LMFDB - Embedded newform 735.2.q.e.79.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(79,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("735.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.5
Root			$-0.531325 - 1.98293i$ of defining polynomial
Character	$\chi$	$=$	735.79
Dual form			735.2.q.e.214.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.64823 + 0.951606i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.811108 + 1.40488i) q^{4} +(1.76210 + 1.37659i) q^{5} +1.90321 q^{6} -0.719004i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.64823 + 0.951606i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.811108 + 1.40488i) q^{4} +(1.76210 + 1.37659i) q^{5} +1.90321 q^{6} -0.719004i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.59438 + 3.94576i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(1.40488 + 0.811108i) q^{12} +6.42864i q^{13} +(2.21432 + 0.311108i) q^{15} +(2.30642 - 3.99484i) q^{16} +(3.83531 - 2.21432i) q^{17} +(1.64823 - 0.951606i) q^{18} +(-1.21432 + 2.10326i) q^{19} +(-0.504684 + 3.59210i) q^{20} -3.80642i q^{22} +(1.19320 + 0.688892i) q^{23} +(-0.359502 - 0.622675i) q^{24} +(1.21002 + 4.85138i) q^{25} +(-6.11753 + 10.5959i) q^{26} -1.00000i q^{27} -0.755569 q^{29} +(3.35366 + 2.61994i) q^{30} +(-2.59210 - 4.48966i) q^{31} +(6.35768 - 3.67061i) q^{32} +(-1.73205 - 1.00000i) q^{33} +8.42864 q^{34} +1.62222 q^{36} +(-6.59292 - 3.80642i) q^{37} +(-4.00296 + 2.31111i) q^{38} +(3.21432 + 5.56737i) q^{39} +(0.989771 - 1.26696i) q^{40} -8.23506 q^{41} -10.1017i q^{43} +(1.62222 - 2.80976i) q^{44} +(2.07321 - 0.837733i) q^{45} +(1.31111 + 2.27091i) q^{46} +(-2.38639 - 1.37778i) q^{47} -4.61285i q^{48} +(-2.62222 + 9.14764i) q^{50} +(2.21432 - 3.83531i) q^{51} +(-9.03147 + 5.21432i) q^{52} +(-7.95376 + 4.59210i) q^{53} +(0.951606 - 1.64823i) q^{54} +(0.622216 - 4.42864i) q^{55} +2.42864i q^{57} +(-1.24535 - 0.719004i) q^{58} +(7.05086 + 12.2124i) q^{59} +(1.35898 + 3.36320i) q^{60} +(-3.42864 + 5.93858i) q^{61} -9.86665i q^{62} +4.74620 q^{64} +(-8.84958 + 11.3279i) q^{65} +(-1.90321 - 3.29646i) q^{66} +(2.38639 - 1.37778i) q^{67} +(6.22171 + 3.59210i) q^{68} +1.37778 q^{69} +2.00000 q^{71} +(-0.622675 - 0.359502i) q^{72} +(1.36084 - 0.785680i) q^{73} +(-7.24443 - 12.5477i) q^{74} +(3.47359 + 3.59641i) q^{75} -3.93978 q^{76} +12.2351i q^{78} +(-2.42864 + 4.20653i) q^{79} +(9.56341 - 3.86433i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-13.5733 - 7.83654i) q^{82} -11.6128i q^{83} +(9.80642 + 1.37778i) q^{85} +(9.61285 - 16.6499i) q^{86} +(-0.654342 + 0.377784i) q^{87} +(-1.24535 + 0.719004i) q^{88} +(2.31111 - 4.00296i) q^{89} +(4.21432 + 0.592104i) q^{90} +2.23506i q^{92} +(-4.48966 - 2.59210i) q^{93} +(-2.62222 - 4.54181i) q^{94} +(-5.03508 + 2.03455i) q^{95} +(3.67061 - 6.35768i) q^{96} -11.9398i q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 10 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{9}+O(q^{10}) $ 12 * q + 10 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^9	$ 12 q + 10 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{9} + 12 q^{10} - 12 q^{11} - 26 q^{16} + 12 q^{19} - 60 q^{20} - 18 q^{24} + 2 q^{25} - 20 q^{26} - 8 q^{29} + 10 q^{30} - 4 q^{31} + 48 q^{34} + 20 q^{36} + 12 q^{39} - 4 q^{40} + 8 q^{41} + 20 q^{44} + 2 q^{45} + 16 q^{46} - 32 q^{50} - 2 q^{54} + 8 q^{55} + 32 q^{59} + 8 q^{60} + 12 q^{61} - 52 q^{64} - 32 q^{65} + 4 q^{66} + 16 q^{69} + 24 q^{71} - 88 q^{74} - 8 q^{75} + 8 q^{76} + 24 q^{79} - 46 q^{80} - 6 q^{81} + 64 q^{85} + 8 q^{86} + 28 q^{89} + 24 q^{90} - 32 q^{94} - 4 q^{95} + 58 q^{96} - 24 q^{99}+O(q^{100}) $ 12 * q + 10 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^9 + 12 * q^10 - 12 * q^11 - 26 * q^16 + 12 * q^19 - 60 * q^20 - 18 * q^24 + 2 * q^25 - 20 * q^26 - 8 * q^29 + 10 * q^30 - 4 * q^31 + 48 * q^34 + 20 * q^36 + 12 * q^39 - 4 * q^40 + 8 * q^41 + 20 * q^44 + 2 * q^45 + 16 * q^46 - 32 * q^50 - 2 * q^54 + 8 * q^55 + 32 * q^59 + 8 * q^60 + 12 * q^61 - 52 * q^64 - 32 * q^65 + 4 * q^66 + 16 * q^69 + 24 * q^71 - 88 * q^74 - 8 * q^75 + 8 * q^76 + 24 * q^79 - 46 * q^80 - 6 * q^81 + 64 * q^85 + 8 * q^86 + 28 * q^89 + 24 * q^90 - 32 * q^94 - 4 * q^95 + 58 * q^96 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.64823	+	0.951606i	1.16547	+	0.672887i	0.952610	−	0.304195i	$-0.0983873\pi$
$2$	1.64823	+	0.951606i	1.16547	+	0.672887i	0.212865	+	0.977082i	$0.431721\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.811108	+	1.40488i	0.405554	+	0.702440i
$5$	1.76210	+	1.37659i	0.788037	+	0.615628i
$5$	1.76210	+	1.37659i	0.788037	+	0.615628i
$6$	1.90321			0.776983
$7$		0			0
$7$		0			0
$8$		−	0.719004i		−	0.254206i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.59438	+	3.94576i	0.504188	+	1.24776i
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$	1.40488	+	0.811108i	0.405554	+	0.234147i
$13$			6.42864i			1.78298i	0.453037	+	0.891492i	$0.350341\pi$
$13$			6.42864i			1.78298i	−0.453037	+	0.891492i	$0.649659\pi$
$14$		0			0
$15$	2.21432	+	0.311108i	0.571735	+	0.0803277i
$16$	2.30642	−	3.99484i	0.576606	−	0.998711i
$17$	3.83531	−	2.21432i	0.930200	−	0.537051i	0.0433254	−	0.999061i	$-0.486205\pi$
$17$	3.83531	−	2.21432i	0.930200	−	0.537051i	0.886875	+	0.462010i	$0.152871\pi$
$18$	1.64823	−	0.951606i	0.388492	−	0.224296i
$19$	−1.21432	+	2.10326i	−0.278584	+	0.482522i	−0.971033	−	0.238945i	$-0.923198\pi$
$19$	−1.21432	+	2.10326i	−0.278584	+	0.482522i	0.692449	+	0.721467i	$0.256532\pi$
$20$	−0.504684	+	3.59210i	−0.112851	+	0.803219i
$21$		0			0
$22$		−	3.80642i		−	0.811532i
$23$	1.19320	+	0.688892i	0.248799	+	0.143644i	0.619214	−	0.785222i	$-0.287451\pi$
$23$	1.19320	+	0.688892i	0.248799	+	0.143644i	−0.370415	+	0.928866i	$0.620785\pi$
$24$	−0.359502	−	0.622675i	−0.0733830	−	0.127103i
$25$	1.21002	+	4.85138i	0.242003	+	0.970275i
$26$	−6.11753	+	10.5959i	−1.19975	+	2.07802i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−0.755569			−0.140306			−0.0701528	−	0.997536i	$-0.522349\pi$
$29$	−0.755569			−0.140306			−0.0701528	+	0.997536i	$0.522349\pi$
$30$	3.35366	+	2.61994i	0.612291	+	0.478333i
$31$	−2.59210	−	4.48966i	−0.465556	−	0.806366i	0.533671	−	0.845692i	$-0.320812\pi$
$31$	−2.59210	−	4.48966i	−0.465556	−	0.806366i	−0.999226	+	0.0393263i	$0.987479\pi$
$32$	6.35768	−	3.67061i	1.12389	−	0.648878i
$33$	−1.73205	−	1.00000i	−0.301511	−	0.174078i
$34$	8.42864			1.44550
$35$		0			0
$36$	1.62222			0.270369
$37$	−6.59292	−	3.80642i	−1.08387	−	0.625772i	−0.151932	−	0.988391i	$-0.548549\pi$
$37$	−6.59292	−	3.80642i	−1.08387	−	0.625772i	−0.931938	+	0.362619i	$0.881883\pi$
$38$	−4.00296	+	2.31111i	−0.649365	+	0.374911i
$39$	3.21432	+	5.56737i	0.514703	+	0.891492i
$40$	0.989771	−	1.26696i	0.156497	−	0.200324i
$41$	−8.23506			−1.28610			−0.643050	−	0.765824i	$-0.722331\pi$
$41$	−8.23506			−1.28610			−0.643050	+	0.765824i	$0.722331\pi$
$42$		0			0
$43$		−	10.1017i		−	1.54050i	−0.637744	−	0.770248i	$-0.720132\pi$
$43$		−	10.1017i		−	1.54050i	0.637744	−	0.770248i	$-0.279868\pi$
$44$	1.62222	−	2.80976i	0.244558	−	0.423587i
$45$	2.07321	−	0.837733i	0.309056	−	0.124882i
$46$	1.31111	+	2.27091i	0.193312	+	0.334827i
$47$	−2.38639	−	1.37778i	−0.348091	−	0.200971i	0.315753	−	0.948841i	$-0.397743\pi$
$47$	−2.38639	−	1.37778i	−0.348091	−	0.200971i	−0.663844	+	0.747871i	$0.731076\pi$
$48$		−	4.61285i		−	0.665807i
$49$		0			0
$50$	−2.62222	+	9.14764i	−0.370837	+	1.29367i
$51$	2.21432	−	3.83531i	0.310067	−	0.537051i
$52$	−9.03147	+	5.21432i	−1.25244	+	0.723096i
$53$	−7.95376	+	4.59210i	−1.09253	+	0.630774i	−0.934250	−	0.356620i	$-0.883929\pi$
$53$	−7.95376	+	4.59210i	−1.09253	+	0.630774i	−0.158283	+	0.987394i	$0.550596\pi$
$54$	0.951606	−	1.64823i	0.129497	−	0.224296i
$55$	0.622216	−	4.42864i	0.0838995	−	0.597158i
$56$		0			0
$57$			2.42864i			0.321681i
$58$	−1.24535	−	0.719004i	−0.163523	−	0.0944098i
$59$	7.05086	+	12.2124i	0.917943	+	1.58992i	0.802534	+	0.596606i	$0.203485\pi$
$59$	7.05086	+	12.2124i	0.917943	+	1.58992i	0.115409	+	0.993318i	$0.463182\pi$
$60$	1.35898	+	3.36320i	0.175444	+	0.434187i
$61$	−3.42864	+	5.93858i	−0.438992	+	0.760357i	−0.997612	−	0.0690669i	$-0.977998\pi$
$61$	−3.42864	+	5.93858i	−0.438992	+	0.760357i	0.558620	+	0.829424i	$0.311331\pi$
$62$		−	9.86665i		−	1.25307i
$63$		0			0
$64$	4.74620			0.593275
$65$	−8.84958	+	11.3279i	−1.09766	+	1.40506i
$66$	−1.90321	−	3.29646i	−0.234269	−	0.405766i
$67$	2.38639	−	1.37778i	0.291544	−	0.168323i	−0.347094	−	0.937830i	$-0.612831\pi$
