LMFDB - Embedded newform 637.2.bd.a.293.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(97,637)]

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([6, 5]))

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

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

chi := DirichletCharacter("637.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bd (of order $12$, degree $4$, 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:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			293.3
Character	$\chi$	$=$	637.293
Dual form			637.2.bd.a.587.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.278342 + 0.0745816i) q^{2} +(0.923129 + 0.532969i) q^{3} +(-1.66014 + 0.958482i) q^{4} +(0.365574 - 0.365574i) q^{5} +(-0.296695 - 0.0794993i) q^{6} +(0.798123 - 0.798123i) q^{8} +(-0.931889 - 1.61408i) q^{9} +O(q^{10})$	\(q+(-0.278342 + 0.0745816i) q^{2} +(0.923129 + 0.532969i) q^{3} +(-1.66014 + 0.958482i) q^{4} +(0.365574 - 0.365574i) q^{5} +(-0.296695 - 0.0794993i) q^{6} +(0.798123 - 0.798123i) q^{8} +(-0.931889 - 1.61408i) q^{9} +(-0.0744896 + 0.129020i) q^{10} +(-0.990856 - 3.69793i) q^{11} -2.04336 q^{12} +(-1.12494 - 3.42557i) q^{13} +(0.532311 - 0.142632i) q^{15} +(1.75434 - 3.03860i) q^{16} +(-2.26016 - 3.91471i) q^{17} +(0.379765 + 0.379765i) q^{18} +(2.97757 + 0.797839i) q^{19} +(-0.256508 + 0.957300i) q^{20} +(0.551594 + 0.955389i) q^{22} +(7.51600 + 4.33936i) q^{23} +(1.16214 - 0.311396i) q^{24} +4.73271i q^{25} +(0.568604 + 0.869580i) q^{26} -5.18448i q^{27} +(1.26720 - 2.19486i) q^{29} +(-0.137527 + 0.0794012i) q^{30} +(-0.739278 + 0.739278i) q^{31} +(-0.845949 + 3.15712i) q^{32} +(1.05619 - 3.94176i) q^{33} +(0.921063 + 0.921063i) q^{34} +(3.09413 + 1.78640i) q^{36} +(-0.0474003 - 0.176900i) q^{37} -0.888289 q^{38} +(0.787251 - 3.76180i) q^{39} -0.583546i q^{40} +(-1.79081 - 6.68338i) q^{41} +(4.59244 - 2.65145i) q^{43} +(5.18935 + 5.18935i) q^{44} +(-0.930740 - 0.249391i) q^{45} +(-2.41566 - 0.647273i) q^{46} +(-6.61286 - 6.61286i) q^{47} +(3.23896 - 1.87001i) q^{48} +(-0.352973 - 1.31731i) q^{50} -4.81838i q^{51} +(5.15091 + 4.60868i) q^{52} -1.02507 q^{53} +(0.386667 + 1.44306i) q^{54} +(-1.71410 - 0.989634i) q^{55} +(2.32346 + 2.32346i) q^{57} +(-0.189020 + 0.705432i) q^{58} +(-0.134868 + 0.503336i) q^{59} +(-0.747000 + 0.747000i) q^{60} +(-7.39280 + 4.26823i) q^{61} +(0.150636 - 0.260909i) q^{62} +6.07549i q^{64} +(-1.66355 - 0.841047i) q^{65} +1.17593i q^{66} +(6.83871 - 1.83243i) q^{67} +(7.50436 + 4.33264i) q^{68} +(4.62549 + 8.01158i) q^{69} +(1.96522 - 7.33429i) q^{71} +(-2.03200 - 0.544472i) q^{72} +(-8.74565 - 8.74565i) q^{73} +(0.0263870 + 0.0457036i) q^{74} +(-2.52239 + 4.36890i) q^{75} +(-5.70790 + 1.52943i) q^{76} +(0.0614358 + 1.10578i) q^{78} -7.55600 q^{79} +(-0.469493 - 1.75217i) q^{80} +(-0.0325003 + 0.0562921i) q^{81} +(0.996914 + 1.72671i) q^{82} +(-6.42827 + 6.42827i) q^{83} +(-2.25737 - 0.604861i) q^{85} +(-1.08052 + 1.08052i) q^{86} +(2.33958 - 1.35076i) q^{87} +(-3.74222 - 2.16057i) q^{88} +(11.7065 - 3.13675i) q^{89} +0.277664 q^{90} -16.6368 q^{92} +(-1.07646 + 0.288437i) q^{93} +(2.33384 + 1.34744i) q^{94} +(1.38019 - 0.796855i) q^{95} +(-2.46357 + 2.46357i) q^{96} +(13.1956 + 3.53575i) q^{97} +(-5.04538 + 5.04538i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} - 6 q^{3} + 6 q^{4} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q + 4 * q^2 - 6 * q^3 + 6 * q^4 + 12 * q^6 - 4 * q^8 + 6 * q^9	$ 28 q + 4 q^{2} - 6 q^{3} + 6 q^{4} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} - 4 q^{11} - 16 q^{12} + 10 q^{15} - 2 q^{16} - 6 q^{17} + 2 q^{18} + 22 q^{19} - 36 q^{20} - 8 q^{22} + 6 q^{23} - 30 q^{24} - 8 q^{29} + 30 q^{30} + 34 q^{31} + 10 q^{32} - 30 q^{33} + 12 q^{34} + 54 q^{36} + 26 q^{37} - 8 q^{39} + 18 q^{41} + 48 q^{43} + 12 q^{44} - 18 q^{45} - 42 q^{46} + 36 q^{47} + 12 q^{48} + 10 q^{50} + 2 q^{52} - 24 q^{53} - 6 q^{55} + 12 q^{57} - 16 q^{58} + 48 q^{59} - 26 q^{60} + 30 q^{61} - 36 q^{62} - 26 q^{65} + 14 q^{67} - 30 q^{68} + 42 q^{69} - 42 q^{71} - 8 q^{72} + 26 q^{73} - 6 q^{74} - 20 q^{75} + 52 q^{76} - 62 q^{78} - 8 q^{79} + 18 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} + 48 q^{86} - 42 q^{87} + 6 q^{88} + 30 q^{89} - 72 q^{90} - 156 q^{92} - 34 q^{93} - 18 q^{94} + 6 q^{95} - 84 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q + 4 * q^2 - 6 * q^3 + 6 * q^4 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 - 4 * q^11 - 16 * q^12 + 10 * q^15 - 2 * q^16 - 6 * q^17 + 2 * q^18 + 22 * q^19 - 36 * q^20 - 8 * q^22 + 6 * q^23 - 30 * q^24 - 8 * q^29 + 30 * q^30 + 34 * q^31 + 10 * q^32 - 30 * q^33 + 12 * q^34 + 54 * q^36 + 26 * q^37 - 8 * q^39 + 18 * q^41 + 48 * q^43 + 12 * q^44 - 18 * q^45 - 42 * q^46 + 36 * q^47 + 12 * q^48 + 10 * q^50 + 2 * q^52 - 24 * q^53 - 6 * q^55 + 12 * q^57 - 16 * q^58 + 48 * q^59 - 26 * q^60 + 30 * q^61 - 36 * q^62 - 26 * q^65 + 14 * q^67 - 30 * q^68 + 42 * q^69 - 42 * q^71 - 8 * q^72 + 26 * q^73 - 6 * q^74 - 20 * q^75 + 52 * q^76 - 62 * q^78 - 8 * q^79 + 18 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 + 48 * q^86 - 42 * q^87 + 6 * q^88 + 30 * q^89 - 72 * q^90 - 156 * q^92 - 34 * q^93 - 18 * q^94 + 6 * q^95 - 84 * q^96 + 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.278342	+	0.0745816i	−0.196818	+	0.0527371i	−0.355881	−	0.934531i	$-0.615819\pi$
$2$	−0.278342	+	0.0745816i	−0.196818	+	0.0527371i	0.159063	+	0.987268i	$0.449153\pi$
$3$	0.923129	+	0.532969i	0.532969	+	0.307710i	0.742224	−	0.670151i	$-0.233771\pi$
$3$	0.923129	+	0.532969i	0.532969	+	0.307710i	−0.209256	+	0.977861i	$0.567104\pi$
$4$	−1.66014	+	0.958482i	−0.830069	+	0.479241i
$5$	0.365574	−	0.365574i	0.163490	−	0.163490i	−0.620621	−	0.784111i	$-0.713119\pi$
$5$	0.365574	−	0.365574i	0.163490	−	0.163490i	0.784111	+	0.620621i	$0.213119\pi$
$6$	−0.296695	−	0.0794993i	−0.121125	−	0.0324554i
$7$		0			0
$7$		0			0
$8$	0.798123	−	0.798123i	0.282179	−	0.282179i
$9$	−0.931889	−	1.61408i	−0.310630	−	0.538026i
$10$	−0.0744896	+	0.129020i	−0.0235557	+	0.0407996i
$11$	−0.990856	−	3.69793i	−0.298754	−	1.11497i	−0.938190	−	0.346122i	$-0.887498\pi$
$11$	−0.990856	−	3.69793i	−0.298754	−	1.11497i	0.639435	−	0.768845i	$-0.279168\pi$
$12$	−2.04336			−0.589868
$13$	−1.12494	−	3.42557i	−0.312003	−	0.950081i
$13$	−1.12494	−	3.42557i	−0.312003	−	0.950081i
$14$		0			0
$15$	0.532311	−	0.142632i	0.137442	−	0.0368275i
$16$	1.75434	−	3.03860i	0.438584	−	0.759650i
$17$	−2.26016	−	3.91471i	−0.548169	−	0.949457i	−0.998400	−	0.0565446i	$-0.981992\pi$
$17$	−2.26016	−	3.91471i	−0.548169	−	0.949457i	0.450231	−	0.892912i	$-0.351342\pi$
$18$	0.379765	+	0.379765i	0.0895114	+	0.0895114i
$19$	2.97757	+	0.797839i	0.683103	+	0.183037i	0.583650	−	0.812006i	$-0.301624\pi$
$19$	2.97757	+	0.797839i	0.683103	+	0.183037i	0.0994528	+	0.995042i	$0.468291\pi$
$20$	−0.256508	+	0.957300i	−0.0573569	+	0.214059i
$21$		0			0
$22$	0.551594	+	0.955389i	0.117600	+	0.203690i
$23$	7.51600	+	4.33936i	1.56719	+	0.904820i	0.996494	+	0.0836605i	$0.0266611\pi$
$23$	7.51600	+	4.33936i	1.56719	+	0.904820i	0.570699	+	0.821159i	$0.306672\pi$
$24$	1.16214	−	0.311396i	0.237222	−	0.0635634i
$25$			4.73271i			0.946542i
$26$	0.568604	+	0.869580i	0.111512	+	0.170539i
$27$		−	5.18448i		−	0.997754i
$28$		0			0
$29$	1.26720	−	2.19486i	0.235314	−	0.407575i	−0.724050	−	0.689747i	$-0.757722\pi$
$29$	1.26720	−	2.19486i	0.235314	−	0.407575i	0.959364	+	0.282172i	$0.0910549\pi$
$30$	−0.137527	+	0.0794012i	−0.0251089	+	0.0144966i
$31$	−0.739278	+	0.739278i	−0.132778	+	0.132778i	−0.770372	−	0.637594i	$-0.779930\pi$
$31$	−0.739278	+	0.739278i	−0.132778	+	0.132778i	0.637594	+	0.770372i	$0.279930\pi$
$32$	−0.845949	+	3.15712i	−0.149544	+	0.558106i
$33$	1.05619	−	3.94176i	0.183859	−	0.686172i
$34$	0.921063	+	0.921063i	0.157961	+	0.157961i
$35$		0			0
$36$	3.09413	+	1.78640i	0.515688	+	0.297733i
$37$	−0.0474003	−	0.176900i	−0.00779255	−	0.0290822i	0.961920	−	0.273331i	$-0.0881254\pi$
$37$	−0.0474003	−	0.176900i	−0.00779255	−	0.0290822i	−0.969713	+	0.244249i	$0.921459\pi$
$38$	−0.888289			−0.144099
$39$	0.787251	−	3.76180i	0.126061	−	0.602370i
$40$		−	0.583546i		−	0.0922667i
$41$	−1.79081	−	6.68338i	−0.279677	−	1.04377i	−0.952642	−	0.304094i	$-0.901646\pi$
$41$	−1.79081	−	6.68338i	−0.279677	−	1.04377i	0.672965	−	0.739674i	$-0.265020\pi$
$42$		0			0
$43$	4.59244	−	2.65145i	0.700341	−	0.404342i	−0.107134	−	0.994245i	$-0.534167\pi$
$43$	4.59244	−	2.65145i	0.700341	−	0.404342i	0.807474	+	0.589903i	$0.200834\pi$
$44$	5.18935	+	5.18935i	0.782324	+	0.782324i
$45$	−0.930740	−	0.249391i	−0.138746	−	0.0371770i
$46$	−2.41566	−	0.647273i	−0.356169	−	0.0954352i
$47$	−6.61286	−	6.61286i	−0.964585	−	0.964585i	0.0348092	−	0.999394i	$-0.488918\pi$
$47$	−6.61286	−	6.61286i	−0.964585	−	0.964585i	−0.999394	+	0.0348092i	$0.988918\pi$
$48$	3.23896	−	1.87001i	0.467503	−	0.269913i
$49$		0			0
$50$	−0.352973	−	1.31731i	−0.0499179	−	0.186296i
$51$		−	4.81838i		−	0.674708i
$52$	5.15091	+	4.60868i	0.714302	+	0.639108i
