	+	0.952427i	$0.598578\pi$
$384$	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	−0.389455	−	0.921046i	$-0.627337\pi$
$389$	4.21022	−	2.43077i	0.213467	−	0.123245i	0.602921	+	0.797801i	$0.294003\pi$
$390$	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	−0.268895	−	0.963170i	$-0.586658\pi$
$397$	13.8333	−	13.8333i	0.694275	−	0.694275i	0.963170	+	0.268895i	$0.0866584\pi$
$398$	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	−0.988118	−	0.153700i	$-0.950881\pi$
$401$	−1.11204	+	4.15019i	−0.0555327	+	0.207251i	0.932585	+	0.360951i	$0.117548\pi$
$402$	−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	−0.895585	−	0.444891i	$-0.853242\pi$
$409$	−29.2989	+	7.85062i	−1.44874	+	0.388188i	−0.553154	+	0.833079i	$0.686576\pi$
$410$	−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	0.658386	−	0.752680i	$-0.271239\pi$
$419$	6.87240	+	3.96778i	0.335739	+	0.193839i	−0.322647	+	0.946519i	$0.604573\pi$
$420$		0			0
$421$	−5.98090	+	5.98090i	−0.291491	+	0.291491i	−0.837669	−	0.546178i	$-0.816082\pi$
$421$	−5.98090	+	5.98090i	−0.291491	+	0.291491i	0.546178	+	0.837669i	$0.316082\pi$
$422$	−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	−0.697185	−	0.716891i	$-0.745565\pi$
$431$	0.409100	−	0.409100i	0.0197057	−	0.0197057i	0.716891	+	0.697185i	$0.245565\pi$
$432$	−17.1274	+	9.88850i	−0.824042	+	0.475761i
$433$	−4.11334	−	7.12452i	−0.197675	−	0.342382i	0.750099	−	0.661325i	$-0.230006\pi$
$433$	−4.11334	−	7.12452i	−0.197675	−	0.342382i	−0.947774	+	0.318943i	$0.896672\pi$
$434$		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	0.673328	−	0.739344i	$-0.264864\pi$
$439$	−6.36168	−	11.0188i	−0.303626	−	0.525896i	−0.976955	+	0.213447i	$0.931531\pi$
$440$	−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	−0.838313	−	0.545189i	$-0.816458\pi$
$443$	1.11534	−	1.93182i	0.0529912	−	0.0917834i	0.891304	+	0.453406i	$0.149791\pi$
$444$	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	−0.141088	−	0.989997i	$-0.545060\pi$
$449$	10.0883	−	37.6500i	0.476096	−	1.77682i	0.617184	−	0.786819i	$-0.288273\pi$
$450$	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	−0.302174	−	0.953253i	$-0.597712\pi$
$457$	−22.2431	−	5.96003i	−1.04049	−	0.278798i	−0.738316	+	0.674455i	$0.764379\pi$
$458$		−	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	0.504859	+	0.863202i	$0.331544\pi$
$461$	−7.81461	+	29.1645i	−0.363962	+	1.35833i	−0.868822	+	0.495125i	$0.835122\pi$
$462$		0			0
$463$	2.19856	+	2.19856i	0.102176	+	0.102176i	0.756347	−	0.654171i	$-0.226982\pi$
$463$	2.19856	+	2.19856i	0.102176	+	0.102176i	−0.654171	+	0.756347i	$0.726982\pi$
$464$	−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	−0.999932	−	0.0116879i	$-0.996280\pi$
$467$	−10.5856	+	18.3348i	−0.489844	+	0.848434i	0.510088	+	0.860122i	$0.329613\pi$
$468$	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	−0.979126	−	0.203255i	$-0.934848\pi$
$479$	−16.9808	+	16.9808i	−0.775871	+	0.775871i	0.203255	+	0.979126i	$0.434848\pi$
$480$	−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	−0.813694	−	0.581294i	$-0.802547\pi$
$487$	−8.81975	−	32.9158i	−0.399661	−	1.49156i	0.414032	−	0.910262i	$-0.364120\pi$
$488$	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	0.750605	−	0.660751i	$-0.229762\pi$
$491$	12.2688	+	7.08337i	0.553681	+	0.319668i	−0.196924	+	0.980419i	$0.563095\pi$