$67$	2.38639	−	1.37778i	0.291544	−	0.168323i	0.638638	+	0.769507i	$0.279498\pi$
$68$	6.22171	+	3.59210i	0.754493	+	0.435607i
$69$	1.37778			0.165866
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	−0.622675	−	0.359502i	−0.0733830	−	0.0423677i
$73$	1.36084	−	0.785680i	0.159274	−	0.0919569i	−0.418244	−	0.908335i	$-0.637354\pi$
$73$	1.36084	−	0.785680i	0.159274	−	0.0919569i	0.577519	+	0.816378i	$0.304021\pi$
$74$	−7.24443	−	12.5477i	−0.842148	−	1.45864i
$75$	3.47359	+	3.59641i	0.401096	+	0.415277i
$76$	−3.93978			−0.451923
$77$		0			0
$78$			12.2351i			1.38535i
$79$	−2.42864	+	4.20653i	−0.273243	+	0.473271i	−0.969690	−	0.244337i	$-0.921430\pi$
$79$	−2.42864	+	4.20653i	−0.273243	+	0.473271i	0.696447	+	0.717608i	$0.254763\pi$
$80$	9.56341	−	3.86433i	1.06922	−	0.432046i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−13.5733	−	7.83654i	−1.49892	−	0.865401i
$83$		−	11.6128i		−	1.27468i	−0.770585	−	0.637338i	$-0.780036\pi$
$83$		−	11.6128i		−	1.27468i	0.770585	−	0.637338i	$-0.219964\pi$
$84$		0			0
$85$	9.80642	+	1.37778i	1.06366	+	0.149442i
$86$	9.61285	−	16.6499i	1.03658	−	1.79541i
$87$	−0.654342	+	0.377784i	−0.0701528	+	0.0405027i
$88$	−1.24535	+	0.719004i	−0.132755	+	0.0766461i
$89$	2.31111	−	4.00296i	0.244977	−	0.424313i	−0.717148	−	0.696921i	$-0.754553\pi$
$89$	2.31111	−	4.00296i	0.244977	−	0.424313i	0.962125	+	0.272608i	$0.0878863\pi$
$90$	4.21432	+	0.592104i	0.444228	+	0.0624133i
$91$		0			0
$92$			2.23506i			0.233021i
$93$	−4.48966	−	2.59210i	−0.465556	−	0.268789i
$94$	−2.62222	−	4.54181i	−0.270461	−	0.468452i
$95$	−5.03508	+	2.03455i	−0.516589	+	0.208740i
$96$	3.67061	−	6.35768i	0.374630	−	0.648878i
$97$		−	11.9398i		−	1.21230i	−0.795350	−	0.606150i	$-0.792713\pi$
$97$		−	11.9398i		−	1.21230i	0.795350	−	0.606150i	$-0.207287\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$	−5.83415	+	5.63492i	−0.583415	+	0.563492i
$101$	−0.739747	−	1.28128i	−0.0736076	−	0.127492i	0.826872	−	0.562390i	$-0.190118\pi$
$101$	−0.739747	−	1.28128i	−0.0736076	−	0.127492i	−0.900480	+	0.434898i	$0.856785\pi$
$102$	7.29942	−	4.21432i	0.722750	−	0.417280i
$103$	−7.67063	−	4.42864i	−0.755809	−	0.436367i	0.0719797	−	0.997406i	$-0.477068\pi$
$103$	−7.67063	−	4.42864i	−0.755809	−	0.436367i	−0.827789	+	0.561039i	$0.810402\pi$
$104$	4.62222			0.453246
$105$		0			0
$106$	−17.4795			−1.69776
$107$	−1.52848	−	0.882468i	−0.147764	−	0.0853114i	0.424295	−	0.905524i	$-0.360522\pi$
$107$	−1.52848	−	0.882468i	−0.147764	−	0.0853114i	−0.572059	+	0.820212i	$0.693855\pi$
$108$	1.40488	−	0.811108i	0.135185	−	0.0780489i
$109$	2.80642	+	4.86087i	0.268807	+	0.465587i	0.968554	−	0.248804i	$-0.0800374\pi$
$109$	2.80642	+	4.86087i	0.268807	+	0.465587i	−0.699747	+	0.714390i	$0.746704\pi$
$110$	5.23987	−	6.70731i	0.499602	−	0.639517i
$111$	−7.61285			−0.722580
$112$		0			0
$113$			11.2859i			1.06169i	0.847469	+	0.530845i	$0.178125\pi$
$113$			11.2859i			1.06169i	−0.847469	+	0.530845i	$0.821875\pi$
$114$	−2.31111	+	4.00296i	−0.216455	+	0.374911i
$115$	1.15421	+	2.85644i	0.107631	+	0.266364i
$116$	−0.612848	−	1.06148i	−0.0569015	−	0.0985563i
$117$	5.56737	+	3.21432i	0.514703	+	0.297164i
$118$			26.8385i			2.47069i
$119$		0			0
$120$	0.223688	−	1.59210i	0.0204198	−	0.145339i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−11.3024	+	6.52543i	−1.02327	+	0.590784i
$123$	−7.13177	+	4.11753i	−0.643050	+	0.371265i
$124$	4.20495	−	7.28319i	0.377616	−	0.654050i
$125$	−4.54617	+	10.2143i	−0.406622	+	0.913597i
$126$		0			0
$127$		−	12.8573i		−	1.14090i	−0.821333	−	0.570450i	$-0.806769\pi$
$127$		−	12.8573i		−	1.14090i	0.821333	−	0.570450i	$-0.193231\pi$
$128$	−4.89253	−	2.82471i	−0.432443	−	0.249671i
$129$	−5.05086	−	8.74834i	−0.444703	−	0.770248i
$130$	−25.3659	+	10.2497i	−2.22473	+	0.898959i
$131$	1.05086	−	1.82013i	0.0918136	−	0.159026i	−0.816461	−	0.577401i	$-0.804067\pi$
$131$	1.05086	−	1.82013i	0.0918136	−	0.159026i	0.908274	+	0.418375i	$0.137400\pi$
$132$		−	3.24443i		−	0.282391i
$133$		0			0
$134$	5.24443			0.453050
$135$	1.37659	−	1.76210i	0.118478	−	0.151658i
$136$	−1.59210	−	2.75761i	−0.136522	−	0.236463i
$137$	13.8043	−	7.96989i	1.17938	−	0.680914i	0.223506	−	0.974702i	$-0.428250\pi$
$137$	13.8043	−	7.96989i	1.17938	−	0.680914i	0.955870	+	0.293789i	$0.0949163\pi$
$138$	2.27091	+	1.31111i	0.193312	+	0.111609i
$139$	−11.6731			−0.990097			−0.495048	−	0.868865i	$-0.664850\pi$
$139$	−11.6731			−0.990097			−0.495048	+	0.868865i	$0.664850\pi$
$140$		0			0
$141$	−2.75557			−0.232061
$142$	3.29646	+	1.90321i	0.276633	+	0.159714i
$143$	11.1347	−	6.42864i	0.931133	−	0.537590i
$144$	−2.30642	−	3.99484i	−0.192202	−	0.332904i
$145$	−1.33139	−	1.04011i	−0.110566	−	0.0863761i
$146$	2.99063			0.247506
$147$		0			0
$148$		−	12.3497i		−	1.01514i
$149$	−10.6128	+	18.3820i	−0.869438	+	1.50591i	−0.00686675	+	0.999976i	$0.502186\pi$
$149$	−10.6128	+	18.3820i	−0.869438	+	1.50591i	−0.862572	+	0.505935i	$0.831148\pi$
$150$	2.30292	+	9.23320i	0.188032	+	0.753888i
$151$	−8.42864	−	14.5988i	−0.685913	−	1.18804i	−0.973149	−	0.230176i	$-0.926070\pi$
$151$	−8.42864	−	14.5988i	−0.685913	−	1.18804i	0.287236	−	0.957860i	$-0.407264\pi$
$152$	1.51225	+	0.873100i	0.122660	+	0.0708178i
$153$		−	4.42864i		−	0.358034i
$154$		0			0
$155$	1.61285	−	11.4795i	0.129547	−	0.922055i
$156$	−5.21432	+	9.03147i	−0.417480	+	0.723096i
$157$	−9.03147	+	5.21432i	−0.720790	+	0.416148i	−0.815043	−	0.579400i	$-0.803287\pi$
$157$	−9.03147	+	5.21432i	−0.720790	+	0.416148i	0.0942537	+	0.995548i	$0.469954\pi$
$158$	−8.00591	+	4.62222i	−0.636916	+	0.367724i
$159$	−4.59210	+	7.95376i	−0.364178	+	0.630774i
$160$	16.2558	+	2.28391i	1.28513	+	0.180559i
$161$		0			0
$162$		−	1.90321i		−	0.149530i
$163$	18.0629	+	10.4286i	1.41480	+	0.816834i	0.995835	−	0.0911693i	$-0.0290605\pi$
$163$	18.0629	+	10.4286i	1.41480	+	0.816834i	0.418963	+	0.908003i	$0.362394\pi$
$164$	−6.67952	−	11.5693i	−0.521583	−	0.903409i
$165$	−1.67547	−	4.14642i	−0.130435	−	0.322799i
$166$	11.0509	−	19.1406i	0.857713	−	1.48560i
$167$			15.3461i			1.18752i	0.804642	+	0.593760i	$0.202357\pi$
$167$			15.3461i			1.18752i	−0.804642	+	0.593760i	$0.797643\pi$
$168$		0			0
$169$	−28.3274			−2.17903
$170$	14.8521	+	11.6028i	1.13911	+	0.889891i
$171$	1.21432	+	2.10326i	0.0928614	+	0.160841i
$172$	14.1917	−	8.19358i	1.08211	−	0.624754i
$173$	1.78421	+	1.03011i	0.135651	+	0.0783179i	0.566290	−	0.824206i	$-0.308378\pi$
$173$	1.78421	+	1.03011i	0.135651	+	0.0783179i	−0.430639	+	0.902524i	$0.641712\pi$
$174$	−1.43801			−0.109015
$175$		0			0
$176$	−9.22570			−0.695413
$177$	12.2124	+	7.05086i	0.917943	+	0.529975i
$178$	7.61847	−	4.39853i	0.571029	−	0.329684i
$179$	5.00000	+	8.66025i	0.373718	+	0.647298i	0.990134	−	0.140122i	$-0.0447496\pi$
$179$	5.00000	+	8.66025i	0.373718	+	0.647298i	−0.616417	+	0.787420i	$0.711416\pi$
$180$	2.85851	+	2.23312i	0.213061	+	0.166447i
$181$	−12.1017			−0.899513			−0.449757	−	0.893151i	$-0.648489\pi$
$181$	−12.1017			−0.899513			−0.449757	+	0.893151i	$0.648489\pi$
$182$		0			0
$183$			6.85728i			0.506905i
$184$	0.495316	−	0.857913i	0.0365152	−	0.0632462i
$185$	−6.37753	−	15.7830i	−0.468885	−	1.16039i
$186$	−4.93332	−	8.54477i	−0.361729	−	0.626533i
$187$	−7.67063	−	4.42864i	−0.560932	−	0.323854i
$188$		−	4.47013i		−	0.326017i
$189$		0			0
$190$	−10.2351	−	1.43801i	−0.742530	−	0.104324i
$191$	−0.244431	+	0.423367i	−0.0176864	+	0.0306338i	−0.874733	−	0.484605i	$-0.838963\pi$
$191$	−0.244431	+	0.423367i	−0.0176864	+	0.0306338i	0.857047	+	0.515239i	$0.172297\pi$
$192$	4.11033	−	2.37310i	0.296638	−	0.171264i
$193$	19.8831	−	11.4795i	1.43121	−	0.826312i	0.434001	−	0.900912i	$-0.357101\pi$
$193$	19.8831	−	11.4795i	1.43121	−	0.826312i	0.997214	+	0.0746003i	$0.0237681\pi$
$194$	11.3620	−	19.6795i	0.815741	−	1.41291i
$195$	−2.00000	+	14.2351i	−0.143223	+	1.01939i
$196$		0			0
$197$		−	1.18421i		−	0.0843713i	−0.999110	−	0.0421857i	$-0.986568\pi$
$197$		−	1.18421i		−	0.0843713i	0.999110	−	0.0421857i	$-0.0134321\pi$
$198$	−3.29646	−	1.90321i	−0.234269	−	0.135255i
$199$	4.39853	+	7.61847i	0.311803	+	0.540059i	0.978753	−	0.205044i	$-0.0657336\pi$
$199$	4.39853	+	7.61847i	0.311803	+	0.540059i	−0.666949	+	0.745103i	$0.732400\pi$
$200$	3.48816	−	0.870006i	0.246650	−	0.0615187i
$201$	1.37778	−	2.38639i	0.0971814	−	0.168323i
$202$		−	2.81579i		−	0.198118i
$203$		0			0
$204$	7.18421			0.502995
$205$	−14.5110	−	11.3363i	−1.01349	−	0.791760i