$53$	−1.02507			−0.140804			−0.0704019	−	0.997519i	$-0.522428\pi$
$53$	−1.02507			−0.140804			−0.0704019	+	0.997519i	$0.522428\pi$
$54$	0.386667	+	1.44306i	0.0526187	+	0.196376i
$55$	−1.71410	−	0.989634i	−0.231129	−	0.133442i
$56$		0			0
$57$	2.32346	+	2.32346i	0.307750	+	0.307750i
$58$	−0.189020	+	0.705432i	−0.0248195	+	0.0926278i
$59$	−0.134868	+	0.503336i	−0.0175584	+	0.0655287i	−0.974149	−	0.225906i	$-0.927466\pi$
$59$	−0.134868	+	0.503336i	−0.0175584	+	0.0655287i	0.956591	+	0.291434i	$0.0941325\pi$
$60$	−0.747000	+	0.747000i	−0.0964373	+	0.0964373i
$61$	−7.39280	+	4.26823i	−0.946551	+	0.546491i	−0.892008	−	0.452020i	$-0.850704\pi$
$61$	−7.39280	+	4.26823i	−0.946551	+	0.546491i	−0.0545432	+	0.998511i	$0.517370\pi$
$62$	0.150636	−	0.260909i	0.0191308	−	0.0331355i
$63$		0			0
$64$			6.07549i			0.759437i
$65$	−1.66355	−	0.841047i	−0.206338	−	0.104319i
$66$			1.17593i			0.144747i
$67$	6.83871	−	1.83243i	0.835482	−	0.223867i	0.184378	−	0.982855i	$-0.440973\pi$
$67$	6.83871	−	1.83243i	0.835482	−	0.223867i	0.651104	+	0.758989i	$0.274306\pi$
$68$	7.50436	+	4.33264i	0.910037	+	0.525410i
$69$	4.62549	+	8.01158i	0.556843	+	0.964481i
$70$		0			0
$71$	1.96522	−	7.33429i	0.233228	−	0.870420i	−0.745711	−	0.666269i	$-0.767890\pi$
$71$	1.96522	−	7.33429i	0.233228	−	0.870420i	0.978940	−	0.204150i	$-0.0654432\pi$
$72$	−2.03200	−	0.544472i	−0.239473	−	0.0641666i
$73$	−8.74565	−	8.74565i	−1.02360	−	1.02360i	−0.999715	−	0.0238860i	$-0.992396\pi$
$73$	−8.74565	−	8.74565i	−1.02360	−	1.02360i	−0.0238860	−	0.999715i	$-0.507604\pi$
$74$	0.0263870	+	0.0457036i	0.00306742	+	0.00531294i
$75$	−2.52239	+	4.36890i	−0.291260	+	0.504477i
$76$	−5.70790	+	1.52943i	−0.654741	+	0.175437i
$77$		0			0
$78$	0.0614358	+	1.10578i	0.00695623	+	0.125205i
$79$	−7.55600			−0.850116			−0.425058	−	0.905166i	$-0.639746\pi$
$79$	−7.55600			−0.850116			−0.425058	+	0.905166i	$0.639746\pi$
$80$	−0.469493	−	1.75217i	−0.0524910	−	0.195899i
$81$	−0.0325003	+	0.0562921i	−0.00361114	+	0.00625468i
$82$	0.996914	+	1.72671i	0.110091	+	0.190683i
$83$	−6.42827	+	6.42827i	−0.705594	+	0.705594i	−0.965606	−	0.260011i	$-0.916274\pi$
$83$	−6.42827	+	6.42827i	−0.705594	+	0.705594i	0.260011	+	0.965606i	$0.416274\pi$
$84$		0			0
$85$	−2.25737	−	0.604861i	−0.244846	−	0.0656064i
$86$	−1.08052	+	1.08052i	−0.116516	+	0.116516i
$87$	2.33958	−	1.35076i	0.250830	−	0.144817i
$88$	−3.74222	−	2.16057i	−0.398922	−	0.230318i
$89$	11.7065	−	3.13675i	1.24089	−	0.332495i	0.422078	−	0.906560i	$-0.361301\pi$
$89$	11.7065	−	3.13675i	1.24089	−	0.332495i	0.818810	+	0.574065i	$0.194634\pi$
$90$	0.277664			0.0292684
$91$		0			0
$92$	−16.6368			−1.73451
$93$	−1.07646	+	0.288437i	−0.111624	+	0.0299095i
$94$	2.33384	+	1.34744i	0.240717	+	0.138978i
$95$	1.38019	−	0.796855i	0.141605	−	0.0817556i
$96$	−2.46357	+	2.46357i	−0.251437	+	0.251437i
$97$	13.1956	+	3.53575i	1.33981	+	0.359001i	0.856364	−	0.516373i	$-0.172718\pi$
$97$	13.1956	+	3.53575i	1.33981	+	0.359001i	0.483446	+	0.875374i	$0.339385\pi$
$98$		0			0
$99$	−5.04538	+	5.04538i	−0.507079	+	0.507079i
$100$	−4.53622	−	7.85696i	−0.453622	−	0.785696i
$101$	−0.555807	+	0.962686i	−0.0553049	+	0.0957909i	−0.892352	−	0.451339i	$-0.850946\pi$
$101$	−0.555807	+	0.962686i	−0.0553049	+	0.0957909i	0.837048	+	0.547130i	$0.184280\pi$
$102$	0.359362	+	1.34116i	0.0355821	+	0.132794i
$103$	0.428376			0.0422091			0.0211046	−	0.999777i	$-0.493282\pi$
$103$	0.428376			0.0422091			0.0211046	+	0.999777i	$0.493282\pi$
$104$	−3.63187	−	1.83618i	−0.356134	−	0.180052i
$105$		0			0
$106$	0.285320	−	0.0764512i	0.0277127	−	0.00742559i
$107$	−2.50817	+	4.34428i	−0.242474	+	0.419977i	−0.961418	−	0.275090i	$-0.911292\pi$
$107$	−2.50817	+	4.34428i	−0.242474	+	0.419977i	0.718944	+	0.695068i	$0.244626\pi$
$108$	4.96923	+	8.60696i	0.478164	+	0.828205i
$109$	0.600467	+	0.600467i	0.0575143	+	0.0575143i	0.735279	−	0.677765i	$-0.237051\pi$
$109$	0.600467	+	0.600467i	0.0575143	+	0.0575143i	−0.677765	+	0.735279i	$0.737051\pi$
$110$	0.550914	+	0.147617i	0.0525276	+	0.0140747i
$111$	0.0505257	−	0.188564i	0.00479569	−	0.0178977i
$112$		0			0
$113$	2.44889	+	4.24160i	0.230372	+	0.399016i	0.957918	−	0.287043i	$-0.0926724\pi$
$113$	2.44889	+	4.24160i	0.230372	+	0.399016i	−0.727546	+	0.686059i	$0.759339\pi$
$114$	−0.820005	−	0.473430i	−0.0768005	−	0.0443408i
$115$	4.33401	−	1.16129i	0.404149	−	0.108291i
$116$			4.85836i			0.451088i
$117$	−4.48081	+	5.00800i	−0.414251	+	0.462989i
$118$		−	0.150158i		−	0.0138232i
$119$		0			0
$120$	0.311012	−	0.538688i	0.0283914	−	0.0491753i
$121$	−3.16658	+	1.82822i	−0.287871	+	0.166202i
$122$	1.73940	−	1.73940i	0.157478	−	0.157478i
$123$	1.90889	−	7.12406i	0.172119	−	0.642355i
$124$	0.518720	−	1.93589i	0.0465824	−	0.173848i
$125$	3.55803	+	3.55803i	0.318240	+	0.318240i
$126$		0			0
$127$	−3.00665	−	1.73589i	−0.266797	−	0.154035i	0.360634	−	0.932707i	$-0.382560\pi$
$127$	−3.00665	−	1.73589i	−0.266797	−	0.154035i	−0.627431	+	0.778672i	$0.715894\pi$
$128$	−2.14502	−	8.00532i	−0.189595	−	0.707577i
$129$	5.65255			0.497679
$130$	0.525762	+	0.110029i	0.0461124	+	0.00965018i
$131$		−	17.3386i		−	1.51488i	−0.652903	−	0.757442i	$-0.726449\pi$
$131$		−	17.3386i		−	1.51488i	0.652903	−	0.757442i	$-0.273551\pi$
$132$	2.02468	+	7.55620i	0.176226	+	0.657683i
$133$		0			0
$134$	−1.76684	+	1.02008i	−0.152631	+	0.0881218i
$135$	−1.89531	−	1.89531i	−0.163122	−	0.163122i
$136$	−4.92831	−	1.32054i	−0.422599	−	0.113235i
$137$	9.12446	+	2.44489i	0.779555	+	0.208881i	0.626589	−	0.779350i	$-0.284451\pi$
$137$	9.12446	+	2.44489i	0.779555	+	0.208881i	0.152966	+	0.988231i	$0.451117\pi$
$138$	−1.88499	−	1.88499i	−0.160461	−	0.160461i
$139$	−13.1525	+	7.59358i	−1.11558	+	0.644079i	−0.940268	−	0.340434i	$-0.889426\pi$
$139$	−13.1525	+	7.59358i	−1.11558	+	0.644079i	−0.175310	+	0.984513i	$0.556093\pi$
$140$		0			0
$141$	−2.58007	−	9.62897i	−0.217281	−	0.810905i
$142$			2.18801i			0.183614i
$143$	−11.5528	+	7.55420i	−0.966096	+	0.631714i
$144$	−6.53939			−0.544949
$145$	−0.339127	−	1.26564i	−0.0281630	−	0.105106i
$146$	3.08655	+	1.78202i	0.255444	+	0.147481i
$147$		0			0
$148$	0.248247	+	0.248247i	0.0204057	+	0.0204057i
$149$	−3.71806	+	13.8760i	−0.304595	+	1.13677i	0.628698	+	0.777650i	$0.283588\pi$
$149$	−3.71806	+	13.8760i	−0.304595	+	1.13677i	−0.933293	+	0.359116i	$0.883078\pi$
$150$	0.376247	−	1.40417i	0.0307205	−	0.114650i
$151$	3.50995	−	3.50995i	0.285636	−	0.285636i	−0.549716	−	0.835352i	$-0.685264\pi$
$151$	3.50995	−	3.50995i	0.285636	−	0.285636i	0.835352	+	0.549716i	$0.185264\pi$
$152$	3.01324	−	1.73970i	0.244406	−	0.141108i
$153$	−4.21243	+	7.29615i	−0.340555	+	0.589859i
$154$		0			0
$155$			0.540522i			0.0434157i
$156$	2.29867	+	6.99967i	0.184041	+	0.560422i
$157$			3.49186i			0.278681i	0.990245	+	0.139340i	$0.0444983\pi$
$157$			3.49186i			0.278681i	−0.990245	+	0.139340i	$0.955502\pi$
$158$	2.10315	−	0.563538i	0.167318	−	0.0448327i
$159$	−0.946269	−	0.546329i	−0.0750440	−	0.0433267i
$160$	0.844906	+	1.46342i	0.0667957	+	0.115693i
$161$		0			0
$162$	0.00484784	−	0.0180924i	0.000380882	−	0.00142147i
$163$	−2.21764	−	0.594214i	−0.173699	−	0.0465424i	0.170921	−	0.985285i	$-0.445326\pi$
$163$	−2.21764	−	0.594214i	−0.173699	−	0.0465424i	−0.344620	+	0.938742i	$0.611992\pi$
$164$	9.37888	+	9.37888i	0.732368	+	0.732368i
$165$	−1.05489	−	1.82712i	−0.0821229	−	0.142241i
$166$	1.30983	−	2.26869i	0.101662	−	0.176085i
$167$	20.2547	−	5.42723i	1.56736	−	0.419972i	0.632372	−	0.774665i	$-0.282081\pi$
$167$	20.2547	−	5.42723i	1.56736	−	0.419972i	0.934983	+	0.354693i	$0.115415\pi$
$168$		0			0
$169$	−10.4690	+	7.70714i	−0.805308	+	0.592857i
$170$	0.673433			0.0516500
$171$	−1.48699	−	5.54954i	−0.113713	−	0.424384i
$172$	−5.08273	+	8.80354i	−0.387554	+	0.671263i
$173$	10.0438	+	17.3963i	0.763613	+	1.32262i	0.940977	+	0.338472i	$0.109910\pi$
$173$	10.0438	+	17.3963i	0.763613	+	1.32262i	−0.177363	+	0.984145i	$0.556757\pi$
$174$	−0.550463	+	0.550463i	−0.0417305	+	0.0417305i
$175$		0			0
$176$	−12.9748	−	3.47659i	−0.978013	−	0.262058i
$177$	−0.392763	+	0.392763i	−0.0295219	+	0.0295219i
$178$	−3.02447	+	1.74618i	−0.226694	+	0.130882i
$179$	18.5574	+	10.7141i	1.38704	+	0.800810i	0.992981	−	0.118274i	$-0.0377360\pi$
$179$	18.5574	+	10.7141i	1.38704	+	0.800810i	0.394062	+	0.919084i	$0.371069\pi$
$180$	1.78419	−	0.478073i	0.132986	−	0.0356335i
$181$	−19.7532			−1.46824			−0.734121	−	0.679019i	$-0.762405\pi$
$181$	−19.7532			−1.46824			−0.734121	+	0.679019i	$0.762405\pi$
$182$		0			0
$183$	−9.09934			−0.672643
$184$	9.46203	−	2.53534i	0.697550	−	0.186908i
$185$	−0.0819984	−	0.0473418i	−0.00602864	−	0.00348064i
$186$	0.278112	−	0.160568i	0.0203922	−	0.0117734i
$187$	−12.2368	+	12.2368i	−0.894844	+	0.894844i
$188$	17.3166	+	4.63996i	1.26294	+	0.338404i
$189$		0			0
$190$	−0.324735	+	0.324735i	−0.0235588	+	0.0235588i
$191$	2.14939	+	3.72284i	0.155524	+	0.269376i	0.933250	−	0.359228i	$-0.116960\pi$
$191$	2.14939	+	3.72284i	0.155524	+	0.269376i	−0.777726	+	0.628604i	$0.783627\pi$