$492$	−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	−0.892032	−	0.451972i	$-0.850721\pi$
$499$	−7.71779	−	28.8032i	−0.345496	−	1.28941i	0.546536	−	0.837436i	$-0.315946\pi$
$500$	−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	−0.739709	−	0.672927i	$-0.765037\pi$
$503$	−11.8147	+	6.82122i	−0.526791	+	0.304143i	0.212918	+	0.977070i	$0.431703\pi$
$504$		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	−0.948921	−	0.315515i	$-0.897823\pi$
$509$	0.690957	−	2.57869i	0.0306261	−	0.114298i	0.979547	+	0.201216i	$0.0644895\pi$
$510$	−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	−0.175182	−	0.984536i	$-0.556052\pi$
$521$	13.4638	−	7.77333i	0.589860	−	0.340556i	0.765042	+	0.643980i	$0.222718\pi$
$522$	1.59521	−	1.59521i	0.0698204	−	0.0698204i
$523$	−0.102601	+	0.0592367i	−0.00448643	+	0.00259024i	−0.502242	−	0.864727i	$-0.667491\pi$
$523$	−0.102601	+	0.0592367i	−0.00448643	+	0.00259024i	0.497755	+	0.867318i	$0.334158\pi$
$524$	−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	−0.161432	−	0.986884i	$-0.551611\pi$
$541$	4.47060	−	1.19789i	0.192206	−	0.0515014i	0.353638	+	0.935382i	$0.384945\pi$
$542$	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	0.727137	−	0.686492i	$-0.240850\pi$
$557$	0.959258	+	0.959258i	0.0406451	+	0.0406451i	−0.686492	+	0.727137i	$0.740850\pi$
$558$	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	−0.279995	−	0.960001i	$-0.590333\pi$
$563$	16.4050	−	28.4143i	0.691388	−	1.19752i	0.971383	−	0.237517i	$-0.0763337\pi$
$564$	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	0.152552	−	0.988296i	$-0.451251\pi$
$569$	25.8745	−	14.9387i	1.08472	−	0.626261i	0.932165	+	0.362034i	$0.117918\pi$
$570$	18.5178	−	18.5178i	0.775626	−	0.775626i
$571$	−0.640877	+	0.370010i	−0.0268198	+	0.0154844i	−0.513350	−	0.858179i	$-0.671596\pi$
$571$	−0.640877	+	0.370010i	−0.0268198	+	0.0154844i	0.486530	+	0.873664i	$0.338262\pi$
$572$	−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	0.496454	+	0.868063i	$0.334635\pi$
$577$	−8.82812	+	32.9470i	−0.367519	+	1.37160i	−0.863973	+	0.503538i	$0.832031\pi$
$578$	−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	−0.497316	−	0.867569i	$-0.665681\pi$
$587$	−11.9740	+	3.20842i	−0.494219	+	0.132426i	0.00309648	+	0.999995i	$0.499014\pi$
$588$		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	0.974405	+	0.224800i	$0.0721728\pi$
$593$	5.91611	+	22.0792i	0.242945	+	0.906685i	−0.731460	+	0.681885i	$0.761161\pi$
$594$	−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	0.839425	−	0.543476i	$-0.182892\pi$
$599$	−1.24701	−	2.15989i	−0.0509516	−	0.0882508i	−0.890376	+	0.455225i	$0.849559\pi$
$600$	−2.59553	+	9.68666i	−0.105962	+	0.395456i
$601$	18.5873	+	10.7314i	0.758193	+	0.437743i	0.828647	−	0.559772i	$-0.189111\pi$
$601$	18.5873	+	10.7314i	0.758193	+	0.437743i	−0.0704537	+	0.997515i	$0.522445\pi$
$602$		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	$-0.894463\pi$
$607$		−	16.0396i		−	0.651028i	0.945537	−	0.325514i	$-0.105537\pi$
$608$	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	−0.798901	−	0.601462i	$-0.794585\pi$
$613$	−4.88837	+	4.88837i	−0.197440	+	0.197440i	0.601462	+	0.798901i	$0.294585\pi$
$614$	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	0.756223	−	0.654314i	$-0.227043\pi$