$206$	−8.42864	−	14.5988i	−0.587251	−	1.01715i
$207$	1.19320	−	0.688892i	0.0829329	−	0.0478813i
$208$	25.6814	+	14.8272i	1.78069	+	1.02808i
$209$	4.85728			0.335985
$210$		0			0
$211$	23.2257			1.59892			0.799461	−	0.600717i	$-0.205118\pi$
$211$	23.2257			1.59892			0.799461	+	0.600717i	$0.205118\pi$
$212$	−12.9027	−	7.44938i	−0.886162	−	0.511626i
$213$	1.73205	−	1.00000i	0.118678	−	0.0685189i
$214$	−1.67952	−	2.90902i	−0.114810	−	0.198857i
$215$	13.9059	−	17.8003i	0.948373	−	1.21397i
$216$	−0.719004			−0.0489220
$217$		0			0
$218$			10.6824i			0.723506i
$219$	0.785680	−	1.36084i	0.0530914	−	0.0919569i
$220$	6.72639	−	2.71797i	0.453493	−	0.183245i
$221$	14.2351	+	24.6559i	0.957554	+	1.65853i
$222$	−12.5477	−	7.24443i	−0.842148	−	0.486214i
$223$			15.2257i			1.01959i	0.860297	+	0.509794i	$0.170278\pi$
$223$			15.2257i			1.01959i	−0.860297	+	0.509794i	$0.829722\pi$
$224$		0			0
$225$	4.80642	+	1.37778i	0.320428	+	0.0918523i
$226$	−10.7397	+	18.6018i	−0.714397	+	1.23737i
$227$	−12.4434	+	7.18421i	−0.825898	+	0.476833i	−0.852446	−	0.522815i	$-0.824882\pi$
$227$	−12.4434	+	7.18421i	−0.825898	+	0.476833i	0.0265479	+	0.999648i	$0.491549\pi$
$228$	−3.41195	+	1.96989i	−0.225962	+	0.130459i
$229$	−2.80642	+	4.86087i	−0.185454	+	0.321215i	−0.943729	−	0.330719i	$-0.892709\pi$
$229$	−2.80642	+	4.86087i	−0.185454	+	0.321215i	0.758276	+	0.651934i	$0.226042\pi$
$230$	−0.815792	+	5.80642i	−0.0537917	+	0.382864i
$231$		0			0
$232$			0.543257i			0.0356666i
$233$	20.1662	+	11.6430i	1.32113	+	0.762756i	0.983909	−	0.178669i	$-0.0571793\pi$
$233$	20.1662	+	11.6430i	1.32113	+	0.762756i	0.337222	+	0.941425i	$0.390513\pi$
$234$	6.11753	+	10.5959i	0.399916	+	0.692674i
$235$	−2.30843	−	5.71288i	−0.150585	−	0.372667i
$236$	−11.4380	+	19.8112i	−0.744551	+	1.28960i
$237$			4.85728i			0.315514i
$238$		0			0
$239$	8.48886			0.549099			0.274549	−	0.961573i	$-0.411471\pi$
$239$	8.48886			0.549099			0.274549	+	0.961573i	$0.411471\pi$
$240$	6.34999	−	8.12831i	0.409890	−	0.524680i
$241$	3.62222	+	6.27386i	0.233327	+	0.404135i	0.958785	−	0.284132i	$-0.0917053\pi$
$241$	3.62222	+	6.27386i	0.233327	+	0.404135i	−0.725458	+	0.688267i	$0.758372\pi$
$242$	11.5376	−	6.66124i	0.741666	−	0.428201i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−11.1240			−0.712140
$245$		0			0
$246$	−15.6731			−0.999278
$247$	−13.5211	−	7.80642i	−0.860328	−	0.496711i
$248$	−3.22808	+	1.86373i	−0.204983	+	0.118347i
$249$	−5.80642	−	10.0570i	−0.367967	−	0.637338i
$250$	−17.2131	+	12.5094i	−1.08865	+	0.791163i
$251$	27.6128			1.74291			0.871454	−	0.490478i	$-0.163178\pi$
$251$	27.6128			1.74291			0.871454	+	0.490478i	$0.163178\pi$
$252$		0			0
$253$		−	2.75557i		−	0.173241i
$254$	12.2351	−	21.1918i	0.767696	−	1.32969i
$255$	9.18150	−	3.71002i	0.574968	−	0.232330i
$256$	−10.1222	−	17.5322i	−0.632638	−	1.09576i
$257$	0.371213	+	0.214320i	0.0231556	+	0.0133689i	0.511533	−	0.859264i	$-0.329078\pi$
$257$	0.371213	+	0.214320i	0.0231556	+	0.0133689i	−0.488378	+	0.872632i	$0.662411\pi$
$258$		−	19.2257i		−	1.19694i
$259$		0			0
$260$	−23.0923	−	3.24443i	−1.43213	−	0.201211i
$261$	−0.377784	+	0.654342i	−0.0233843	+	0.0405027i
$262$	3.46410	−	2.00000i	0.214013	−	0.123560i
$263$	8.12140	−	4.68889i	0.500787	−	0.289129i	−0.228252	−	0.973602i	$-0.573301\pi$
$263$	8.12140	−	4.68889i	0.500787	−	0.289129i	0.729038	+	0.684473i	$0.239968\pi$
$264$	−0.719004	+	1.24535i	−0.0442516	+	0.0766461i
$265$	−20.3368	−	2.85728i	−1.24928	−	0.175521i
$266$		0			0
$267$		−	4.62222i		−	0.282875i
$268$	3.87124	+	2.23506i	0.236474	+	0.136528i
$269$	0.873100	+	1.51225i	0.0532339	+	0.0922038i	0.891414	−	0.453189i	$-0.149714\pi$
$269$	0.873100	+	1.51225i	0.0532339	+	0.0922038i	−0.838181	+	0.545393i	$0.816380\pi$
$270$	3.94576	−	1.59438i	0.240131	−	0.0970310i
$271$	1.34767	−	2.33424i	0.0818653	−	0.141795i	−0.822186	−	0.569219i	$-0.807246\pi$
$271$	1.34767	−	2.33424i	0.0818653	−	0.141795i	0.904051	+	0.427424i	$0.140579\pi$
$272$		−	20.4286i		−	1.23867i
$273$		0			0
$274$	30.3368			1.83271
$275$	7.19282	−	6.94719i	0.433743	−	0.418931i
$276$	1.11753	+	1.93562i	0.0672675	+	0.116511i
$277$	−4.43750	+	2.56199i	−0.266624	+	0.153935i	−0.627352	−	0.778736i	$-0.715861\pi$
$277$	−4.43750	+	2.56199i	−0.266624	+	0.153935i	0.360729	+	0.932671i	$0.382528\pi$
$278$	−19.2399	−	11.1082i	−1.15393	−	0.666223i
$279$	−5.18421			−0.310370
$280$		0			0
$281$	23.9813			1.43060			0.715301	−	0.698816i	$-0.246290\pi$
$281$	23.9813			1.43060			0.715301	+	0.698816i	$0.246290\pi$
$282$	−4.54181	−	2.62222i	−0.270461	−	0.156151i
$283$	−2.05111	+	1.18421i	−0.121926	+	0.0703939i	−0.559723	−	0.828680i	$-0.689092\pi$
$283$	−2.05111	+	1.18421i	−0.121926	+	0.0703939i	0.437797	+	0.899074i	$0.355759\pi$
$284$	1.62222	+	2.80976i	0.0962608	+	0.166729i
$285$	−3.34323	+	4.27951i	−0.198036	+	0.253497i
$286$	24.4701			1.44695
$287$		0			0
$288$		−	7.34122i		−	0.432585i
$289$	1.30642	−	2.26279i	0.0768485	−	0.133105i
$290$	−1.20467	−	2.98129i	−0.0707404	−	0.175068i
$291$	−5.96989	−	10.3402i	−0.349961	−	0.606150i
$292$	2.20757	+	1.27454i	0.129188	+	0.0745870i
$293$		−	8.42864i		−	0.492406i	−0.969218	−	0.246203i	$-0.920817\pi$
$293$		−	8.42864i		−	0.492406i	0.969218	−	0.246203i	$-0.0791831\pi$
$294$		0			0
$295$	−4.38715	+	31.2257i	−0.255430	+	1.81803i
$296$	−2.73683	+	4.74033i	−0.159075	+	0.275526i
$297$	−1.73205	+	1.00000i	−0.100504	+	0.0580259i
$298$	−34.9848	+	20.1985i	−2.02662	+	1.17007i
$299$	−4.42864	+	7.67063i	−0.256115	+	0.443604i
$300$	−2.23506	+	7.79706i	−0.129041	+	0.450163i
$301$		0			0
$302$		−	32.0830i		−	1.84617i
$303$	−1.28128	−	0.739747i	−0.0736076	−	0.0424974i
$304$	5.60147	+	9.70203i	0.321266	+	0.556450i
$305$	−14.2166	+	5.74457i	−0.814039	+	0.328933i
$306$	4.21432	−	7.29942i	0.240917	−	0.417280i
$307$		−	22.5718i		−	1.28824i	−0.764923	−	0.644121i	$-0.777223\pi$
$307$		−	22.5718i		−	1.28824i	0.764923	−	0.644121i	$-0.222777\pi$
$308$		0			0
$309$	−8.85728			−0.503873
$310$	13.5823	−	17.3861i	0.771423	−	0.987461i
$311$	12.0415	+	20.8565i	0.682810	+	1.18266i	0.974120	+	0.226033i	$0.0725757\pi$
$311$	12.0415	+	20.8565i	0.682810	+	1.18266i	−0.291310	+	0.956629i	$0.594091\pi$
$312$	4.00296	−	2.31111i	0.226623	−	0.130841i
$313$	8.36090	+	4.82717i	0.472586	+	0.272848i	0.717322	−	0.696742i	$-0.245368\pi$
$313$	8.36090	+	4.82717i	0.472586	+	0.272848i	−0.244736	+	0.969590i	$0.578701\pi$
$314$	−19.8479			−1.12008
$315$		0			0
$316$	−7.87955			−0.443260
$317$	5.23208	+	3.02074i	0.293863	+	0.169662i	0.639683	−	0.768639i	$-0.279066\pi$
$317$	5.23208	+	3.02074i	0.293863	+	0.169662i	−0.345820	+	0.938301i	$0.612399\pi$
$318$	−15.1377	+	8.73975i	−0.848879	+	0.490101i
$319$	0.755569	+	1.30868i	0.0423037	+	0.0732722i
$320$	8.36330	+	6.53356i	0.467522	+	0.365237i
$321$	−1.76494			−0.0985092
$322$		0			0
$323$			10.7556i			0.598456i
$324$	0.811108	−	1.40488i	0.0450615	−	0.0780489i
$325$	−31.1878	+	7.77875i	−1.72999	+	0.431488i
$326$	19.8479	+	34.3776i	1.09927	+	1.90400i
$327$	4.86087	+	2.80642i	0.268807	+	0.155196i
$328$			5.92104i			0.326935i
$329$		0			0
$330$	1.18421	−	8.42864i	0.0651885	−	0.463981i
$331$	−6.75557	+	11.7010i	−0.371320	+	0.643144i	−0.989769	−	0.142680i	$-0.954428\pi$
$331$	−6.75557	+	11.7010i	−0.371320	+	0.643144i	0.618449	+	0.785825i	$0.287761\pi$
$332$	16.3147	−	9.41927i	0.895383	−	0.516950i
$333$	−6.59292	+	3.80642i	−0.361290	+	0.208591i
$334$	−14.6035	+	25.2940i	−0.799067	+	1.38402i
$335$	6.10171	+	0.857279i	0.333372	+	0.0468382i
$336$		0			0
$337$			10.4889i			0.571365i	0.958324	+	0.285682i	$0.0922202\pi$
$337$			10.4889i			0.571365i	−0.958324	+	0.285682i	$0.907780\pi$
$338$	−46.6901	−	26.9565i	−2.53961	−	1.46624i
$339$	5.64296	+	9.77389i	0.306483	+	0.530845i
$340$	6.01845	+	14.8944i	0.326396	+	0.807761i
$341$	−5.18421	+	8.97931i	−0.280741	+	0.486257i
$342$			4.62222i			0.249941i
$343$		0			0
$344$	−7.26317			−0.391604
$345$	2.42780	+	1.89664i	0.130708	+	0.102112i
$346$	1.96052	+	3.39572i	0.105398	+	0.182555i
$347$	−14.4833	+	8.36196i	−0.777507	+	0.448894i	−0.835546	−	0.549421i	$-0.814848\pi$
$347$	−14.4833	+	8.36196i	−0.777507	+	0.448894i	0.0580392	+	0.998314i	$0.481515\pi$
$348$	−1.06148	−	0.612848i	−0.0569015	−	0.0328521i
$349$	16.3684			0.876181			0.438091	−	0.898931i	$-0.355655\pi$
$349$	16.3684			0.876181			0.438091	+	0.898931i	$0.355655\pi$
$350$		0			0
$351$	6.42864			0.343135
$352$	−12.7154	−	7.34122i	−0.677731	−	0.391288i
$353$	−0.475522	+	0.274543i	−0.0253095	+	0.0146124i	−0.512601	−	0.858627i	$-0.671318\pi$