$192$	−3.23805	+	5.60846i	−0.233686	+	0.404756i
$193$	−3.50795	−	13.0919i	−0.252508	−	0.942372i	−0.969460	−	0.245250i	$-0.921130\pi$
$193$	−3.50795	−	13.0919i	−0.252508	−	0.942372i	0.716952	−	0.697123i	$-0.245537\pi$
$194$	−3.93659			−0.282631
$195$	−1.08742	−	1.66301i	−0.0778716	−	0.119091i
$196$		0			0
$197$	3.69905	−	0.991158i	0.263546	−	0.0706171i	−0.124626	−	0.992204i	$-0.539773\pi$
$197$	3.69905	−	0.991158i	0.263546	−	0.0706171i	0.388173	+	0.921587i	$0.373106\pi$
$198$	1.02805	−	1.78063i	0.0730603	−	0.126544i
$199$	−5.25409	−	9.10036i	−0.372453	−	0.645107i	0.617489	−	0.786579i	$-0.288150\pi$
$199$	−5.25409	−	9.10036i	−0.372453	−	0.645107i	−0.989942	+	0.141472i	$0.954817\pi$
$200$	3.77729	+	3.77729i	0.267094	+	0.267094i
$201$	7.28964	+	1.95325i	0.514171	+	0.137772i
$202$	0.0829059	−	0.309409i	0.00583324	−	0.0217700i
$203$		0			0
$204$	4.61832	+	7.99917i	0.323347	+	0.560054i
$205$	−3.09794	−	1.78860i	−0.216370	−	0.124921i
$206$	−0.119235	+	0.0319489i	−0.00830750	+	0.00222599i
$207$		−	16.1752i		−	1.12426i
$208$	−12.3825	−	2.59134i	−0.858569	−	0.179677i
$209$		−	11.8014i		−	0.816319i
$210$		0			0
$211$	−3.87722	+	6.71554i	−0.266919	+	0.462317i	−0.968065	−	0.250701i	$-0.919339\pi$
$211$	−3.87722	+	6.71554i	−0.266919	+	0.462317i	0.701146	+	0.713018i	$0.252672\pi$
$212$	1.70175	−	0.982508i	0.116877	−	0.0674790i
$213$	5.72309	−	5.72309i	0.392140	−	0.392140i
$214$	0.374126	−	1.39626i	0.0255748	−	0.0954463i
$215$	0.709577	−	2.64818i	0.0483927	−	0.180604i
$216$	−4.13785	−	4.13785i	−0.281545	−	0.281545i
$217$		0			0
$218$	−0.211919	−	0.122352i	−0.0143530	−	0.00828669i
$219$	−3.41220	−	12.7345i	−0.230575	−	0.860519i
$220$	3.79418			0.255804
$221$	−10.8675	+	12.1462i	−0.731030	+	0.817039i
$222$			0.0562537i			0.00377550i
$223$	6.07469	+	22.6710i	0.406791	+	1.51817i	0.800728	+	0.599028i	$0.204446\pi$
$223$	6.07469	+	22.6710i	0.406791	+	1.51817i	−0.393937	+	0.919138i	$0.628887\pi$
$224$		0			0
$225$	7.63897	−	4.41036i	0.509265	−	0.294024i
$226$	−0.997974	−	0.997974i	−0.0663842	−	0.0663842i
$227$	−5.95236	−	1.59493i	−0.395072	−	0.105859i	0.0558131	−	0.998441i	$-0.482225\pi$
$227$	−5.95236	−	1.59493i	−0.395072	−	0.105859i	−0.450885	+	0.892582i	$0.648892\pi$
$228$	−6.08426	−	1.63027i	−0.402940	−	0.107968i
$229$	8.05289	+	8.05289i	0.532150	+	0.532150i	0.921212	−	0.389062i	$-0.127201\pi$
$229$	8.05289	+	8.05289i	0.532150	+	0.532150i	−0.389062	+	0.921212i	$0.627201\pi$
$230$	−1.11973	+	0.646475i	−0.0738326	+	0.0426273i
$231$		0			0
$232$	−0.740385	−	2.76315i	−0.0486086	−	0.181410i
$233$			14.9044i			0.976417i	0.872727	+	0.488208i	$0.162349\pi$
$233$			14.9044i			0.976417i	−0.872727	+	0.488208i	$0.837651\pi$
$234$	0.873695	−	1.72812i	0.0571152	−	0.112971i
$235$	−4.83498			−0.315399
$236$	−0.258538	−	0.964876i	−0.0168294	−	0.0628081i
$237$	−6.97516	−	4.02711i	−0.453085	−	0.261589i
$238$		0			0
$239$	20.4619	+	20.4619i	1.32357	+	1.32357i	0.910864	+	0.412706i	$0.135416\pi$
$239$	20.4619	+	20.4619i	1.32357	+	1.32357i	0.412706	+	0.910864i	$0.364584\pi$
$240$	0.500451	−	1.86771i	0.0323039	−	0.120560i
$241$	−4.76037	+	17.7659i	−0.306642	+	1.14440i	0.624880	+	0.780721i	$0.285148\pi$
$241$	−4.76037	+	17.7659i	−0.306642	+	1.14440i	−0.931522	+	0.363684i	$0.881519\pi$
$242$	0.745040	−	0.745040i	0.0478930	−	0.0478930i
$243$	−13.5297	+	7.81137i	−0.867930	+	0.501099i
$244$	8.18205	−	14.1717i	0.523802	−	0.907252i
$245$		0			0
$246$			2.12530i			0.135504i
$247$	−0.616557	−	11.0974i	−0.0392306	−	0.706111i
$248$			1.18007i			0.0749345i
$249$	−9.36019	+	2.50806i	−0.593178	+	0.158942i
$250$	−1.25571	−	0.724986i	−0.0794182	−	0.0458521i
$251$	−3.43367	−	5.94730i	−0.216731	−	0.375390i	0.737075	−	0.675811i	$-0.236206\pi$
$251$	−3.43367	−	5.94730i	−0.216731	−	0.375390i	−0.953807	+	0.300421i	$0.902873\pi$
$252$		0			0
$253$	8.59937	−	32.0933i	0.540638	−	2.01769i
$254$	0.966343	+	0.258931i	0.0606338	+	0.0162468i
$255$	−1.76147	−	1.76147i	−0.110308	−	0.110308i
$256$	−4.88140	−	8.45483i	−0.305087	−	0.528427i
$257$	4.16483	−	7.21370i	0.259795	−	0.449978i	−0.706392	−	0.707821i	$-0.749678\pi$
$257$	4.16483	−	7.21370i	0.259795	−	0.449978i	0.966187	+	0.257843i	$0.0830117\pi$
$258$	−1.57334	+	0.421576i	−0.0979521	+	0.0262462i
$259$		0			0
$260$	3.56785	−	0.198225i	0.221269	−	0.0122934i
$261$	−4.72357			−0.292382
$262$	1.29314	+	4.82607i	0.0798906	+	0.298156i
$263$	1.35186	−	2.34149i	0.0833593	−	0.144383i	−0.821332	−	0.570451i	$-0.806768\pi$
$263$	1.35186	−	2.34149i	0.0833593	−	0.144383i	0.904691	+	0.426069i	$0.140102\pi$
$264$	−2.30304	−	3.98898i	−0.141742	−	0.245505i
$265$	−0.374738	+	0.374738i	−0.0230200	+	0.0230200i
$266$		0			0
$267$	12.4784	+	3.34358i	0.763666	+	0.204624i
$268$	−9.59686	+	9.59686i	−0.586222	+	0.586222i
$269$	20.2332	−	11.6816i	1.23364	−	0.712242i	0.265853	−	0.964014i	$-0.414346\pi$
$269$	20.2332	−	11.6816i	1.23364	−	0.712242i	0.967787	+	0.251771i	$0.0810130\pi$
$270$	0.668901	+	0.386190i	0.0407080	+	0.0235028i
$271$	−12.8394	+	3.44030i	−0.779936	+	0.208983i	−0.626756	−	0.779215i	$-0.715618\pi$
$271$	−12.8394	+	3.44030i	−0.779936	+	0.208983i	−0.153179	+	0.988198i	$0.548951\pi$
$272$	−15.8603			−0.961673
$273$		0			0
$274$	−2.72207			−0.164446
$275$	17.5012	−	4.68944i	1.05536	−	0.282784i
$276$	−15.3579	−	8.86689i	−0.924437	−	0.533724i
$277$	−4.19252	+	2.42055i	−0.251904	+	0.145437i	−0.620636	−	0.784099i	$-0.713125\pi$
$277$	−4.19252	+	2.42055i	−0.251904	+	0.145437i	0.368732	+	0.929536i	$0.379792\pi$
$278$	3.09455	−	3.09455i	0.185599	−	0.185599i
$279$	1.88218	+	0.504328i	0.112683	+	0.0301933i
$280$		0			0
$281$	8.60836	−	8.60836i	0.513532	−	0.513532i	−0.402075	−	0.915607i	$-0.631711\pi$
$281$	8.60836	−	8.60836i	0.513532	−	0.513532i	0.915607	+	0.402075i	$0.131711\pi$
$282$	1.43629	+	2.48772i	0.0855297	+	0.148142i
$283$	0.527867	−	0.914293i	0.0313784	−	0.0543491i	−0.849910	−	0.526928i	$-0.823344\pi$
$283$	0.527867	−	0.914293i	0.0313784	−	0.0543491i	0.881288	+	0.472579i	$0.156677\pi$
$284$	3.76725	+	14.0596i	0.223545	+	0.834281i
$285$	1.69879			0.100628
$286$	2.65224	−	2.96428i	0.156830	−	0.175282i
$287$		0			0
$288$	5.88418	−	1.57666i	0.346729	−	0.0929056i
$289$	−1.71664	+	2.97331i	−0.100979	+	0.174900i
$290$	0.188787	+	0.326989i	0.0110860	+	0.0192014i
$291$	10.2968	+	10.2968i	0.603608	+	0.603608i
$292$	22.9015	+	6.13645i	1.34021	+	0.359108i
$293$	5.31237	−	19.8260i	0.310352	−	1.15825i	−0.617888	−	0.786266i	$-0.712011\pi$
$293$	5.31237	−	19.8260i	0.310352	−	1.15825i	0.928240	−	0.371983i	$-0.121322\pi$
$294$		0			0
$295$	0.134702	+	0.233311i	0.00784266	+	0.0135839i
$296$	−0.179019	−	0.103357i	−0.0104053	−	0.00600749i
$297$	−19.1718	+	5.13708i	−1.11246	+	0.298083i
$298$		−	4.13957i		−	0.239799i
$299$	6.40969	−	30.6281i	0.370682	−	1.77127i
$300$		−	9.67064i		−	0.558335i
$301$		0			0
$302$	−0.715189	+	1.23874i	−0.0411545	+	0.0712817i
$303$	−1.02616	+	0.592456i	−0.0589515	+	0.0340357i
$304$	7.64798	−	7.64798i	0.438642	−	0.438642i
$305$	−1.14226	+	4.26297i	−0.0654056	+	0.244097i
$306$	0.628340	−	2.34500i	0.0359198	−	0.134055i
$307$	−7.23927	−	7.23927i	−0.413167	−	0.413167i	0.469673	−	0.882840i	$-0.344372\pi$
$307$	−7.23927	−	7.23927i	−0.413167	−	0.413167i	−0.882840	+	0.469673i	$0.844372\pi$
$308$		0			0
$309$	0.395446	+	0.228311i	0.0224961	+	0.0129881i
$310$	−0.0403130	−	0.150450i	−0.00228962	−	0.00854499i
$311$	9.72413			0.551405			0.275702	−	0.961243i	$-0.411090\pi$
$311$	9.72413			0.551405			0.275702	+	0.961243i	$0.411090\pi$
$312$	−2.37405	−	3.63070i	−0.134404	−	0.205548i
$313$		−	16.6820i		−	0.942923i	−0.881887	−	0.471461i	$-0.843727\pi$
$313$		−	16.6820i		−	0.942923i	0.881887	−	0.471461i	$-0.156273\pi$
$314$	−0.260429	−	0.971933i	−0.0146968	−	0.0548494i
$315$		0			0
$316$	12.5440	−	7.24228i	0.705655	−	0.407410i
$317$	7.53574	+	7.53574i	0.423249	+	0.423249i	0.886321	−	0.463071i	$-0.153253\pi$
$317$	7.53574	+	7.53574i	0.423249	+	0.423249i	−0.463071	+	0.886321i	$0.653253\pi$
$318$	0.304133	+	0.0814921i	0.0170549	+	0.00456985i
$319$	−9.37205	−	2.51123i	−0.524734	−	0.140602i
$320$	2.22104	+	2.22104i	0.124160	+	0.124160i
$321$	−4.63073	+	2.67355i	−0.258462	+	0.149223i
$322$		0			0
$323$	−3.60649	−	13.4596i	−0.200670	−	0.748911i
$324$		−	0.124604i		−	0.00692242i
$325$	16.2122	−	5.32404i	0.899292	−	0.295324i
$326$	0.661579			0.0366415
$327$	0.234278	+	0.874339i	0.0129556	+	0.0483510i
$328$	−6.76344	−	3.90488i	−0.373449	−	0.215611i
$329$		0			0
$330$	0.429889	+	0.429889i	0.0236646	+	0.0236646i
$331$	8.87424	−	33.1191i	0.487772	−	1.82039i	−0.0794669	−	0.996838i	$-0.525322\pi$
$331$	8.87424	−	33.1191i	0.487772	−	1.82039i	0.567239	−	0.823553i	$-0.308012\pi$
$332$	4.51044	−	16.8332i	0.247543	−	0.923842i
$333$	−0.241359	+	0.241359i	−0.0132264	+	0.0132264i
$334$	−5.23296	+	3.02125i	−0.286335	+	0.165316i
$335$	1.83017	−	3.16994i	0.0999927	−	0.173192i
$336$		0			0
$337$			32.8040i			1.78695i	0.449117	+	0.893473i	$0.351739\pi$
$337$			32.8040i			1.78695i	−0.449117	+	0.893473i	$0.648261\pi$
$338$	2.33915	−	2.92602i	0.127233	−	0.159154i
