LMFDB - Embedded newform 289.3.e.l.131.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [289,3,Mod(40,289)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(289, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([15])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("289.40"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	289.e (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,8,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.87467964001$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			131.1
Root			$0.382683 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	289.131
Dual form			289.3.e.l.214.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.509666 + 1.23044i) q^{2} +(-2.23044 + 1.49033i) q^{3} +(1.57420 - 1.57420i) q^{4} +(-1.59379 - 0.317025i) q^{5} +(-2.97055 - 1.98486i) q^{6} +(-8.69552 + 1.72965i) q^{7} +(7.66104 + 3.17331i) q^{8} +(-0.690373 + 1.66671i) q^{9} +(-0.422221 - 2.12265i) q^{10} +(4.60119 - 6.88617i) q^{11} +(-1.16508 + 5.85724i) q^{12} +(-16.1480 - 16.1480i) q^{13} +(-6.56004 - 9.81779i) q^{14} +(4.02734 - 1.66818i) q^{15} +2.13880i q^{16} -2.40265 q^{18} +(-0.500280 - 1.20778i) q^{19} +(-3.00801 + 2.00989i) q^{20} +(16.8171 - 16.8171i) q^{21} +(10.8181 + 2.15186i) q^{22} +(-22.2452 - 14.8638i) q^{23} +(-21.8168 + 4.33963i) q^{24} +(-20.6573 - 8.55654i) q^{25} +(11.6391 - 28.0993i) q^{26} +(-5.65414 - 28.4253i) q^{27} +(-10.9657 + 16.4113i) q^{28} +(-3.22816 + 16.2291i) q^{29} +(4.10520 + 4.10520i) q^{30} +(-7.63208 - 11.4222i) q^{31} +(28.0125 - 11.6032i) q^{32} +22.2165i q^{33} +14.4072 q^{35} +(1.53694 + 3.71051i) q^{36} +(16.0776 - 10.7427i) q^{37} +(1.23113 - 1.23113i) q^{38} +(60.0832 + 11.9513i) q^{39} +(-11.2041 - 7.48635i) q^{40} +(25.9249 - 5.15679i) q^{41} +(29.2636 + 12.1214i) q^{42} +(-9.06895 + 21.8944i) q^{43} +(-3.59701 - 18.0834i) q^{44} +(1.62870 - 2.43752i) q^{45} +(6.95139 - 34.9470i) q^{46} +(-26.8680 - 26.8680i) q^{47} +(-3.18752 - 4.77046i) q^{48} +(27.3503 - 11.3288i) q^{49} -29.7786i q^{50} -50.8404 q^{52} +(10.8340 + 26.1557i) q^{53} +(32.0939 - 21.4445i) q^{54} +(-9.51644 + 9.51644i) q^{55} +(-72.1055 - 14.3427i) q^{56} +(2.91584 + 1.94830i) q^{57} +(-21.6142 + 4.29933i) q^{58} +(-22.0193 - 9.12070i) q^{59} +(3.71379 - 8.96587i) q^{60} +(10.0745 + 50.6480i) q^{61} +(10.1646 - 15.2124i) q^{62} +(3.12033 - 15.6870i) q^{63} +(34.6035 + 34.6035i) q^{64} +(20.6173 + 30.8560i) q^{65} +(-27.3362 + 11.3230i) q^{66} +70.4415i q^{67} +71.7687 q^{69} +(7.34286 + 17.7272i) q^{70} +(-87.2049 + 58.2684i) q^{71} +(-10.5780 + 10.5780i) q^{72} +(-34.9000 - 6.94205i) q^{73} +(21.4125 + 14.3074i) q^{74} +(58.8271 - 11.7014i) q^{75} +(-2.68883 - 1.11375i) q^{76} +(-28.0991 + 67.8373i) q^{77} +(15.9170 + 80.0201i) q^{78} +(4.03239 - 6.03490i) q^{79} +(0.678052 - 3.40880i) q^{80} +(43.4936 + 43.4936i) q^{81} +(19.5582 + 29.2709i) q^{82} +(-124.385 + 51.5218i) q^{83} -52.9469i q^{84} -31.5619 q^{86} +(-16.9865 - 41.0090i) q^{87} +(57.1019 - 38.1543i) q^{88} +(-38.6522 + 38.6522i) q^{89} +(3.82932 + 0.761700i) q^{90} +(168.346 + 112.485i) q^{91} +(-58.4169 + 11.6198i) q^{92} +(34.0458 + 14.1023i) q^{93} +(19.3658 - 46.7533i) q^{94} +(0.414445 + 2.08356i) q^{95} +(-45.1877 + 67.6282i) q^{96} +(-15.4672 + 77.7590i) q^{97} +(27.8790 + 27.8790i) q^{98} +(8.30069 + 12.4229i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 16 q^{5} + 8 q^{6} - 40 q^{7} + 40 q^{8} - 8 q^{9} + 48 q^{10} + 8 q^{11} - 72 q^{12} - 16 q^{13} - 104 q^{14} + 56 q^{18} + 48 q^{19} + 16 q^{20} + 64 q^{21} + 24 q^{22} - 56 q^{23} - 24 q^{24}+ \cdots - 128 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 16 * q^5 + 8 * q^6 - 40 * q^7 + 40 * q^8 - 8 * q^9 + 48 * q^10 + 8 * q^11 - 72 * q^12 - 16 * q^13 - 104 * q^14 + 56 * q^18 + 48 * q^19 + 16 * q^20 + 64 * q^21 + 24 * q^22 - 56 * q^23 - 24 * q^24 + 32 * q^25 + 48 * q^26 + 24 * q^27 - 8 * q^28 + 128 * q^29 - 16 * q^30 + 40 * q^31 + 88 * q^32 - 160 * q^35 + 24 * q^36 + 96 * q^37 + 120 * q^38 + 96 * q^39 - 112 * q^40 + 48 * q^41 - 128 * q^42 + 112 * q^43 - 120 * q^44 + 112 * q^45 - 72 * q^46 - 192 * q^47 + 136 * q^48 + 80 * q^49 - 384 * q^52 + 128 * q^53 + 64 * q^54 - 224 * q^55 - 200 * q^56 - 48 * q^57 + 120 * q^59 - 48 * q^60 - 288 * q^61 - 8 * q^62 + 120 * q^63 + 64 * q^64 + 64 * q^65 + 96 * q^66 + 240 * q^69 - 480 * q^70 - 344 * q^71 - 40 * q^72 - 200 * q^73 + 208 * q^74 + 104 * q^75 - 160 * q^76 - 80 * q^77 + 512 * q^78 - 328 * q^79 - 64 * q^80 + 424 * q^81 + 64 * q^82 - 336 * q^83 + 832 * q^86 + 80 * q^87 - 8 * q^88 - 160 * q^89 + 224 * q^90 + 544 * q^91 - 24 * q^92 + 208 * q^93 - 432 * q^94 + 192 * q^95 - 64 * q^96 - 240 * q^97 + 120 * q^98 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{13}{16}\right)$

Coefficient data

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

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

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

$2$	0.509666	+	1.23044i	0.254833	+	0.615221i	0.998582	−	0.0532379i	$-0.0169542\pi$
$2$	0.509666	+	1.23044i	0.254833	+	0.615221i	−0.743749	+	0.668459i	$0.766954\pi$
$3$	−2.23044	+	1.49033i	−0.743481	+	0.496778i	−0.868692	−	0.495352i	$-0.835039\pi$
$3$	−2.23044	+	1.49033i	−0.743481	+	0.496778i	0.125211	+	0.992130i	$0.460039\pi$
$4$	1.57420	−	1.57420i	0.393549	−	0.393549i
$5$	−1.59379	−	0.317025i	−0.318759	−	0.0634051i	0.0331178	−	0.999451i	$-0.489456\pi$
$5$	−1.59379	−	0.317025i	−0.318759	−	0.0634051i	−0.351877	+	0.936046i	$0.614456\pi$
$6$	−2.97055	−	1.98486i	−0.495092	−	0.330810i
$7$	−8.69552	+	1.72965i	−1.24222	+	0.247092i	−0.772094	−	0.635509i	$-0.780790\pi$
$7$	−8.69552	+	1.72965i	−1.24222	+	0.247092i	−0.470123	+	0.882601i	$0.655790\pi$
$8$	7.66104	+	3.17331i	0.957631	+	0.396664i
$9$	−0.690373	+	1.66671i	−0.0767081	+	0.185190i
$10$	−0.422221	−	2.12265i	−0.0422221	−	0.212265i
$11$	4.60119	−	6.88617i	0.418290	−	0.626015i	−0.561159	−	0.827708i	$-0.689644\pi$
$11$	4.60119	−	6.88617i	0.418290	−	0.626015i	0.979449	+	0.201693i	$0.0646442\pi$
$12$	−1.16508	+	5.85724i	−0.0970898	+	0.488103i
$13$	−16.1480	−	16.1480i	−1.24216	−	1.24216i	−0.959105	−	0.283051i	$-0.908654\pi$
$13$	−16.1480	−	16.1480i	−1.24216	−	1.24216i	−0.283051	−	0.959105i	$-0.591346\pi$
$14$	−6.56004	−	9.81779i	−0.468574	−	0.701271i
$15$	4.02734	−	1.66818i	0.268489	−	0.111212i
$16$			2.13880i			0.133675i
$17$		0			0
$17$		0			0
$18$	−2.40265			−0.133480
$19$	−0.500280	−	1.20778i	−0.0263305	−	0.0635675i	0.910167	−	0.414241i	$-0.135953\pi$
$19$	−0.500280	−	1.20778i	−0.0263305	−	0.0635675i	−0.936498	+	0.350673i	$0.885953\pi$
$20$	−3.00801	+	2.00989i	−0.150400	+	0.100494i
$21$	16.8171	−	16.8171i	0.800814	−	0.800814i
$22$	10.8181	+	2.15186i	0.491732	+	0.0978116i
$23$	−22.2452	−	14.8638i	−0.967183	−	0.646251i	−0.0316533	−	0.999499i	$-0.510077\pi$
$23$	−22.2452	−	14.8638i	−0.967183	−	0.646251i	−0.935530	+	0.353248i	$0.885077\pi$
$24$	−21.8168	+	4.33963i	−0.909034	+	0.180818i
$25$	−20.6573	−	8.55654i	−0.826293	−	0.342262i
$26$	11.6391	−	28.0993i	0.447658	−	1.08074i
$27$	−5.65414	−	28.4253i	−0.209412	−	1.05279i
$28$	−10.9657	+	16.4113i	−0.391631	+	0.586117i
$29$	−3.22816	+	16.2291i	−0.111316	+	0.559623i	0.884366	+	0.466794i	$0.154591\pi$
$29$	−3.22816	+	16.2291i	−0.111316	+	0.559623i	−0.995682	+	0.0928290i	$0.970409\pi$
$30$	4.10520	+	4.10520i	0.136840	+	0.136840i
$31$	−7.63208	−	11.4222i	−0.246196	−	0.368459i	0.687705	−	0.725991i	$-0.258618\pi$
$31$	−7.63208	−	11.4222i	−0.246196	−	0.368459i	−0.933901	+	0.357532i	$0.883618\pi$
$32$	28.0125	−	11.6032i	0.875391	−	0.362599i
$33$			22.2165i			0.673228i
$34$		0			0
$35$	14.4072			0.411634
$36$	1.53694	+	3.71051i	0.0426929	+	0.103070i
$37$	16.0776	−	10.7427i	0.434530	−	0.290344i	−0.319003	−	0.947754i	$-0.603348\pi$
$37$	16.0776	−	10.7427i	0.434530	−	0.290344i	0.753533	+	0.657410i	$0.228348\pi$
$38$	1.23113	−	1.23113i	0.0323982	−	0.0323982i
$39$	60.0832	+	11.9513i	1.54059	+	0.306443i
$40$	−11.2041	−	7.48635i	−0.280103	−	0.187159i
$41$	25.9249	−	5.15679i	0.632315	−	0.125775i	0.131481	−	0.991319i	$-0.458027\pi$
$41$	25.9249	−	5.15679i	0.632315	−	0.125775i	0.500834	+	0.865543i	$0.333027\pi$
$42$	29.2636	+	12.1214i	0.696752	+	0.288604i
$43$	−9.06895	+	21.8944i	−0.210906	+	0.509172i	−0.993563	−	0.113281i	$-0.963864\pi$
$43$	−9.06895	+	21.8944i	−0.210906	+	0.509172i	0.782657	+	0.622453i	$0.213864\pi$
$44$	−3.59701	−	18.0834i	−0.0817502	−	0.410986i
$45$	1.62870	−	2.43752i	0.0361933	−	0.0541672i
$46$	6.95139	−	34.9470i	0.151117	−	0.759718i
$47$	−26.8680	−	26.8680i	−0.571660	−	0.571660i	0.360932	−	0.932592i	$-0.382459\pi$
$47$	−26.8680	−	26.8680i	−0.571660	−	0.571660i	−0.932592	+	0.360932i	$0.882459\pi$
$48$	−3.18752	−	4.77046i	−0.0664067	−	0.0993846i
$49$	27.3503	−	11.3288i	0.558169	−	0.231201i
$50$		−	29.7786i		−	0.595572i
$51$		0			0
$52$	−50.8404			−0.977699
$53$	10.8340	+	26.1557i	0.204416	+	0.493503i	0.992526	−	0.122031i	$-0.0389406\pi$
$53$	10.8340	+	26.1557i	0.204416	+	0.493503i	−0.788111	+	0.615533i	$0.788941\pi$
$54$	32.0939	−	21.4445i	0.594332	−	0.397120i
$55$	−9.51644	+	9.51644i	−0.173026	+	0.173026i
$56$	−72.1055	−	14.3427i	−1.28760	−	0.256119i
$57$	2.91584	+	1.94830i	0.0511551	+	0.0341808i
$58$	−21.6142	+	4.29933i	−0.372659	+	0.0741265i
$59$	−22.0193	−	9.12070i	−0.373209	−	0.154588i	0.188192	−	0.982132i	$-0.439737\pi$
