LMFDB - Embedded newform 289.3.e.k.249.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,3,Mod(40,289)]

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

lf = mfeigenbasis(mf)

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")

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

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			249.1
Root			$-0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	289.249
Dual form			289.3.e.k.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.79690 + 1.15851i) q^{2} +(-0.158513 - 0.796897i) q^{3} +(3.65205 + 3.65205i) q^{4} +(-6.67619 - 4.46088i) q^{5} +(0.479872 - 2.41248i) q^{6} +(6.53073 - 4.36370i) q^{7} +(1.34942 + 3.25778i) q^{8} +(7.70500 - 3.19151i) q^{9} +O(q^{10})$	\(q+(2.79690 + 1.15851i) q^{2} +(-0.158513 - 0.796897i) q^{3} +(3.65205 + 3.65205i) q^{4} +(-6.67619 - 4.46088i) q^{5} +(0.479872 - 2.41248i) q^{6} +(6.53073 - 4.36370i) q^{7} +(1.34942 + 3.25778i) q^{8} +(7.70500 - 3.19151i) q^{9} +(-13.5046 - 20.2111i) q^{10} +(7.92030 + 1.57545i) q^{11} +(2.33141 - 3.48921i) q^{12} +(0.798835 - 0.798835i) q^{13} +(23.3212 - 4.63887i) q^{14} +(-2.49661 + 6.02734i) q^{15} -9.98414i q^{16} +25.2475 q^{18} +(-2.59882 - 1.07647i) q^{19} +(-8.09040 - 40.6732i) q^{20} +(-4.51262 - 4.51262i) q^{21} +(20.3271 + 13.5821i) q^{22} +(-1.67393 + 8.41543i) q^{23} +(2.38222 - 1.59175i) q^{24} +(15.1049 + 36.4664i) q^{25} +(3.15972 - 1.30880i) q^{26} +(-7.82730 - 11.7144i) q^{27} +(39.7870 + 7.91414i) q^{28} +(-1.70587 + 2.55301i) q^{29} +(-13.9655 + 13.9655i) q^{30} +(-12.5915 + 2.50461i) q^{31} +(16.9644 - 40.9557i) q^{32} -6.56139i q^{33} -63.0663 q^{35} +(39.7946 + 16.4835i) q^{36} +(4.61798 + 23.2161i) q^{37} +(-6.02153 - 6.02153i) q^{38} +(-0.763215 - 0.509964i) q^{39} +(5.52363 - 27.7692i) q^{40} +(-18.1595 + 12.1338i) q^{41} +(-7.39341 - 17.8493i) q^{42} +(21.4671 - 8.89197i) q^{43} +(23.1717 + 34.6790i) q^{44} +(-65.6770 - 13.0640i) q^{45} +(-14.4312 + 21.5978i) q^{46} +(-55.6597 + 55.6597i) q^{47} +(-7.95633 + 1.58261i) q^{48} +(4.85715 - 11.7262i) q^{49} +119.492i q^{50} +5.83478 q^{52} +(55.5080 + 22.9922i) q^{53} +(-8.32089 - 41.8320i) q^{54} +(-45.8495 - 45.8495i) q^{55} +(23.0287 + 15.3873i) q^{56} +(-0.445887 + 2.24162i) q^{57} +(-7.72882 + 5.16424i) q^{58} +(-10.5100 - 25.3733i) q^{59} +(-31.1299 + 12.8944i) q^{60} +(20.2562 + 30.3155i) q^{61} +(-38.1189 - 7.58231i) q^{62} +(36.3925 - 54.4652i) q^{63} +(66.6561 - 66.6561i) q^{64} +(-8.89668 + 1.76966i) q^{65} +(7.60145 - 18.3515i) q^{66} -117.219i q^{67} +6.97157 q^{69} +(-176.390 - 73.0632i) q^{70} +(20.6737 + 103.934i) q^{71} +(20.7945 + 20.7945i) q^{72} +(50.7486 + 33.9091i) q^{73} +(-13.9802 + 70.2832i) q^{74} +(26.6657 - 17.8174i) q^{75} +(-5.55971 - 13.4223i) q^{76} +(58.6001 - 24.2730i) q^{77} +(-1.54383 - 2.31051i) q^{78} +(93.4553 + 18.5894i) q^{79} +(-44.5381 + 66.6560i) q^{80} +(44.9799 - 44.9799i) q^{81} +(-64.8474 + 12.8989i) q^{82} +(-45.4770 + 109.791i) q^{83} -32.9607i q^{84} +70.3428 q^{86} +(2.30489 + 0.954715i) q^{87} +(5.55533 + 27.9285i) q^{88} +(61.4534 + 61.4534i) q^{89} +(-168.557 - 112.626i) q^{90} +(1.73111 - 8.70285i) q^{91} +(-36.8469 + 24.6203i) q^{92} +(3.99184 + 9.63715i) q^{93} +(-220.157 + 91.1920i) q^{94} +(12.5482 + 18.7797i) q^{95} +(-35.3266 - 7.02689i) q^{96} +(13.6621 - 20.4467i) q^{97} +(27.1699 - 27.1699i) q^{98} +(66.0539 - 13.1389i) 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}+O(q^{10}) $ 8 * q + 8 * q^2 - 16 * q^5 - 8 * q^6 + 40 * q^7 + 40 * q^8 - 8 * q^9	\( 8 q + 8 q^{2} - 16 q^{5} - 8 q^{6} + 40 q^{7} + 40 q^{8} - 8 q^{9} - 48 q^{10} - 8 q^{11} + 72 q^{12} - 16 q^{13} + 104 q^{14} + 56 q^{18} + 48 q^{19} - 16 q^{20} + 64 q^{21} - 24 q^{22} + 56 q^{23} + 24 q^{24} + 32 q^{25} + 48 q^{26} - 24 q^{27} + 8 q^{28} - 128 q^{29} - 16 q^{30} - 40 q^{31} + 88 q^{32} - 160 q^{35} + 24 q^{36} - 96 q^{37} + 120 q^{38} - 96 q^{39} + 112 q^{40} - 48 q^{41} - 128 q^{42} + 112 q^{43} + 120 q^{44} - 112 q^{45} + 72 q^{46} - 192 q^{47} - 136 q^{48} + 80 q^{49} - 384 q^{52} + 128 q^{53} - 64 q^{54} - 224 q^{55} + 200 q^{56} + 48 q^{57} + 120 q^{59} - 48 q^{60} + 288 q^{61} + 8 q^{62} - 120 q^{63} + 64 q^{64} - 64 q^{65} + 96 q^{66} + 240 q^{69} - 480 q^{70} + 344 q^{71} - 40 q^{72} + 200 q^{73} - 208 q^{74} - 104 q^{75} - 160 q^{76} - 80 q^{77} - 512 q^{78} + 328 q^{79} + 64 q^{80} + 424 q^{81} - 64 q^{82} - 336 q^{83} + 832 q^{86} + 80 q^{87} + 8 q^{88} - 160 q^{89} - 224 q^{90} - 544 q^{91} + 24 q^{92} + 208 q^{93} - 432 q^{94} - 192 q^{95} + 64 q^{96} + 240 q^{97} + 120 q^{98} + 128 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{16}\right)$