$339$			5.22072i			0.283551i
$340$	4.32730	−	1.15950i	0.234681	−	0.0628825i
$341$	3.46631	+	2.00128i	0.187711	+	0.108375i
$342$	0.827787	+	1.43377i	0.0447616	+	0.0775293i
$343$		0			0
$344$	1.54915	−	5.78151i	0.0835247	−	0.311718i
$345$	4.61978	+	1.23787i	0.248721	+	0.0666445i
$346$	−4.09305	−	4.09305i	−0.220044	−	0.220044i
$347$	−4.53276	−	7.85096i	−0.243331	−	0.421462i	0.718330	−	0.695703i	$-0.244907\pi$
$347$	−4.53276	−	7.85096i	−0.243331	−	0.421462i	−0.961661	+	0.274241i	$0.911573\pi$
$348$	−2.58936	+	4.48490i	−0.138804	+	0.240416i
$349$	27.6016	−	7.39582i	1.47748	−	0.395889i	0.571990	−	0.820261i	$-0.306172\pi$
$349$	27.6016	−	7.39582i	1.47748	−	0.395889i	0.905488	+	0.424372i	$0.139505\pi$
$350$		0			0
$351$	−17.7598	+	5.83225i	−0.947947	+	0.311303i
$352$	12.5130			0.666947
$353$	−5.20313	−	19.4183i	−0.276935	−	1.03353i	−0.954534	−	0.298103i	$-0.903646\pi$
$353$	−5.20313	−	19.4183i	−0.276935	−	1.03353i	0.677599	−	0.735431i	$-0.263020\pi$
$354$	0.0800296	−	0.138615i	0.00425353	−	0.00736733i
$355$	−1.96279	−	3.39966i	−0.104174	−	0.180435i
$356$	−16.4279	+	16.4279i	−0.870678	+	0.870678i
$357$		0			0
$358$	−5.96438	−	1.59815i	−0.315227	−	0.0844649i
$359$	21.8093	−	21.8093i	1.15105	−	1.15105i	0.164706	−	0.986343i	$-0.447332\pi$
$359$	21.8093	−	21.8093i	1.15105	−	1.15105i	0.986343	−	0.164706i	$-0.0526676\pi$
$360$	−0.941889	+	0.543800i	−0.0496419	+	0.0286608i
$361$	−8.22508	−	4.74875i	−0.432899	−	0.249934i
$362$	5.49814	−	1.47322i	0.288976	−	0.0774309i
$363$	−3.89754			−0.204568
$364$		0			0
$365$	−6.39436			−0.334696
$366$	2.53273	−	0.678643i	0.132388	−	0.0354733i
$367$	4.59522	+	2.65305i	0.239869	+	0.138488i	0.615116	−	0.788436i	$-0.289109\pi$
$367$	4.59522	+	2.65305i	0.239869	+	0.138488i	−0.375248	+	0.926925i	$0.622442\pi$
$368$	26.3712	−	15.2254i	1.37469	−	0.793679i
$369$	−9.11867	+	9.11867i	−0.474699	+	0.474699i
$370$	0.0263544	+	0.00706165i	0.00137010	+	0.000367118i
$371$		0			0
$372$	1.51061	−	1.51061i	0.0783216	−	0.0783216i
$373$	12.2831	+	21.2749i	0.635993	+	1.10157i	0.986304	+	0.164938i	$0.0527425\pi$
$373$	12.2831	+	21.2749i	0.635993	+	1.10157i	−0.350311	+	0.936633i	$0.613924\pi$
$374$	2.49338	−	4.31866i	0.128930	−	0.223313i
$375$	1.38820	+	5.18083i	0.0716863	+	0.267537i
$376$	−10.5558			−0.544371
$377$	−8.94417	−	1.87179i	−0.460648	−	0.0964022i
$378$		0			0
$379$	21.0045	−	5.62815i	1.07893	−	0.289099i	0.324773	−	0.945792i	$-0.394712\pi$
$379$	21.0045	−	5.62815i	1.07893	−	0.289099i	0.754158	+	0.656693i	$0.228045\pi$
$380$	−1.52754	+	2.64578i	−0.0783612	+	0.135726i
$381$	−1.85035	−	3.20490i	−0.0947963	−	0.164192i
$382$	−0.875920	−	0.875920i	−0.0448160	−	0.0448160i
$383$	11.3422	+	3.03913i	0.579558	+	0.155292i	0.536677	−	0.843788i	$-0.319679\pi$
$383$	11.3422	+	3.03913i	0.579558	+	0.155292i	0.0428816	+	0.999080i	$0.486346\pi$
$384$	2.28645	−	8.53317i	0.116680	−	0.435456i
$385$		0			0
$386$	1.95282	+	3.38239i	0.0993961	+	0.172159i
$387$	−8.55929	−	4.94171i	−0.435093	−	0.251201i
$388$	−25.2955	+	6.77790i	−1.28418	+	0.344096i
$389$			35.0116i			1.77516i	0.460653	+	0.887580i	$0.347615\pi$
$389$			35.0116i			1.77516i	−0.460653	+	0.887580i	$0.652385\pi$
$390$	0.426704	+	0.381786i	0.0216070	+	0.0193325i
$391$		−	39.2306i		−	1.98398i
$392$		0			0
$393$	9.24095	−	16.0058i	0.466144	−	0.807385i
$394$	−0.955680	+	0.551762i	−0.0481465	+	0.0277974i
$395$	−2.76228	+	2.76228i	−0.138985	+	0.138985i
$396$	3.54012	−	13.2119i	0.177898	−	0.663924i
$397$	2.07243	−	7.73441i	0.104012	−	0.388179i	−0.894219	−	0.447630i	$-0.852268\pi$
$397$	2.07243	−	7.73441i	0.104012	−	0.388179i	0.998231	+	0.0594508i	$0.0189349\pi$
$398$	2.14116	+	2.14116i	0.107326	+	0.107326i
$399$		0			0
$400$	14.3808	+	8.30277i	0.719041	+	0.415139i
$401$	7.07012	+	26.3860i	0.353065	+	1.31766i	0.882902	+	0.469557i	$0.155586\pi$
$401$	7.07012	+	26.3860i	0.353065	+	1.31766i	−0.529837	+	0.848099i	$0.677747\pi$
$402$	−2.17469			−0.108464
$403$	3.36409	+	1.70080i	0.167577	+	0.0847228i
$404$		−	2.13092i		−	0.106017i
$405$	0.00869768	+	0.0324602i	0.000432191	+	0.00161296i
$406$		0			0
$407$	−0.607197	+	0.350565i	−0.0300976	+	0.0173769i
$408$	−3.84566	−	3.84566i	−0.190388	−	0.190388i
$409$	5.52667	+	1.48087i	0.273276	+	0.0732242i	0.392855	−	0.919601i	$-0.371488\pi$
$409$	5.52667	+	1.48087i	0.273276	+	0.0732242i	−0.119578	+	0.992825i	$0.538154\pi$
$410$	0.995685	+	0.266793i	0.0491734	+	0.0131760i
$411$	7.12000	+	7.12000i	0.351204	+	0.351204i
$412$	−0.711163	+	0.410590i	−0.0350365	+	0.0202283i
$413$		0			0
$414$	1.20637	+	4.50225i	0.0592900	+	0.221273i
$415$			4.70002i			0.230715i
$416$	11.7666	−	0.653736i	0.576904	−	0.0320520i
$417$	−16.1886			−0.792757
$418$	0.880167	+	3.28483i	0.0430504	+	0.160666i
$419$	13.3221	+	7.69152i	0.650828	+	0.375755i	0.788773	−	0.614684i	$-0.210717\pi$
$419$	13.3221	+	7.69152i	0.650828	+	0.375755i	−0.137946	+	0.990440i	$0.544050\pi$
$420$		0			0
$421$	4.76255	+	4.76255i	0.232112	+	0.232112i	0.813574	−	0.581462i	$-0.197519\pi$
$421$	4.76255	+	4.76255i	0.232112	+	0.232112i	−0.581462	+	0.813574i	$0.697519\pi$
$422$	0.578338	−	2.15839i	0.0281531	−	0.105069i
$423$	−4.51123	+	16.8361i	−0.219343	+	0.818601i
$424$	−0.818130	+	0.818130i	−0.0397319	+	0.0397319i
$425$	18.5272	−	10.6967i	0.898701	−	0.518865i
$426$	−1.16614	+	2.01982i	−0.0564997	+	0.0978604i
$427$		0			0
$428$		−	9.61614i		−	0.464814i
$429$	−14.6909	+	0.816207i	−0.709283	+	0.0394068i
$430$			0.790021i			0.0380982i
$431$	−16.3021	+	4.36813i	−0.785244	+	0.210406i	−0.629095	−	0.777328i	$-0.716575\pi$
$431$	−16.3021	+	4.36813i	−0.785244	+	0.210406i	−0.156149	+	0.987734i	$0.549908\pi$
$432$	−15.7536	−	9.09533i	−0.757944	−	0.437599i
$433$	4.63490	+	8.02787i	0.222739	+	0.385795i	0.955639	−	0.294542i	$-0.0951669\pi$
$433$	4.63490	+	8.02787i	0.222739	+	0.385795i	−0.732900	+	0.680337i	$0.761834\pi$
$434$		0			0
$435$	0.361488	−	1.34909i	0.0173320	−	0.0646841i
$436$	−1.57240	−	0.421322i	−0.0753041	−	0.0201777i
$437$	18.9173	+	18.9173i	0.904939	+	0.904939i
$438$	1.89952	+	3.29007i	0.0907626	+	0.157205i
$439$	−8.70664	+	15.0803i	−0.415545	+	0.719745i	−0.995486	−	0.0949136i	$-0.969743\pi$
$439$	−8.70664	+	15.0803i	−0.415545	+	0.719745i	0.579940	+	0.814659i	$0.303076\pi$
$440$	−2.15791	+	0.578210i	−0.102874	+	0.0275651i
$441$		0			0
$442$	2.11902	−	4.19131i	0.100791	−	0.199360i
$443$	10.1954			0.484397			0.242198	−	0.970227i	$-0.422132\pi$
$443$	10.1954			0.484397			0.242198	+	0.970227i	$0.422132\pi$
$444$	0.0968559	+	0.361471i	0.00459658	+	0.0171547i
$445$	3.13288	−	5.42631i	0.148513	−	0.257232i
$446$	−3.38168	−	5.85725i	−0.160127	−	0.277349i
$447$	−10.8277	+	10.8277i	−0.512133	+	0.512133i
$448$		0			0
$449$	−17.5974	−	4.71520i	−0.830471	−	0.222524i	−0.181552	−	0.983381i	$-0.558112\pi$
$449$	−17.5974	−	4.71520i	−0.830471	−	0.222524i	−0.648919	+	0.760857i	$0.724779\pi$
$450$	−1.79732	+	1.79732i	−0.0847263	+	0.0847263i
$451$	−22.9402	+	13.2445i	−1.08021	+	0.623661i
$452$	−8.13099	−	4.69443i	−0.382449	−	0.220807i
$453$	5.11083	−	1.36944i	0.240128	−	0.0643420i
$454$	1.77575			0.0833399
$455$		0			0
$456$	3.70882			0.173681
$457$	−32.5856	+	8.73128i	−1.52429	+	0.408432i	−0.921151	−	0.389204i	$-0.872750\pi$
$457$	−32.5856	+	8.73128i	−1.52429	+	0.408432i	−0.603138	+	0.797637i	$0.706083\pi$
$458$	−2.84206	−	1.64086i	−0.132801	−	0.0766725i
$459$	−20.2957	+	11.7178i	−0.947324	+	0.546938i
$460$	−6.08198	+	6.08198i	−0.283574	+	0.283574i
$461$	10.9633	+	2.93760i	0.510611	+	0.136818i	0.504920	−	0.863166i	$-0.331522\pi$
$461$	10.9633	+	2.93760i	0.510611	+	0.136818i	0.00569051	+	0.999984i	$0.498189\pi$
$462$		0			0
$463$	−4.05208	+	4.05208i	−0.188316	+	0.188316i	−0.794968	−	0.606652i	$-0.792512\pi$
$463$	−4.05208	+	4.05208i	−0.188316	+	0.188316i	0.606652	+	0.794968i	$0.292512\pi$
$464$	−4.44620	−	7.70105i	−0.206410	−	0.357512i
$465$	−0.288081	+	0.498971i	−0.0133594	+	0.0231392i
$466$	−1.11159	−	4.14851i	−0.0514934	−	0.192176i
$467$	−36.3712			−1.68306			−0.841529	−	0.540211i	$-0.818344\pi$
$467$	−36.3712			−1.68306			−0.841529	+	0.540211i	$0.818344\pi$
$468$	2.63870	−	12.6087i	0.121974	−	0.582839i
$469$		0			0
$470$	1.34578	−	0.360600i	0.0620762	−	0.0166333i
$471$	−1.86105	+	3.22344i	−0.0857528	+	0.148528i
$472$	0.294082	+	0.509365i	0.0135362	+	0.0234454i
$473$	−14.3553	−	14.3553i	−0.660057	−	0.660057i
$474$	2.24183	+	0.600696i	0.102971	+	0.0275909i
$475$	−3.77594	+	14.0920i	−0.173252	+	0.646585i
$476$		0			0
$477$	0.955249	+	1.65454i	0.0437379	+	0.0757562i
$478$	−7.22149	−	4.16933i	−0.330303	−	0.190701i
$479$	23.4789	−	6.29114i	1.07278	−	0.287449i	0.321143	−	0.947031i	$-0.395933\pi$
$479$	23.4789	−	6.29114i	1.07278	−	0.287449i	0.751633	+	0.659581i	$0.229266\pi$
$480$			1.80123i			0.0822147i
$481$	−0.552660	+	0.361375i	−0.0251991	+	0.0164773i
$482$		−	5.30005i		−	0.241411i
$483$		0			0
$484$	3.50464	−	6.07021i	0.159302	−	0.275919i
$485$	6.11654	−	3.53139i	0.277738	−	0.160352i
$486$	3.18330	−	3.18330i	0.144397	−	0.144397i
$487$	6.89506	−	25.7327i	0.312445	−	1.16606i	−0.613899	−	0.789384i	$-0.710400\pi$