$59$	−22.0193	−	9.12070i	−0.373209	−	0.154588i	−0.561401	+	0.827544i	$0.689737\pi$
$60$	3.71379	−	8.96587i	0.0618964	−	0.149431i
$61$	10.0745	+	50.6480i	0.165156	+	0.830295i	0.971168	+	0.238396i	$0.0766216\pi$
$61$	10.0745	+	50.6480i	0.165156	+	0.830295i	−0.806012	+	0.591899i	$0.798378\pi$
$62$	10.1646	−	15.2124i	0.163945	−	0.245361i
$63$	3.12033	−	15.6870i	0.0495291	−	0.249000i
$64$	34.6035	+	34.6035i	0.540679	+	0.540679i
$65$	20.6173	+	30.8560i	0.317189	+	0.474707i
$66$	−27.3362	+	11.3230i	−0.414184	+	0.171561i
$67$			70.4415i			1.05137i	0.850681	+	0.525683i	$0.176190\pi$
$67$			70.4415i			1.05137i	−0.850681	+	0.525683i	$0.823810\pi$
$68$		0			0
$69$	71.7687			1.04013
$70$	7.34286	+	17.7272i	0.104898	+	0.253246i
$71$	−87.2049	+	58.2684i	−1.22824	+	0.820682i	−0.988657	−	0.150194i	$-0.952010\pi$
$71$	−87.2049	+	58.2684i	−1.22824	+	0.820682i	−0.239581	+	0.970876i	$0.577010\pi$
$72$	−10.5780	+	10.5780i	−0.146916	+	0.146916i
$73$	−34.9000	−	6.94205i	−0.478083	−	0.0950966i	−0.0498341	−	0.998758i	$-0.515869\pi$
$73$	−34.9000	−	6.94205i	−0.478083	−	0.0950966i	−0.428249	+	0.903661i	$0.640869\pi$
$74$	21.4125	+	14.3074i	0.289358	+	0.193343i
$75$	58.8271	−	11.7014i	0.784361	−	0.156019i
$76$	−2.68883	−	1.11375i	−0.0353793	−	0.0146546i
$77$	−28.0991	+	67.8373i	−0.364924	+	0.881003i
$78$	15.9170	+	80.0201i	0.204064	+	1.02590i
$79$	4.03239	−	6.03490i	0.0510429	−	0.0763911i	−0.805070	−	0.593179i	$-0.797873\pi$
$79$	4.03239	−	6.03490i	0.0510429	−	0.0763911i	0.856113	+	0.516788i	$0.172873\pi$
$80$	0.678052	−	3.40880i	0.00847565	−	0.0426100i
$81$	43.4936	+	43.4936i	0.536958	+	0.536958i
$82$	19.5582	+	29.2709i	0.238514	+	0.356962i
$83$	−124.385	+	51.5218i	−1.49861	+	0.620745i	−0.973170	−	0.230085i	$-0.926099\pi$
$83$	−124.385	+	51.5218i	−1.49861	+	0.620745i	−0.525441	+	0.850830i	$0.676099\pi$
$84$		−	52.9469i		−	0.630320i
$85$		0			0
$86$	−31.5619			−0.366999
$87$	−16.9865	−	41.0090i	−0.195247	−	0.471368i
$88$	57.1019	−	38.1543i	0.648885	−	0.433571i
$89$	−38.6522	+	38.6522i	−0.434294	+	0.434294i	−0.890086	−	0.455792i	$-0.849356\pi$
$89$	−38.6522	+	38.6522i	−0.434294	+	0.434294i	0.455792	+	0.890086i	$0.349356\pi$
$90$	3.82932	+	0.761700i	0.0425480	+	0.00846333i
$91$	168.346	+	112.485i	1.84995	+	1.23610i
$92$	−58.4169	+	11.6198i	−0.634966	+	0.126303i
$93$	34.0458	+	14.1023i	0.366084	+	0.151637i
$94$	19.3658	−	46.7533i	0.206020	−	0.497375i
$95$	0.414445	+	2.08356i	0.00436258	+	0.0219322i
$96$	−45.1877	+	67.6282i	−0.470705	+	0.704460i
$97$	−15.4672	+	77.7590i	−0.159456	+	0.801640i	0.815416	+	0.578875i	$0.196508\pi$
$97$	−15.4672	+	77.7590i	−0.159456	+	0.801640i	−0.974872	+	0.222765i	$0.928492\pi$
$98$	27.8790	+	27.8790i	0.284480	+	0.284480i
$99$	8.30069	+	12.4229i	0.0838454	+	0.125483i
$100$	−45.9884	+	19.0490i	−0.459884	+	0.190490i
$101$		−	140.647i		−	1.39254i	−0.717779	−	0.696271i	$-0.754841\pi$
$101$		−	140.647i		−	1.39254i	0.717779	−	0.696271i	$-0.245159\pi$
$102$		0			0
$103$	−42.3283			−0.410954			−0.205477	−	0.978662i	$-0.565875\pi$
$103$	−42.3283			−0.410954			−0.205477	+	0.978662i	$0.565875\pi$
$104$	−72.4681	−	174.953i	−0.696808	−	1.68224i
$105$	−32.1344	+	21.4715i	−0.306042	+	0.204491i
$106$	−26.6613	+	26.6613i	−0.251522	+	0.251522i
$107$	−72.3344	−	14.3882i	−0.676022	−	0.134469i	−0.154872	−	0.987934i	$-0.549497\pi$
$107$	−72.3344	−	14.3882i	−0.676022	−	0.134469i	−0.521150	+	0.853465i	$0.674497\pi$
$108$	−53.6477	−	35.8462i	−0.496738	−	0.331910i
$109$	206.191	−	41.0140i	1.89166	−	0.376275i	0.894211	−	0.447645i	$-0.147737\pi$
$109$	206.191	−	41.0140i	1.89166	−	0.376275i	0.997450	+	0.0713703i	$0.0227372\pi$
$110$	−16.5596	−	6.85923i	−0.150542	−	0.0623566i
$111$	−19.8500	+	47.9220i	−0.178828	+	0.431730i
$112$	−3.69936	−	18.5979i	−0.0330300	−	0.166053i
$113$	79.8003	−	119.430i	0.706198	−	1.05690i	−0.288838	−	0.957378i	$-0.593269\pi$
$113$	79.8003	−	119.430i	0.706198	−	1.05690i	0.995035	−	0.0995215i	$-0.0317312\pi$
$114$	−0.911170	+	4.58076i	−0.00799272	+	0.0401821i
$115$	30.7421	+	30.7421i	0.267323	+	0.267323i
$116$	20.4660	+	30.6295i	0.176431	+	0.264048i
$117$	38.0622	−	15.7659i	0.325318	−	0.134751i
$118$		−	31.7420i		−	0.269000i
$119$		0			0
$120$	36.1473			0.301227
$121$	20.0563	+	48.4202i	0.165755	+	0.400167i
$122$	−57.1848	+	38.2097i	−0.468728	+	0.313194i
$123$	−50.1387	+	50.1387i	−0.407632	+	0.407632i
$124$	−29.9952	−	5.96643i	−0.241897	−	0.0481163i
$125$	63.9897	+	42.7565i	0.511918	+	0.342052i
$126$	20.8923	−	4.15573i	0.165812	−	0.0329820i
$127$	−100.009	−	41.4251i	−0.787472	−	0.326182i	−0.0475454	−	0.998869i	$-0.515140\pi$
$127$	−100.009	−	41.4251i	−0.787472	−	0.326182i	−0.739927	+	0.672687i	$0.765140\pi$
$128$	21.4713	−	51.8363i	0.167744	−	0.404971i
$129$	−12.4022	−	62.3499i	−0.0961408	−	0.483333i
$130$	−27.4585	+	41.0946i	−0.211220	+	0.316112i
$131$	18.0821	−	90.9051i	0.138032	−	0.693932i	−0.848347	−	0.529441i	$-0.822402\pi$
$131$	18.0821	−	90.9051i	0.138032	−	0.693932i	0.986379	−	0.164491i	$-0.0525982\pi$
$132$	34.9732	+	34.9732i	0.264948	+	0.264948i
$133$	6.43923	+	9.63698i	0.0484152	+	0.0724585i
$134$	−86.6742	+	35.9016i	−0.646822	+	0.267923i
$135$			47.0965i			0.348863i
$136$		0			0
$137$	102.046			0.744863			0.372431	−	0.928060i	$-0.378524\pi$
$137$	102.046			0.744863			0.372431	+	0.928060i	$0.378524\pi$
$138$	36.5780	+	88.3072i	0.265058	+	0.639907i
$139$	25.6379	−	17.1307i	0.184445	−	0.123242i	−0.459920	−	0.887961i	$-0.652122\pi$
$139$	25.6379	−	17.1307i	0.184445	−	0.123242i	0.644365	+	0.764718i	$0.277122\pi$
$140$	22.6798	−	22.6798i	0.161999	−	0.161999i
$141$	99.9699	+	19.8853i	0.709006	+	0.141030i
$142$	−116.141	−	77.6032i	−0.817897	−	0.546501i
$143$	−185.498	+	36.8979i	−1.29719	+	0.258027i
$144$	−3.56475	−	1.47657i	−0.0247552	−	0.0102539i
$145$	10.2900	−	24.8424i	0.0709659	−	0.171327i
$146$	−9.24557	−	46.4806i	−0.0633258	−	0.318360i
$147$	−44.1194	+	66.0294i	−0.300132	+	0.449179i
$148$	8.39818	−	42.2205i	0.0567445	−	0.285274i
$149$	−23.3099	−	23.3099i	−0.156443	−	0.156443i	0.624546	−	0.780988i	$-0.285284\pi$
$149$	−23.3099	−	23.3099i	−0.156443	−	0.156443i	−0.780988	+	0.624546i	$0.785284\pi$
$150$	44.3801	+	66.4195i	0.295867	+	0.442797i
$151$	130.239	−	53.9466i	0.862507	−	0.357262i	0.0928198	−	0.995683i	$-0.470412\pi$
$151$	130.239	−	53.9466i	0.862507	−	0.357262i	0.769688	+	0.638421i	$0.220412\pi$
$152$		−	10.8404i		−	0.0713185i
$153$		0			0
$154$	−97.7910			−0.635006
$155$	8.54284	+	20.6242i	0.0551151	+	0.133060i
$156$	113.397	−	75.7691i	0.726901	−	0.485699i
$157$	78.3942	−	78.3942i	0.499326	−	0.499326i	−0.411902	−	0.911228i	$-0.635135\pi$
$157$	78.3942	−	78.3942i	0.499326	−	0.499326i	0.911228	+	0.411902i	$0.135135\pi$
$158$	9.48077	+	1.88584i	0.0600049	+	0.0119357i
$159$	−63.1453	−	42.1924i	−0.397140	−	0.265361i
$160$	−48.3247	+	9.61238i	−0.302029	+	0.0600773i
$161$	219.143	+	90.7719i	1.36113	+	0.563800i
$162$	−31.3491	+	75.6835i	−0.193513	+	0.467182i
$163$	31.8642	+	160.192i	0.195486	+	0.982774i	0.946553	+	0.322548i	$0.104539\pi$
$163$	31.8642	+	160.192i	0.195486	+	0.982774i	−0.751067	+	0.660226i	$0.770461\pi$
$164$	32.6932	−	48.9288i	0.199349	−	0.298346i
$165$	7.04320	−	35.4086i	0.0426861	−	0.214597i
$166$	−126.789	−	126.789i	−0.763791	−	0.763791i
$167$	−92.6251	−	138.623i	−0.554641	−	0.830079i	0.443154	−	0.896445i	$-0.353859\pi$
$167$	−92.6251	−	138.623i	−0.554641	−	0.830079i	−0.997795	+	0.0663664i	$0.978859\pi$
$168$	182.202	−	75.4707i	1.08454	−	0.449230i
$169$			352.517i			2.08590i
$170$		0			0
$171$	2.35840			0.0137918
$172$	20.1898	+	48.7424i	0.117382	+	0.283386i
$173$	13.8988	−	9.28690i	0.0803401	−	0.0536815i	−0.514751	−	0.857339i	$-0.672116\pi$
$173$	13.8988	−	9.28690i	0.0803401	−	0.0536815i	0.595092	+	0.803658i	$0.297116\pi$
$174$	41.8018	−	41.8018i	0.240240	−	0.240240i
$175$	194.426	+	38.6737i	1.11100	+	0.220993i
$176$	14.7281	+	9.84101i	0.0836824	+	0.0559148i
$177$	62.7057	−	12.4729i	0.354270	−	0.0704686i
$178$	−67.2590	−	27.8596i	−0.377859	−	0.156514i
$179$	−14.8215	+	35.7824i	−0.0828019	+	0.199901i	−0.959858	−	0.280487i	$-0.909504\pi$
$179$	−14.8215	+	35.7824i	−0.0828019	+	0.199901i	0.877056	+	0.480388i	$0.159504\pi$
$180$	−1.27325	−	6.40104i	−0.00707359	−	0.0355613i
$181$	−23.9973	+	35.9145i	−0.132582	+	0.198423i	−0.891820	−	0.452390i	$-0.850572\pi$
$181$	−23.9973	+	35.9145i	−0.132582	+	0.198423i	0.759238	+	0.650813i	$0.225572\pi$
$182$	−52.6063	+	264.470i	−0.289045	+	1.45313i
$183$	−97.9531	−	97.9531i	−0.535263	−	0.535263i
$184$	−123.254	−	184.463i	−0.669860	−	1.00252i
$185$	−29.0301	+	12.0247i	−0.156920	+	0.0649982i
$186$			49.0789i			0.263865i
$187$		0			0
$188$	−84.5912			−0.449953
$189$	98.3313	+	237.393i	0.520271	+	1.25605i
$190$	−2.35247	+	1.57187i	−0.0123814	+	0.00827300i
$191$	107.196	−	107.196i	0.561234	−	0.561234i	−0.368424	−	0.929658i	$-0.620102\pi$
$191$	107.196	−	107.196i	0.561234	−	0.561234i	0.929658	+	0.368424i	$0.120102\pi$
$192$	−128.752	−	25.6103i	−0.670582	−	0.133387i
$193$	−171.004	−	114.261i	−0.886033	−	0.592028i	0.0271259	−	0.999632i	$-0.491364\pi$
$193$	−171.004	−	114.261i	−0.886033	−	0.592028i	−0.913159	+	0.407604i	$0.866364\pi$
$194$	−103.561	+	20.5996i	−0.533820	+	0.106183i
$195$	−91.9714	−	38.0958i	−0.471648	−	0.195363i
$196$	25.2209	−	60.8886i	0.128678	−	0.310656i
$197$	−27.3151	−	137.322i	−0.138655	−	0.697067i	−0.986096	−	0.166177i	$-0.946858\pi$