$353$	−0.475522	+	0.274543i	−0.0253095	+	0.0146124i	0.487292	+	0.873239i	$0.337985\pi$
$354$	13.4193	+	23.2429i	0.713226	+	1.23534i
$355$	3.52421	+	2.75317i	0.187045	+	0.146123i
$356$	7.49823			0.397405
$357$		0			0
$358$			19.0321i			1.00588i
$359$	−0.142721	+	0.247200i	−0.00753253	+	0.0130467i	−0.869767	−	0.493462i	$-0.835731\pi$
$359$	−0.142721	+	0.247200i	−0.00753253	+	0.0130467i	0.862235	+	0.506509i	$0.169064\pi$
$360$	−0.602333	−	1.49065i	−0.0317457	−	0.0785640i
$361$	6.55086	+	11.3464i	0.344782	+	0.597180i
$362$	−19.9464	−	11.5161i	−1.04836	−	0.605271i
$363$		−	7.00000i		−	0.367405i
$364$		0			0
$365$	3.47949	+	0.488863i	0.182125	+	0.0255882i
$366$	−6.52543	+	11.3024i	−0.341090	+	0.590784i
$367$	1.48485	−	0.857279i	0.0775086	−	0.0447496i	−0.460745	−	0.887533i	$-0.652418\pi$
$367$	1.48485	−	0.857279i	0.0775086	−	0.0447496i	0.538253	+	0.842783i	$0.319084\pi$
$368$	5.50403	−	3.17775i	0.286918	−	0.165652i
$369$	−4.11753	+	7.13177i	−0.214350	+	0.371265i
$370$	4.50760	−	32.0830i	0.234339	−	1.66791i
$371$		0			0
$372$		−	8.40990i		−	0.436033i
$373$	13.8564	+	8.00000i	0.717458	+	0.414224i	0.813816	−	0.581122i	$-0.197386\pi$
$373$	13.8564	+	8.00000i	0.717458	+	0.414224i	−0.0963587	+	0.995347i	$0.530720\pi$
$374$	−8.42864	−	14.5988i	−0.435835	−	0.754888i
$375$	1.17006	+	11.1189i	0.0604216	+	0.574180i
$376$	−0.990632	+	1.71583i	−0.0510879	+	0.0884869i
$377$		−	4.85728i		−	0.250163i
$378$		0			0
$379$	4.85728			0.249502			0.124751	−	0.992188i	$-0.460187\pi$
$379$	4.85728			0.249502			0.124751	+	0.992188i	$0.460187\pi$
$380$	−6.94229	−	5.42345i	−0.356132	−	0.278217i
$381$	−6.42864	−	11.1347i	−0.329349	−	0.570450i
$382$	−0.805758	+	0.465205i	−0.0412262	+	0.0238019i
$383$	−7.26349	−	4.19358i	−0.371147	−	0.214282i	0.302813	−	0.953050i	$-0.402074\pi$
$383$	−7.26349	−	4.19358i	−0.371147	−	0.214282i	−0.673959	+	0.738768i	$0.735408\pi$
$384$	−5.64941			−0.288295
$385$		0			0
$386$	43.6958			2.22406
$387$	−8.74834	−	5.05086i	−0.444703	−	0.256749i
$388$	16.7740	−	9.68445i	0.851568	−	0.491653i
$389$	4.47949	+	7.75871i	0.227119	+	0.393382i	0.956953	−	0.290242i	$-0.0937359\pi$
$389$	4.47949	+	7.75871i	0.227119	+	0.393382i	−0.729834	+	0.683625i	$0.760403\pi$
$390$	−16.8426	+	21.5594i	−0.852860	+	1.09170i
$391$	6.10171			0.308577
$392$		0			0
$393$		−	2.10171i		−	0.106017i
$394$	1.12690	−	1.95185i	0.0567724	−	0.0983326i
$395$	−10.0702	+	4.06910i	−0.506685	+	0.204739i
$396$	−1.62222	−	2.80976i	−0.0815194	−	0.141196i
$397$	2.20757	+	1.27454i	0.110795	+	0.0639675i	0.554373	−	0.832268i	$-0.312958\pi$
$397$	2.20757	+	1.27454i	0.110795	+	0.0639675i	−0.443579	+	0.896236i	$0.646291\pi$
$398$			16.7427i			0.839234i
$399$		0			0
$400$	22.1713	+	6.35551i	1.10857	+	0.317775i
$401$	−0.479495	+	0.830509i	−0.0239448	+	0.0414736i	−0.877750	−	0.479120i	$-0.840956\pi$
$401$	−0.479495	+	0.830509i	−0.0239448	+	0.0414736i	0.853805	+	0.520593i	$0.174289\pi$
$402$	4.54181	−	2.62222i	0.226525	−	0.130784i
$403$	28.8624	−	16.6637i	1.43774	−	0.830078i
$404$	1.20003	−	2.07851i	0.0597037	−	0.103410i
$405$	0.311108	−	2.21432i	0.0154591	−	0.110030i
$406$		0			0
$407$			15.2257i			0.754710i
$408$	−2.75761	−	1.59210i	−0.136522	−	0.0788209i
$409$	−15.9906	−	27.6966i	−0.790686	−	1.36951i	−0.925543	−	0.378643i	$-0.876391\pi$
$409$	−15.9906	−	27.6966i	−0.790686	−	1.36951i	0.134857	−	0.990865i	$-0.456943\pi$
$410$	−13.1298	−	32.4936i	−0.648437	−	1.60474i
$411$	7.96989	−	13.8043i	0.393126	−	0.680914i
$412$		−	14.3684i		−	0.707881i
$413$		0			0
$414$	2.62222			0.128875
$415$	15.9861	−	20.4630i	0.784727	−	1.00449i
$416$	23.5970	+	40.8712i	1.15694	+	2.00388i
$417$	−10.1092	+	5.83654i	−0.495048	+	0.285816i
$418$	8.00591	+	4.62222i	0.391582	+	0.226080i
$419$	0.470127			0.0229672			0.0114836	−	0.999934i	$-0.496345\pi$
$419$	0.470127			0.0229672			0.0114836	+	0.999934i	$0.496345\pi$
$420$		0			0
$421$	−33.6128			−1.63819			−0.819095	−	0.573658i	$-0.805524\pi$
$421$	−33.6128			−1.63819			−0.819095	+	0.573658i	$0.805524\pi$
$422$	38.2813	+	22.1017i	1.86350	+	1.07589i
$423$	−2.38639	+	1.37778i	−0.116030	+	0.0669902i
$424$	3.30174	+	5.71878i	0.160347	+	0.277729i
$425$	15.3833	+	15.9272i	0.746199	+	0.772582i
$426$	3.80642			0.184422
$427$		0			0
$428$		−	2.86311i		−	0.138394i
$429$	6.42864	−	11.1347i	0.310378	−	0.537590i
$430$	39.8589	−	16.1060i	1.92217	−	0.776700i
$431$	−5.85728	−	10.1451i	−0.282135	−	0.488673i	0.689775	−	0.724024i	$-0.257709\pi$
$431$	−5.85728	−	10.1451i	−0.282135	−	0.488673i	−0.971910	+	0.235351i	$0.924376\pi$
$432$	−3.99484	−	2.30642i	−0.192202	−	0.110968i
$433$			0.0602231i			0.00289414i	0.999999	+	0.00144707i	$0.000460616\pi$
$433$			0.0602231i			0.00289414i	−0.999999	+	0.00144707i	$0.999539\pi$
$434$		0			0
$435$	−1.67307	−	0.235063i	−0.0802176	−	0.0112704i
$436$	−4.55262	+	7.88538i	−0.218031	+	0.377641i
$437$	−2.89784	+	1.67307i	−0.138623	+	0.0800338i
$438$	2.58996	−	1.49532i	0.123753	−	0.0714490i
$439$	−11.2143	+	19.4238i	−0.535230	+	0.927046i	0.463922	+	0.885876i	$0.346442\pi$
$439$	−11.2143	+	19.4238i	−0.535230	+	0.927046i	−0.999152	+	0.0411699i	$0.986892\pi$
$440$	−3.18421	−	0.447375i	−0.151801	−	0.0213278i
$441$		0			0
$442$			54.1847i			2.57730i
$443$	−20.7410	−	11.9748i	−0.985434	−	0.568940i	−0.0815275	−	0.996671i	$-0.525980\pi$
$443$	−20.7410	−	11.9748i	−0.985434	−	0.568940i	−0.903906	+	0.427731i	$0.859313\pi$
$444$	−6.17484	−	10.6951i	−0.293045	−	0.507569i
$445$	9.58283	−	3.87218i	0.454270	−	0.183559i
$446$	−14.4889	+	25.0954i	−0.686068	+	1.18830i
$447$			21.2257i			1.00394i
$448$		0			0
$449$	−29.4291			−1.38885			−0.694423	−	0.719567i	$-0.744340\pi$
$449$	−29.4291			−1.38885			−0.694423	+	0.719567i	$0.744340\pi$
$450$	6.61098	+	6.84473i	0.311645	+	0.322664i
$451$	8.23506	+	14.2635i	0.387774	+	0.671644i
$452$	−15.8554	+	9.15410i	−0.745773	+	0.430572i
$453$	−14.5988	−	8.42864i	−0.685913	−	0.396012i
$454$	−27.3461			−1.28342
$455$		0			0
$456$	1.74620			0.0817733
$457$	2.72168	+	1.57136i	0.127315	+	0.0735051i	0.562305	−	0.826930i	$-0.309915\pi$
$457$	2.72168	+	1.57136i	0.127315	+	0.0735051i	−0.434990	+	0.900435i	$0.643248\pi$
$458$	−9.25126	+	5.34122i	−0.432283	+	0.249579i
$459$	−2.21432	−	3.83531i	−0.103356	−	0.179017i
$460$	−3.07676	+	3.93841i	−0.143455	+	0.183629i
$461$	−3.37778			−0.157319			−0.0786596	−	0.996902i	$-0.525064\pi$
$461$	−3.37778			−0.157319			−0.0786596	+	0.996902i	$0.525064\pi$
$462$		0			0
$463$		−	20.8573i		−	0.969320i	−0.874703	−	0.484660i	$-0.838943\pi$
$463$		−	20.8573i		−	0.969320i	0.874703	−	0.484660i	$-0.161057\pi$
$464$	−1.74266	+	3.01838i	−0.0809010	+	0.140125i
$465$	−4.34298	−	10.7480i	−0.201401	−	0.498425i
$466$	22.1590	+	38.3805i	1.02650	+	1.77794i
$467$	12.4434	+	7.18421i	0.575813	+	0.332446i	0.759467	−	0.650545i	$-0.225460\pi$
$467$	12.4434	+	7.18421i	0.575813	+	0.332446i	−0.183655	+	0.982991i	$0.558793\pi$
$468$			10.4286i			0.482064i
$469$		0			0
$470$	1.63158	−	11.6128i	0.0752593	−	0.535661i
$471$	−5.21432	+	9.03147i	−0.240263	+	0.416148i
$472$	8.78079	−	5.06959i	0.404169	−	0.233347i
$473$	−17.4967	+	10.1017i	−0.804498	+	0.464477i
$474$	−4.62222	+	8.00591i	−0.212305	+	0.367724i
$475$	−11.6731	−	3.34614i	−0.535597	−	0.153532i
$476$		0			0
$477$			9.18421i			0.420516i
$478$	13.9916	+	8.07805i	0.639961	+	0.369482i
$479$	3.18421	+	5.51521i	0.145490	+	0.251996i	0.929556	−	0.368682i	$-0.120191\pi$
$479$	3.18421	+	5.51521i	0.145490	+	0.251996i	−0.784066	+	0.620678i	$0.786857\pi$
$480$	15.2199	−	6.14998i	0.694690	−	0.280707i
$481$	24.4701	−	42.3835i	1.11574	−	1.93252i
$482$			13.7877i			0.628012i
$483$		0			0
$484$	11.3555			0.516160
$485$	16.4361	−	21.0391i	0.746327	−	0.955337i
$486$	−0.951606	−	1.64823i	−0.0431657	−	0.0747652i
$487$	15.0060	−	8.66370i	0.679986	−	0.392590i	−0.119864	−	0.992790i	$-0.538246\pi$
$487$	15.0060	−	8.66370i	0.679986	−	0.392590i	0.799850	+	0.600200i	$0.204913\pi$
$488$	4.26986	+	2.46520i	0.193287	+	0.111595i
$489$	20.8573			0.943199
$490$		0			0
$491$	2.00000			0.0902587			0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000			0.0902587			0.0451294	+	0.998981i	$0.485630\pi$
$492$	−11.5693	−	6.67952i	−0.521583	−	0.301136i
$493$	−2.89784	+	1.67307i	−0.130512	+	0.0753513i
$494$	−14.8573	−	25.7336i	−0.668461	−	1.15781i
$495$	−3.52421	−	2.75317i	−0.158401	−	0.123746i
$496$	−23.9140			−1.07377
$497$		0			0
$498$		−	22.1017i		−	0.990401i
$499$	11.6731	−	20.2184i	0.522558	−	0.905098i	−0.477097	−	0.878851i	$-0.658311\pi$