$487$	6.89506	−	25.7327i	0.312445	−	1.16606i	0.926345	−	0.376677i	$-0.122933\pi$
$488$	−2.49379	+	9.30694i	−0.112888	+	0.421305i
$489$	−1.73047	−	1.73047i	−0.0782544	−	0.0782544i
$490$		0			0
$491$	−15.2520	−	8.80574i	−0.688313	−	0.397398i	0.114667	−	0.993404i	$-0.463420\pi$
$491$	−15.2520	−	8.80574i	−0.688313	−	0.397398i	−0.802980	+	0.596006i	$0.796753\pi$
$492$	3.65927	+	13.6566i	0.164972	+	0.615686i
$493$	−11.4563			−0.515967
$494$	0.999276	+	3.04289i	0.0449595	+	0.136906i
$495$			3.68892i			0.165804i
$496$	0.949428	+	3.54331i	0.0426306	+	0.159099i
$497$		0			0
$498$	2.41828	−	1.39620i	0.108366	−	0.0625650i
$499$	−10.7462	−	10.7462i	−0.481067	−	0.481067i	0.424406	−	0.905472i	$-0.360483\pi$
$499$	−10.7462	−	10.7462i	−0.481067	−	0.481067i	−0.905472	+	0.424406i	$0.860483\pi$
$500$	−9.31712	−	2.49651i	−0.416674	−	0.111648i
$501$	21.5902	+	5.78508i	0.964580	+	0.258459i
$502$	1.39929	+	1.39929i	0.0624536	+	0.0624536i
$503$	−3.91743	+	2.26173i	−0.174669	+	0.100845i	−0.584786	−	0.811188i	$-0.698821\pi$
$503$	−3.91743	+	2.26173i	−0.174669	+	0.100845i	0.410116	+	0.912033i	$0.365488\pi$
$504$		0			0
$505$	0.148744	+	0.555122i	0.00661904	+	0.0247026i
$506$			9.57427i			0.425628i
$507$	−13.7719	+	1.53504i	−0.611632	+	0.0681733i
$508$	6.65528			0.295280
$509$	9.94708	+	37.1230i	0.440897	+	1.64545i	0.726548	+	0.687115i	$0.241123\pi$
$509$	9.94708	+	37.1230i	0.440897	+	1.64545i	−0.285652	+	0.958334i	$0.592210\pi$
$510$	0.621666	+	0.358919i	0.0275278	+	0.0158932i
$511$		0			0
$512$	13.7099	+	13.7099i	0.605896	+	0.605896i
$513$	4.13638	−	15.4372i	0.182626	−	0.681568i
$514$	−0.621239	+	2.31850i	−0.0274017	+	0.102265i
$515$	0.156603	−	0.156603i	0.00690075	−	0.00690075i
$516$	−9.38402	+	5.41787i	−0.413108	+	0.238508i
$517$	−17.9015	+	31.0063i	−0.787306	+	1.36365i
$518$		0			0
$519$			21.4121i			0.939885i
$520$	−1.99898	+	0.656457i	−0.0876609	+	0.0287875i
$521$			36.6665i			1.60639i	0.595716	+	0.803195i	$0.296868\pi$
$521$			36.6665i			1.60639i	−0.595716	+	0.803195i	$0.703132\pi$
$522$	1.31477	−	0.352291i	0.0575459	−	0.0154194i
$523$	−9.11850	−	5.26457i	−0.398724	−	0.230203i	0.287209	−	0.957868i	$-0.407272\pi$
$523$	−9.11850	−	5.26457i	−0.398724	−	0.230203i	−0.685933	+	0.727664i	$0.740606\pi$
$524$	16.6188	+	28.7845i	0.725994	+	1.25746i
$525$		0			0
$526$	−0.201648	+	0.752560i	−0.00879226	+	0.0328132i
$527$	4.56495	+	1.22317i	0.198852	+	0.0532823i
$528$	−10.1245	−	10.1245i	−0.440613	−	0.440613i
$529$	26.1601	+	45.3107i	1.13740	+	1.97003i
$530$	0.0763569	−	0.132254i	0.00331673	−	0.00574475i
$531$	0.938106	−	0.251365i	0.0407103	−	0.0109083i
$532$		0			0
$533$	−20.8798	+	13.6530i	−0.904404	+	0.591375i
$534$	−3.72264			−0.161094
$535$	0.671233	+	2.50508i	0.0290199	+	0.108304i
$536$	3.99563	−	6.92064i	0.172585	−	0.298926i
$537$	11.4206	+	19.7810i	0.492834	+	0.853613i
$538$	−4.76052	+	4.76052i	−0.205241	+	0.205241i
$539$		0			0
$540$	4.96310	+	1.32986i	0.213578	+	0.0572280i
$541$	8.67352	−	8.67352i	0.372904	−	0.372904i	−0.495630	−	0.868534i	$-0.665063\pi$
$541$	8.67352	−	8.67352i	0.372904	−	0.372904i	0.868534	+	0.495630i	$0.165063\pi$
$542$	3.31715	−	1.91516i	0.142484	−	0.0822632i
$543$	−18.2347	−	10.5278i	−0.782527	−	0.451792i
$544$	14.2712	−	3.82396i	0.611873	−	0.163951i
$545$	0.439030			0.0188060
$546$		0			0
$547$	−46.5673			−1.99108			−0.995538	−	0.0943609i	$-0.969919\pi$
$547$	−46.5673			−1.99108			−0.995538	+	0.0943609i	$0.969919\pi$
$548$	−17.4912	+	4.68677i	−0.747189	+	0.200209i
$549$	13.7785	+	7.95504i	0.588054	+	0.339513i
$550$	−4.52158	+	2.61054i	−0.192801	+	0.111314i
$551$	5.52434	−	5.52434i	0.235345	−	0.235345i
$552$	10.0859	+	2.70252i	0.429286	+	0.115027i
$553$		0			0
$554$	0.986426	−	0.986426i	0.0419092	−	0.0419092i
$555$	−0.0504634	−	0.0874051i	−0.00214205	−	0.00371014i
$556$	14.5566	−	25.2128i	0.617338	−	1.06926i
$557$	−4.86405	−	18.1529i	−0.206097	−	0.769163i	−0.989113	−	0.147161i	$-0.952986\pi$
$557$	−4.86405	−	18.1529i	−0.206097	−	0.769163i	0.783016	−	0.622002i	$-0.213680\pi$
$558$	−0.561503			−0.0237703
$559$	−14.2489	−	12.7490i	−0.602666	−	0.539224i
$560$		0			0
$561$	−17.8180	+	4.77432i	−0.752276	+	0.201572i
$562$	−1.75404	+	3.03809i	−0.0739899	+	0.128154i
$563$	−9.35345	−	16.2007i	−0.394201	−	0.682776i	0.598798	−	0.800900i	$-0.295645\pi$
$563$	−9.35345	−	16.2007i	−0.394201	−	0.682776i	−0.992999	+	0.118124i	$0.962312\pi$
$564$	13.5125	+	13.5125i	0.568978	+	0.568978i
$565$	2.44587	+	0.655368i	0.102898	+	0.0275715i
$566$	−0.0787383	+	0.293855i	−0.00330962	+	0.0123517i
$567$		0			0
$568$	−4.28518	−	7.42215i	−0.179802	−	0.311426i
$569$	−5.84529	−	3.37478i	−0.245047	−	0.141478i	0.372447	−	0.928053i	$-0.378519\pi$
$569$	−5.84529	−	3.37478i	−0.245047	−	0.141478i	−0.617494	+	0.786575i	$0.711852\pi$
$570$	−0.472846	+	0.126699i	−0.0198054	+	0.00530683i
$571$		−	6.15900i		−	0.257746i	−0.991661	−	0.128873i	$-0.958864\pi$
$571$		−	6.15900i		−	0.257746i	0.991661	−	0.128873i	$-0.0411360\pi$
$572$	11.9387	−	23.6142i	0.499184	−	0.987359i
$573$			4.58222i			0.191425i
$574$		0			0
$575$	−20.5369	+	35.5710i	−0.856450	+	1.48341i
$576$	9.80633	−	5.66169i	0.408597	−	0.235904i
$577$	14.3180	−	14.3180i	0.596066	−	0.596066i	−0.343197	−	0.939263i	$-0.611510\pi$
$577$	14.3180	−	14.3180i	0.596066	−	0.596066i	0.939263	+	0.343197i	$0.111510\pi$
$578$	0.256059	−	0.955626i	0.0106507	−	0.0397488i
$579$	3.73926	−	13.9551i	0.155398	−	0.579954i
$580$	1.77609	+	1.77609i	0.0737482	+	0.0737482i
$581$		0			0
$582$	−3.63398	−	2.09808i	−0.150633	−	0.0869682i
$583$	1.01569	+	3.79062i	0.0420658	+	0.156992i
$584$	−13.9602			−0.577677
$585$	0.192725	+	3.46886i	0.00796821	+	0.143420i
$586$			5.91463i			0.244331i
$587$	−3.35452	−	12.5192i	−0.138456	−	0.516725i	−0.999960	−	0.00897355i	$-0.997144\pi$
$587$	−3.35452	−	12.5192i	−0.138456	−	0.516725i	0.861504	−	0.507751i	$-0.169523\pi$
$588$		0			0
$589$	−2.79108	+	1.61143i	−0.115004	+	0.0663979i
$590$	−0.0548940	−	0.0548940i	−0.00225995	−	0.00225995i
$591$	3.94296	+	1.05651i	0.162192	+	0.0434591i
$592$	−0.620685	−	0.166312i	−0.0255100	−	0.00683538i
$593$	1.85060	+	1.85060i	0.0759950	+	0.0759950i	0.744083	−	0.668088i	$-0.232887\pi$
$593$	1.85060	+	1.85060i	0.0759950	+	0.0759950i	−0.668088	+	0.744083i	$0.732887\pi$
$594$	4.95320	−	2.85973i	0.203232	−	0.117336i
$595$		0			0
$596$	−7.12739	−	26.5998i	−0.291949	−	1.08957i
$597$		−	11.2011i		−	0.458429i
$598$	0.500202	+	9.00313i	0.0204548	+	0.368166i
$599$	23.6717			0.967200			0.483600	−	0.875289i	$-0.339329\pi$
$599$	23.6717			0.967200			0.483600	+	0.875289i	$0.339329\pi$
$600$	1.47375	+	5.50010i	0.0601654	+	0.224540i
$601$	39.8779	+	23.0235i	1.62665	+	0.939149i	0.985082	+	0.172087i	$0.0550511\pi$
$601$	39.8779	+	23.0235i	1.62665	+	0.939149i	0.641573	+	0.767062i	$0.278282\pi$
$602$		0			0
$603$	−9.33060	−	9.33060i	−0.379971	−	0.379971i
$604$	−2.46278	+	9.19122i	−0.100209	+	0.373986i
$605$	−0.489267	+	1.82597i	−0.0198915	+	0.0742362i
$606$	0.241438	−	0.241438i	0.00980776	−	0.00980776i
$607$	7.28556	−	4.20632i	0.295712	−	0.170729i	−0.344803	−	0.938675i	$-0.612054\pi$
$607$	7.28556	−	4.20632i	0.295712	−	0.170729i	0.640515	+	0.767946i	$0.278721\pi$
$608$	−5.03775	+	8.72564i	−0.204308	+	0.353872i
$609$		0			0
$610$		−	1.27176i		−	0.0514919i
$611$	−15.2137	+	30.0919i	−0.615480	+	1.21739i
$612$		−	16.1502i		−	0.652832i
$613$	20.4788	−	5.48728i	0.827131	−	0.221629i	0.179669	−	0.983727i	$-0.442497\pi$
$613$	20.4788	−	5.48728i	0.827131	−	0.221629i	0.647462	+	0.762098i	$0.275831\pi$
$614$	2.55491	+	1.47508i	0.103108	+	0.0595293i
$615$	−1.90653	−	3.30221i	−0.0768788	−	0.133158i
$616$		0			0
$617$	7.51730	−	28.0549i	0.302635	−	1.12945i	−0.632327	−	0.774702i	$-0.717900\pi$
$617$	7.51730	−	28.0549i	0.302635	−	1.12945i	0.934962	−	0.354748i	$-0.115433\pi$
$618$	−0.127097	−	0.0340556i	−0.00511259	−	0.00136992i
$619$	18.2033	+	18.2033i	0.731654	+	0.731654i	0.970947	−	0.239293i	$-0.0769157\pi$
$619$	18.2033	+	18.2033i	0.731654	+	0.731654i	−0.239293	+	0.970947i	$0.576916\pi$
$620$	−0.518080	−	0.897341i	−0.0208066	−	0.0360381i
$621$	22.4973	−	38.9665i	0.902787	−	1.56367i
$622$	−2.70664	+	0.725241i	−0.108526	+	0.0290795i
$623$		0			0
$624$	−10.0495	−	8.99160i	−0.402302	−	0.359952i
$625$	−21.0621			−0.842485
$626$	1.24417	+	4.64331i	0.0497270	+	0.185584i
$627$	6.28977	−	10.8942i	0.251189	−	0.435073i
$628$	−3.34689	−	5.79698i	−0.133555	−	0.231325i
$629$	−0.585381	+	0.585381i	−0.0233407	+	0.0233407i
$630$		0			0
$631$	4.24248	+	1.13677i	0.168891	+	0.0452541i	0.342273	−	0.939600i	$-0.388803\pi$
$631$	4.24248	+	1.13677i	0.168891	+	0.0452541i	−0.173383	+	0.984855i	$0.555470\pi$
$632$	−6.03061	+	6.03061i	−0.239885	+	0.239885i
$633$	−7.15834	+	4.13287i	−0.284519	+	0.164267i
$634$	−2.65954	−	1.53549i	−0.105624	−	0.0609820i
$635$	−1.73375	+	0.464557i	−0.0688018	+	0.0184354i
$636$	2.09458			0.0830557
$637$		0			0
$638$	2.79593			0.110692
$639$	−13.6695	+	3.66273i	−0.540756	+	0.144895i
$640$	−3.71070	−	2.14237i	−0.146678	−	0.0846847i