$197$	−27.3151	−	137.322i	−0.138655	−	0.697067i	0.847441	−	0.530890i	$-0.178142\pi$
$198$	−11.0550	+	16.5450i	−0.0558335	+	0.0835608i
$199$	28.9262	−	145.422i	0.145358	−	0.730763i	−0.837506	−	0.546429i	$-0.815987\pi$
$199$	28.9262	−	145.422i	0.145358	−	0.730763i	0.982864	−	0.184335i	$-0.0590130\pi$
$200$	−131.104	−	131.104i	−0.655520	−	0.655520i
$201$	−104.981	−	157.116i	−0.522295	−	0.781670i
$202$	173.058	−	71.6828i	0.856721	−	0.354865i
$203$		−	146.704i		−	0.722678i
$204$		0			0
$205$	−42.9538			−0.209531
$206$	−21.5733	−	52.0825i	−0.104725	−	0.252828i
$207$	40.1310	−	26.8147i	0.193870	−	0.129540i
$208$	34.5373	−	34.5373i	0.166045	−	0.166045i
$209$	−10.6189	−	2.11223i	−0.0508080	−	0.0101063i
$210$	−42.7973	−	28.5963i	−0.203797	−	0.136173i
$211$	−200.746	+	39.9308i	−0.951401	+	0.189245i	−0.646308	−	0.763077i	$-0.723688\pi$
$211$	−200.746	+	39.9308i	−0.951401	+	0.189245i	−0.305094	+	0.952322i	$0.598688\pi$
$212$	58.2291	+	24.1193i	0.274665	+	0.113770i
$213$	107.666	−	259.929i	0.505474	−	1.22032i
$214$	−19.1625	−	96.3364i	−0.0895444	−	0.450170i
$215$	21.3951	−	32.0200i	0.0995121	−	0.148930i
$216$	46.8855	−	235.709i	0.217063	−	1.09125i
$217$	86.1213	+	86.1213i	0.396872	+	0.396872i
$218$	155.554	+	232.803i	0.713550	+	1.06790i
$219$	88.1885	−	36.5289i	0.402687	−	0.166799i
$220$			29.9615i			0.136189i
$221$		0			0
$222$	−69.0821			−0.311181
$223$	−44.4897	−	107.408i	−0.199506	−	0.481649i	0.792187	−	0.610278i	$-0.208942\pi$
$223$	−44.4897	−	107.408i	−0.199506	−	0.481649i	−0.991693	+	0.128629i	$0.958942\pi$
$224$	−223.514	+	149.347i	−0.997830	+	0.666729i
$225$	28.5225	−	28.5225i	0.126767	−	0.126767i
$226$	187.623	+	37.3205i	0.830190	+	0.165135i
$227$	−127.562	−	85.2339i	−0.561945	−	0.375480i	0.241916	−	0.970297i	$-0.422224\pi$
$227$	−127.562	−	85.2339i	−0.561945	−	0.375480i	−0.803861	+	0.594818i	$0.797224\pi$
$228$	7.65713	−	1.52310i	0.0335839	−	0.00668025i
$229$	−8.91000	−	3.69064i	−0.0389083	−	0.0161164i	0.363144	−	0.931733i	$-0.381703\pi$
$229$	−8.91000	−	3.69064i	−0.0389083	−	0.0161164i	−0.402053	+	0.915617i	$0.631703\pi$
$230$	−22.1582	+	53.4946i	−0.0963399	+	0.232585i
$231$	−38.4267	−	193.184i	−0.166349	−	0.836295i
$232$	−76.2309	+	114.088i	−0.328582	+	0.491757i
$233$	−76.0950	+	382.555i	−0.326588	+	1.64187i	0.373369	+	0.927683i	$0.378203\pi$
$233$	−76.0950	+	382.555i	−0.326588	+	1.64187i	−0.699956	+	0.714185i	$0.746797\pi$
$234$	38.7980	+	38.7980i	0.165803	+	0.165803i
$235$	34.3043	+	51.3399i	0.145976	+	0.218468i
$236$	−49.0206	+	20.3050i	−0.207714	+	0.0860381i
$237$			19.4701i			0.0821523i
$238$		0			0
$239$	372.281			1.55766			0.778831	−	0.627233i	$-0.215813\pi$
$239$	372.281			1.55766			0.778831	+	0.627233i	$0.215813\pi$
$240$	3.56789	+	8.61365i	0.0148662	+	0.0358902i
$241$	115.562	−	77.2160i	0.479510	−	0.320398i	−0.292217	−	0.956352i	$-0.594393\pi$
$241$	115.562	−	77.2160i	0.479510	−	0.320398i	0.771727	+	0.635954i	$0.219393\pi$
$242$	−49.3563	+	49.3563i	−0.203952	+	0.203952i
$243$	93.9975	+	18.6973i	0.386821	+	0.0769434i
$244$	95.5892	+	63.8707i	0.391759	+	0.261765i
$245$	−47.1822	+	9.38513i	−0.192580	+	0.0383066i
$246$	−87.2468	−	36.1388i	−0.354662	−	0.146906i
$247$	−11.4248	+	27.5818i	−0.0462541	+	0.111667i
$248$	−22.2235	−	111.725i	−0.0896109	−	0.450504i
$249$	200.648	−	300.291i	0.805816	−	1.20599i
$250$	−19.9961	+	100.527i	−0.0799844	+	0.402109i
$251$	−154.052	−	154.052i	−0.613754	−	0.613754i	0.330168	−	0.943922i	$-0.392894\pi$
$251$	−154.052	−	154.052i	−0.613754	−	0.613754i	−0.943922	+	0.330168i	$0.892894\pi$
$252$	−19.7824	−	29.6064i	−0.0785015	−	0.117486i
$253$	−204.709	+	84.7932i	−0.809126	+	0.335151i
$254$		−	144.168i		−	0.567591i
$255$		0			0
$256$	270.472			1.05653
$257$	−162.362	−	391.977i	−0.631760	−	1.52520i	−0.837408	−	0.546578i	$-0.815930\pi$
$257$	−162.362	−	391.977i	−0.631760	−	1.52520i	0.205648	−	0.978626i	$-0.434070\pi$
$258$	70.3970	−	47.0378i	0.272857	−	0.182317i
$259$	−121.222	+	121.222i	−0.468039	+	0.468039i
$260$	81.0291	+	16.1177i	0.311650	+	0.0619911i
$261$	−24.8205	−	16.5845i	−0.0950976	−	0.0635422i
$262$	121.069	−	24.0822i	0.462097	−	0.0919168i
$263$	132.058	+	54.7003i	0.502122	+	0.207986i	0.619344	−	0.785120i	$-0.287399\pi$
$263$	132.058	+	54.7003i	0.502122	+	0.207986i	−0.117221	+	0.993106i	$0.537399\pi$
$264$	−70.4999	+	170.202i	−0.267045	+	0.644704i
$265$	−8.97520	−	45.1214i	−0.0338687	−	0.170269i
$266$	−8.57590	+	12.8347i	−0.0322402	+	0.0482509i
$267$	28.6068	−	143.816i	0.107142	−	0.538637i
$268$	110.889	+	110.889i	0.413764	+	0.413764i
$269$	−25.4480	−	38.0856i	−0.0946022	−	0.141582i	0.781149	−	0.624344i	$-0.214634\pi$
$269$	−25.4480	−	38.0856i	−0.0946022	−	0.141582i	−0.875752	+	0.482762i	$0.839634\pi$
$270$	−57.9495	+	24.0035i	−0.214628	+	0.0889018i
$271$		−	329.809i		−	1.21701i	−0.793550	−	0.608504i	$-0.791770\pi$
$271$		−	329.809i		−	1.21701i	0.793550	−	0.608504i	$-0.208230\pi$
$272$		0			0
$273$	−543.126			−1.98947
$274$	52.0095	+	125.562i	0.189816	+	0.458255i
$275$	−153.970	+	102.880i	−0.559891	+	0.374107i
$276$	112.978	−	112.978i	0.409341	−	0.409341i
$277$	−276.779	−	55.0547i	−0.999201	−	0.198753i	−0.331718	−	0.943379i	$-0.607628\pi$
$277$	−276.779	−	55.0547i	−0.999201	−	0.198753i	−0.667483	+	0.744625i	$0.732628\pi$
$278$	34.1451	+	22.8150i	0.122824	+	0.0820684i
$279$	24.3065	−	4.83486i	0.0871200	−	0.0173292i
$280$	110.374	+	45.7185i	0.394194	+	0.163280i
$281$	58.4999	−	141.231i	0.208185	−	0.502603i	−0.784953	−	0.619556i	$-0.787313\pi$
$281$	58.4999	−	141.231i	0.208185	−	0.502603i	0.993137	+	0.116953i	$0.0373127\pi$
$282$	26.4836	+	133.142i	0.0939135	+	0.472135i
$283$	−176.613	+	264.320i	−0.624073	+	0.933992i	0.375900	+	0.926660i	$0.377334\pi$
$283$	−176.613	+	264.320i	−0.624073	+	0.933992i	−0.999973	+	0.00733142i	$0.997666\pi$
$284$	−45.5517	+	229.004i	−0.160393	+	0.806351i
$285$	−4.02959	−	4.02959i	−0.0141389	−	0.0141389i
$286$	−139.943	−	209.439i	−0.489311	−	0.732305i
$287$	−216.511	+	89.6819i	−0.754395	+	0.312480i
$288$			54.6992i			0.189928i
$289$		0			0
$290$	35.8116			0.123488
$291$	−81.3882	−	196.488i	−0.279684	−	0.675218i
$292$	−65.8677	+	44.0114i	−0.225574	+	0.150724i
$293$	27.2633	−	27.2633i	0.0930488	−	0.0930488i	−0.659050	−	0.752099i	$-0.729042\pi$
$293$	27.2633	−	27.2633i	0.0930488	−	0.0930488i	0.752099	+	0.659050i	$0.229042\pi$
$294$	−103.732	−	20.6335i	−0.352828	−	0.0701819i
$295$	32.2028	+	21.5172i	0.109162	+	0.0729397i
$296$	157.261	−	31.2812i	0.531288	−	0.105680i
$297$	−221.757	−	91.8547i	−0.746656	−	0.309275i
$298$	16.8013	−	40.5618i	0.0563801	−	0.136114i
$299$	119.196	+	599.237i	0.398647	+	2.00414i
$300$	74.1851	−	111.026i	0.247284	−	0.370086i
$301$	40.9897	−	206.069i	0.136178	−	0.684615i
$302$	132.756	+	132.756i	0.439591	+	0.439591i
$303$	209.610	+	313.704i	0.691784	+	1.03533i
$304$	2.58320	−	1.07000i	0.00849736	−	0.00351972i
$305$		−	83.9164i		−	0.275136i
$306$		0			0
$307$	−4.80965			−0.0156666			−0.00783330	−	0.999969i	$-0.502493\pi$
$307$	−4.80965			−0.0156666			−0.00783330	+	0.999969i	$0.502493\pi$
$308$	62.5557	+	151.023i	0.203103	+	0.490334i
$309$	94.4108	−	63.0833i	0.305537	−	0.204153i
$310$	−21.0229	+	21.0229i	−0.0678159	+	0.0678159i
$311$	−471.395	−	93.7663i	−1.51574	−	0.301499i	−0.634037	−	0.773303i	$-0.718603\pi$
$311$	−471.395	−	93.7663i	−1.51574	−	0.301499i	−0.881704	+	0.471804i	$0.843603\pi$
$312$	422.375	+	282.222i	1.35377	+	0.904557i
$313$	86.9871	−	17.3028i	0.277914	−	0.0552805i	−0.0541654	−	0.998532i	$-0.517250\pi$
$313$	86.9871	−	17.3028i	0.277914	−	0.0552805i	0.332079	+	0.943251i	$0.392250\pi$
$314$	136.414	+	56.5047i	0.434441	+	0.179951i
$315$	−9.94634	+	24.0126i	−0.0315757	+	0.0762305i
$316$	−3.15234	−	15.8479i	−0.00997577	−	0.0501516i
$317$	66.8346	−	100.025i	0.210835	−	0.315537i	−0.710947	−	0.703246i	$-0.751733\pi$
$317$	66.8346	−	100.025i	0.210835	−	0.315537i	0.921782	+	0.387709i	$0.126733\pi$
$318$	19.7323	−	99.2007i	0.0620511	−	0.311952i
$319$	96.9027	+	96.9027i	0.303770	+	0.303770i
$320$	−44.1806	−	66.1210i	−0.138064	−	0.206628i
$321$	182.781	−	75.7103i	0.569411	−	0.235858i
$322$			315.906i			0.981074i
$323$		0			0
$324$	136.935			0.422639
$325$	195.404	+	471.746i	0.601242	+	1.45153i
$326$	−180.867	+	120.852i	−0.554807	+	0.370710i
$327$	−398.773	+	398.773i	−1.21949	+	1.21949i
$328$	214.976	+	42.7614i	0.655415	+	0.130370i
$329$	280.104	+	187.159i	0.851379	+	0.568873i
$330$	47.1579	−	9.38028i	0.142903	−	0.0284251i
$331$	−93.9184	−	38.9023i	−0.283741	−	0.117530i	0.236274	−	0.971687i	$-0.424074\pi$
$331$	−93.9184	−	38.9023i	−0.283741	−	0.117530i	−0.520015	+	0.854157i	$0.674074\pi$
$332$	−114.701	+	276.912i	−0.345484	+	0.834071i
$333$	6.80542	+	34.2132i	0.0204367	+	0.102742i
$334$	123.360	−	184.621i	0.369341	−	0.552758i
$335$	22.3317	−	112.269i	0.0666619	−	0.335132i
$336$	35.9683	+	35.9683i	0.107049	+	0.107049i
$337$	305.344	+	456.980i	0.906066	+	1.35602i	0.934325	+	0.356423i	$0.116004\pi$
$337$	305.344	+	456.980i	0.906066	+	1.35602i	−0.0282592	+	0.999601i	$0.508996\pi$
$338$	−433.752	+	179.666i	−1.28329	+	0.531556i
$339$			385.310i			1.13661i
$340$		0			0
$341$	−113.772			−0.333642
$342$	1.20200	+	2.90187i	0.00351461	+	0.00848501i
$343$	142.984	−	95.5387i	0.416862	−	0.278538i
$344$	−138.955	+	138.955i	−0.403940	+	0.403940i
$345$	−114.384	−	22.7525i	−0.331549	−	0.0659492i