$499$	11.6731	−	20.2184i	0.522558	−	0.905098i	0.999655	−	0.0262471i	$-0.00835568\pi$
$500$	−18.0373	+	1.89809i	−0.806654	+	0.0848852i
$501$	7.67307	+	13.2901i	0.342808	+	0.593760i
$502$	45.5123	+	26.2766i	2.03131	+	1.17278i
$503$		−	0.387152i		−	0.0172623i	−0.999963	−	0.00863113i	$-0.997253\pi$
$503$		−	0.387152i		−	0.0172623i	0.999963	−	0.00863113i	$-0.00274741\pi$
$504$		0			0
$505$	0.460282	−	3.27607i	0.0204823	−	0.145783i
$506$	2.62222	−	4.54181i	0.116572	−	0.201908i
$507$	−24.5323	+	14.1637i	−1.08952	+	0.629032i
$508$	18.0629	−	10.4286i	0.801413	−	0.462696i
$509$	−14.9748	+	25.9371i	−0.663747	+	1.14964i	0.315877	+	0.948800i	$0.397701\pi$
$509$	−14.9748	+	25.9371i	−0.663747	+	1.14964i	−0.979623	+	0.200843i	$0.935632\pi$
$510$	18.6637	+	2.62222i	0.826443	+	0.116114i
$511$		0			0
$512$		−	27.2306i		−	1.20343i
$513$	2.10326	+	1.21432i	0.0928614	+	0.0536135i
$514$	0.407896	+	0.706496i	0.0179915	+	0.0311622i
$515$	−7.42003	−	18.3630i	−0.326966	−	0.809171i
$516$	8.19358	−	14.1917i	0.360702	−	0.624754i
$517$			5.51114i			0.242380i
$518$		0			0
$519$	2.06022			0.0904338
$520$	8.14482	+	6.36288i	0.357174	+	0.279031i
$521$	9.26025	+	16.0392i	0.405699	+	0.702691i	0.994403	−	0.105658i	$-0.0336948\pi$
$521$	9.26025	+	16.0392i	0.405699	+	0.702691i	−0.588704	+	0.808349i	$0.700361\pi$
$522$	−1.24535	+	0.719004i	−0.0545075	+	0.0314699i
$523$	−3.46410	−	2.00000i	−0.151475	−	0.0874539i	0.422347	−	0.906434i	$-0.361206\pi$
$523$	−3.46410	−	2.00000i	−0.151475	−	0.0874539i	−0.573822	+	0.818980i	$0.694540\pi$
$524$	3.40943			0.148942
$525$		0			0
$526$	17.8479			0.778206
$527$	−19.8831	−	11.4795i	−0.866120	−	0.500055i
$528$	−7.98969	+	4.61285i	−0.347706	+	0.200748i
$529$	−10.5509	−	18.2746i	−0.458733	−	0.794549i
$530$	−30.8007	−	24.0620i	−1.33790	−	1.04519i
$531$	14.1017			0.611962
$532$		0			0
$533$		−	52.9403i		−	2.29310i
$534$	4.39853	−	7.61847i	0.190343	−	0.329684i
$535$	−1.47854	−	3.65909i	−0.0639231	−	0.158196i
$536$	−0.990632	−	1.71583i	−0.0427888	−	0.0741124i
$537$	8.66025	+	5.00000i	0.373718	+	0.215766i
$538$			3.32339i			0.143282i
$539$		0			0
$540$	3.59210	+	0.504684i	0.154580	+	0.0217181i
$541$	−7.29529	+	12.6358i	−0.313649	+	0.543256i	−0.979149	−	0.203142i	$-0.934885\pi$
$541$	−7.29529	+	12.6358i	−0.313649	+	0.543256i	0.665501	+	0.746397i	$0.268218\pi$
$542$	4.44255	−	2.56491i	0.190824	−	0.110172i
$543$	−10.4804	+	6.05086i	−0.449757	+	0.259667i
$544$	16.2558	−	28.1559i	0.696962	−	1.20717i
$545$	−1.74620	+	12.4286i	−0.0747990	+	0.532384i
$546$		0			0
$547$		−	18.7556i		−	0.801930i	−0.916093	−	0.400965i	$-0.868675\pi$
$547$		−	18.7556i		−	0.801930i	0.916093	−	0.400965i	$-0.131325\pi$
$548$	22.3935	+	12.9289i	0.956602	+	0.552294i
$549$	3.42864	+	5.93858i	0.146331	+	0.253452i
$550$	18.4664	−	4.60583i	0.787410	−	0.196393i
$551$	0.917502	−	1.58916i	0.0390869	−	0.0677005i
$552$		−	0.990632i		−	0.0421641i
$553$		0			0
$554$	−9.75203			−0.414324
$555$	−13.4146	−	10.4797i	−0.569419	−	0.444841i
$556$	−9.46812	−	16.3993i	−0.401538	−	0.695484i
$557$	27.6059	−	15.9382i	1.16970	−	0.675325i	0.216089	−	0.976374i	$-0.430670\pi$
$557$	27.6059	−	15.9382i	1.16970	−	0.675325i	0.953609	+	0.301049i	$0.0973366\pi$
$558$	−8.54477	−	4.93332i	−0.361729	−	0.208844i
$559$	64.9403			2.74668
$560$		0			0
$561$	−8.85728			−0.373955
$562$	39.5266	+	22.8207i	1.66733	+	0.962634i
$563$	1.74828	−	1.00937i	0.0736811	−	0.0425398i	−0.462707	−	0.886511i	$-0.653122\pi$
$563$	1.74828	−	1.00937i	0.0736811	−	0.0425398i	0.536388	+	0.843972i	$0.319788\pi$
$564$	−2.23506	−	3.87124i	−0.0941131	−	0.163009i
$565$	−15.5361	+	19.8870i	−0.653607	+	0.836650i
$566$	−4.50760			−0.189468
$567$		0			0
$568$		−	1.43801i		−	0.0603375i
$569$	−14.4795	+	25.0792i	−0.607012	+	1.05138i	0.384718	+	0.923034i	$0.374299\pi$
$569$	−14.4795	+	25.0792i	−0.607012	+	1.05138i	−0.991730	+	0.128341i	$0.959035\pi$
$570$	−9.58283	+	3.87218i	−0.401381	+	0.162188i
$571$	−4.48886	−	7.77494i	−0.187853	−	0.325371i	0.756681	−	0.653784i	$-0.226820\pi$
$571$	−4.48886	−	7.77494i	−0.187853	−	0.325371i	−0.944534	+	0.328413i	$0.893486\pi$
$572$	18.0629	+	10.4286i	0.755249	+	0.436043i
$573$			0.488863i			0.0204225i
$574$		0			0
$575$	−1.89829	+	6.62222i	−0.0791642	+	0.276165i
$576$	2.37310	−	4.11033i	0.0988792	−	0.171264i
$577$	24.8347	−	14.3383i	1.03388	−	0.596911i	0.115787	−	0.993274i	$-0.463061\pi$
$577$	24.8347	−	14.3383i	1.03388	−	0.596911i	0.918094	+	0.396363i	$0.129728\pi$
$578$	4.30657	−	2.48640i	0.179130	−	0.103421i
$579$	11.4795	−	19.8831i	0.477072	−	0.826312i
$580$	0.381323	−	2.71408i	0.0158336	−	0.112696i
$581$		0			0
$582$		−	22.7239i		−	0.941937i
$583$	15.9075	+	9.18421i	0.658822	+	0.380371i
$584$	−0.564907	−	0.978448i	−0.0233760	−	0.0404885i
$585$	5.38548	+	13.3279i	0.222662	+	0.551042i
$586$	8.02074	−	13.8923i	0.331334	−	0.573887i
$587$			45.2070i			1.86589i	0.360018	+	0.932945i	$0.382771\pi$
$587$			45.2070i			1.86589i	−0.360018	+	0.932945i	$0.617229\pi$
$588$		0			0
$589$	12.5906			0.518786
$590$	−36.9456	+	47.2923i	−1.52103	+	1.94699i
$591$	−0.592104	−	1.02555i	−0.0243559	−	0.0421857i
$592$	−30.4121	+	17.5585i	−1.24993	+	0.721648i
$593$	−15.8168	−	9.13182i	−0.649517	−	0.374999i	0.138754	−	0.990327i	$-0.455690\pi$
$593$	−15.8168	−	9.13182i	−0.649517	−	0.374999i	−0.788271	+	0.615328i	$0.789024\pi$
$594$	−3.80642			−0.156179
$595$		0			0
$596$	−34.4327			−1.41042
$597$	7.61847	+	4.39853i	0.311803	+	0.180020i
$598$	−14.5988	+	8.42864i	−0.596991	+	0.344673i
$599$	−11.3684	−	19.6907i	−0.464501	−	0.804539i	0.534678	−	0.845056i	$-0.320433\pi$
$599$	−11.3684	−	19.6907i	−0.464501	−	0.804539i	−0.999179	+	0.0405167i	$0.987100\pi$
$600$	2.58583	−	2.49753i	0.105566	−	0.101961i
$601$	0.488863			0.0199411			0.00997056	−	0.999950i	$-0.496826\pi$
$601$	0.488863			0.0199411			0.00997056	+	0.999950i	$0.496826\pi$
$602$		0			0
$603$		−	2.75557i		−	0.112215i
$604$	13.6731	−	23.6825i	0.556349	−	0.963625i
$605$	14.5125	−	5.86413i	0.590016	−	0.238411i
$606$	−1.40790	−	2.43855i	−0.0571919	−	0.0990592i
$607$	−17.4967	−	10.1017i	−0.710168	−	0.410016i	0.100955	−	0.994891i	$-0.467810\pi$
$607$	−17.4967	−	10.1017i	−0.710168	−	0.410016i	−0.811123	+	0.584875i	$0.801143\pi$
$608$			17.8292i			0.723069i
$609$		0			0
$610$	−28.8988	−	4.06022i	−1.17008	−	0.164394i
$611$	8.85728	−	15.3413i	0.358327	−	0.620641i
$612$	6.22171	−	3.59210i	0.251498	−	0.145202i
$613$	8.97931	−	5.18421i	0.362671	−	0.209388i	−0.307581	−	0.951522i	$-0.599519\pi$
$613$	8.97931	−	5.18421i	0.362671	−	0.209388i	0.670252	+	0.742134i	$0.266186\pi$
$614$	21.4795	−	37.2036i	0.866842	−	1.50141i
$615$	−18.2351	−	2.56199i	−0.735309	−	0.103310i
$616$		0			0
$617$			39.2859i			1.58159i	0.612080	+	0.790796i	$0.290333\pi$
$617$			39.2859i			1.58159i	−0.612080	+	0.790796i	$0.709667\pi$
$618$	−14.5988	−	8.42864i	−0.587251	−	0.339050i
$619$	21.4494	+	37.1514i	0.862123	+	1.49324i	0.869875	+	0.493272i	$0.164199\pi$
$619$	21.4494	+	37.1514i	0.862123	+	1.49324i	−0.00775178	+	0.999970i	$0.502467\pi$
$620$	17.4355	−	7.04525i	0.700227	−	0.282944i
$621$	0.688892	−	1.19320i	0.0276443	−	0.0478813i
$622$			45.8350i			1.83782i
$623$		0			0
$624$	29.6543			1.18712
$625$	−22.0717	+	11.7405i	−0.882869	+	0.469619i
$626$	9.18712	+	15.9126i	0.367191	+	0.635994i
$627$	4.20653	−	2.42864i	0.167993	−	0.0969905i
$628$	−14.6510	−	8.45875i	−0.584638	−	0.337541i
$629$	−33.7146			−1.34429
$630$		0			0
$631$	15.3461			0.610920			0.305460	−	0.952205i	$-0.401190\pi$
$631$	15.3461			0.610920			0.305460	+	0.952205i	$0.401190\pi$
$632$	3.02451	+	1.74620i	0.120308	+	0.0694601i
$633$	20.1140	−	11.6128i	0.799461	−	0.461569i
$634$	5.74912	+	9.95776i	0.228327	+	0.395473i
$635$	17.6992	−	22.6559i	0.702370	−	0.899070i
$636$	−14.8988			−0.590775
$637$		0			0
$638$			2.87601i			0.113863i
$639$	1.00000	−	1.73205i	0.0395594	−	0.0685189i
$640$	−4.73270	−	11.7124i	−0.187076	−	0.462974i
$641$	−15.3368	−	26.5641i	−0.605766	−	1.04922i	−0.991930	−	0.126787i	$-0.959533\pi$
$641$	−15.3368	−	26.5641i	−0.605766	−	1.04922i	0.386164	−	0.922430i	$-0.373800\pi$
$642$	−2.90902	−	1.67952i	−0.114810	−	0.0662855i
$643$		−	49.0607i		−	1.93477i	−0.253320	−	0.967383i	$-0.581523\pi$
$643$		−	49.0607i		−	1.93477i	0.253320	−	0.967383i	$-0.418477\pi$
$644$		0			0
$645$	3.14272	−	22.3684i	0.123745	−	0.880756i
$646$	−10.2351	+	17.7276i	−0.402693	+	0.697485i
$647$	13.2901	−	7.67307i	0.522490	−	0.301660i	−0.215463	−	0.976512i	$-0.569126\pi$
$647$	13.2901	−	7.67307i	0.522490	−	0.301660i	0.737953	+	0.674852i	$0.235793\pi$