$641$	17.4189	−	10.0568i	0.688005	−	0.397220i	−0.114859	−	0.993382i	$-0.536642\pi$
$641$	17.4189	−	10.0568i	0.688005	−	0.397220i	0.802864	+	0.596162i	$0.203308\pi$
$642$	1.08953	−	1.08953i	0.0430003	−	0.0430003i
$643$	−3.80955	−	1.02077i	−0.150234	−	0.0402551i	0.182918	−	0.983128i	$-0.441446\pi$
$643$	−3.80955	−	1.02077i	−0.150234	−	0.0402551i	−0.333152	+	0.942873i	$0.608112\pi$
$644$		0			0
$645$	2.06643	−	2.06643i	0.0813654	−	0.0813654i
$646$	2.00767	+	3.47739i	0.0789909	+	0.136816i
$647$	3.76152	−	6.51515i	0.147881	−	0.256137i	−0.782563	−	0.622571i	$-0.786088\pi$
$647$	3.76152	−	6.51515i	0.147881	−	0.256137i	0.930444	+	0.366434i	$0.119421\pi$
$648$	0.0189888	+	0.0708672i	0.000745951	+	0.00278393i
$649$	1.99493			0.0783080
$650$	−4.11547	+	2.69104i	−0.161422	+	0.105551i
$651$		0			0
$652$	4.25113	−	1.13909i	0.166487	−	0.0446100i
$653$	5.29139	−	9.16495i	0.207068	−	0.358652i	−0.743722	−	0.668489i	$-0.766941\pi$
$653$	5.29139	−	9.16495i	0.207068	−	0.358652i	0.950790	+	0.309837i	$0.100275\pi$
$654$	−0.130419	−	0.225893i	−0.00509979	−	0.00883310i
$655$	−6.33855	−	6.33855i	−0.247668	−	0.247668i
$656$	−23.4498	−	6.28336i	−0.915561	−	0.245324i
$657$	−5.96619	+	22.2661i	−0.232763	+	0.868685i
$658$		0			0
$659$	2.76883	+	4.79576i	0.107858	+	0.186816i	0.914902	−	0.403675i	$-0.132267\pi$
$659$	2.76883	+	4.79576i	0.107858	+	0.186816i	−0.807044	+	0.590491i	$0.798934\pi$
$660$	3.50252	+	2.02218i	0.136335	+	0.0787133i
$661$	12.8542	−	3.44429i	0.499972	−	0.133967i	−1.48350e−5	−	1.00000i	$-0.500005\pi$
$661$	12.8542	−	3.44429i	0.499972	−	0.133967i	0.499987	+	0.866033i	$0.333338\pi$
$662$			9.88030i			0.384009i
$663$	−16.5057	+	5.42040i	−0.641027	+	0.210511i
$664$			10.2611i			0.398208i
$665$		0			0
$666$	0.0491795	−	0.0851813i	0.00190567	−	0.00330071i
$667$	19.0486	−	10.9977i	0.737564	−	0.425833i
$668$	−28.4237	+	28.4237i	−1.09975	+	1.09975i
$669$	−6.47524	+	24.1659i	−0.250347	+	0.934308i
$670$	−0.272994	+	1.01883i	−0.0105467	+	0.0393607i
$671$	23.1088	+	23.1088i	0.892106	+	0.892106i
$672$		0			0
$673$	12.8942	+	7.44448i	0.497035	+	0.286963i	0.727488	−	0.686120i	$-0.240687\pi$
$673$	12.8942	+	7.44448i	0.497035	+	0.286963i	−0.230453	+	0.973083i	$0.574021\pi$
$674$	−2.44657	−	9.13073i	−0.0942384	−	0.351703i
$675$	24.5367			0.944416
$676$	9.99284	−	22.8293i	0.384340	−	0.878049i
$677$		−	12.3765i		−	0.475669i	−0.971306	−	0.237835i	$-0.923562\pi$
$677$		−	12.3765i		−	0.475669i	0.971306	−	0.237835i	$-0.0764376\pi$
$678$	−0.389370	−	1.45315i	−0.0149536	−	0.0558078i
$679$		0			0
$680$	−2.28441	+	1.31891i	−0.0876033	+	0.0505778i
$681$	−4.64475	−	4.64475i	−0.177987	−	0.177987i
$682$	−1.11408	−	0.298517i	−0.0426603	−	0.0114308i
$683$	−27.4570	−	7.35708i	−1.05061	−	0.281511i	−0.308108	−	0.951351i	$-0.599696\pi$
$683$	−27.4570	−	7.35708i	−1.05061	−	0.281511i	−0.742505	+	0.669841i	$0.766362\pi$
$684$	7.78775	+	7.78775i	0.297772	+	0.297772i
$685$	4.22945	−	2.44188i	0.161599	−	0.0932993i
$686$		0			0
$687$	3.14192	+	11.7258i	0.119872	+	0.447367i
$688$		−	18.6061i		−	0.709352i
$689$	1.15314	+	3.51144i	0.0439313	+	0.133775i
$690$	−1.37820			−0.0524673
$691$	3.02975	+	11.3072i	0.115257	+	0.430145i	0.999306	−	0.0372491i	$-0.0118595\pi$
$691$	3.02975	+	11.3072i	0.115257	+	0.430145i	−0.884049	+	0.467394i	$0.845193\pi$
$692$	−33.3481	−	19.2535i	−1.26770	−	0.731909i
$693$		0			0
$694$	1.84719	+	1.84719i	0.0701186	+	0.0701186i
$695$	−2.03219	+	7.58422i	−0.0770852	+	0.287686i
$696$	0.789203	−	2.94535i	0.0299147	−	0.111643i
$697$	−22.1160	+	22.1160i	−0.837703	+	0.837703i
$698$	−7.13109	+	4.11714i	−0.269916	+	0.155836i
$699$	−7.94355	+	13.7586i	−0.300453	+	0.520399i
$700$		0			0
$701$			0.431477i			0.0162966i	0.999967	+	0.00814832i	$0.00259372\pi$
$701$			0.431477i			0.0162966i	−0.999967	+	0.00814832i	$0.997406\pi$
$702$	4.50832	−	2.94792i	0.170156	−	0.111262i
$703$		−	0.564551i		−	0.0212925i
$704$	22.4667	−	6.01994i	0.846747	−	0.226885i
$705$	−4.46331	−	2.57689i	−0.168098	−	0.0970514i
$706$	2.89650	+	5.01689i	0.109011	+	0.188813i
$707$		0			0
$708$	0.275585	−	1.02850i	0.0103571	−	0.0386533i
$709$	4.10081	+	1.09881i	0.154009	+	0.0412666i	0.335000	−	0.942218i	$-0.391264\pi$
$709$	4.10081	+	1.09881i	0.154009	+	0.0412666i	−0.180991	+	0.983485i	$0.557930\pi$
$710$	0.799880	+	0.799880i	0.0300190	+	0.0300190i
$711$	7.04135	+	12.1960i	0.264071	+	0.457385i
$712$	6.83973	−	11.8468i	0.256330	−	0.443976i
$713$	−8.76441	+	2.34842i	−0.328230	+	0.0879488i
$714$		0			0
$715$	−1.46179	+	6.98503i	−0.0546680	+	0.261225i
$716$	−41.0771			−1.53512
$717$	7.98342	+	29.7945i	0.298146	+	1.11270i
$718$	−4.44387	+	7.69701i	−0.165844	+	0.287250i
$719$	−5.89574	−	10.2117i	−0.219874	−	0.380833i	0.734895	−	0.678180i	$-0.237231\pi$
$719$	−5.89574	−	10.2117i	−0.219874	−	0.380833i	−0.954769	+	0.297348i	$0.903898\pi$
$720$	−2.39063	+	2.39063i	−0.0890935	+	0.0890935i
$721$		0			0
$722$	2.64356	+	0.708339i	0.0983830	+	0.0263616i
$723$	−13.8631	+	13.8631i	−0.515575	+	0.515575i
$724$	32.7930	−	18.9330i	1.21874	−	0.703641i
$725$	10.3876	+	5.99731i	0.385787	+	0.222734i
$726$	1.08485	−	0.290685i	0.0402626	−	0.0107883i
$727$	9.73102			0.360904			0.180452	−	0.983584i	$-0.442244\pi$
$727$	9.73102			0.360904			0.180452	+	0.983584i	$0.442244\pi$
$728$		0			0
$729$	−16.4579			−0.609550
$730$	1.77982	−	0.476902i	0.0658741	−	0.0176509i
$731$	−20.7593	−	11.9854i	−0.767810	−	0.443295i
$732$	15.1062	−	8.72155i	0.558340	−	0.322358i
$733$	−10.7236	+	10.7236i	−0.396084	+	0.396084i	−0.876849	−	0.480765i	$-0.840359\pi$
$733$	−10.7236	+	10.7236i	−0.396084	+	0.396084i	0.480765	+	0.876849i	$0.340359\pi$
$734$	−1.47691	−	0.395738i	−0.0545139	−	0.0146069i
$735$		0			0
$736$	−20.0581	+	20.0581i	−0.739350	+	0.739350i
$737$	−13.5524	−	23.4734i	−0.499207	−	0.864653i
$738$	1.85803	−	3.21820i	0.0683949	−	0.118463i
$739$	0.607767	+	2.26822i	0.0223571	+	0.0834378i	0.976203	−	0.216859i	$-0.0695811\pi$
$739$	0.607767	+	2.26822i	0.0223571	+	0.0834378i	−0.953846	+	0.300296i	$0.902914\pi$
$740$	0.181505			0.00667225
$741$	5.34541	−	10.5729i	0.196368	−	0.388407i
$742$		0			0
$743$	27.0211	−	7.24029i	0.991309	−	0.265620i	0.273509	−	0.961870i	$-0.411816\pi$
$743$	27.0211	−	7.24029i	0.991309	−	0.265620i	0.717800	+	0.696249i	$0.245149\pi$
$744$	−0.628940	+	1.08936i	−0.0230581	+	0.0399377i
$745$	3.71348	+	6.43193i	0.136051	+	0.235648i
$746$	−5.00561	−	5.00561i	−0.183268	−	0.183268i
$747$	16.3662	+	4.38530i	0.598807	+	0.160450i
$748$	8.58605	−	32.0436i	0.313937	−	1.17163i
$749$		0			0
$750$	−0.772789	−	1.33851i	−0.0282183	−	0.0488755i
$751$	4.51677	+	2.60776i	0.164819	+	0.0951584i	0.580141	−	0.814516i	$-0.302998\pi$
$751$	4.51677	+	2.60776i	0.164819	+	0.0951584i	−0.415321	+	0.909675i	$0.636331\pi$
$752$	−31.6950	+	8.49266i	−1.15580	+	0.309695i
$753$		−	7.32016i		−	0.266761i
$754$	2.62914	−	0.146072i	0.0957477	−	0.00531961i
$755$		−	2.56629i		−	0.0933969i
$756$		0			0
$757$	10.3674	−	17.9569i	0.376811	−	0.652656i	−0.613785	−	0.789473i	$-0.710354\pi$
$757$	10.3674	−	17.9569i	0.376811	−	0.652656i	0.990596	+	0.136817i	$0.0436872\pi$
$758$	−5.42669	+	3.13310i	−0.197106	+	0.113799i
$759$	25.0430	−	25.0430i	0.909005	−	0.909005i
$760$	0.465576	−	1.73755i	0.0168882	−	0.0630276i
$761$	−10.1793	+	37.9896i	−0.368999	+	1.37712i	0.492919	+	0.870075i	$0.335930\pi$
$761$	−10.1793	+	37.9896i	−0.368999	+	1.37712i	−0.861918	+	0.507048i	$0.830737\pi$
$762$	0.754057	+	0.754057i	0.0273166	+	0.0273166i
$763$		0			0
$764$	−7.13656	−	4.12029i	−0.258192	−	0.149067i
$765$	1.12733	+	4.20724i	0.0407586	+	0.152113i
$766$	−3.38367			−0.122257
$767$	1.87593	−	0.104224i	0.0677359	−	0.00376331i
$768$		−	10.4065i		−	0.375513i
$769$	2.96518	+	11.0662i	0.106927	+	0.399057i	0.998557	−	0.0537084i	$-0.0171041\pi$
$769$	2.96518	+	11.0662i	0.106927	+	0.399057i	−0.891630	+	0.452765i	$0.850437\pi$
$770$		0			0
$771$	7.68935	−	4.43945i	0.276925	−	0.159883i
$772$	18.3720	+	18.3720i	0.661222	+	0.661222i
$773$	−45.2574	−	12.1267i	−1.62780	−	0.436167i	−0.674518	−	0.738258i	$-0.735649\pi$
$773$	−45.2574	−	12.1267i	−1.62780	−	0.436167i	−0.953279	+	0.302091i	$0.902315\pi$
$774$	2.75097	+	0.737121i	0.0988816	+	0.0264953i
$775$	−3.49879	−	3.49879i	−0.125680	−	0.125680i
$776$	13.3537	−	7.70974i	0.479369	−	0.276764i
$777$		0			0
$778$	−2.61122	−	9.74522i	−0.0936169	−	0.349383i
$779$		−	21.3290i		−	0.764192i
$780$	3.39923	+	1.71856i	0.121712	+	0.0615345i
$781$	−29.0689			−1.04017
$782$	2.92588	+	10.9195i	0.104629	+	0.390482i
$783$	−11.3792	−	6.56979i	−0.406660	−	0.234785i
$784$		0			0
$785$	1.27653	+	1.27653i	0.0455615	+	0.0455615i
$786$	−1.37841	+	5.14429i	−0.0491662	+	0.183491i
$787$	2.09890	−	7.83322i	0.0748179	−	0.279224i	−0.918374	−	0.395713i	$-0.870497\pi$
$787$	2.09890	−	7.83322i	0.0748179	−	0.279224i	0.993192	+	0.116489i	$0.0371641\pi$
$788$	−5.19093	+	5.19093i	−0.184919	+	0.184919i
$789$	2.49588	−	1.44100i	0.0888558	−	0.0513009i
$790$	0.562843	−	0.974873i	0.0200251	−	0.0346844i
$791$		0			0
$792$			8.05366i			0.286174i
$793$	22.9376	+	20.5230i	0.814538	+	0.728793i