$346$	18.5108	+	12.3685i	0.0534993	+	0.0357471i
$347$	−250.376	+	49.8028i	−0.721544	+	0.143524i	−0.542184	−	0.840260i	$-0.682403\pi$
$347$	−250.376	+	49.8028i	−0.721544	+	0.143524i	−0.179360	+	0.983784i	$0.557403\pi$
$348$	−91.2964	−	37.8162i	−0.262346	−	0.108667i
$349$	−212.580	+	513.215i	−0.609113	+	1.47053i	0.254854	+	0.966980i	$0.417973\pi$
$349$	−212.580	+	513.215i	−0.609113	+	1.47053i	−0.863967	+	0.503549i	$0.832027\pi$
$350$	51.5065	+	258.940i	0.147161	+	0.739830i
$351$	−367.709	+	550.315i	−1.04760	+	1.56785i
$352$	48.9896	−	246.287i	0.139175	−	0.699680i
$353$	408.644	+	408.644i	1.15763	+	1.15763i	0.984984	+	0.172648i	$0.0552323\pi$
$353$	408.644	+	408.644i	1.15763	+	1.15763i	0.172648	+	0.984984i	$0.444768\pi$
$354$	47.3062	+	70.7988i	0.133633	+	0.199997i
$355$	157.459	−	65.2217i	0.443547	−	0.183723i
$356$			121.692i			0.341832i
$357$		0			0
$358$	−51.5822			−0.144084
$359$	−66.0778	−	159.526i	−0.184061	−	0.444362i	0.804735	−	0.593634i	$-0.202307\pi$
$359$	−66.0778	−	159.526i	−0.184061	−	0.444362i	−0.988796	+	0.149272i	$0.952307\pi$
$360$	20.2126	−	13.5056i	0.0561460	−	0.0375155i
$361$	254.057	−	254.057i	0.703759	−	0.703759i
$362$	−56.4214	−	11.2229i	−0.155860	−	0.0310025i
$363$	−116.897	−	78.1079i	−0.322030	−	0.215173i
$364$	442.083	−	87.9358i	1.21451	−	0.241582i
$365$	53.4227	+	22.1284i	0.146363	+	0.0606257i
$366$	70.6023	−	170.449i	0.192902	−	0.465708i
$367$	3.98311	+	20.0244i	0.0108531	+	0.0545625i	0.985832	−	0.167734i	$-0.0536448\pi$
$367$	3.98311	+	20.0244i	0.0108531	+	0.0545625i	−0.974979	+	0.222296i	$0.928645\pi$
$368$	31.7906	−	47.5779i	0.0863874	−	0.129288i
$369$	−9.30301	+	46.7694i	−0.0252114	+	0.126746i
$370$	−29.5913	−	29.5913i	−0.0799766	−	0.0799766i
$371$	−139.448	−	208.698i	−0.375869	−	0.562528i
$372$	75.7946	−	31.3952i	0.203749	−	0.0843956i
$373$		−	690.960i		−	1.85244i	−0.376983	−	0.926220i	$-0.623039\pi$
$373$		−	690.960i		−	1.85244i	0.376983	−	0.926220i	$-0.376961\pi$
$374$		0			0
$375$	−206.447			−0.550525
$376$	−120.577	−	291.098i	−0.320682	−	0.774196i
$377$	314.196	−	209.939i	0.833410	−	0.556867i
$378$	−241.982	+	241.982i	−0.640164	+	0.640164i
$379$	171.489	+	34.1112i	0.452477	+	0.0900032i	0.416067	−	0.909334i	$-0.363408\pi$
$379$	171.489	+	34.1112i	0.452477	+	0.0900032i	0.0364093	+	0.999337i	$0.488408\pi$
$380$	3.93235	+	2.62751i	0.0103483	+	0.00691451i
$381$	284.801	−	56.6505i	0.747510	−	0.148689i
$382$	186.532	+	77.2642i	0.488304	+	0.202262i
$383$	182.466	−	440.512i	0.476412	−	1.15016i	−0.484868	−	0.874588i	$-0.661132\pi$
$383$	182.466	−	440.512i	0.476412	−	1.15016i	0.961280	−	0.275574i	$-0.0888678\pi$
$384$	29.3629	+	147.617i	0.0764658	+	0.384420i
$385$	66.2903	−	99.2105i	0.172183	−	0.257690i
$386$	53.4371	−	268.646i	0.138438	−	0.695975i
$387$	−30.2306	−	30.2306i	−0.0781151	−	0.0781151i
$388$	98.0596	+	146.757i	0.252731	+	0.378239i
$389$	−204.196	+	84.5808i	−0.524926	+	0.217431i	−0.629379	−	0.777098i	$-0.716691\pi$
$389$	−204.196	+	84.5808i	−0.524926	+	0.217431i	0.104453	+	0.994530i	$0.466691\pi$
$390$		−	132.582i		−	0.339953i
$391$		0			0
$392$	245.482			0.626228
$393$	95.1478	+	229.707i	0.242106	+	0.584496i
$394$	155.045	−	103.598i	0.393516	−	0.262939i
$395$	−8.34002	+	8.34002i	−0.0211140	+	0.0211140i
$396$	32.6230	+	6.48911i	0.0823812	+	0.0163866i
$397$	−100.601	−	67.2191i	−0.253402	−	0.169318i	0.422381	−	0.906418i	$-0.361194\pi$
$397$	−100.601	−	67.2191i	−0.253402	−	0.169318i	−0.675783	+	0.737101i	$0.736194\pi$
$398$	193.676	−	38.5245i	0.486623	−	0.0967953i
$399$	−28.7246	−	11.8981i	−0.0719916	−	0.0298199i
$400$	18.3007	−	44.1818i	0.0457517	−	0.110454i
$401$	−101.865	−	512.110i	−0.254028	−	1.27708i	−0.871463	−	0.490461i	$-0.836828\pi$
$401$	−101.865	−	512.110i	−0.254028	−	1.27708i	0.617435	−	0.786622i	$-0.288172\pi$
$402$	139.816	−	209.250i	0.347802	−	0.520522i
$403$	−61.2032	+	307.689i	−0.151869	+	0.763497i
$404$	−221.406	−	221.406i	−0.548034	−	0.548034i
$405$	−55.5312	−	83.1084i	−0.137114	−	0.205206i
$406$	180.510	−	74.7699i	0.444607	−	0.184162i
$407$		−	160.142i		−	0.393471i
$408$		0			0
$409$	136.013			0.332550			0.166275	−	0.986079i	$-0.446826\pi$
$409$	136.013			0.332550			0.166275	+	0.986079i	$0.446826\pi$
$410$	−21.8921	−	52.8522i	−0.0533954	−	0.128908i
$411$	−227.608	+	152.083i	−0.553791	+	0.370032i
$412$	−66.6331	+	66.6331i	−0.161731	+	0.161731i
$413$	207.245	+	41.2236i	0.501804	+	0.0998150i
$414$	53.4474	+	35.7124i	0.129100	+	0.0862618i
$415$	214.577	−	42.6821i	0.517054	−	0.102848i
$416$	−639.715	−	264.979i	−1.53778	−	0.636968i
$417$	−31.6534	+	76.4181i	−0.0759074	+	0.183257i
$418$	−2.81311	−	14.1424i	−0.00672992	−	0.0338336i
$419$	−208.077	+	311.409i	−0.496604	+	0.743220i	−0.992108	−	0.125386i	$-0.959983\pi$
$419$	−208.077	+	311.409i	−0.496604	+	0.743220i	0.495505	+	0.868605i	$0.334983\pi$
$420$	−16.7855	+	84.3864i	−0.0399655	+	0.200920i
$421$	273.997	+	273.997i	0.650824	+	0.650824i	0.953192	−	0.302367i	$-0.0977769\pi$
$421$	273.997	+	273.997i	0.650824	+	0.650824i	−0.302367	+	0.953192i	$0.597777\pi$
$422$	−151.446	−	226.655i	−0.358876	−	0.537096i
$423$	63.3301	−	26.2322i	0.149716	−	0.0620146i
$424$			234.759i			0.553678i
$425$		0			0
$426$	374.701			0.879580
$427$	−175.206	−	422.985i	−0.410319	−	0.990598i
$428$	−136.518	+	91.2187i	−0.318968	+	0.213128i
$429$	358.753	−	358.753i	0.836254	−	0.836254i
$430$	50.3032	+	10.0059i	0.116984	+	0.0232696i
$431$	57.2309	+	38.2405i	0.132786	+	0.0887250i	0.620189	−	0.784452i	$-0.287056\pi$
$431$	57.2309	+	38.2405i	0.132786	+	0.0887250i	−0.487403	+	0.873177i	$0.662056\pi$
$432$	60.7958	−	12.0930i	0.140731	−	0.0279931i
$433$	251.710	+	104.262i	0.581317	+	0.240790i	0.653910	−	0.756572i	$-0.273127\pi$
$433$	251.710	+	104.262i	0.581317	+	0.240790i	−0.0725929	+	0.997362i	$0.523127\pi$
$434$	−62.0742	+	149.860i	−0.143028	+	0.345301i
$435$	14.0721	+	70.7451i	0.0323496	+	0.162632i
$436$	260.021	−	389.150i	0.596379	−	0.892545i
$437$	−6.82337	+	34.3034i	−0.0156141	+	0.0784975i
$438$	89.8934	+	89.8934i	0.205236	+	0.205236i
$439$	81.7913	+	122.409i	0.186313	+	0.278837i	0.912854	−	0.408286i	$-0.133873\pi$
$439$	81.7913	+	122.409i	0.186313	+	0.278837i	−0.726541	+	0.687123i	$0.758873\pi$
$440$	−103.105	+	42.7073i	−0.234328	+	0.0970620i
$441$			53.4060i			0.121102i
$442$		0			0
$443$	−619.331			−1.39804			−0.699019	−	0.715103i	$-0.746380\pi$
$443$	−619.331			−1.39804			−0.699019	+	0.715103i	$0.746380\pi$
$444$	44.1910	+	106.687i	0.0995293	+	0.240285i
$445$	73.8573	−	49.3499i	0.165971	−	0.110899i
$446$	109.484	−	109.484i	0.245480	−	0.245480i
$447$	86.7311	+	17.2519i	0.194029	+	0.0385948i
$448$	−360.747	−	241.043i	−0.805239	−	0.538043i
$449$	−615.365	+	122.404i	−1.37052	+	0.272614i	−0.824835	−	0.565374i	$-0.808732\pi$
$449$	−615.365	+	122.404i	−1.37052	+	0.272614i	−0.545688	+	0.837988i	$0.683732\pi$
$450$	49.6322	+	20.5583i	0.110294	+	0.0456852i
$451$	83.7750	−	202.251i	0.185754	−	0.448450i
$452$	−62.3844	−	313.627i	−0.138019	−	0.693866i
$453$	−210.091	+	314.424i	−0.463778	+	0.694092i
$454$	39.8616	−	200.398i	0.0878009	−	0.441405i
$455$	−232.648	−	232.648i	−0.511314	−	0.511314i
$456$	16.1558	+	24.1789i	0.0354295	+	0.0530239i
$457$	127.865	−	52.9634i	0.279792	−	0.115894i	−0.238375	−	0.971173i	$-0.576615\pi$
$457$	127.865	−	52.9634i	0.279792	−	0.115894i	0.518167	+	0.855280i	$0.326615\pi$
$458$		−	12.8442i		−	0.0280442i
$459$		0			0
$460$	96.7883			0.210409
$461$	−56.1709	−	135.609i	−0.121846	−	0.294162i	0.851174	−	0.524884i	$-0.175891\pi$
$461$	−56.1709	−	135.609i	−0.121846	−	0.294162i	−0.973020	+	0.230722i	$0.925891\pi$
$462$	218.117	−	145.741i	0.472115	−	0.315457i
$463$	−522.332	+	522.332i	−1.12815	+	1.12815i	−0.137669	+	0.990478i	$0.543961\pi$
$463$	−522.332	+	522.332i	−1.12815	+	1.12815i	−0.990478	+	0.137669i	$0.956039\pi$
$464$	−34.7106	−	6.90438i	−0.0748074	−	0.0148801i
$465$	−49.7913	−	33.2695i	−0.107078	−	0.0715473i
$466$	−509.495	+	101.345i	−1.09334	+	0.217478i
$467$	7.06740	+	2.92741i	0.0151336	+	0.00626855i	0.390237	−	0.920714i	$-0.372393\pi$
$467$	7.06740	+	2.92741i	0.0151336	+	0.00626855i	−0.375104	+	0.926983i	$0.622393\pi$
$468$	35.0988	−	84.7360i	0.0749974	−	0.181060i
$469$	−121.839	−	612.525i	−0.259784	−	1.30602i
$470$	−45.6871	+	68.3756i	−0.0972067	+	0.145480i
$471$	−58.0202	+	291.687i	−0.123185	+	0.619294i
$472$	−139.748	−	139.748i	−0.296077	−	0.296077i
$473$	109.040	+	163.191i	0.230529	+	0.345012i
$474$	−23.9568	+	9.92325i	−0.0505419	+	0.0209351i
$475$			29.2302i			0.0615372i
$476$		0			0
$477$	−51.0733			−0.107072
$478$	189.739	+	458.071i	0.396944	+	0.958307i
$479$	−629.340	+	420.512i	−1.31386	+	0.877895i	−0.997495	−	0.0707413i	$-0.977464\pi$
$479$	−629.340	+	420.512i	−1.31386	+	0.877895i	−0.316368	+	0.948636i	$0.602464\pi$
$480$	93.4598	−	93.4598i	0.194708	−	0.194708i
$481$	−433.095	−	86.1480i	−0.900406	−	0.179102i
$482$	153.908	+	102.838i	0.319311	+	0.213357i
$483$	−624.066	+	124.134i	−1.29206	+	0.257007i
$484$	107.796	+	44.6504i	0.222718	+	0.0922529i
$485$	49.3032	−	119.028i	0.101656	−	0.245419i
$486$	24.9014	+	125.188i	0.0512375	+	0.257588i
$487$	−4.90730	+	7.34429i	−0.0100766	+	0.0150807i	−0.836474	−	0.548007i	$-0.815387\pi$
$487$	−4.90730	+	7.34429i	−0.0100766	+	0.0150807i	0.826397	+	0.563088i	$0.190387\pi$
$488$	−83.5404	+	419.986i	−0.171189	+	0.860627i
$489$	−309.811	−	309.811i	−0.633561	−	0.633561i