$648$	−0.622675	+	0.359502i	−0.0244610	+	0.0141226i
$649$	14.1017	−	24.4249i	0.553541	−	0.958760i
$650$	−58.8069	−	16.8573i	−2.30660	−	0.661197i
$651$		0			0
$652$			33.8350i			1.32508i
$653$	16.8612	+	9.73483i	0.659830	+	0.380953i	0.792212	−	0.610246i	$-0.208929\pi$
$653$	16.8612	+	9.73483i	0.659830	+	0.380953i	−0.132382	+	0.991199i	$0.542263\pi$
$654$	5.34122	+	9.25126i	0.208858	+	0.361753i
$655$	4.35729	−	1.76067i	0.170253	−	0.0687951i
$656$	−18.9935	+	32.8978i	−0.741573	+	1.28444i
$657$		−	1.57136i		−	0.0613046i
$658$		0			0
$659$	−30.9403			−1.20526			−0.602631	−	0.798020i	$-0.705881\pi$
$659$	−30.9403			−1.20526			−0.602631	+	0.798020i	$0.705881\pi$
$660$	4.46624	−	5.71702i	0.173848	−	0.222535i
$661$	−23.8988	−	41.3939i	−0.929554	−	1.61004i	−0.784068	−	0.620675i	$-0.786859\pi$
$661$	−23.8988	−	41.3939i	−0.929554	−	1.61004i	−0.145486	−	0.989360i	$-0.546475\pi$
$662$	−22.2695	+	12.8573i	−0.865527	+	0.499712i
$663$	24.6559	+	14.2351i	0.957554	+	0.552844i
$664$	−8.34968			−0.324030
$665$		0			0
$666$	−14.4889			−0.561432
$667$	−0.901542	−	0.520505i	−0.0349078	−	0.0201540i
$668$	−21.5595	+	12.4474i	−0.834162	+	0.481603i
$669$	7.61285	+	13.1858i	0.294330	+	0.509794i
$670$	9.24123	+	7.21942i	0.357020	+	0.278910i
$671$	13.7146			0.529445
$672$		0			0
$673$			27.8163i			1.07224i	0.844142	+	0.536119i	$0.180110\pi$
$673$			27.8163i			1.07224i	−0.844142	+	0.536119i	$0.819890\pi$
$674$	−9.98126	+	17.2881i	−0.384464	+	0.665911i
$675$	4.85138	−	1.21002i	0.186730	−	0.0465735i
$676$	−22.9766	−	39.7966i	−0.883715	−	1.53064i
$677$	−16.4549	−	9.50024i	−0.632413	−	0.365124i	0.149273	−	0.988796i	$-0.452307\pi$
$677$	−16.4549	−	9.50024i	−0.632413	−	0.365124i	−0.781686	+	0.623672i	$0.785640\pi$
$678$			21.4795i			0.824915i
$679$		0			0
$680$	0.990632	−	7.05086i	0.0379890	−	0.270388i
$681$	−7.18421	+	12.4434i	−0.275299	+	0.476833i
$682$	−17.0895	+	9.86665i	−0.654392	+	0.377813i
$683$	3.91487	−	2.26025i	0.149798	−	0.0864862i	−0.423227	−	0.906024i	$-0.639103\pi$
$683$	3.91487	−	2.26025i	0.149798	−	0.0864862i	0.573026	+	0.819537i	$0.305769\pi$
$684$	−1.96989	+	3.41195i	−0.0753206	+	0.130459i
$685$	35.2958	+	4.95899i	1.34858	+	0.189473i
$686$		0			0
$687$			5.61285i			0.214143i
$688$	−40.3547	−	23.2988i	−1.53851	−	0.888259i
$689$	−29.5210	−	51.1318i	−1.12466	−	1.94797i
$690$	2.19672	+	5.43641i	0.0836275	+	0.206960i
$691$	0.592104	−	1.02555i	0.0225247	−	0.0390139i	−0.854543	−	0.519380i	$-0.826163\pi$
$691$	0.592104	−	1.02555i	0.0225247	−	0.0390139i	0.877068	+	0.480366i	$0.159496\pi$
$692$			3.34213i			0.127049i
$693$		0			0
$694$	−31.8292			−1.20822
$695$	−20.5692	−	16.0690i	−0.780233	−	0.609532i
$696$	0.271628	+	0.470474i	0.0102960	+	0.0178333i
$697$	−31.5841	+	18.2351i	−1.19633	+	0.690702i
$698$	26.9789	+	15.5763i	1.02117	+	0.589571i
$699$	23.2859			0.880754
$700$		0			0
$701$	−26.6735			−1.00745			−0.503723	−	0.863865i	$-0.668037\pi$
$701$	−26.6735			−1.00745			−0.503723	+	0.863865i	$0.668037\pi$
$702$	10.5959	+	6.11753i	0.399916	+	0.230891i
$703$	16.0118	−	9.24443i	0.603897	−	0.348660i
$704$	−4.74620	−	8.22066i	−0.178879	−	0.309828i
$705$	−4.85560	−	3.79328i	−0.182872	−	0.142863i
$706$	−1.04503			−0.0393301
$707$		0			0
$708$			22.8760i			0.859733i
$709$	−9.10171	+	15.7646i	−0.341822	+	0.592053i	−0.984771	−	0.173856i	$-0.944377\pi$
$709$	−9.10171	+	15.7646i	−0.341822	+	0.592053i	0.642949	+	0.765909i	$0.277711\pi$
$710$	3.18877	+	7.89152i	0.119672	+	0.296163i
$711$	2.42864	+	4.20653i	0.0910811	+	0.157757i
$712$	−2.87814	−	1.66170i	−0.107863	−	0.0622747i
$713$		−	7.14272i		−	0.267497i
$714$		0			0
$715$	28.4701	+	4.00000i	1.06472	+	0.149592i
$716$	−8.11108	+	14.0488i	−0.303125	+	0.525028i
$717$	7.35157	−	4.24443i	0.274549	−	0.158511i
$718$	−0.470474	+	0.271628i	−0.0175579	+	0.0101371i
$719$	2.42864	−	4.20653i	0.0905730	−	0.156877i	−0.817179	−	0.576383i	$-0.804463\pi$
$719$	2.42864	−	4.20653i	0.0905730	−	0.156877i	0.907752	+	0.419506i	$0.137797\pi$
$720$	1.43509	−	10.2143i	0.0534828	−	0.380665i
$721$		0			0
$722$			24.9353i			0.927997i
$723$	6.27386	+	3.62222i	0.233327	+	0.134712i
$724$	−9.81579	−	17.0015i	−0.364801	−	0.631854i
$725$	−0.914250	−	3.66555i	−0.0339544	−	0.136135i
$726$	6.66124	−	11.5376i	0.247222	−	0.428201i
$727$		−	21.0607i		−	0.781098i	−0.920582	−	0.390549i	$-0.872285\pi$
$727$		−	21.0607i		−	0.781098i	0.920582	−	0.390549i	$-0.127715\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	5.26980	+	4.11687i	0.195044	+	0.152372i
$731$	−22.3684	−	38.7432i	−0.827326	−	1.43297i
$732$	−9.63365	+	5.56199i	−0.356070	+	0.205577i
$733$	−8.18473	−	4.72546i	−0.302310	−	0.174539i	0.341170	−	0.940002i	$-0.389177\pi$
$733$	−8.18473	−	4.72546i	−0.302310	−	0.174539i	−0.643480	+	0.765463i	$0.722510\pi$
$734$	3.26317			0.120446
$735$		0			0
$736$	10.1146			0.372830
$737$	−4.77279	−	2.75557i	−0.175808	−	0.101503i
$738$	−13.5733	+	7.83654i	−0.499639	+	0.288467i
$739$	−4.10171	−	7.10437i	−0.150884	−	0.261338i	0.780669	−	0.624945i	$-0.214879\pi$
$739$	−4.10171	−	7.10437i	−0.150884	−	0.261338i	−0.931553	+	0.363607i	$0.881545\pi$
$740$	17.0004	−	21.7614i	0.624948	−	0.799965i
$741$	−15.6128			−0.573552
$742$		0			0
$743$			8.33677i			0.305847i	0.988238	+	0.152923i	$0.0488687\pi$
$743$			8.33677i			0.305847i	−0.988238	+	0.152923i	$0.951131\pi$
$744$	−1.86373	+	3.22808i	−0.0683277	+	0.118347i
$745$	−44.0053	+	17.7815i	−1.61223	+	0.651462i
$746$	15.2257	+	26.3717i	0.557452	+	0.965536i
$747$	−10.0570	−	5.80642i	−0.367967	−	0.212446i
$748$		−	14.3684i		−	0.525361i
$749$		0			0
$750$	−8.65233	+	19.4400i	−0.315938	+	0.709849i
$751$	12.9590	−	22.4456i	0.472880	−	0.819053i	−0.526638	−	0.850090i	$-0.676548\pi$
$751$	12.9590	−	22.4456i	0.472880	−	0.819053i	0.999518	+	0.0310371i	$0.00988099\pi$
$752$	−11.0081	+	6.35551i	−0.401423	+	0.231762i
$753$	23.9134	−	13.8064i	0.871454	−	0.503134i
$754$	4.62222	−	8.00591i	0.168331	−	0.291558i
$755$	5.24443	−	37.3274i	0.190864	−	1.35848i
$756$		0			0
$757$		−	8.94025i		−	0.324939i	−0.986714	−	0.162470i	$-0.948054\pi$
$757$		−	8.94025i		−	0.324939i	0.986714	−	0.162470i	$-0.0519459\pi$
$758$	8.00591	+	4.62222i	0.290788	+	0.167886i
$759$	−1.37778	−	2.38639i	−0.0500104	−	0.0866206i
$760$	1.46285	+	3.62024i	0.0530631	+	0.131320i
$761$	0.412818	−	0.715022i	0.0149646	−	0.0259195i	−0.858446	−	0.512904i	$-0.828570\pi$
$761$	0.412818	−	0.715022i	0.0149646	−	0.0259195i	0.873411	+	0.486984i	$0.161903\pi$
$762$		−	24.4701i		−	0.886459i
$763$		0			0
$764$	−0.793040			−0.0286912
$765$	6.09641	−	7.80372i	0.220416	−	0.282144i
$766$	−7.98126	−	13.8240i	−0.288375	−	0.499480i
$767$	−78.5094	+	45.3274i	−2.83481	+	1.63668i
$768$	−17.5322	−	10.1222i	−0.632638	−	0.365254i
$769$	−21.2257			−0.765418			−0.382709	−	0.923869i	$-0.625009\pi$
$769$	−21.2257			−0.765418			−0.382709	+	0.923869i	$0.625009\pi$
$770$		0			0
$771$	0.428639			0.0154371
$772$	32.2546	+	18.6222i	1.16087	+	0.670228i
$773$	25.5385	−	14.7447i	0.918557	−	0.530329i	0.0353823	−	0.999374i	$-0.488735\pi$
$773$	25.5385	−	14.7447i	0.918557	−	0.530329i	0.883174	+	0.469045i	$0.155402\pi$
$774$	−9.61285	−	16.6499i	−0.345527	−	0.598470i
$775$	18.6445	−	18.0078i	0.669731	−	0.646860i
$776$	−8.58474			−0.308174
$777$		0			0
$778$			17.0509i			0.611303i
$779$	10.0000	−	17.3205i	0.358287	−	0.620572i
$780$	−21.6208	+	8.73641i	−0.774148	+	0.312814i
$781$	−2.00000	−	3.46410i	−0.0715656	−	0.123955i
$782$	10.0570	+	5.80642i	0.359638	+	0.207637i
$783$			0.755569i			0.0270018i
$784$		0			0
$785$	−23.0923	−	3.24443i	−0.824201	−	0.115799i
$786$	2.00000	−	3.46410i	0.0713376	−	0.123560i
$787$	29.8358	−	17.2257i	1.06353	−	0.614030i	0.137124	−	0.990554i	$-0.456214\pi$
$787$	29.8358	−	17.2257i	1.06353	−	0.614030i	0.926407	+	0.376524i	$0.122881\pi$
$788$	1.66367	−	0.960521i	0.0592658	−	0.0342171i
$789$	4.68889	−	8.12140i	0.166929	−	0.289129i
$790$	−20.4701	−	2.87601i	−0.728294	−	0.102324i
$791$		0			0
$792$			1.43801i			0.0510974i
$793$	−38.1770	−	22.0415i	−1.35570	−	0.782716i
$794$	2.42573	+	4.20148i	0.0860858	+	0.149105i
$795$	−19.0408	+	7.69391i	−0.675308	+	0.272875i
$796$	−7.13536	+	12.3588i	−0.252906	+	0.438046i
$797$		−	18.9175i		−	0.670092i	−0.942202	−	0.335046i	$-0.891248\pi$
$797$		−	18.9175i		−	0.670092i	0.942202	−	0.335046i	$-0.108752\pi$
$798$		0			0
$799$	−12.2034			−0.431726
$800$	25.5004	+	26.4020i	0.901576	+	0.933452i
$801$	−2.31111	−	4.00296i	−0.0816590	−	0.141438i
$802$	−1.58063	+	0.912580i	−0.0558142	+	0.0322243i