$794$			2.30738i			0.0818858i
$795$	−0.545655	+	0.146208i	−0.0193524	+	0.00518546i
$796$	17.4451	+	10.0719i	0.618323	+	0.356989i
$797$	−5.11594	−	8.86106i	−0.181216	−	0.313875i	0.761079	−	0.648659i	$-0.224670\pi$
$797$	−5.11594	−	8.86106i	−0.181216	−	0.313875i	−0.942295	+	0.334784i	$0.891337\pi$
$798$		0			0
$799$	−10.9413	+	40.8335i	−0.387076	+	1.44459i
$800$	−14.9418	−	4.00363i	−0.528271	−	0.141550i
$801$	−15.9721	−	15.9721i	−0.564348	−	0.564348i
$802$	−3.93583	−	6.81705i	−0.138979	−	0.240718i
$803$	−23.6751	+	41.0064i	−0.835475	+	1.44709i
$804$	−13.9740	+	3.74431i	−0.492824	+	0.132052i
$805$		0			0
$806$	−1.06322	−	0.222505i	−0.0374502	−	0.00783740i
$807$	24.9038			0.876655
$808$	0.324740	+	1.21194i	0.0114243	+	0.0426361i
$809$	−5.83752	+	10.1109i	−0.205236	+	0.355480i	−0.950208	−	0.311616i	$-0.899130\pi$
$809$	−5.83752	+	10.1109i	−0.205236	+	0.355480i	0.744972	+	0.667096i	$0.232463\pi$
$810$	−0.00484186	−	0.00838635i	−0.000170126	−	0.000294666i
$811$	−19.1328	+	19.1328i	−0.671843	+	0.671843i	−0.958141	−	0.286298i	$-0.907575\pi$
$811$	−19.1328	+	19.1328i	−0.671843	+	0.671843i	0.286298	+	0.958141i	$0.407575\pi$
$812$		0			0
$813$	−13.6860	−	3.66714i	−0.479988	−	0.128612i
$814$	0.142863	−	0.142863i	0.00500734	−	0.00500734i
$815$	−1.02794	+	0.593481i	−0.0360071	+	0.0207887i
$816$	−14.6411	−	8.45306i	−0.512542	−	0.295916i
$817$	15.7898	−	4.23085i	0.552414	−	0.148019i
$818$	−1.64875			−0.0576472
$819$		0			0
$820$	6.85735			0.239469
$821$	26.2162	−	7.02461i	0.914952	−	0.245161i	0.229526	−	0.973303i	$-0.426283\pi$
$821$	26.2162	−	7.02461i	0.914952	−	0.245161i	0.685426	+	0.728142i	$0.259616\pi$
$822$	−2.51282	−	1.45078i	−0.0876446	−	0.0506016i
$823$	−24.0565	+	13.8890i	−0.838557	+	0.484141i	−0.856773	−	0.515693i	$-0.827534\pi$
$823$	−24.0565	+	13.8890i	−0.838557	+	0.484141i	0.0182167	+	0.999834i	$0.494201\pi$
$824$	0.341896	−	0.341896i	0.0119105	−	0.0119105i
$825$	18.6552	+	4.99864i	0.649491	+	0.174030i
$826$		0			0
$827$	30.1851	−	30.1851i	1.04964	−	1.04964i	0.0509356	−	0.998702i	$-0.483780\pi$
$827$	30.1851	−	30.1851i	1.04964	−	1.04964i	0.998702	−	0.0509356i	$-0.0162203\pi$
$828$	15.5036	+	26.8531i	0.538789	+	0.933210i
$829$	−13.9806	+	24.2150i	−0.485565	+	0.841023i	−0.999862	−	0.0165887i	$-0.994719\pi$
$829$	−13.9806	+	24.2150i	−0.485565	+	0.841023i	0.514297	+	0.857612i	$0.328053\pi$
$830$	−0.350535	−	1.30821i	−0.0121672	−	0.0454088i
$831$	−5.16031			−0.179009
$832$	20.8120	−	6.83459i	0.721527	−	0.236947i
$833$		0			0
$834$	4.50596	−	1.20737i	0.156029	−	0.0418078i
$835$	5.42053	−	9.38864i	0.187585	−	0.324907i
$836$	11.3114	+	19.5920i	0.391214	+	0.677602i
$837$	3.83277	+	3.83277i	0.132480	+	0.132480i
$838$	−4.28175	−	1.14729i	−0.147911	−	0.0396325i
$839$	8.74827	−	32.6490i	0.302024	−	1.12717i	−0.633453	−	0.773781i	$-0.718363\pi$
$839$	8.74827	−	32.6490i	0.302024	−	1.12717i	0.935477	−	0.353387i	$-0.114970\pi$
$840$		0			0
$841$	11.2884	+	19.5521i	0.389255	+	0.674209i
$842$	−1.68082	−	0.970419i	−0.0579247	−	0.0334429i
$843$	12.5346	−	3.35864i	0.431715	−	0.115678i
$844$		−	14.8650i		−	0.511673i
$845$	−1.00966	+	6.64472i	−0.0347335	+	0.228585i
$846$		−	5.02266i		−	0.172683i
$847$		0			0
$848$	−1.79831	+	3.11477i	−0.0617544	+	0.106962i
$849$	0.974579	−	0.562673i	0.0334475	−	0.0193109i
$850$	−4.35913	+	4.35913i	−0.149517	+	0.149517i
$851$	0.411374	−	1.53527i	0.0141017	−	0.0526283i
$852$	−4.01565	+	14.9866i	−0.137574	+	0.513433i
$853$	−18.1560	−	18.1560i	−0.621649	−	0.621649i	0.324304	−	0.945953i	$-0.394870\pi$
$853$	−18.1560	−	18.1560i	−0.621649	−	0.621649i	−0.945953	+	0.324304i	$0.894870\pi$
$854$		0			0
$855$	−2.57237	−	1.48516i	−0.0879733	−	0.0507914i
$856$	1.46544	+	5.46910i	0.0500877	+	0.186930i
$857$	−1.88417			−0.0643620			−0.0321810	−	0.999482i	$-0.510245\pi$
$857$	−1.88417			−0.0643620			−0.0321810	+	0.999482i	$0.510245\pi$
$858$	4.02822	−	1.32286i	0.137521	−	0.0451615i
$859$			1.51994i			0.0518599i	0.999664	+	0.0259299i	$0.00825468\pi$
$859$			1.51994i			0.0518599i	−0.999664	+	0.0259299i	$0.991745\pi$
$860$	1.36023	+	5.07646i	0.0463835	+	0.173106i
$861$		0			0
$862$	4.21178	−	2.43167i	0.143454	−	0.0828231i
$863$	6.49601	+	6.49601i	0.221127	+	0.221127i	0.808973	−	0.587846i	$-0.200024\pi$
$863$	6.49601	+	6.49601i	0.221127	+	0.221127i	−0.587846	+	0.808973i	$0.700024\pi$
$864$	16.3681	+	4.38581i	0.556853	+	0.149208i
$865$	10.0314	+	2.68790i	0.341077	+	0.0913914i
$866$	−1.88882	−	1.88882i	−0.0641847	−	0.0641847i
$867$	−3.16936	+	1.82983i	−0.107637	+	0.0621443i
$868$		0			0
$869$	7.48691	+	27.9415i	0.253976	+	0.947851i
$870$			0.402470i			0.0136450i
$871$	−13.9703	−	21.3651i	−0.473365	−	0.723928i
$872$	0.958493			0.0324587
$873$	−6.58985	−	24.5937i	−0.223033	−	0.832369i
$874$	−6.67638	−	3.85461i	−0.225832	−	0.130384i
$875$		0			0
$876$	17.8705	+	17.8705i	0.603789	+	0.603789i
$877$	−0.734191	+	2.74004i	−0.0247919	+	0.0925245i	−0.977213	−	0.212260i	$-0.931918\pi$
$877$	−0.734191	+	2.74004i	−0.0247919	+	0.0925245i	0.952421	+	0.304784i	$0.0985844\pi$
$878$	1.29871	−	4.84685i	0.0438293	−	0.163573i
$879$	15.4707	−	15.4707i	0.521812	−	0.521812i
$880$	−6.01421	+	3.47230i	−0.202739	+	0.117051i
$881$	16.7491	−	29.0103i	0.564292	−	0.977383i	−0.432823	−	0.901479i	$-0.642483\pi$
$881$	16.7491	−	29.0103i	0.564292	−	0.977383i	0.997115	−	0.0759037i	$-0.0241842\pi$
$882$		0			0
$883$		−	36.3459i		−	1.22314i	−0.791192	−	0.611568i	$-0.790539\pi$
$883$		−	36.3459i		−	1.22314i	0.791192	−	0.611568i	$-0.209461\pi$
$884$	6.39977	−	30.5806i	0.215247	−	1.02854i
$885$			0.287168i			0.00965304i
$886$	−2.83780	+	0.760387i	−0.0953378	+	0.0255457i
$887$	−21.2724	−	12.2816i	−0.714258	−	0.412377i	0.0983776	−	0.995149i	$-0.468635\pi$
$887$	−21.2724	−	12.2816i	−0.714258	−	0.412377i	−0.812636	+	0.582772i	$0.801968\pi$
$888$	−0.110172	−	0.190823i	−0.00369713	−	0.00640361i
$889$		0			0
$890$	−0.467311	+	1.74403i	−0.0156643	+	0.0584599i
$891$	0.240367	+	0.0644062i	0.00805260	+	0.00215769i
$892$	−31.8146	−	31.8146i	−1.06523	−	1.06523i
$893$	−14.4143	−	24.9663i	−0.482356	−	0.835465i
$894$	2.20626	−	3.82136i	0.0737885	−	0.127805i
$895$	10.7009	−	2.86730i	0.357691	−	0.0958431i
$896$		0			0
$897$	22.2408	−	24.8575i	0.742598	−	0.829968i
$898$	5.24976			0.175187
$899$	0.685797	+	2.55943i	0.0228726	+	0.0853617i
$900$	−8.45450	+	14.6436i	−0.281817	+	0.488121i
$901$	2.31682	+	4.01284i	0.0771843	+	0.133687i
$902$	5.39743	−	5.39743i	0.179715	−	0.179715i
$903$		0			0
$904$	5.33983	+	1.43080i	0.177600	+	0.0475878i
$905$	−7.22125	+	7.22125i	−0.240042	+	0.240042i
$906$	−1.32042	+	0.762347i	−0.0438681	+	0.0253273i
$907$	29.6238	+	17.1033i	0.983641	+	0.567905i	0.903367	−	0.428868i	$-0.141087\pi$
$907$	29.6238	+	17.1033i	0.983641	+	0.567905i	0.0802733	+	0.996773i	$0.474421\pi$
$908$	11.4105	−	3.05742i	0.378669	−	0.101464i
$909$	2.07180			0.0687173
$910$		0			0
$911$	49.8898			1.65292			0.826462	−	0.562993i	$-0.190350\pi$
$911$	49.8898			1.65292			0.826462	+	0.562993i	$0.190350\pi$
$912$	11.1362	−	2.98394i	0.368757	−	0.0988081i
$913$	30.1408	+	17.4018i	0.997514	+	0.575915i
$914$	8.41875	−	4.86057i	0.278468	−	0.160773i
$915$	−3.32648	+	3.32648i	−0.109970	+	0.109970i
$916$	−21.0875	−	5.65037i	−0.696750	−	0.186694i
$917$		0			0
$918$	4.77523	−	4.77523i	0.157606	−	0.157606i
$919$	1.35826	+	2.35258i	0.0448049	+	0.0776044i	0.887558	−	0.460696i	$-0.152400\pi$
$919$	1.35826	+	2.35258i	0.0448049	+	0.0776044i	−0.842753	+	0.538300i	$0.819067\pi$
$920$	2.53222	−	4.38593i	0.0834848	−	0.144600i
$921$	−2.82448	−	10.5411i	−0.0930696	−	0.347341i
$922$	−3.27063			−0.107713
$923$	−27.3348	+	1.51869i	−0.899737	+	0.0499882i
$924$		0			0
$925$	0.837217	−	0.224332i	0.0275275	−	0.00737598i
$926$	0.825655	−	1.43008i	0.0271327	−	0.0469952i
$927$	−0.399198	−	0.691432i	−0.0131114	−	0.0227096i
$928$	5.85746	+	5.85746i	0.192281	+	0.192281i
$929$	−24.2713	−	6.50346i	−0.796314	−	0.213372i	−0.162349	−	0.986733i	$-0.551907\pi$
$929$	−24.2713	−	6.50346i	−0.796314	−	0.213372i	−0.633965	+	0.773362i	$0.718574\pi$
$930$	0.0429711	−	0.160370i	0.00140908	−	0.00525875i
$931$		0			0
$932$	−14.2855	−	24.7433i	−0.467939	−	0.810494i
$933$	8.97662	+	5.18266i	0.293881	+	0.169673i
$934$	10.1236	−	2.71262i	0.331256	−	0.0887597i
$935$			8.94692i			0.292596i
$936$	0.420759	+	7.57323i	0.0137529	+	0.247539i
$937$		−	3.14878i		−	0.102866i	−0.998676	−	0.0514330i	$-0.983621\pi$
$937$		−	3.14878i		−	0.102866i	0.998676	−	0.0514330i	$-0.0163789\pi$
$938$		0			0
$939$	8.89099	−	15.3996i	0.290146	−	0.502548i
$940$	8.02674	−	4.63424i	0.261803	−	0.151152i
$941$	−6.84616	+	6.84616i	−0.223178	+	0.223178i	−0.809836	−	0.586657i	$-0.800444\pi$
$941$	−6.84616	+	6.84616i	−0.223178	+	0.223178i	0.586657	+	0.809836i	$0.300444\pi$
$942$	0.277601	−	1.03602i	0.00904472	−	0.0337553i
$943$	15.5419	−	58.0032i	0.506114	−	1.88884i
$944$	1.29283	+	1.29283i	0.0420781	+	0.0420781i
$945$		0			0
$946$	5.06633	+	2.92504i	0.164720	+	0.0951014i
$947$	−11.3728	−	42.4440i	−0.369568	−	1.37925i	−0.861122	−	0.508399i	$-0.830238\pi$