$490$	−35.5950	−	53.2717i	−0.0726429	−	0.108718i
$491$	542.252	−	224.608i	1.10438	−	0.457450i	0.245383	−	0.969426i	$-0.421086\pi$
$491$	542.252	−	224.608i	1.10438	−	0.457450i	0.859000	+	0.511976i	$0.171086\pi$
$492$			157.857i			0.320847i
$493$		0			0
$494$	−39.7607			−0.0804871
$495$	−9.29123	−	22.4310i	−0.0187702	−	0.0453152i
$496$	24.4298	−	16.3235i	0.0492536	−	0.0329102i
$497$	657.508	−	657.508i	1.32295	−	1.32295i
$498$	471.755	+	93.8378i	0.947299	+	0.188429i
$499$	−93.1992	−	62.2737i	−0.186772	−	0.124797i	0.458669	−	0.888607i	$-0.348326\pi$
$499$	−93.1992	−	62.2737i	−0.186772	−	0.124797i	−0.645441	+	0.763810i	$0.723326\pi$
$500$	168.040	−	33.4252i	0.336079	−	0.0668503i
$501$	413.190	+	171.149i	0.824730	+	0.341614i
$502$	111.037	−	268.067i	0.221190	−	0.533999i
$503$	93.2434	+	468.766i	0.185375	+	0.931941i	0.955712	+	0.294304i	$0.0950879\pi$
$503$	93.2434	+	468.766i	0.185375	+	0.931941i	−0.770337	+	0.637637i	$0.779912\pi$
$504$	73.6847	−	110.277i	0.146200	−	0.218803i
$505$	−44.5886	+	224.162i	−0.0882942	+	0.443885i
$506$	−208.666	−	208.666i	−0.412384	−	0.412384i
$507$	−525.368	−	786.269i	−1.03623	−	1.55083i
$508$	−222.645	+	92.2226i	−0.438278	+	0.181541i
$509$			235.103i			0.461891i	0.972967	+	0.230946i	$0.0741820\pi$
$509$			235.103i			0.461891i	−0.972967	+	0.230946i	$0.925818\pi$
$510$		0			0
$511$	315.481			0.617380
$512$	51.9650	+	125.455i	0.101494	+	0.245029i
$513$	−31.5029	+	21.0495i	−0.0614091	+	0.0410322i
$514$	399.555	−	399.555i	0.777345	−	0.777345i
$515$	67.4626	+	13.4191i	0.130995	+	0.0260566i
$516$	−117.675	−	78.6276i	−0.228051	−	0.152379i
$517$	−308.643	+	61.3929i	−0.596988	+	0.118748i
$518$	−210.940	−	87.3740i	−0.407219	−	0.168676i
$519$	−17.1600	+	41.4278i	−0.0330635	+	0.0798223i
$520$	60.0345	+	301.814i	0.115451	+	0.580411i
$521$	336.082	−	502.982i	0.645071	−	0.965417i	−0.354468	−	0.935068i	$-0.615338\pi$
$521$	336.082	−	502.982i	0.645071	−	0.965417i	0.999539	−	0.0303489i	$-0.00966184\pi$
$522$	7.75613	−	38.9927i	0.0148585	−	0.0746987i
$523$	−721.650	−	721.650i	−1.37983	−	1.37983i	−0.844894	−	0.534934i	$-0.820336\pi$
$523$	−721.650	−	721.650i	−1.37983	−	1.37983i	−0.534934	−	0.844894i	$-0.679664\pi$
$524$	−114.638	−	171.567i	−0.218774	−	0.327419i
$525$	−491.292	+	203.500i	−0.935795	+	0.387619i
$526$			190.369i			0.361918i
$527$		0			0
$528$	−47.5166			−0.0899935
$529$	71.4781	+	172.563i	0.135119	+	0.326207i
$530$	50.9449	−	34.0403i	0.0961225	−	0.0642270i
$531$	30.4031	−	30.4031i	0.0572563	−	0.0572563i
$532$	25.3071	+	5.03390i	0.0475698	+	0.00946222i
$533$	−501.908	−	335.364i	−0.941666	−	0.629201i
$534$	191.537	−	38.0991i	0.358684	−	0.0713467i
$535$	110.725	+	45.8636i	0.206962	+	0.0857264i
$536$	−223.533	+	539.655i	−0.417038	+	1.00682i
$537$	−20.2691	−	101.900i	−0.0377450	−	0.189757i
$538$	33.8922	−	50.7232i	0.0629966	−	0.0942811i
$539$	47.8314	−	240.465i	0.0887410	−	0.446131i
$540$	74.1392	+	74.1392i	0.137295	+	0.137295i
$541$	−315.825	−	472.665i	−0.583779	−	0.873688i	0.415577	−	0.909558i	$-0.363580\pi$
$541$	−315.825	−	472.665i	−0.583779	−	0.873688i	−0.999356	+	0.0358703i	$0.988580\pi$
$542$	405.812	−	168.093i	0.748730	−	0.310134i
$543$		−	115.869i		−	0.213387i
$544$		0			0
$545$	−341.629			−0.626841
$546$	−276.813	−	668.285i	−0.506983	−	1.22397i
$547$	−305.074	+	203.844i	−0.557723	+	0.372658i	−0.802254	−	0.596983i	$-0.796366\pi$
$547$	−305.074	+	203.844i	−0.557723	+	0.372658i	0.244531	+	0.969641i	$0.421366\pi$
$548$	160.641	−	160.641i	0.293140	−	0.293140i
$549$	−91.3705	−	18.1747i	−0.166431	−	0.0331052i
$550$	−205.061	−	137.017i	−0.372837	−	0.249122i
$551$	21.2162	−	4.22016i	0.0385048	−	0.00765908i
$552$	549.823	+	227.744i	0.996056	+	0.412580i
$553$	−24.6255	+	59.4512i	−0.0445307	+	0.107507i
$554$	−73.3230	−	368.620i	−0.132352	−	0.665379i
$555$	46.8292	−	70.0849i	0.0843770	−	0.126279i
$556$	13.3920	−	67.3262i	0.0240864	−	0.121090i
$557$	146.512	+	146.512i	0.263038	+	0.263038i	0.826287	−	0.563249i	$-0.190449\pi$
$557$	146.512	+	146.512i	0.263038	+	0.263038i	−0.563249	+	0.826287i	$0.690449\pi$
$558$	18.3372	+	27.4436i	0.0328624	+	0.0491820i
$559$	499.996	−	207.105i	0.894448	−	0.370493i
$560$			30.8141i			0.0550251i
$561$		0			0
$562$	203.593			0.362264
$563$	328.584	+	793.273i	0.583631	+	1.40901i	0.889499	+	0.456936i	$0.151053\pi$
$563$	328.584	+	793.273i	0.583631	+	1.40901i	−0.305868	+	0.952074i	$0.598947\pi$
$564$	188.676	−	126.069i	0.334531	−	0.223527i
$565$	−165.048	+	165.048i	−0.292120	+	0.292120i
$566$	−415.244	−	82.5971i	−0.733646	−	0.145931i
$567$	−453.428	−	302.971i	−0.799696	−	0.534340i
$568$	−852.984	+	169.669i	−1.50173	+	0.298713i
$569$	−292.003	−	120.952i	−0.513187	−	0.212569i	0.111034	−	0.993817i	$-0.464584\pi$
$569$	−292.003	−	120.952i	−0.513187	−	0.212569i	−0.624221	+	0.781248i	$0.714584\pi$
$570$	2.90444	−	7.01193i	0.00509550	−	0.0123016i
$571$	−52.7480	−	265.182i	−0.0923782	−	0.464417i	−0.999089	−	0.0426646i	$-0.986415\pi$
$571$	−52.7480	−	265.182i	−0.0923782	−	0.464417i	0.906711	−	0.421752i	$-0.138585\pi$
$572$	−233.926	+	350.095i	−0.408962	+	0.612055i
$573$	−79.3365	+	398.852i	−0.138458	+	0.696076i
$574$	−220.697	−	220.697i	−0.384489	−	0.384489i
$575$	332.344	+	497.388i	0.577989	+	0.865022i
$576$	−81.5632	+	33.7846i	−0.141603	+	0.0586538i
$577$		−	63.2031i		−	0.109537i	−0.998499	−	0.0547687i	$-0.982558\pi$
$577$		−	63.2031i		−	0.109537i	0.998499	−	0.0547687i	$-0.0174421\pi$
$578$		0			0
$579$	551.703			0.952855
$580$	−22.9082	−	55.3054i	−0.0394970	−	0.0953541i
$581$	992.475	−	663.151i	1.70822	−	1.14140i
$582$	200.287	−	200.287i	0.344136	−	0.344136i
$583$	229.962	+	45.7422i	0.394446	+	0.0784601i
$584$	−245.342	−	163.932i	−0.420105	−	0.280705i
$585$	−65.6614	+	13.0609i	−0.112242	+	0.0223263i
$586$	47.4411	+	19.6507i	0.0809575	+	0.0335337i
$587$	283.753	−	685.040i	0.483395	−	1.16702i	−0.474592	−	0.880206i	$-0.657404\pi$
$587$	283.753	−	685.040i	0.483395	−	1.16702i	0.957987	−	0.286812i	$-0.0925956\pi$
$588$	34.4906	+	173.396i	0.0586575	+	0.294891i
$589$	−9.97738	+	14.9322i	−0.0169395	+	0.0253518i
$590$	−10.0630	+	50.5903i	−0.0170560	+	0.0857462i
$591$	265.581	+	265.581i	0.449375	+	0.449375i
$592$	22.9765	+	34.3867i	0.0388116	+	0.0580857i
$593$	185.647	−	76.8977i	0.313065	−	0.129676i	−0.220618	−	0.975360i	$-0.570808\pi$
$593$	185.647	−	76.8977i	0.313065	−	0.129676i	0.533683	+	0.845685i	$0.320808\pi$
$594$		−	319.674i		−	0.538172i
$595$		0			0
$596$	−73.3889			−0.123136
$597$	152.209	+	367.465i	0.254956	+	0.615519i
$598$	−676.576	+	452.074i	−1.13140	+	0.755976i
$599$	−457.825	+	457.825i	−0.764316	+	0.764316i	−0.977099	−	0.212784i	$-0.931747\pi$
$599$	−457.825	+	457.825i	−0.764316	+	0.764316i	0.212784	+	0.977099i	$0.431747\pi$
$600$	487.809	+	97.0312i	0.813015	+	0.161719i
$601$	596.295	+	398.432i	0.992171	+	0.662948i	0.941937	−	0.335790i	$-0.109003\pi$
$601$	596.295	+	398.432i	0.992171	+	0.662948i	0.0502343	+	0.998737i	$0.484003\pi$
$602$	274.447	−	54.5909i	0.455892	−	0.0906826i
$603$	−117.405	−	48.6309i	−0.194702	−	0.0806482i
$604$	120.099	−	289.944i	0.198839	−	0.480040i
$605$	−16.6152	−	83.5302i	−0.0274631	−	0.138067i
$606$	−279.164	+	417.798i	−0.460666	+	0.689436i
$607$	202.623	−	1018.65i	0.333810	−	1.67818i	−0.340903	−	0.940098i	$-0.610733\pi$
$607$	202.623	−	1018.65i	0.333810	−	1.67818i	0.674713	−	0.738080i	$-0.264267\pi$
$608$	−28.0282	−	28.0282i	−0.0460990	−	0.0460990i
$609$	218.638	+	327.214i	0.359011	+	0.537297i
$610$	103.254	−	42.7693i	0.169269	−	0.0701136i
$611$			867.731i			1.42018i
$612$		0			0
$613$	−626.391			−1.02185			−0.510923	−	0.859627i	$-0.670696\pi$
$613$	−626.391			−1.02185			−0.510923	+	0.859627i	$0.670696\pi$
$614$	−2.45131	−	5.91799i	−0.00399237	−	0.00963842i
$615$	95.8060	−	64.0155i	0.155782	−	0.104090i
$616$	−430.537	+	430.537i	−0.698924	+	0.698924i
$617$	657.155	+	130.716i	1.06508	+	0.211858i	0.696368	−	0.717685i	$-0.254798\pi$
$617$	657.155	+	130.716i	1.06508	+	0.211858i	0.368714	+	0.929543i	$0.379798\pi$
$618$	125.738	+	84.0157i	0.203460	+	0.135948i
$619$	771.905	−	153.541i	1.24702	−	0.248047i	0.472916	−	0.881107i	$-0.343201\pi$
$619$	771.905	−	153.541i	1.24702	−	0.248047i	0.774103	+	0.633060i	$0.218201\pi$
$620$	45.9147	+	19.0185i	0.0740560	+	0.0306750i
$621$	−296.729	+	716.368i	−0.477825	+	1.15357i
$622$	−124.880	−	627.814i	−0.200772	−	1.00935i
$623$	269.246	−	402.955i	0.432177	−	0.646798i
$624$	−25.5614	+	128.506i	−0.0409637	+	0.205938i
$625$	306.829	+	306.829i	0.490927	+	0.490927i
$626$	65.6245	+	98.2140i	0.104831	+	0.156891i
$627$	26.8327	−	11.1145i	0.0427954	−	0.0177264i
$628$		−	246.816i		−	0.393019i
$629$		0			0
$630$	−34.6154			−0.0549451
$631$	−317.894	−	767.465i	−0.503794	−	1.21627i	−0.947402	−	0.320046i	$-0.896302\pi$
$631$	−317.894	−	767.465i	−0.503794	−	1.21627i	0.443608	−	0.896221i	$-0.353698\pi$
$632$	50.0429	−	33.4376i	0.0791818	−	0.0529076i
$633$	388.241	−	388.241i	0.613336	−	0.613336i
$634$	157.138	+	31.2568i	0.247852	+	0.0493009i
$635$	146.261	+	97.7284i	0.230332	+	0.153903i
$636$	−165.822	+	32.9841i	−0.260727	+	0.0518618i
$637$	−624.591	−	258.714i	−0.980520	−	0.406145i
$638$	−69.8452	+	168.621i	−0.109475	+	0.264297i
$639$	−36.9126	−	185.572i	−0.0577661	−	0.290410i
$640$	−50.6542	+	75.8094i	−0.0791472	+	0.118452i
$641$	164.996	−	829.492i	0.257404	−	1.29406i	−0.608381	−	0.793645i	$-0.708181\pi$