$617$	26.9254	+	7.21463i	1.08397	+	0.290450i	0.327751	+	0.944764i	$0.393709\pi$
$618$	10.3143	+	10.3143i	0.414901	+	0.414901i
$619$	13.3912	+	3.58815i	0.538237	+	0.144220i	0.517689	−	0.855569i	$-0.326792\pi$
$619$	13.3912	+	3.58815i	0.538237	+	0.144220i	0.0205475	+	0.999789i	$0.493459\pi$
$620$	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	−0.694764	−	0.719237i	$-0.744491\pi$
$631$	6.69536	−	24.9874i	0.266538	−	0.994733i	0.961302	−	0.275496i	$-0.0888419\pi$
$632$	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	0.699405	−	0.714726i	$-0.253449\pi$
$641$	10.8902	+	6.28745i	0.430136	+	0.248339i	−0.269269	+	0.963065i	$0.586782\pi$
$642$	−15.1449	+	4.05806i	−0.597720	+	0.160159i
$643$	6.40174	−	23.8916i	0.252460	−	0.942193i	−0.717026	−	0.697046i	$-0.754497\pi$
$643$	6.40174	−	23.8916i	0.252460	−	0.942193i	0.969486	−	0.245147i	$-0.0788361\pi$
$644$		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	0.999108	+	0.0422314i	$0.0134467\pi$
$653$	13.7001	+	23.7293i	0.536127	+	0.928600i	−0.462980	+	0.886368i	$0.653220\pi$
$654$	−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	0.904795	−	0.425847i	$-0.140024\pi$
$659$	2.14617	+	3.71728i	0.0836031	+	0.144805i	−0.821192	+	0.570652i	$0.806691\pi$
$660$	−0.357797	+	0.206574i	−0.0139272	+	0.00804090i
$661$	10.7570	−	10.7570i	0.418399	−	0.418399i	−0.466252	−	0.884652i	$-0.654396\pi$
$661$	10.7570	−	10.7570i	0.418399	−	0.418399i	0.884652	+	0.466252i	$0.154396\pi$
$662$	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	0.912314	−	0.409492i	$-0.134294\pi$
$673$	26.3013	+	15.1851i	1.01384	+	0.585341i	0.101526	+	0.994833i	$0.467627\pi$
$674$	−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	0.965048	−	0.262073i	$-0.0844060\pi$
$677$	31.7593	+	18.3363i	1.22061	+	0.704720i	0.255562	+	0.966793i	$0.417739\pi$
$678$	−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	−0.542219	−	0.840237i	$-0.682416\pi$
$683$	−15.4630	+	4.14330i	−0.591676	+	0.158539i	−0.0494567	+	0.998776i	$0.515749\pi$
$684$	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	−0.818161	−	0.574989i	$-0.805006\pi$
$691$	4.67596	−	17.4509i	0.177882	−	0.663864i	0.996043	−	0.0888748i	$-0.0283271\pi$
$692$	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	$-0.748355\pi$
$701$		−	37.6363i		−	1.42150i	0.703444	−	0.710751i	$-0.251645\pi$
$702$	−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	0.537252	−	0.843422i	$-0.319462\pi$
$709$	−8.15239	−	8.15239i	−0.306169	−	0.306169i	−0.843422	+	0.537252i	$0.819462\pi$
$710$	−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	−0.804428	−	0.594050i	$-0.797528\pi$
$733$	−32.5986	+	8.73478i	−1.20406	+	0.322626i	−0.399630	+	0.916676i	$0.630861\pi$
$734$	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	0.679052	−	0.734090i	$-0.262391\pi$
$739$	−1.49619	−	1.49619i	−0.0550382	−	0.0550382i	−0.734090	+	0.679052i	$0.762391\pi$
$740$	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	−0.964058	−	0.265692i	$-0.914400\pi$
$743$	−7.14174	−	26.6533i	−0.262005	−	0.977816i	0.702053	−	0.712125i	$-0.252267\pi$
$744$	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	−0.376194	−	0.926541i	$-0.622767\pi$
$751$	6.52544	−	3.76747i	0.238117	−	0.137477i	0.614311	+	0.789064i	$0.289434\pi$
$752$	−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	0.172512	+	0.985007i	$0.444812\pi$