$803$	−2.72168	−	1.57136i	−0.0960459	−	0.0554521i
$804$	4.47013			0.157649
$805$		0			0
$806$	63.4291			2.23420
$807$	1.51225	+	0.873100i	0.0532339	+	0.0307346i
$808$	−0.921245	+	0.531881i	−0.0324093	+	0.0187115i
$809$	10.6128	+	18.3820i	0.373128	+	0.646276i	0.990045	−	0.140752i	$-0.0449519\pi$
$809$	10.6128	+	18.3820i	0.373128	+	0.646276i	−0.616917	+	0.787028i	$0.711619\pi$
$810$	2.61994	−	3.35366i	0.0920552	−	0.117835i
$811$	−21.5081			−0.755251			−0.377625	−	0.925958i	$-0.623259\pi$
$811$	−21.5081			−0.755251			−0.377625	+	0.925958i	$0.623259\pi$
$812$		0			0
$813$		−	2.69535i		−	0.0945299i
$814$	−14.4889	+	25.0954i	−0.507834	+	0.879595i
$815$	17.4728	+	43.2415i	0.612046	+	1.51469i
$816$	−10.2143	−	17.6917i	−0.357573	−	0.619334i
$817$	21.2466	+	12.2667i	0.743323	+	0.429158i
$818$		−	60.8671i		−	2.12817i
$819$		0			0
$820$	4.15610	−	29.5812i	0.145137	−	1.03302i
$821$	23.1017	−	40.0133i	0.806255	−	1.39648i	−0.109185	−	0.994021i	$-0.534824\pi$
$821$	23.1017	−	40.0133i	0.806255	−	1.39648i	0.915440	−	0.402454i	$-0.131843\pi$
$822$	26.2724	−	15.1684i	0.916356	−	0.529058i
$823$	−15.4456	+	8.91750i	−0.538399	+	0.310845i	−0.744430	−	0.667701i	$-0.767279\pi$
$823$	−15.4456	+	8.91750i	−0.538399	+	0.310845i	0.206031	+	0.978545i	$0.433945\pi$
$824$	−3.18421	+	5.51521i	−0.110927	+	0.192131i
$825$	2.75557	−	9.61285i	0.0959366	−	0.334676i
$826$		0			0
$827$		−	35.2128i		−	1.22447i	−0.790676	−	0.612234i	$-0.790271\pi$
$827$		−	35.2128i		−	1.22447i	0.790676	−	0.612234i	$-0.209729\pi$
$828$	1.93562	+	1.11753i	0.0672675	+	0.0388369i
$829$	7.19358	+	12.4596i	0.249843	+	0.432741i	0.963482	−	0.267773i	$-0.0862876\pi$
$829$	7.19358	+	12.4596i	0.249843	+	0.432741i	−0.713639	+	0.700514i	$0.752954\pi$
$830$	45.8215	−	18.5153i	1.59049	−	0.642676i
$831$	−2.56199	+	4.43750i	−0.0888745	+	0.153935i
$832$			30.5116i			1.05780i
$833$		0			0
$834$	−22.2163			−0.769289
$835$	−21.1253	+	27.0415i	−0.731071	+	0.935809i
$836$	3.93978	+	6.82389i	0.136260	+	0.236009i
$837$	−4.48966	+	2.59210i	−0.155185	+	0.0895962i
$838$	0.774877	+	0.447375i	0.0267677	+	0.0154543i
$839$	−1.51114			−0.0521703			−0.0260851	−	0.999660i	$-0.508304\pi$
$839$	−1.51114			−0.0521703			−0.0260851	+	0.999660i	$0.508304\pi$
$840$		0			0
$841$	−28.4291			−0.980314
$842$	−55.4017	−	31.9862i	−1.90927	−	1.10232i
$843$	20.7684	−	11.9906i	0.715301	−	0.412979i
$844$	18.8385	+	32.6293i	0.648449	+	1.12315i
$845$	−49.9158	−	38.9951i	−1.71716	−	1.34147i
$846$	−5.24443			−0.180307
$847$		0			0
$848$			42.3654i			1.45483i
$849$	−1.18421	+	2.05111i	−0.0406419	+	0.0703939i
$850$	10.1988	+	40.8905i	0.349815	+	1.40253i
$851$	−5.24443	−	9.08362i	−0.179777	−	0.311383i
$852$	2.80976	+	1.62222i	0.0962608	+	0.0555762i
$853$		−	15.4064i		−	0.527504i	−0.964591	−	0.263752i	$-0.915040\pi$
$853$		−	15.4064i		−	0.527504i	0.964591	−	0.263752i	$-0.0849600\pi$
$854$		0			0
$855$	−0.755569	+	5.37778i	−0.0258399	+	0.183916i
$856$	−0.634498	+	1.09898i	−0.0216867	+	0.0375625i
$857$	−17.1973	+	9.92888i	−0.587449	+	0.339164i	−0.764088	−	0.645112i	$-0.776811\pi$
$857$	−17.1973	+	9.92888i	−0.587449	+	0.339164i	0.176639	+	0.984276i	$0.443477\pi$
$858$	21.1918	−	12.2351i	0.723474	−	0.417698i
$859$	1.21432	−	2.10326i	0.0414321	−	0.0717624i	−0.844566	−	0.535452i	$-0.820141\pi$
$859$	1.21432	−	2.10326i	0.0414321	−	0.0717624i	0.885998	+	0.463689i	$0.153475\pi$
$860$	36.2864	+	5.09817i	1.23736	+	0.173846i
$861$		0			0
$862$		−	22.2953i		−	0.759380i
$863$	34.0311	+	19.6479i	1.15843	+	0.668822i	0.950928	−	0.309412i	$-0.100132\pi$
$863$	34.0311	+	19.6479i	1.15843	+	0.668822i	0.207505	+	0.978234i	$0.433466\pi$
$864$	−3.67061	−	6.35768i	−0.124877	−	0.216293i
$865$	1.72592	+	4.27128i	0.0586829	+	0.145228i
$866$	−0.0573086	+	0.0992614i	−0.00194743	+	0.00337304i
$867$		−	2.61285i		−	0.0887370i
$868$		0			0
$869$	9.71456			0.329544
$870$	−2.53392	−	1.97954i	−0.0859078	−	0.0671128i
$871$	8.85728	+	15.3413i	0.300117	+	0.519819i
$872$	3.49498	−	2.01783i	0.118355	−	0.0683323i
$873$	−10.3402	−	5.96989i	−0.349961	−	0.202050i
$874$	−6.36842			−0.215415
$875$		0			0
$876$	2.54909			0.0861256
$877$	−48.7454	−	28.1432i	−1.64602	−	0.950328i	−0.978633	−	0.205614i	$-0.934081\pi$
$877$	−48.7454	−	28.1432i	−1.64602	−	0.950328i	−0.667384	−	0.744714i	$-0.732586\pi$
$878$	−36.9676	+	21.3432i	−1.24759	+	0.720299i
$879$	−4.21432	−	7.29942i	−0.142145	−	0.246203i
$880$	−16.2566	−	12.7000i	−0.548011	−	0.428116i
$881$	−2.33677			−0.0787279			−0.0393640	−	0.999225i	$-0.512533\pi$
$881$	−2.33677			−0.0787279			−0.0393640	+	0.999225i	$0.512533\pi$
$882$		0			0
$883$			33.7146i			1.13459i	0.823516	+	0.567293i	$0.192009\pi$
$883$			33.7146i			1.13459i	−0.823516	+	0.567293i	$0.807991\pi$
$884$	−23.0923	+	39.9971i	−0.776680	+	1.34525i
$885$	11.8135	+	29.2358i	0.397105	+	0.982751i
$886$	−22.7906	−	39.4745i	−0.765665	−	1.32617i
$887$	41.4820	+	23.9496i	1.39283	+	0.804150i	0.993627	−	0.112714i	$-0.0359544\pi$
$887$	41.4820	+	23.9496i	1.39283	+	0.804150i	0.399200	+	0.916864i	$0.369288\pi$
$888$			5.47367i			0.183684i
$889$		0			0
$890$	19.4795	+	2.73683i	0.652954	+	0.0917388i
$891$	−1.00000	+	1.73205i	−0.0335013	+	0.0580259i
$892$	−21.3903	+	12.3497i	−0.716199	+	0.413498i
$893$	5.79569	−	3.34614i	0.193945	−	0.111974i
$894$	−20.1985	+	34.9848i	−0.675539	+	1.17007i
$895$	−3.11108	+	22.1432i	−0.103992	+	0.740165i
$896$		0			0
$897$			8.85728i			0.295736i
$898$	−48.5059	−	28.0049i	−1.61866	−	0.934536i
$899$	1.95851	+	3.39224i	0.0653201	+	0.113138i
$900$	1.96291	+	7.86998i	0.0654302	+	0.262333i
$901$	−20.3368	+	35.2243i	−0.677516	+	1.17349i
$902$			31.3461i			1.04371i
$903$		0			0
$904$	8.11462			0.269888
$905$	−21.3245	−	16.6591i	−0.708849	−	0.553766i
$906$	−16.0415	−	27.7847i	−0.532943	−	0.923084i
$907$	−20.5760	+	11.8796i	−0.683215	+	0.394454i	−0.801065	−	0.598577i	$-0.795733\pi$
$907$	−20.5760	+	11.8796i	−0.683215	+	0.394454i	0.117851	+	0.993031i	$0.462400\pi$
$908$	−20.1859	−	11.6543i	−0.669893	−	0.386763i
$909$	−1.47949			−0.0490717
$910$		0			0
$911$	22.9403			0.760045			0.380022	−	0.924977i	$-0.375916\pi$
$911$	22.9403			0.760045			0.380022	+	0.924977i	$0.375916\pi$
$912$	9.70203	+	5.60147i	0.321266	+	0.185483i
$913$	−20.1140	+	11.6128i	−0.665678	+	0.384329i
$914$	2.99063	+	5.17993i	0.0989213	+	0.171337i
$915$	−9.43964	+	12.0832i	−0.312065	+	0.399459i
$916$	−9.10525			−0.300846
$917$		0			0
$918$		−	8.42864i		−	0.278187i
$919$	8.48886	−	14.7031i	0.280022	−	0.485012i	−0.691368	−	0.722503i	$-0.742992\pi$
$919$	8.48886	−	14.7031i	0.280022	−	0.485012i	0.971390	+	0.237491i	$0.0763250\pi$
$920$	2.05379	−	0.829885i	0.0677114	−	0.0273605i
$921$	−11.2859	−	19.5478i	−0.371884	−	0.644121i
$922$	−5.56737	−	3.21432i	−0.183351	−	0.105858i
$923$			12.8573i			0.423202i
$924$		0			0
$925$	10.4889	−	36.5906i	0.344872	−	1.20309i
$926$	19.8479	−	34.3776i	0.652243	−	1.12972i
$927$	−7.67063	+	4.42864i	−0.251936	+	0.145456i
$928$	−4.80367	+	2.77340i	−0.157688	+	0.0910412i
$929$	19.6702	−	34.0697i	0.645357	−	1.11779i	−0.338862	−	0.940836i	$-0.610042\pi$
$929$	19.6702	−	34.0697i	0.645357	−	1.11779i	0.984219	−	0.176955i	$-0.0566247\pi$
$930$	3.06959	−	21.8479i	0.100656	−	0.716421i
$931$		0			0
$932$			37.7748i			1.23735i
$933$	20.8565	+	12.0415i	0.682810	+	0.394221i
$934$	13.6731	+	23.6825i	0.447397	+	0.774914i
$935$	−7.42003	−	18.3630i	−0.242661	−	0.600535i
$936$	2.31111	−	4.00296i	0.0755409	−	0.130841i
$937$			17.7748i			0.580677i	0.956924	+	0.290338i	$0.0937679\pi$
$937$			17.7748i			0.580677i	−0.956924	+	0.290338i	$0.906232\pi$
$938$		0			0
$939$	9.65433			0.315057
$940$	6.15352	−	7.87682i	0.200706	−	0.256914i
$941$	−17.7906	−	30.8142i	−0.579957	−	1.00452i	−0.995484	−	0.0949340i	$-0.969736\pi$
$941$	−17.7906	−	30.8142i	−0.579957	−	1.00452i	0.415527	−	0.909581i	$-0.363597\pi$
$942$	−17.1888	+	9.92396i	−0.560041	+	0.323340i
$943$	−9.82605	−	5.67307i	−0.319980	−	0.184741i
$944$	65.0490			2.11717
$945$		0			0
$946$	−38.4514			−1.25016
$947$	26.4153	+	15.2509i	0.858382	+	0.495587i	0.863470	−	0.504400i	$-0.168286\pi$
$947$	26.4153	+	15.2509i	0.858382	+	0.495587i	−0.00508803	+	0.999987i	$0.501620\pi$
$948$	−6.82389	+	3.93978i	−0.221630	+	0.127958i
$949$	5.05086	+	8.74834i	0.163958	+	0.283983i
$950$	−16.0557	−	16.6234i	−0.520916	−	0.539333i
$951$	6.04149			0.195909
$952$		0			0
$953$		−	51.1655i		−	1.65741i	−0.559684	−	0.828706i	$-0.689077\pi$
$953$		−	51.1655i		−	1.65741i	0.559684	−	0.828706i	$-0.310923\pi$
$954$	−8.73975	+	15.1377i	−0.282960	+	0.490101i