$641$	164.996	−	829.492i	0.257404	−	1.29406i	0.865786	−	0.500415i	$-0.166819\pi$
$642$	186.314	+	186.314i	0.290209	+	0.290209i
$643$	410.655	+	614.589i	0.638655	+	0.955814i	0.999729	+	0.0232773i	$0.00741006\pi$
$643$	410.655	+	614.589i	0.638655	+	0.955814i	−0.361074	+	0.932537i	$0.617590\pi$
$644$	487.867	−	202.081i	0.757557	−	0.313790i
$645$			103.305i			0.160162i
$646$		0			0
$647$	874.070			1.35096			0.675479	−	0.737379i	$-0.263937\pi$
$647$	874.070			1.35096			0.675479	+	0.737379i	$0.263937\pi$
$648$	195.188	+	471.225i	0.301216	+	0.727199i
$649$	−164.122	+	109.663i	−0.252884	+	0.168972i
$650$	−480.866	+	480.866i	−0.739793	+	0.739793i
$651$	−320.438	−	63.7391i	−0.492225	−	0.0979096i
$652$	302.335	+	202.014i	0.463704	+	0.309837i
$653$	1133.57	−	225.482i	1.73595	−	0.345301i	0.777133	−	0.629337i	$-0.216673\pi$
$653$	1133.57	−	225.482i	1.73595	−	0.345301i	0.958814	+	0.284036i	$0.0916734\pi$
$654$	−693.908	−	287.426i	−1.06102	−	0.439489i
$655$	−57.6384	+	139.151i	−0.0879976	+	0.212445i
$656$	11.0293	+	55.4481i	0.0168130	+	0.0845246i
$657$	35.6644	−	53.3755i	0.0542837	−	0.0812413i
$658$	−87.5294	+	440.040i	−0.133023	+	0.668754i
$659$	318.726	+	318.726i	0.483651	+	0.483651i	0.906295	−	0.422645i	$-0.138898\pi$
$659$	318.726	+	318.726i	0.483651	+	0.483651i	−0.422645	+	0.906295i	$0.638898\pi$
$660$	−44.6527	−	66.8275i	−0.0676556	−	0.101254i
$661$	−461.408	+	191.121i	−0.698045	+	0.289140i	−0.703347	−	0.710846i	$-0.748312\pi$
$661$	−461.408	+	191.121i	−0.698045	+	0.289140i	0.00530241	+	0.999986i	$0.498312\pi$
$662$		−	135.388i		−	0.204514i
$663$		0			0
$664$	−1116.41			−1.68134
$665$	−7.20763	−	17.4008i	−0.0108385	−	0.0261666i
$666$	−38.6288	+	25.8110i	−0.0580012	+	0.0387552i
$667$	313.036	−	313.036i	0.469320	−	0.469320i
$668$	−364.030	−	72.4102i	−0.544956	−	0.108398i
$669$	259.305	+	173.262i	0.387601	+	0.258987i
$670$	149.523	−	29.7419i	0.223168	−	0.0443909i
$671$	395.126	+	163.666i	0.588861	+	0.243914i
$672$	275.958	−	666.221i	0.410651	−	0.991400i
$673$	183.323	+	921.629i	0.272397	+	1.36943i	0.838411	+	0.545038i	$0.183485\pi$
$673$	183.323	+	921.629i	0.272397	+	1.36943i	−0.566014	+	0.824396i	$0.691515\pi$
$674$	−406.664	+	608.615i	−0.603359	+	0.902990i
$675$	−126.423	+	635.569i	−0.187293	+	0.941584i
$676$	554.932	+	554.932i	0.820905	+	0.820905i
$677$	−618.247	−	925.272i	−0.913216	−	1.36672i	−0.930272	−	0.366870i	$-0.880430\pi$
$677$	−618.247	−	925.272i	−0.913216	−	1.36672i	0.0170566	−	0.999855i	$-0.494570\pi$
$678$	−474.102	+	196.379i	−0.699265	+	0.289645i
$679$		−	702.908i		−	1.03521i
$680$		0			0
$681$	411.546			0.604325
$682$	−57.9857	−	139.990i	−0.0850231	−	0.205264i
$683$	1093.01	−	730.324i	1.60030	−	1.06929i	0.649110	−	0.760695i	$-0.275142\pi$
$683$	1093.01	−	730.324i	1.60030	−	1.06929i	0.951194	−	0.308594i	$-0.0998583\pi$
$684$	3.71259	−	3.71259i	0.00542776	−	0.00542776i
$685$	−162.641	−	32.3512i	−0.237432	−	0.0472281i
$686$	190.429	+	127.240i	0.277593	+	0.185482i
$687$	25.3735	−	5.04711i	0.0369338	−	0.00734660i
$688$	−46.8276	−	19.3966i	−0.0680634	−	0.0281928i
$689$	247.414	−	597.310i	0.359091	−	0.866923i
$690$	−30.3022	−	152.340i	−0.0439163	−	0.220782i
$691$	−266.235	+	398.449i	−0.385290	+	0.576627i	−0.972528	−	0.232787i	$-0.925215\pi$
$691$	−266.235	+	398.449i	−0.385290	+	0.576627i	0.587238	+	0.809415i	$0.300215\pi$
$692$	7.26009	−	36.4989i	0.0104915	−	0.0527441i
$693$	−93.6660	−	93.6660i	−0.135160	−	0.135160i
$694$	−188.887	−	282.690i	−0.272172	−	0.407334i
$695$	−46.2924	+	19.1749i	−0.0666078	+	0.0275898i
$696$		−	368.075i		−	0.528844i
$697$		0			0
$698$	−739.826			−1.05992
$699$	−400.410	−	966.675i	−0.572832	−	1.38294i
$700$	366.945	−	245.185i	0.524207	−	0.350264i
$701$	−777.458	+	777.458i	−1.10907	+	1.10907i	−0.115796	+	0.993273i	$0.536942\pi$
$701$	−777.458	+	777.458i	−1.10907	+	1.10907i	−0.993273	+	0.115796i	$0.963058\pi$
$702$	−864.539	−	171.968i	−1.23154	−	0.244968i
$703$	−21.0182	−	14.0439i	−0.0298978	−	0.0199771i
$704$	397.503	−	79.0682i	0.564635	−	0.112313i
$705$	−153.027	−	63.3860i	−0.217060	−	0.0899092i
$706$	−294.541	+	711.085i	−0.417197	+	1.00720i
$707$	243.269	+	1223.00i	0.344086	+	1.72984i
$708$	79.0764	−	118.346i	0.111690	−	0.167156i
$709$	−101.816	+	511.863i	−0.143605	+	0.721951i	0.840138	+	0.542372i	$0.182474\pi$
$709$	−101.816	+	511.863i	−0.143605	+	0.721951i	−0.983744	+	0.179579i	$0.942526\pi$
$710$	160.503	+	160.503i	0.226061	+	0.226061i
$711$	7.27456	+	10.8871i	0.0102314	+	0.0153124i
$712$	−418.771	+	173.461i	−0.588162	+	0.243625i
$713$			367.531i			0.515472i
$714$		0			0
$715$	307.343			0.429851
$716$	32.9965	+	79.6605i	0.0460845	+	0.111258i
$717$	−830.352	+	554.824i	−1.15809	+	0.773813i
$718$	162.610	−	162.610i	0.226476	−	0.226476i
$719$	609.667	+	121.270i	0.847938	+	0.168665i	0.599890	−	0.800082i	$-0.295211\pi$
$719$	609.667	+	121.270i	0.847938	+	0.168665i	0.248048	+	0.968748i	$0.420211\pi$
$720$	5.21336	+	3.48346i	0.00724078	+	0.00483813i
$721$	368.066	−	73.2130i	0.510494	−	0.101544i
$722$	442.087	+	183.118i	0.612309	+	0.253627i
$723$	−142.677	+	344.452i	−0.197340	+	0.476420i
$724$	18.7600	+	94.3131i	0.0259117	+	0.130267i
$725$	205.550	−	307.627i	0.283517	−	0.424313i
$726$	36.5290	−	183.644i	0.0503154	−	0.252953i
$727$	−181.405	−	181.405i	−0.249526	−	0.249526i	0.571250	−	0.820776i	$-0.306459\pi$
$727$	−181.405	−	181.405i	−0.249526	−	0.249526i	−0.820776	+	0.571250i	$0.806459\pi$
$728$	932.755	+	1395.97i	1.28126	+	1.91754i
$729$	−748.965	+	310.231i	−1.02739	+	0.425557i
$730$			77.0116i			0.105495i
$731$		0			0
$732$	−308.395			−0.421305
$733$	84.8211	+	204.776i	0.115718	+	0.279367i	0.971118	−	0.238600i	$-0.0766886\pi$
$733$	84.8211	+	204.776i	0.115718	+	0.279367i	−0.855400	+	0.517968i	$0.826689\pi$
$734$	−22.6088	+	15.1067i	−0.0308022	+	0.0205814i
$735$	91.2502	−	91.2502i	0.124150	−	0.124150i
$736$	−795.611	−	158.257i	−1.08099	−	0.215023i
$737$	485.072	+	324.115i	0.658171	+	0.439776i
$738$	−62.2884	+	12.3899i	−0.0844017	+	0.0167885i
$739$	−272.978	−	113.071i	−0.369388	−	0.153006i	0.190265	−	0.981733i	$-0.439065\pi$
$739$	−272.978	−	113.071i	−0.369388	−	0.153006i	−0.559653	+	0.828727i	$0.689065\pi$
$740$	−26.7699	+	64.6284i	−0.0361756	+	0.0873356i
$741$	−15.6238	−	78.5464i	−0.0210848	−	0.106000i
$742$	185.719	−	277.948i	0.250295	−	0.374594i
$743$	146.076	−	734.372i	0.196602	−	0.988387i	−0.748878	−	0.662708i	$-0.769407\pi$
$743$	146.076	−	734.372i	0.196602	−	0.988387i	0.945480	−	0.325679i	$-0.105593\pi$
$744$	216.076	+	216.076i	0.290425	+	0.290425i
$745$	29.7614	+	44.5411i	0.0399482	+	0.0597867i
$746$	850.187	−	352.159i	1.13966	−	0.472063i
$747$		−	242.882i		−	0.325143i
$748$		0			0
$749$	653.871			0.872992
$750$	−105.219	−	254.021i	−0.140292	−	0.338695i
$751$	−579.170	+	386.989i	−0.771199	+	0.515298i	−0.877814	−	0.479002i	$-0.840999\pi$
$751$	−579.170	+	386.989i	−0.771199	+	0.515298i	0.106615	+	0.994300i	$0.465999\pi$
$752$	57.4652	−	57.4652i	0.0764165	−	0.0764165i
$753$	573.194	+	114.015i	0.761213	+	0.151415i
$754$	418.453	+	279.601i	0.554977	+	0.370824i
$755$	−224.676	+	44.6908i	−0.297584	+	0.0591931i
$756$	528.496	+	218.910i	0.699069	+	0.289564i
$757$	−262.415	+	633.525i	−0.346651	+	0.836889i	0.650360	+	0.759626i	$0.274618\pi$
$757$	−262.415	+	633.525i	−0.346651	+	0.836889i	−0.997011	+	0.0772631i	$0.975382\pi$
$758$	45.4301	+	228.392i	0.0599341	+	0.301309i
$759$	330.221	−	494.211i	0.435074	−	0.651135i
$760$	−3.43669	+	17.2774i	−0.00452195	+	0.0227334i
$761$	305.005	+	305.005i	0.400795	+	0.400795i	0.878513	−	0.477718i	$-0.158536\pi$
$761$	305.005	+	305.005i	0.400795	+	0.400795i	−0.477718	+	0.878513i	$0.658536\pi$
$762$	214.859	+	321.559i	0.281967	+	0.421993i
$763$	−1722.00	+	713.275i	−2.25688	+	0.934830i
$764$		−	337.495i		−	0.441747i
$765$		0			0
$766$	635.021			0.829009
$767$	208.287	+	502.850i	0.271561	+	0.655606i
$768$	−603.271	+	403.093i	−0.785509	+	0.524861i
$769$	−303.275	+	303.275i	−0.394376	+	0.394376i	−0.876244	−	0.481868i	$-0.839959\pi$
$769$	−303.275	+	303.275i	−0.394376	+	0.394376i	0.481868	+	0.876244i	$0.339959\pi$
$770$	155.859	+	31.0022i	0.202414	+	0.0402626i
$771$	946.317	+	632.309i	1.22739	+	0.820115i
$772$	−449.065	+	89.3246i	−0.581690	+	0.115705i
$773$	192.675	+	79.8088i	0.249257	+	0.103246i	0.503814	−	0.863812i	$-0.331930\pi$
$773$	192.675	+	79.8088i	0.249257	+	0.103246i	−0.254557	+	0.967058i	$0.581930\pi$
$774$	21.7895	−	52.6045i	0.0281518	−	0.0679644i
$775$	59.9237	+	301.257i	0.0773209	+	0.388718i
$776$	−365.249	+	546.633i	−0.470681	+	0.704424i
$777$	89.7175	−	451.040i	0.115467	−	0.580489i
$778$	−208.144	−	208.144i	−0.267537	−	0.267537i
$779$	−19.1980	−	28.7318i	−0.0246444	−	0.0368830i
$780$	−204.751	+	84.8108i	−0.262502	+	0.108732i
$781$			868.612i			1.11218i
$782$		0			0
$783$	479.568			0.612475
$784$	24.2301	+	58.4966i	0.0309057	+	0.0746130i
$785$	−149.797	+	100.091i	−0.190824	+	0.127505i
$786$	−234.148	+	234.148i	−0.297898	+	0.297898i
$787$	−1084.81	−	215.783i	−1.37842	−	0.274184i	−0.550407	−	0.834896i	$-0.685527\pi$
$787$	−1084.81	−	215.783i	−1.37842	−	0.274184i	−0.828011	+	0.560712i	$0.810527\pi$
$788$	−259.172	−	173.173i	−0.328898	−	0.219763i
$789$	−376.070	+	74.8050i	−0.476641	+	0.0948098i
$790$	−14.5125	−	6.01129i	−0.0183703	−	0.00760922i
$791$	−487.334	+	1176.53i	−0.616099	+	1.48739i
$792$	24.1704	+	121.513i	0.0305182	+	0.153425i