$947$	−11.3728	−	42.4440i	−0.369568	−	1.37925i	0.491554	−	0.870847i	$-0.336429\pi$
$948$	15.4396			0.501456
$949$	−20.1204	+	39.7972i	−0.653137	+	1.29187i
$950$		−	4.20402i		−	0.136396i
$951$	2.94015	+	10.9728i	0.0953408	+	0.355817i
$952$		0			0
$953$	−17.0074	+	9.81922i	−0.550923	+	0.318076i	−0.749494	−	0.662011i	$-0.769703\pi$
$953$	−17.0074	+	9.81922i	−0.550923	+	0.318076i	0.198571	+	0.980086i	$0.436370\pi$
$954$	−0.389284	−	0.389284i	−0.0126035	−	0.0126035i
$955$	2.14673	+	0.575216i	0.0694667	+	0.0186135i
$956$	−53.5819	−	14.3572i	−1.73296	−	0.464346i
$957$	−7.31320	−	7.31320i	−0.236402	−	0.236402i
$958$	−6.06595	+	3.50218i	−0.195982	+	0.113150i
$959$		0			0
$960$	0.866562	+	3.23405i	0.0279682	+	0.104379i
$961$			29.9069i			0.964740i
$962$	0.126877	−	0.141804i	0.00409067	−	0.00457196i
$963$	9.34934			0.301278
$964$	−9.12545	−	34.0567i	−0.293911	−	1.09689i
$965$	−6.06846	−	3.50363i	−0.195351	−	0.112786i
$966$		0			0
$967$	−22.4539	−	22.4539i	−0.722068	−	0.722068i	0.246958	−	0.969026i	$-0.420569\pi$
$967$	−22.4539	−	22.4539i	−0.722068	−	0.722068i	−0.969026	+	0.246958i	$0.920569\pi$
$968$	−1.06817	+	3.98646i	−0.0343323	+	0.128130i
$969$	3.84429	−	14.3471i	0.123496	−	0.460894i
$970$	−1.43912	+	1.43912i	−0.0462072	+	0.0462072i
$971$	33.8453	−	19.5406i	1.08615	−	0.627087i	0.153599	−	0.988133i	$-0.450914\pi$
$971$	33.8453	−	19.5406i	1.08615	−	0.627087i	0.932548	+	0.361046i	$0.117580\pi$
$972$	14.9741	−	25.9359i	0.480295	−	0.831895i
$973$		0			0
$974$			7.67675i			0.245979i
$975$	17.8035	+	3.72583i	0.570168	+	0.119322i
$976$			29.9517i			0.958730i
$977$	−26.0701	+	6.98547i	−0.834057	+	0.223485i	−0.650483	−	0.759521i	$-0.725433\pi$
$977$	−26.0701	+	6.98547i	−0.834057	+	0.223485i	−0.183574	+	0.983006i	$0.558767\pi$
$978$	0.610723	+	0.352601i	0.0195288	+	0.0112749i
$979$	−23.1989	−	40.1817i	−0.741441	−	1.28421i
$980$		0			0
$981$	0.409633	−	1.52877i	0.0130786	−	0.0488099i
$982$	4.90202	+	1.31349i	0.156430	+	0.0419152i
$983$	8.81863	+	8.81863i	0.281271	+	0.281271i	0.833616	−	0.552345i	$-0.186267\pi$
$983$	8.81863	+	8.81863i	0.281271	+	0.281271i	−0.552345	+	0.833616i	$0.686267\pi$
$984$	−4.16235	−	7.20941i	−0.132691	−	0.229827i
$985$	0.989935	−	1.71462i	0.0315420	−	0.0546323i
$986$	3.18878	−	0.854431i	0.101551	−	0.0272106i
$987$		0			0
$988$	11.6602	+	17.8323i	0.370961	+	0.567320i
$989$	46.0223			1.46343
$990$	−0.275125	−	1.02678i	−0.00874405	−	0.0326332i
$991$	11.0564	−	19.1502i	0.351218	−	0.608327i	−0.635245	−	0.772311i	$-0.719101\pi$
$991$	11.0564	−	19.1502i	0.351218	−	0.608327i	0.986463	+	0.163983i	$0.0524343\pi$
$992$	−1.70860	−	2.95938i	−0.0542481	−	0.0939606i
$993$	25.8435	−	25.8435i	0.820119	−	0.820119i
$994$		0			0
$995$	−5.24761	−	1.40609i	−0.166361	−	0.0445762i
$996$	13.1353	−	13.1353i	0.416208	−	0.416208i
$997$	−29.9386	+	17.2851i	−0.948167	+	0.547424i	−0.892511	−	0.451026i	$-0.851058\pi$
$997$	−29.9386	+	17.2851i	−0.948167	+	0.547424i	−0.0556556	+	0.998450i	$0.517725\pi$
$998$	3.79260	+	2.18966i	0.120053	+	0.0693123i
$999$	−0.917136	+	0.245746i	−0.0290169	+	0.00777505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bd.a.293.3		28
7.2	even	3		637.2.bb.a.423.5		28
7.3	odd	6		637.2.x.a.215.5		28
7.4	even	3		91.2.w.a.33.5	✓	28
7.5	odd	6		91.2.ba.a.59.5	yes	28
7.6	odd	2		637.2.bd.b.293.3		28
13.2	odd	12		637.2.bd.b.587.3		28
21.5	even	6		819.2.et.b.514.3		28
21.11	odd	6		819.2.gh.b.397.3		28
91.2	odd	12		637.2.x.a.80.5		28
91.41	even	12	inner	637.2.bd.a.587.3		28
91.54	even	12		91.2.w.a.80.5	yes	28
91.67	odd	12		91.2.ba.a.54.5	yes	28
91.80	even	12		637.2.bb.a.509.5		28
273.158	even	12		819.2.et.b.145.3		28
273.236	odd	12		819.2.gh.b.262.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.33.5	✓	28	7.4	even	3
91.2.w.a.80.5	yes	28	91.54	even	12
91.2.ba.a.54.5	yes	28	91.67	odd	12
91.2.ba.a.59.5	yes	28	7.5	odd	6
637.2.x.a.80.5		28	91.2	odd	12
637.2.x.a.215.5		28	7.3	odd	6
637.2.bb.a.423.5		28	7.2	even	3
637.2.bb.a.509.5		28	91.80	even	12
637.2.bd.a.293.3		28	1.1	even	1	trivial
637.2.bd.a.587.3		28	91.41	even	12	inner
637.2.bd.b.293.3		28	7.6	odd	2
637.2.bd.b.587.3		28	13.2	odd	12
819.2.et.b.145.3		28	273.158	even	12
819.2.et.b.514.3		28	21.5	even	6
819.2.gh.b.262.3		28	273.236	odd	12
819.2.gh.b.397.3		28	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.278342 + 0.0745816i) q^{2} +(0.923129 + 0.532969i) q^{3} +(-1.66014 + 0.958482i) q^{4} +(0.365574 - 0.365574i) q^{5} +(-0.296695 - 0.0794993i) q^{6} +(0.798123 - 0.798123i) q^{8} +(-0.931889 - 1.61408i) q^{9} +O(q^{10})\)	\(q+(-0.278342 + 0.0745816i) q^{2} +(0.923129 + 0.532969i) q^{3} +(-1.66014 + 0.958482i) q^{4} +(0.365574 - 0.365574i) q^{5} +(-0.296695 - 0.0794993i) q^{6} +(0.798123 - 0.798123i) q^{8} +(-0.931889 - 1.61408i) q^{9} +(-0.0744896 + 0.129020i) q^{10} +(-0.990856 - 3.69793i) q^{11} -2.04336 q^{12} +(-1.12494 - 3.42557i) q^{13} +(0.532311 - 0.142632i) q^{15} +(1.75434 - 3.03860i) q^{16} +(-2.26016 - 3.91471i) q^{17} +(0.379765 + 0.379765i) q^{18} +(2.97757 + 0.797839i) q^{19} +(-0.256508 + 0.957300i) q^{20} +(0.551594 + 0.955389i) q^{22} +(7.51600 + 4.33936i) q^{23} +(1.16214 - 0.311396i) q^{24} +4.73271i q^{25} +(0.568604 + 0.869580i) q^{26} -5.18448i q^{27} +(1.26720 - 2.19486i) q^{29} +(-0.137527 + 0.0794012i) q^{30} +(-0.739278 + 0.739278i) q^{31} +(-0.845949 + 3.15712i) q^{32} +(1.05619 - 3.94176i) q^{33} +(0.921063 + 0.921063i) q^{34} +(3.09413 + 1.78640i) q^{36} +(-0.0474003 - 0.176900i) q^{37} -0.888289 q^{38} +(0.787251 - 3.76180i) q^{39} -0.583546i q^{40} +(-1.79081 - 6.68338i) q^{41} +(4.59244 - 2.65145i) q^{43} +(5.18935 + 5.18935i) q^{44} +(-0.930740 - 0.249391i) q^{45} +(-2.41566 - 0.647273i) q^{46} +(-6.61286 - 6.61286i) q^{47} +(3.23896 - 1.87001i) q^{48} +(-0.352973 - 1.31731i) q^{50} -4.81838i q^{51} +(5.15091 + 4.60868i) q^{52} -1.02507 q^{53} +(0.386667 + 1.44306i) q^{54} +(-1.71410 - 0.989634i) q^{55} +(2.32346 + 2.32346i) q^{57} +(-0.189020 + 0.705432i) q^{58} +(-0.134868 + 0.503336i) q^{59} +(-0.747000 + 0.747000i) q^{60} +(-7.39280 + 4.26823i) q^{61} +(0.150636 - 0.260909i) q^{62} +6.07549i q^{64} +(-1.66355 - 0.841047i) q^{65} +1.17593i q^{66} +(6.83871 - 1.83243i) q^{67} +(7.50436 + 4.33264i) q^{68} +(4.62549 + 8.01158i) q^{69} +(1.96522 - 7.33429i) q^{71} +(-2.03200 - 0.544472i) q^{72} +(-8.74565 - 8.74565i) q^{73} +(0.0263870 + 0.0457036i) q^{74} +(-2.52239 + 4.36890i) q^{75} +(-5.70790 + 1.52943i) q^{76} +(0.0614358 + 1.10578i) q^{78} -7.55600 q^{79} +(-0.469493 - 1.75217i) q^{80} +(-0.0325003 + 0.0562921i) q^{81} +(0.996914 + 1.72671i) q^{82} +(-6.42827 + 6.42827i) q^{83} +(-2.25737 - 0.604861i) q^{85} +(-1.08052 + 1.08052i) q^{86} +(2.33958 - 1.35076i) q^{87} +(-3.74222 - 2.16057i) q^{88} +(11.7065 - 3.13675i) q^{89} +0.277664 q^{90} -16.6368 q^{92} +(-1.07646 + 0.288437i) q^{93} +(2.33384 + 1.34744i) q^{94} +(1.38019 - 0.796855i) q^{95} +(-2.46357 + 2.46357i) q^{96} +(13.1956 + 3.53575i) q^{97} +(-5.04538 + 5.04538i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} - 6 q^{3} + 6 q^{4} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q + 4 * q^2 - 6 * q^3 + 6 * q^4 + 12 * q^6 - 4 * q^8 + 6 * q^9	\( 28 q + 4 q^{2} - 6 q^{3} + 6 q^{4} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} - 4 q^{11} - 16 q^{12} + 10 q^{15} - 2 q^{16} - 6 q^{17} + 2 q^{18} + 22 q^{19} - 36 q^{20} - 8 q^{22} + 6 q^{23} - 30 q^{24} - 8 q^{29} + 30 q^{30} + 34 q^{31} + 10 q^{32} - 30 q^{33} + 12 q^{34} + 54 q^{36} + 26 q^{37} - 8 q^{39} + 18 q^{41} + 48 q^{43} + 12 q^{44} - 18 q^{45} - 42 q^{46} + 36 q^{47} + 12 q^{48} + 10 q^{50} + 2 q^{52} - 24 q^{53} - 6 q^{55} + 12 q^{57} - 16 q^{58} + 48 q^{59} - 26 q^{60} + 30 q^{61} - 36 q^{62} - 26 q^{65} + 14 q^{67} - 30 q^{68} + 42 q^{69} - 42 q^{71} - 8 q^{72} + 26 q^{73} - 6 q^{74} - 20 q^{75} + 52 q^{76} - 62 q^{78} - 8 q^{79} + 18 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} + 48 q^{86} - 42 q^{87} + 6 q^{88} + 30 q^{89} - 72 q^{90} - 156 q^{92} - 34 q^{93} - 18 q^{94} + 6 q^{95} - 84 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q + 4 * q^2 - 6 * q^3 + 6 * q^4 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 - 4 * q^11 - 16 * q^12 + 10 * q^15 - 2 * q^16 - 6 * q^17 + 2 * q^18 + 22 * q^19 - 36 * q^20 - 8 * q^22 + 6 * q^23 - 30 * q^24 - 8 * q^29 + 30 * q^30 + 34 * q^31 + 10 * q^32 - 30 * q^33 + 12 * q^34 + 54 * q^36 + 26 * q^37 - 8 * q^39 + 18 * q^41 + 48 * q^43 + 12 * q^44 - 18 * q^45 - 42 * q^46 + 36 * q^47 + 12 * q^48 + 10 * q^50 + 2 * q^52 - 24 * q^53 - 6 * q^55 + 12 * q^57 - 16 * q^58 + 48 * q^59 - 26 * q^60 + 30 * q^61 - 36 * q^62 - 26 * q^65 + 14 * q^67 - 30 * q^68 + 42 * q^69 - 42 * q^71 - 8 * q^72 + 26 * q^73 - 6 * q^74 - 20 * q^75 + 52 * q^76 - 62 * q^78 - 8 * q^79 + 18 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 + 48 * q^86 - 42 * q^87 + 6 * q^88 + 30 * q^89 - 72 * q^90 - 156 * q^92 - 34 * q^93 - 18 * q^94 + 6 * q^95 - 84 * q^96 + 62 * q^97 - 36 * q^99

Introduction

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