$955$	−1.01352	+	0.409536i	−0.0327966	+	0.0132523i
$956$	6.88538	+	11.9258i	0.222689	+	0.385709i
$957$	1.30868	+	0.755569i	0.0423037	+	0.0244241i
$958$			12.1204i			0.391594i
$959$		0			0
$960$	10.5096	+	1.47658i	0.339196	+	0.0476564i
$961$	2.06199	−	3.57148i	0.0665159	−	0.115209i
$962$	80.6648	−	46.5718i	2.60074	−	1.50154i
$963$	−1.52848	+	0.882468i	−0.0492546	+	0.0284371i
$964$	−5.87601	+	10.1776i	−0.189254	+	0.327797i
$965$	50.8385	+	7.14272i	1.63655	+	0.229932i
$966$		0			0
$967$		−	47.8992i		−	1.54034i	−0.637841	−	0.770168i	$-0.720172\pi$
$967$		−	47.8992i		−	1.54034i	0.637841	−	0.770168i	$-0.279828\pi$
$968$	−4.35873	−	2.51651i	−0.140095	−	0.0808838i
$969$	5.37778	+	9.31460i	0.172759	+	0.299228i
$970$	47.1115	−	19.0366i	1.51266	−	0.611228i
$971$	−20.3368	+	35.2243i	−0.652638	+	1.13040i	0.329842	+	0.944036i	$0.393004\pi$
$971$	−20.3368	+	35.2243i	−0.652638	+	1.13040i	−0.982480	+	0.186366i	$0.940329\pi$
$972$		−	1.62222i		−	0.0520326i
$973$		0			0
$974$	32.9777			1.05667
$975$	−23.1200	+	22.3305i	−0.740433	+	0.715148i
$976$	15.8158	+	27.3938i	0.506251	+	0.876853i
$977$	23.8065	−	13.7447i	0.761636	−	0.439731i	−0.0682466	−	0.997668i	$-0.521740\pi$
$977$	23.8065	−	13.7447i	0.761636	−	0.439731i	0.829883	+	0.557938i	$0.188407\pi$
$978$	34.3776	+	19.8479i	1.09927	+	0.634666i
$979$	−9.24443			−0.295453
$980$		0			0
$981$	5.61285			0.179204
$982$	3.29646	+	1.90321i	0.105194	+	0.0607339i
$983$	20.7846	−	12.0000i	0.662926	−	0.382741i	−0.130465	−	0.991453i	$-0.541647\pi$
$983$	20.7846	−	12.0000i	0.662926	−	0.382741i	0.793391	+	0.608712i	$0.208314\pi$
$984$	2.96052	+	5.12777i	0.0943779	+	0.163467i
$985$	1.63017	−	2.08670i	0.0519414	−	0.0664877i
$986$	−6.36842			−0.202812
$987$		0			0
$988$		−	25.3274i		−	0.805772i
$989$	6.95899	−	12.0533i	0.221283	−	0.383273i
$990$	−3.18877	−	7.89152i	−0.101346	−	0.250809i
$991$	17.3461	+	30.0444i	0.551018	+	0.954392i	0.998201	+	0.0599493i	$0.0190939\pi$
$991$	17.3461	+	30.0444i	0.551018	+	0.954392i	−0.447183	+	0.894442i	$0.647573\pi$
$992$	−32.9595	−	19.0292i	−1.04647	−	0.604178i
$993$			13.5111i			0.428763i
$994$		0			0
$995$	−2.73683	+	19.4795i	−0.0867634	+	0.617541i
$996$	9.41927	−	16.3147i	0.298461	−	0.516950i
$997$	24.8347	−	14.3383i	0.786522	−	0.454099i	−0.0522147	−	0.998636i	$-0.516628\pi$
$997$	24.8347	−	14.3383i	0.786522	−	0.454099i	0.838737	+	0.544537i	$0.183295\pi$
$998$	38.4798	−	22.2163i	1.21806	−	0.703246i
$999$	−3.80642	+	6.59292i	−0.120430	+	0.208591i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.q.e.79.5		12
5.4	even	2	inner	735.2.q.e.79.2		12
7.2	even	3		105.2.d.b.64.2	✓	6
7.3	odd	6		735.2.q.f.214.2		12
7.4	even	3	inner	735.2.q.e.214.2		12
7.5	odd	6		735.2.d.b.589.2		6
7.6	odd	2		735.2.q.f.79.5		12
21.2	odd	6		315.2.d.e.64.5		6
21.5	even	6		2205.2.d.l.1324.5		6
28.23	odd	6		1680.2.t.k.1009.2		6
35.2	odd	12		525.2.a.j.1.3		3
35.4	even	6	inner	735.2.q.e.214.5		12
35.9	even	6		105.2.d.b.64.5	yes	6
35.12	even	12		3675.2.a.bi.1.3		3
35.19	odd	6		735.2.d.b.589.5		6
35.23	odd	12		525.2.a.k.1.1		3
35.24	odd	6		735.2.q.f.214.5		12
35.33	even	12		3675.2.a.bj.1.1		3
35.34	odd	2		735.2.q.f.79.2		12
84.23	even	6		5040.2.t.v.1009.4		6
105.2	even	12		1575.2.a.x.1.1		3
105.23	even	12		1575.2.a.w.1.3		3
105.44	odd	6		315.2.d.e.64.2		6
105.89	even	6		2205.2.d.l.1324.2		6
140.23	even	12		8400.2.a.dj.1.1		3
140.79	odd	6		1680.2.t.k.1009.5		6
140.107	even	12		8400.2.a.dg.1.3		3
420.359	even	6		5040.2.t.v.1009.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.d.b.64.2	✓	6	7.2	even	3
105.2.d.b.64.5	yes	6	35.9	even	6
315.2.d.e.64.2		6	105.44	odd	6
315.2.d.e.64.5		6	21.2	odd	6
525.2.a.j.1.3		3	35.2	odd	12
525.2.a.k.1.1		3	35.23	odd	12
735.2.d.b.589.2		6	7.5	odd	6
735.2.d.b.589.5		6	35.19	odd	6
735.2.q.e.79.2		12	5.4	even	2	inner
735.2.q.e.79.5		12	1.1	even	1	trivial
735.2.q.e.214.2		12	7.4	even	3	inner
735.2.q.e.214.5		12	35.4	even	6	inner
735.2.q.f.79.2		12	35.34	odd	2
735.2.q.f.79.5		12	7.6	odd	2
735.2.q.f.214.2		12	7.3	odd	6
735.2.q.f.214.5		12	35.24	odd	6
1575.2.a.w.1.3		3	105.23	even	12
1575.2.a.x.1.1		3	105.2	even	12
1680.2.t.k.1009.2		6	28.23	odd	6
1680.2.t.k.1009.5		6	140.79	odd	6
2205.2.d.l.1324.2		6	105.89	even	6
2205.2.d.l.1324.5		6	21.5	even	6
3675.2.a.bi.1.3		3	35.12	even	12
3675.2.a.bj.1.1		3	35.33	even	12
5040.2.t.v.1009.3		6	420.359	even	6
5040.2.t.v.1009.4		6	84.23	even	6
8400.2.a.dg.1.3		3	140.107	even	12
8400.2.a.dj.1.1		3	140.23	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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.64823 + 0.951606i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.811108 + 1.40488i) q^{4} +(1.76210 + 1.37659i) q^{5} +1.90321 q^{6} -0.719004i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.64823 + 0.951606i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.811108 + 1.40488i) q^{4} +(1.76210 + 1.37659i) q^{5} +1.90321 q^{6} -0.719004i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.59438 + 3.94576i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(1.40488 + 0.811108i) q^{12} +6.42864i q^{13} +(2.21432 + 0.311108i) q^{15} +(2.30642 - 3.99484i) q^{16} +(3.83531 - 2.21432i) q^{17} +(1.64823 - 0.951606i) q^{18} +(-1.21432 + 2.10326i) q^{19} +(-0.504684 + 3.59210i) q^{20} -3.80642i q^{22} +(1.19320 + 0.688892i) q^{23} +(-0.359502 - 0.622675i) q^{24} +(1.21002 + 4.85138i) q^{25} +(-6.11753 + 10.5959i) q^{26} -1.00000i q^{27} -0.755569 q^{29} +(3.35366 + 2.61994i) q^{30} +(-2.59210 - 4.48966i) q^{31} +(6.35768 - 3.67061i) q^{32} +(-1.73205 - 1.00000i) q^{33} +8.42864 q^{34} +1.62222 q^{36} +(-6.59292 - 3.80642i) q^{37} +(-4.00296 + 2.31111i) q^{38} +(3.21432 + 5.56737i) q^{39} +(0.989771 - 1.26696i) q^{40} -8.23506 q^{41} -10.1017i q^{43} +(1.62222 - 2.80976i) q^{44} +(2.07321 - 0.837733i) q^{45} +(1.31111 + 2.27091i) q^{46} +(-2.38639 - 1.37778i) q^{47} -4.61285i q^{48} +(-2.62222 + 9.14764i) q^{50} +(2.21432 - 3.83531i) q^{51} +(-9.03147 + 5.21432i) q^{52} +(-7.95376 + 4.59210i) q^{53} +(0.951606 - 1.64823i) q^{54} +(0.622216 - 4.42864i) q^{55} +2.42864i q^{57} +(-1.24535 - 0.719004i) q^{58} +(7.05086 + 12.2124i) q^{59} +(1.35898 + 3.36320i) q^{60} +(-3.42864 + 5.93858i) q^{61} -9.86665i q^{62} +4.74620 q^{64} +(-8.84958 + 11.3279i) q^{65} +(-1.90321 - 3.29646i) q^{66} +(2.38639 - 1.37778i) q^{67} +(6.22171 + 3.59210i) q^{68} +1.37778 q^{69} +2.00000 q^{71} +(-0.622675 - 0.359502i) q^{72} +(1.36084 - 0.785680i) q^{73} +(-7.24443 - 12.5477i) q^{74} +(3.47359 + 3.59641i) q^{75} -3.93978 q^{76} +12.2351i q^{78} +(-2.42864 + 4.20653i) q^{79} +(9.56341 - 3.86433i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-13.5733 - 7.83654i) q^{82} -11.6128i q^{83} +(9.80642 + 1.37778i) q^{85} +(9.61285 - 16.6499i) q^{86} +(-0.654342 + 0.377784i) q^{87} +(-1.24535 + 0.719004i) q^{88} +(2.31111 - 4.00296i) q^{89} +(4.21432 + 0.592104i) q^{90} +2.23506i q^{92} +(-4.48966 - 2.59210i) q^{93} +(-2.62222 - 4.54181i) q^{94} +(-5.03508 + 2.03455i) q^{95} +(3.67061 - 6.35768i) q^{96} -11.9398i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 10 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{9}+O(q^{10}) \) 12 * q + 10 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^9	\( 12 q + 10 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{9} + 12 q^{10} - 12 q^{11} - 26 q^{16} + 12 q^{19} - 60 q^{20} - 18 q^{24} + 2 q^{25} - 20 q^{26} - 8 q^{29} + 10 q^{30} - 4 q^{31} + 48 q^{34} + 20 q^{36} + 12 q^{39} - 4 q^{40} + 8 q^{41} + 20 q^{44} + 2 q^{45} + 16 q^{46} - 32 q^{50} - 2 q^{54} + 8 q^{55} + 32 q^{59} + 8 q^{60} + 12 q^{61} - 52 q^{64} - 32 q^{65} + 4 q^{66} + 16 q^{69} + 24 q^{71} - 88 q^{74} - 8 q^{75} + 8 q^{76} + 24 q^{79} - 46 q^{80} - 6 q^{81} + 64 q^{85} + 8 q^{86} + 28 q^{89} + 24 q^{90} - 32 q^{94} - 4 q^{95} + 58 q^{96} - 24 q^{99}+O(q^{100}) \) 12 * q + 10 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^9 + 12 * q^10 - 12 * q^11 - 26 * q^16 + 12 * q^19 - 60 * q^20 - 18 * q^24 + 2 * q^25 - 20 * q^26 - 8 * q^29 + 10 * q^30 - 4 * q^31 + 48 * q^34 + 20 * q^36 + 12 * q^39 - 4 * q^40 + 8 * q^41 + 20 * q^44 + 2 * q^45 + 16 * q^46 - 32 * q^50 - 2 * q^54 + 8 * q^55 + 32 * q^59 + 8 * q^60 + 12 * q^61 - 52 * q^64 - 32 * q^65 + 4 * q^66 + 16 * q^69 + 24 * q^71 - 88 * q^74 - 8 * q^75 + 8 * q^76 + 24 * q^79 - 46 * q^80 - 6 * q^81 + 64 * q^85 + 8 * q^86 + 28 * q^89 + 24 * q^90 - 32 * q^94 - 4 * q^95 + 58 * q^96 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more