$793$	655.182	−	980.548i	0.826206	−	1.23650i
$794$	31.4366	−	158.042i	0.0395927	−	0.199046i
$795$	87.2646	+	87.2646i	0.109767	+	0.109767i
$796$	−183.387	−	274.458i	−0.230386	−	0.344797i
$797$	56.6619	−	23.4701i	0.0710940	−	0.0294481i	−0.346853	−	0.937919i	$-0.612750\pi$
$797$	56.6619	−	23.4701i	0.0710940	−	0.0294481i	0.417947	+	0.908471i	$0.362750\pi$
$798$		−	41.4081i		−	0.0518899i
$799$		0			0
$800$	−677.946			−0.847433
$801$	−37.7374	−	91.1062i	−0.0471129	−	0.113741i
$802$	578.205	−	386.344i	0.720954	−	0.481726i
$803$	−208.386	+	208.386i	−0.259509	+	0.259509i
$804$	−412.593	−	82.0698i	−0.513175	−	0.102077i
$805$	−320.491	−	214.145i	−0.398126	−	0.266019i
$806$	−409.787	+	81.5117i	−0.508421	+	0.101131i
$807$	113.521	+	47.0217i	0.140670	+	0.0582673i
$808$	446.315	−	1077.50i	0.552370	−	1.33354i
$809$	−158.661	−	797.643i	−0.196120	−	0.985962i	−0.945945	−	0.324326i	$-0.894862\pi$
$809$	−158.661	−	797.643i	−0.196120	−	0.985962i	0.749825	−	0.661636i	$-0.230138\pi$
$810$	73.9577	−	110.685i	0.0913058	−	0.136649i
$811$	−225.686	+	1134.60i	−0.278281	+	1.39901i	0.548340	+	0.836256i	$0.315260\pi$
$811$	−225.686	+	1134.60i	−0.278281	+	1.39901i	−0.826621	+	0.562759i	$0.809740\pi$
$812$	−230.941	−	230.941i	−0.284410	−	0.284410i
$813$	491.526	+	735.621i	0.604583	+	0.904823i
$814$	197.046	−	81.6192i	0.242071	−	0.100269i
$815$		−	265.415i		−	0.325663i
$816$		0			0
$817$	30.9806			0.0379200
$818$	69.3211	+	167.356i	0.0847446	+	0.204592i
$819$	−303.701	+	202.926i	−0.370819	+	0.247773i
$820$	−67.6178	+	67.6178i	−0.0824608	+	0.0824608i
$821$	−981.470	−	195.226i	−1.19546	−	0.237791i	−0.443054	−	0.896495i	$-0.646105\pi$
$821$	−981.470	−	195.226i	−1.19546	−	0.237791i	−0.752402	+	0.658704i	$0.771105\pi$
$822$	−303.133	−	202.547i	−0.368776	−	0.246408i
$823$	−53.1391	+	10.5700i	−0.0645676	+	0.0128433i	−0.227268	−	0.973832i	$-0.572979\pi$
$823$	−53.1391	+	10.5700i	−0.0645676	+	0.0128433i	0.162701	+	0.986675i	$0.447979\pi$
$824$	−324.279	−	134.321i	−0.393542	−	0.163011i
$825$	190.097	−	458.934i	0.230420	−	0.556283i
$826$	54.9025	+	276.013i	0.0664679	+	0.334157i
$827$	−227.897	+	341.072i	−0.275570	+	0.412420i	−0.943278	−	0.332003i	$-0.892276\pi$
$827$	−227.897	+	341.072i	−0.275570	+	0.412420i	0.667708	+	0.744423i	$0.267276\pi$
$828$	20.9625	−	105.386i	0.0253171	−	0.127278i
$829$	153.097	+	153.097i	0.184677	+	0.184677i	0.793390	−	0.608713i	$-0.208314\pi$
$829$	153.097	+	153.097i	0.184677	+	0.184677i	−0.608713	+	0.793390i	$0.708314\pi$
$830$	161.881	+	242.271i	0.195037	+	0.291893i
$831$	699.389	−	289.696i	0.841623	−	0.348612i
$832$		−	1117.56i		−	1.34322i
$833$		0			0
$834$	−110.161			−0.132087
$835$	103.678	+	250.301i	0.124165	+	0.299762i
$836$	−20.0413	+	13.3911i	−0.0239728	+	0.0160181i
$837$	−281.527	+	281.527i	−0.336352	+	0.336352i
$838$	−489.221	−	97.3120i	−0.583796	−	0.116124i
$839$	−235.891	−	157.618i	−0.281158	−	0.187864i	0.406993	−	0.913431i	$-0.366577\pi$
$839$	−235.891	−	157.618i	−0.281158	−	0.187864i	−0.688151	+	0.725568i	$0.741577\pi$
$840$	−314.319	+	62.5220i	−0.374190	+	0.0744309i
$841$	524.021	+	217.057i	0.623093	+	0.258094i
$842$	−197.491	+	476.785i	−0.234549	+	0.566252i
$843$	80.0011	+	402.193i	0.0949005	+	0.477097i
$844$	−253.154	+	378.872i	−0.299946	+	0.448901i
$845$	111.757	−	561.840i	0.132257	−	0.664899i
$846$	64.5544	+	64.5544i	0.0763054	+	0.0763054i
$847$	−258.150	−	386.349i	−0.304782	−	0.456138i
$848$	−55.9416	+	23.1718i	−0.0659689	+	0.0273252i
$849$		−	852.762i		−	1.00443i
$850$		0			0
$851$	−517.327			−0.607905
$852$	−239.692	−	578.667i	−0.281328	−	0.679187i
$853$	−474.002	+	316.718i	−0.555688	+	0.371299i	−0.801478	−	0.598024i	$-0.795953\pi$
$853$	−474.002	+	316.718i	−0.555688	+	0.371299i	0.245790	+	0.969323i	$0.420953\pi$
$854$	431.162	−	431.162i	0.504874	−	0.504874i
$855$	−3.75880	−	0.747672i	−0.00439626	−	0.000874470i
$856$	−508.499	−	339.768i	−0.594040	−	0.396925i
$857$	1303.19	−	259.221i	1.52065	−	0.302475i	0.637086	−	0.770792i	$-0.280139\pi$
$857$	1303.19	−	259.221i	1.52065	−	0.302475i	0.883561	+	0.468317i	$0.155139\pi$
$858$	624.269	+	258.581i	0.727586	+	0.301376i
$859$	107.826	−	260.316i	0.125526	−	0.303046i	−0.848607	−	0.529024i	$-0.822558\pi$
$859$	107.826	−	260.316i	0.125526	−	0.303046i	0.974132	+	0.225979i	$0.0725580\pi$
$860$	−16.7257	−	84.0860i	−0.0194485	−	0.0977744i
$861$	349.260	−	522.704i	0.405645	−	0.607090i
$862$	−17.8841	+	89.9092i	−0.0207472	+	0.104303i
$863$	−44.4457	−	44.4457i	−0.0515014	−	0.0515014i	0.680887	−	0.732388i	$-0.261594\pi$
$863$	−44.4457	−	44.4457i	−0.0515014	−	0.0515014i	−0.732388	+	0.680887i	$0.761594\pi$
$864$	−488.209	−	730.657i	−0.565057	−	0.845668i
$865$	−25.0961	+	10.3951i	−0.0290128	+	0.0120175i
$866$			362.854i			0.419000i
$867$		0			0
$868$	271.144			0.312378
$869$	−23.0035	−	55.5355i	−0.0264713	−	0.0639073i
$870$	−79.8757	+	53.3712i	−0.0918112	+	0.0613463i
$871$	1137.49	−	1137.49i	1.30596	−	1.30596i
$872$	1709.79	+	340.098i	1.96077	+	0.390021i
$873$	−118.923	−	79.4621i	−0.136224	−	0.0910218i
$874$	−45.6860	+	9.08751i	−0.0522723	+	0.0103976i
$875$	−630.377	−	261.111i	−0.720431	−	0.298412i
$876$	81.3225	−	196.330i	0.0928339	−	0.224121i
$877$	−87.9713	−	442.261i	−0.100309	−	0.504289i	−0.997975	−	0.0636113i	$-0.979738\pi$
$877$	−87.9713	−	442.261i	−0.100309	−	0.504289i	0.897665	−	0.440678i	$-0.145262\pi$
$878$	−108.931	+	163.027i	−0.124068	+	0.185680i
$879$	−20.1778	+	101.441i	−0.0229554	+	0.115405i
$880$	−20.3537	−	20.3537i	−0.0231292	−	0.0231292i
$881$	−546.902	−	818.497i	−0.620774	−	0.929054i	−0.999993	−	0.00374731i	$-0.998807\pi$
$881$	−546.902	−	818.497i	−0.620774	−	0.929054i	0.379219	−	0.925307i	$-0.376193\pi$
$882$	−65.7130	+	27.2192i	−0.0745046	+	0.0308608i
$883$			908.452i			1.02882i	0.857543	+	0.514412i	$0.171990\pi$
$883$			908.452i			1.02882i	−0.857543	+	0.514412i	$0.828010\pi$
$884$		0			0
$885$	−103.894			−0.117395
$886$	−315.652	−	762.051i	−0.356266	−	0.860103i
$887$	208.233	−	139.137i	0.234761	−	0.156862i	−0.432626	−	0.901574i	$-0.642413\pi$
$887$	208.233	−	139.137i	0.234761	−	0.156862i	0.667387	+	0.744711i	$0.267413\pi$
$888$	−304.143	+	304.143i	−0.342503	+	0.342503i
$889$	941.280	+	187.232i	1.05881	+	0.210610i
$890$	98.3647	+	65.7252i	0.110522	+	0.0738485i
$891$	499.626	−	99.3819i	0.560748	−	0.111540i
$892$	−239.117	−	99.0454i	−0.268068	−	0.111037i
$893$	−19.0092	+	45.8922i	−0.0212869	+	0.0513911i
$894$	22.9764	+	115.510i	0.0257007	+	0.129206i
$895$	34.9664	−	52.3309i	0.0390686	−	0.0584703i
$896$	−97.0455	+	487.881i	−0.108310	+	0.544510i
$897$	−1158.92	−	1158.92i	−1.29200	−	1.29200i
$898$	−464.241	−	694.786i	−0.516972	−	0.773704i
$899$	210.010	−	86.9888i	0.233604	−	0.0967617i
$900$		−	89.8001i		−	0.0997779i
$901$		0			0
$902$	291.555			0.323232
$903$	215.687	+	520.713i	0.238856	+	0.576648i
$904$	990.341	−	661.725i	1.09551	−	0.731996i
$905$	49.6326	−	49.6326i	0.0548427	−	0.0548427i
$906$	−493.957	−	98.2541i	−0.545206	−	0.108448i
$907$	1443.77	+	964.698i	1.59181	+	1.06361i	0.956653	+	0.291232i	$0.0940650\pi$
$907$	1443.77	+	964.698i	1.59181	+	1.06361i	0.635158	+	0.772382i	$0.280935\pi$
$908$	−334.982	+	66.6321i	−0.368923	+	0.0733833i
$909$	234.417	+	97.0986i	0.257884	+	0.106819i
$910$	167.687	−	404.833i	0.184272	−	0.444871i
$911$	−350.193	−	1760.54i	−0.384405	−	1.93253i	−0.360334	−	0.932823i	$-0.617337\pi$
$911$	−350.193	−	1760.54i	−0.384405	−	1.93253i	−0.0240704	−	0.999710i	$-0.507663\pi$
$912$	−4.16702	+	6.23639i	−0.00456911	+	0.00683815i
$913$	−217.530	+	1093.60i	−0.238258	+	1.19781i
$914$	130.337	+	130.337i	0.142600	+	0.142600i
$915$	125.063	+	187.171i	0.136681	+	0.204558i
$916$	−19.8359	+	8.21630i	−0.0216549	+	0.00896976i
$917$			821.743i			0.896121i
$918$		0			0
$919$	−506.869			−0.551544			−0.275772	−	0.961223i	$-0.588933\pi$
$919$	−506.869			−0.551544			−0.275772	+	0.961223i	$0.588933\pi$
$920$	137.962	+	333.071i	0.149959	+	0.362033i
$921$	10.7276	−	7.16798i	0.0116478	−	0.00778282i
$922$	138.230	−	138.230i	0.149924	−	0.149924i
$923$	2349.11	+	467.266i	2.54508	+	0.506247i
$924$	−364.601	−	243.619i	−0.394590	−	0.263657i
$925$	−424.041	+	84.3470i	−0.458422	+	0.0911859i
$926$	−908.914	−	376.485i	−0.981549	−	0.406571i
$927$	29.2223	−	70.5489i	0.0315235	−	0.0761045i
$928$	97.8796	+	492.074i	0.105474	+	0.530252i
$929$	−774.790	+	1159.56i	−0.834005	+	1.24818i	0.132412	+	0.991195i	$0.457728\pi$
$929$	−774.790	+	1159.56i	−0.834005	+	1.24818i	−0.966416	+	0.256981i	$0.917272\pi$
$930$	15.5593	−	78.2217i	0.0167304	−	0.0841093i
$931$	−27.3656	−	27.3656i	−0.0293937	−	0.0293937i
$932$	482.429	+	722.006i	0.517628	+	0.774685i
$933$	1191.16	−	493.396i	1.27670	−	0.528827i
$934$			10.1880i			0.0109080i
$935$		0			0
$936$	341.626			0.364985
$937$	−76.7261	−	185.233i	−0.0818848	−	0.197687i	0.877634	−	0.479331i	$-0.159121\pi$
$937$	−76.7261	−	185.233i	−0.0818848	−	0.197687i	−0.959519	+	0.281643i	$0.909121\pi$
$938$	691.580	−	462.099i	0.737292	−	0.492643i
$939$	−168.233	+	168.233i	−0.179162	+	0.179162i
$940$	134.821	+	26.8175i	0.143426	+	0.0285293i
$941$	−1269.83	−	848.476i	−1.34945	−	0.901675i	−0.350067	−	0.936725i	$-0.613841\pi$
$941$	−1269.83	−	848.476i	−1.34945	−	0.901675i	−0.999386	+	0.0350495i	$0.988841\pi$
$942$	−388.476	+	77.2726i	−0.412394	+	0.0820303i
$943$	−653.355	−	270.628i	−0.692847	−	0.286987i
$944$	19.5073	−	47.0948i	0.0206645	−	0.0498886i