$757$	−21.0971	+	36.5412i	−0.766786	+	1.32811i	−0.939297	+	0.343104i	$0.888522\pi$
$758$		−	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	−0.684908	−	0.728629i	$-0.740158\pi$
$761$	1.20610	−	1.20610i	0.0437212	−	0.0437212i	0.728629	+	0.684908i	$0.240158\pi$
$762$	−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	−0.321304	−	0.946976i	$-0.604121\pi$
$769$	−3.49612	+	0.936782i	−0.126073	+	0.0337812i	0.195231	+	0.980757i	$0.437454\pi$
$770$		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	−0.691219	−	0.722645i	$-0.742926\pi$
$773$	−25.8153	+	6.91718i	−0.928510	+	0.248794i	−0.237291	+	0.971439i	$0.576259\pi$
$774$	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	−0.802021	−	0.597296i	$-0.796242\pi$
$787$	−11.3925	−	42.5173i	−0.406098	−	1.51558i	0.395923	−	0.918284i	$-0.370425\pi$
$788$	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	0.716340	−	0.697751i	$-0.245816\pi$
$797$	−6.94770	−	12.0338i	−0.246100	−	0.426258i	−0.962440	+	0.271493i	$0.912483\pi$
$798$		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	0.853895	−	0.520446i	$-0.174234\pi$
$811$	9.49597	+	9.49597i	0.333449	+	0.333449i	−0.520446	+	0.853895i	$0.674234\pi$
$812$		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	−0.752135	−	0.659009i	$-0.770976\pi$
$821$	−49.6560	−	13.3053i	−1.73301	−	0.464358i	−0.980873	+	0.194651i	$0.937643\pi$
$822$			15.3735i			0.536213i
$823$	−22.4979	−	12.9892i	−0.784227	−	0.452774i	0.0536991	−	0.998557i	$-0.482899\pi$
$823$	−22.4979	−	12.9892i	−0.784227	−	0.452774i	−0.837926	+	0.545783i	$0.816232\pi$
$824$	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	0.688463	−	0.725272i	$-0.258286\pi$
$827$	−1.05853	−	1.05853i	−0.0368089	−	0.0368089i	−0.725272	+	0.688463i	$0.758286\pi$
$828$	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	−0.0789379	−	0.996880i	$-0.525153\pi$
$839$	−18.7042	−	5.01177i	−0.645740	−	0.173025i	−0.566802	+	0.823854i	$0.691820\pi$
$840$		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	−0.933442	−	0.358728i	$-0.883210\pi$
$853$	−16.7852	+	16.7852i	−0.574713	+	0.574713i	0.358728	+	0.933442i	$0.383210\pi$
$854$		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	−0.858343	−	0.513076i	$-0.828506\pi$
$857$	−25.5716	−	44.2913i	−0.873508	−	1.51296i	−0.0151651	−	0.999885i	$-0.504827\pi$
$858$	7.16743	−	2.58926i	0.244692	−	0.0883958i
$859$	−13.0666	−	7.54398i	−0.445825	−	0.257397i	0.260240	−	0.965544i	$-0.416198\pi$
$859$	−13.0666	−	7.54398i	−0.445825	−	0.257397i	−0.706065	+	0.708147i	$0.749532\pi$
$860$	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	0.883079	−	0.469225i	$-0.155467\pi$
$863$	−3.41659	−	12.7509i	−0.116302	−	0.434045i	−0.999381	+	0.0351791i	$0.988800\pi$
$864$	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	−0.0672193	−	0.997738i	$-0.521413\pi$
$877$	27.5566	−	27.5566i	0.930519	−	0.930519i	0.997738	+	0.0672193i	$0.0214127\pi$
$878$	−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	−0.507974	−	0.861372i	$-0.669605\pi$
$881$	14.6029	−	25.2929i	0.491983	−	0.852140i	0.999957	+	0.00923231i	$0.00293878\pi$
$882$		0			0
$883$			2.58799i			0.0870929i	0.999051	+	0.0435464i	$0.0138656\pi$
$883$			2.58799i			0.0870929i	−0.999051	+	0.0435464i	$0.986134\pi$
$884$	−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	−0.935439	−	0.353488i	$-0.884996\pi$