$945$	−81.4603	−	409.529i	−0.0862014	−	0.433364i
$946$	−145.222	+	217.341i	−0.153512	+	0.229747i
$947$	198.435	−	997.602i	0.209541	−	1.05343i	−0.722580	−	0.691287i	$-0.757044\pi$
$947$	198.435	−	997.602i	0.209541	−	1.05343i	0.932121	−	0.362147i	$-0.117956\pi$
$948$	30.6498	+	30.6498i	0.0323310	+	0.0323310i
$949$	451.466	+	675.667i	0.475728	+	0.711978i
$950$	−35.9661	+	14.8976i	−0.0378590	+	0.0156817i
$951$			322.706i			0.339334i
$952$		0			0
$953$	297.230			0.311889			0.155945	−	0.987766i	$-0.450158\pi$
$953$	297.230			0.311889			0.155945	+	0.987766i	$0.450158\pi$
$954$	−26.0303	−	62.8428i	−0.0272855	−	0.0658730i
$955$	−204.832	+	136.864i	−0.214484	+	0.143313i
$956$	586.045	−	586.045i	0.613017	−	0.613017i
$957$	−360.553	−	71.7185i	−0.376754	−	0.0749410i
$958$	−838.169	−	560.047i	−0.874915	−	0.584600i
$959$	−887.345	+	176.504i	−0.925281	+	0.184050i
$960$	197.085	+	81.6352i	0.205297	+	0.0850366i
$961$	295.540	−	713.498i	0.307534	−	0.742453i
$962$	−114.734	−	576.806i	−0.119266	−	0.599590i
$963$	73.9186	−	110.627i	0.0767586	−	0.114877i
$964$	60.3641	−	303.471i	0.0626183	−	0.314804i
$965$	236.322	+	236.322i	0.244893	+	0.244893i
$966$	−470.805	−	704.610i	−0.487376	−	0.729410i
$967$	1093.12	−	452.787i	1.13043	−	0.468239i	0.262502	−	0.964931i	$-0.415452\pi$
$967$	1093.12	−	452.787i	1.13043	−	0.468239i	0.867927	+	0.496692i	$0.165452\pi$
$968$			434.595i			0.448961i
$969$		0			0
$970$	171.586			0.176893
$971$	211.336	+	510.211i	0.217648	+	0.525449i	0.994561	−	0.104160i	$-0.0332153\pi$
$971$	211.336	+	510.211i	0.217648	+	0.525449i	−0.776913	+	0.629608i	$0.783215\pi$
$972$	177.404	−	118.537i	0.182514	−	0.121952i
$973$	−193.305	+	193.305i	−0.198669	+	0.198669i
$974$	−11.5378	−	2.29501i	−0.0118458	−	0.00235628i
$975$	−1138.90	−	760.986i	−1.16810	−	0.780498i
$976$	−108.326	+	21.5473i	−0.110989	+	0.0220772i
$977$	302.204	+	125.177i	0.309318	+	0.128124i	0.531942	−	0.846781i	$-0.321462\pi$
$977$	302.204	+	125.177i	0.309318	+	0.128124i	−0.222624	+	0.974904i	$0.571462\pi$
$978$	223.305	−	539.105i	0.228328	−	0.551232i
$979$	88.3194	+	444.011i	0.0902138	+	0.453536i
$980$	−59.5001	+	89.0482i	−0.0607144	+	0.0908655i
$981$	−73.9904	+	371.975i	−0.0754235	+	0.379179i
$982$	552.735	+	552.735i	0.562866	+	0.562866i
$983$	−569.276	−	851.982i	−0.579121	−	0.866716i	0.420047	−	0.907503i	$-0.362014\pi$
$983$	−569.276	−	851.982i	−0.579121	−	0.866716i	−0.999168	+	0.0407862i	$0.987014\pi$
$984$	−543.221	+	225.009i	−0.552053	+	0.228668i
$985$			227.523i			0.230988i
$986$		0			0
$987$	−903.685			−0.915587
$988$	25.4344	+	61.4041i	0.0257433	+	0.0621499i
$989$	527.174	−	352.246i	0.533037	−	0.356164i
$990$	22.8646	−	22.8646i	0.0230956	−	0.0230956i
$991$	404.735	+	80.5068i	0.408411	+	0.0812380i	0.395020	−	0.918672i	$-0.370738\pi$
$991$	404.735	+	80.5068i	0.408411	+	0.0812380i	0.0133905	+	0.999910i	$0.495738\pi$
$992$	−346.328	−	231.409i	−0.349121	−	0.233275i
$993$	267.457	−	53.2005i	0.269342	−	0.0535755i
$994$	1144.14	+	473.916i	1.15104	+	0.476777i
$995$	−92.2048	+	222.602i	−0.0926682	+	0.223721i
$996$	−156.858	−	788.578i	−0.157488	−	0.791745i
$997$	−698.922	+	1046.01i	−0.701025	+	1.04916i	0.294590	+	0.955624i	$0.404817\pi$
$997$	−698.922	+	1046.01i	−0.701025	+	1.04916i	−0.995616	+	0.0935352i	$0.970183\pi$
$998$	29.1238	−	146.415i	0.0291821	−	0.146708i
$999$	−396.270	−	396.270i	−0.396666	−	0.396666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.3.e.l.131.1		8
17.2	even	8		289.3.e.m.65.1		8
17.3	odd	16		17.3.e.a.6.1	yes	8
17.4	even	4		289.3.e.d.158.1		8
17.5	odd	16		289.3.e.m.249.1		8
17.6	odd	16		289.3.e.b.75.1		8
17.7	odd	16		289.3.e.k.214.1		8
17.8	even	8		289.3.e.c.224.1		8
17.9	even	8		17.3.e.a.3.1	✓	8
17.10	odd	16	inner	289.3.e.l.214.1		8
17.11	odd	16		289.3.e.d.75.1		8
17.12	odd	16		289.3.e.i.249.1		8
17.13	even	4		289.3.e.b.158.1		8
17.14	odd	16		289.3.e.c.40.1		8
17.15	even	8		289.3.e.i.65.1		8
17.16	even	2		289.3.e.k.131.1		8
51.20	even	16		153.3.p.b.91.1		8
51.26	odd	8		153.3.p.b.37.1		8
68.3	even	16		272.3.bh.c.193.1		8
68.43	odd	8		272.3.bh.c.241.1		8
85.3	even	16		425.3.t.c.74.1		8
85.9	even	8		425.3.u.b.326.1		8
85.37	even	16		425.3.t.a.74.1		8
85.43	odd	8		425.3.t.a.224.1		8
85.54	odd	16		425.3.u.b.176.1		8
85.77	odd	8		425.3.t.c.224.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.3.1	✓	8	17.9	even	8
17.3.e.a.6.1	yes	8	17.3	odd	16
153.3.p.b.37.1		8	51.26	odd	8
153.3.p.b.91.1		8	51.20	even	16
272.3.bh.c.193.1		8	68.3	even	16
272.3.bh.c.241.1		8	68.43	odd	8
289.3.e.b.75.1		8	17.6	odd	16
289.3.e.b.158.1		8	17.13	even	4
289.3.e.c.40.1		8	17.14	odd	16
289.3.e.c.224.1		8	17.8	even	8
289.3.e.d.75.1		8	17.11	odd	16
289.3.e.d.158.1		8	17.4	even	4
289.3.e.i.65.1		8	17.15	even	8
289.3.e.i.249.1		8	17.12	odd	16
289.3.e.k.131.1		8	17.16	even	2
289.3.e.k.214.1		8	17.7	odd	16
289.3.e.l.131.1		8	1.1	even	1	trivial
289.3.e.l.214.1		8	17.10	odd	16	inner
289.3.e.m.65.1		8	17.2	even	8
289.3.e.m.249.1		8	17.5	odd	16
425.3.t.a.74.1		8	85.37	even	16
425.3.t.a.224.1		8	85.43	odd	8
425.3.t.c.74.1		8	85.3	even	16
425.3.t.c.224.1		8	85.77	odd	8
425.3.u.b.176.1		8	85.54	odd	16
425.3.u.b.326.1		8	85.9	even	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	289.e (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.509666 + 1.23044i) q^{2} +(-2.23044 + 1.49033i) q^{3} +(1.57420 - 1.57420i) q^{4} +(-1.59379 - 0.317025i) q^{5} +(-2.97055 - 1.98486i) q^{6} +(-8.69552 + 1.72965i) q^{7} +(7.66104 + 3.17331i) q^{8} +(-0.690373 + 1.66671i) q^{9} +(-0.422221 - 2.12265i) q^{10} +(4.60119 - 6.88617i) q^{11} +(-1.16508 + 5.85724i) q^{12} +(-16.1480 - 16.1480i) q^{13} +(-6.56004 - 9.81779i) q^{14} +(4.02734 - 1.66818i) q^{15} +2.13880i q^{16} -2.40265 q^{18} +(-0.500280 - 1.20778i) q^{19} +(-3.00801 + 2.00989i) q^{20} +(16.8171 - 16.8171i) q^{21} +(10.8181 + 2.15186i) q^{22} +(-22.2452 - 14.8638i) q^{23} +(-21.8168 + 4.33963i) q^{24} +(-20.6573 - 8.55654i) q^{25} +(11.6391 - 28.0993i) q^{26} +(-5.65414 - 28.4253i) q^{27} +(-10.9657 + 16.4113i) q^{28} +(-3.22816 + 16.2291i) q^{29} +(4.10520 + 4.10520i) q^{30} +(-7.63208 - 11.4222i) q^{31} +(28.0125 - 11.6032i) q^{32} +22.2165i q^{33} +14.4072 q^{35} +(1.53694 + 3.71051i) q^{36} +(16.0776 - 10.7427i) q^{37} +(1.23113 - 1.23113i) q^{38} +(60.0832 + 11.9513i) q^{39} +(-11.2041 - 7.48635i) q^{40} +(25.9249 - 5.15679i) q^{41} +(29.2636 + 12.1214i) q^{42} +(-9.06895 + 21.8944i) q^{43} +(-3.59701 - 18.0834i) q^{44} +(1.62870 - 2.43752i) q^{45} +(6.95139 - 34.9470i) q^{46} +(-26.8680 - 26.8680i) q^{47} +(-3.18752 - 4.77046i) q^{48} +(27.3503 - 11.3288i) q^{49} -29.7786i q^{50} -50.8404 q^{52} +(10.8340 + 26.1557i) q^{53} +(32.0939 - 21.4445i) q^{54} +(-9.51644 + 9.51644i) q^{55} +(-72.1055 - 14.3427i) q^{56} +(2.91584 + 1.94830i) q^{57} +(-21.6142 + 4.29933i) q^{58} +(-22.0193 - 9.12070i) q^{59} +(3.71379 - 8.96587i) q^{60} +(10.0745 + 50.6480i) q^{61} +(10.1646 - 15.2124i) q^{62} +(3.12033 - 15.6870i) q^{63} +(34.6035 + 34.6035i) q^{64} +(20.6173 + 30.8560i) q^{65} +(-27.3362 + 11.3230i) q^{66} +70.4415i q^{67} +71.7687 q^{69} +(7.34286 + 17.7272i) q^{70} +(-87.2049 + 58.2684i) q^{71} +(-10.5780 + 10.5780i) q^{72} +(-34.9000 - 6.94205i) q^{73} +(21.4125 + 14.3074i) q^{74} +(58.8271 - 11.7014i) q^{75} +(-2.68883 - 1.11375i) q^{76} +(-28.0991 + 67.8373i) q^{77} +(15.9170 + 80.0201i) q^{78} +(4.03239 - 6.03490i) q^{79} +(0.678052 - 3.40880i) q^{80} +(43.4936 + 43.4936i) q^{81} +(19.5582 + 29.2709i) q^{82} +(-124.385 + 51.5218i) q^{83} -52.9469i q^{84} -31.5619 q^{86} +(-16.9865 - 41.0090i) q^{87} +(57.1019 - 38.1543i) q^{88} +(-38.6522 + 38.6522i) q^{89} +(3.82932 + 0.761700i) q^{90} +(168.346 + 112.485i) q^{91} +(-58.4169 + 11.6198i) q^{92} +(34.0458 + 14.1023i) q^{93} +(19.3658 - 46.7533i) q^{94} +(0.414445 + 2.08356i) q^{95} +(-45.1877 + 67.6282i) q^{96} +(-15.4672 + 77.7590i) q^{97} +(27.8790 + 27.8790i) q^{98} +(8.30069 + 12.4229i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 16 q^{5} + 8 q^{6} - 40 q^{7} + 40 q^{8} - 8 q^{9} + 48 q^{10} + 8 q^{11} - 72 q^{12} - 16 q^{13} - 104 q^{14} + 56 q^{18} + 48 q^{19} + 16 q^{20} + 64 q^{21} + 24 q^{22} - 56 q^{23} - 24 q^{24}+ \cdots - 128 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 16 * q^5 + 8 * q^6 - 40 * q^7 + 40 * q^8 - 8 * q^9 + 48 * q^10 + 8 * q^11 - 72 * q^12 - 16 * q^13 - 104 * q^14 + 56 * q^18 + 48 * q^19 + 16 * q^20 + 64 * q^21 + 24 * q^22 - 56 * q^23 - 24 * q^24 + 32 * q^25 + 48 * q^26 + 24 * q^27 - 8 * q^28 + 128 * q^29 - 16 * q^30 + 40 * q^31 + 88 * q^32 - 160 * q^35 + 24 * q^36 + 96 * q^37 + 120 * q^38 + 96 * q^39 - 112 * q^40 + 48 * q^41 - 128 * q^42 + 112 * q^43 - 120 * q^44 + 112 * q^45 - 72 * q^46 - 192 * q^47 + 136 * q^48 + 80 * q^49 - 384 * q^52 + 128 * q^53 + 64 * q^54 - 224 * q^55 - 200 * q^56 - 48 * q^57 + 120 * q^59 - 48 * q^60 - 288 * q^61 - 8 * q^62 + 120 * q^63 + 64 * q^64 + 64 * q^65 + 96 * q^66 + 240 * q^69 - 480 * q^70 - 344 * q^71 - 40 * q^72 - 200 * q^73 + 208 * q^74 + 104 * q^75 - 160 * q^76 - 80 * q^77 + 512 * q^78 - 328 * q^79 - 64 * q^80 + 424 * q^81 + 64 * q^82 - 336 * q^83 + 832 * q^86 + 80 * q^87 - 8 * q^88 - 160 * q^89 + 224 * q^90 + 544 * q^91 - 24 * q^92 + 208 * q^93 - 432 * q^94 + 192 * q^95 - 64 * q^96 - 240 * q^97 + 120 * q^98 - 128 * q^99

Introduction

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