$887$	−32.6723	+	18.8634i	−1.09703	+	0.633370i	−0.161590	+	0.986858i	$0.551662\pi$
$888$	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	$0.330692\pi$
$907$			51.9116i			1.72369i	−0.507168	+	0.861847i	$0.669308\pi$
$908$	−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	0.00759811	−	0.999971i	$-0.497581\pi$
$929$	−30.2470	−	30.2470i	−0.992373	−	0.992373i	−0.999971	+	0.00759811i	$0.997581\pi$
$930$	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	$0.0784713\pi$
$937$			14.9401i			0.488071i	−0.969766	+	0.244035i	$0.921529\pi$
$938$		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	−0.997176	−	0.0750961i	$-0.976074\pi$
$941$	−2.94635	+	10.9959i	−0.0960482	+	0.358457i	0.901128	+	0.433553i	$0.142740\pi$
$942$	−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	0.688453	+	0.725281i	$0.258290\pi$
$947$	−8.32128	+	31.0554i	−0.270405	+	1.00917i	−0.958858	+	0.283885i	$0.908377\pi$
$948$	−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	0.128428	−	0.991719i	$-0.459007\pi$
$953$	32.4604	−	18.7410i	1.05150	−	0.607081i	0.923068	+	0.384638i	$0.125674\pi$
$954$	−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	−0.509520	−	0.860459i	$-0.670177\pi$
$967$	10.9130	−	10.9130i	0.350939	−	0.350939i	0.860459	+	0.509520i	$0.170177\pi$
$968$	−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	$-0.990881\pi$
$971$		−	1.78526i		−	0.0572916i	0.999590	−	0.0286458i	$-0.00911949\pi$
$972$	−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	−0.732327	−	0.680953i	$-0.761566\pi$
$977$	−1.60581	+	1.60581i	−0.0513743	+	0.0513743i	0.680953	+	0.732327i	$0.261566\pi$
$978$	−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	−0.470835	−	0.882221i	$-0.656047\pi$
$983$	−41.3763	−	11.0868i	−1.31970	−	0.353613i	−0.848865	+	0.528609i	$0.822714\pi$
$984$	−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	−0.311152	−	0.950360i	$-0.600715\pi$
$997$	−40.7247	−	23.5124i	−1.28976	−	0.744645i	−0.978612	+	0.205715i	$0.934048\pi$
$998$		−	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.19.5		32
7.2	even	3		91.2.bc.a.6.4	yes	32
7.3	odd	6		637.2.bb.b.227.4		32
7.4	even	3		637.2.bb.b.227.3		32
7.5	odd	6		91.2.bc.a.6.3	✓	32
7.6	odd	2	inner	637.2.x.b.19.6		32
13.11	odd	12		637.2.bb.b.362.4		32
21.2	odd	6		819.2.fm.g.370.5		32
21.5	even	6		819.2.fm.g.370.6		32
91.11	odd	12	inner	637.2.x.b.570.5		32
91.24	even	12	inner	637.2.x.b.570.6		32
91.37	odd	12		91.2.bc.a.76.3	yes	32
91.76	even	12		637.2.bb.b.362.3		32
91.89	even	12		91.2.bc.a.76.4	yes	32
273.89	odd	12		819.2.fm.g.622.5		32
273.128	even	12		819.2.fm.g.622.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.6.3	✓	32	7.5	odd	6
91.2.bc.a.6.4	yes	32	7.2	even	3
91.2.bc.a.76.3	yes	32	91.37	odd	12
91.2.bc.a.76.4	yes	32	91.89	even	12
637.2.x.b.19.5		32	1.1	even	1	trivial
637.2.x.b.19.6		32	7.6	odd	2	inner
637.2.x.b.570.5		32	91.11	odd	12	inner
637.2.x.b.570.6		32	91.24	even	12	inner
637.2.bb.b.227.3		32	7.4	even	3
637.2.bb.b.227.4		32	7.3	odd	6
637.2.bb.b.362.3		32	91.76	even	12
637.2.bb.b.362.4		32	13.11	odd	12
819.2.fm.g.370.5		32	21.2	odd	6
819.2.fm.g.370.6		32	21.5	even	6
819.2.fm.g.622.5		32	273.89	odd	12
819.2.fm.g.622.6		32	273.128	even	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
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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