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 $

$2$	2.79690	+	1.15851i	1.39845	+	0.579256i	0.949348	−	0.314225i	$-0.101745\pi$
$2$	2.79690	+	1.15851i	1.39845	+	0.579256i	0.449100	+	0.893481i	$0.351745\pi$
$3$	−0.158513	−	0.796897i	−0.0528376	−	0.265632i	0.945332	−	0.326109i	$-0.105738\pi$
$3$	−0.158513	−	0.796897i	−0.0528376	−	0.265632i	−0.998170	+	0.0604771i	$0.980738\pi$
$4$	3.65205	+	3.65205i	0.913014	+	0.913014i
$5$	−6.67619	−	4.46088i	−1.33524	−	0.892177i	−0.336464	−	0.941696i	$-0.609231\pi$
$5$	−6.67619	−	4.46088i	−1.33524	−	0.892177i	−0.998773	+	0.0495193i	$0.984231\pi$
$6$	0.479872	−	2.41248i	0.0799786	−	0.402080i
$7$	6.53073	−	4.36370i	0.932962	−	0.623385i	0.00658318	−	0.999978i	$-0.497904\pi$
$7$	6.53073	−	4.36370i	0.932962	−	0.623385i	0.926379	+	0.376593i	$0.122904\pi$
$8$	1.34942	+	3.25778i	0.168677	+	0.407223i
$9$	7.70500	−	3.19151i	0.856111	−	0.354613i
$10$	−13.5046	−	20.2111i	−1.35046	−	2.02111i
$11$	7.92030	+	1.57545i	0.720027	+	0.143222i	0.541486	−	0.840710i	$-0.317862\pi$
$11$	7.92030	+	1.57545i	0.720027	+	0.143222i	0.178542	+	0.983932i	$0.442862\pi$
$12$	2.33141	−	3.48921i	0.194285	−	0.290767i
$13$	0.798835	−	0.798835i	0.0614489	−	0.0614489i	−0.675715	−	0.737163i	$-0.736165\pi$
$13$	0.798835	−	0.798835i	0.0614489	−	0.0614489i	0.737163	+	0.675715i	$0.236165\pi$
$14$	23.3212	−	4.63887i	1.66580	−	0.331348i
$15$	−2.49661	+	6.02734i	−0.166440	+	0.401823i
$16$		−	9.98414i		−	0.624009i
$17$		0			0
$17$		0			0
$18$	25.2475			1.40264
$19$	−2.59882	−	1.07647i	−0.136780	−	0.0566561i	0.313244	−	0.949673i	$-0.398584\pi$
$19$	−2.59882	−	1.07647i	−0.136780	−	0.0566561i	−0.450023	+	0.893017i	$0.648584\pi$
$20$	−8.09040	−	40.6732i	−0.404520	−	2.03366i
$21$	−4.51262	−	4.51262i	−0.214887	−	0.214887i
$22$	20.3271	+	13.5821i	0.923958	+	0.617369i
$23$	−1.67393	+	8.41543i	−0.0727797	+	0.365888i	−0.999962	−	0.00872222i	$-0.997224\pi$
$23$	−1.67393	+	8.41543i	−0.0727797	+	0.365888i	0.927182	+	0.374611i	$0.122224\pi$
$24$	2.38222	−	1.59175i	0.0992590	−	0.0663228i
$25$	15.1049	+	36.4664i	0.604195	+	1.45866i
$26$	3.15972	−	1.30880i	0.121528	−	0.0503384i
$27$	−7.82730	−	11.7144i	−0.289900	−	0.433866i
$28$	39.7870	+	7.91414i	1.42097	+	0.282648i
$29$	−1.70587	+	2.55301i	−0.0588230	+	0.0880348i	−0.859715	−	0.510774i	$-0.829359\pi$
$29$	−1.70587	+	2.55301i	−0.0588230	+	0.0880348i	0.800892	+	0.598809i	$0.204359\pi$
$30$	−13.9655	+	13.9655i	−0.465517	+	0.465517i
$31$	−12.5915	+	2.50461i	−0.406179	+	0.0807940i	−0.393951	−	0.919131i	$-0.628892\pi$
$31$	−12.5915	+	2.50461i	−0.406179	+	0.0807940i	−0.0122273	+	0.999925i	$0.503892\pi$
$32$	16.9644	−	40.9557i	0.530138	−	1.27987i
$33$		−	6.56139i		−	0.198830i
$34$		0			0
$35$	−63.0663			−1.80190
$36$	39.7946	+	16.4835i	1.10541	+	0.457875i
$37$	4.61798	+	23.2161i	0.124810	+	0.627463i	0.991659	+	0.128892i	$0.0411420\pi$
$37$	4.61798	+	23.2161i	0.124810	+	0.627463i	−0.866848	+	0.498572i	$0.833858\pi$
$38$	−6.02153	−	6.02153i	−0.158461	−	0.158461i
$39$	−0.763215	−	0.509964i	−0.0195696	−	0.0130760i
$40$	5.52363	−	27.7692i	0.138091	−	0.694229i
$41$	−18.1595	+	12.1338i	−0.442914	+	0.295946i	−0.756959	−	0.653462i	$-0.773316\pi$
$41$	−18.1595	+	12.1338i	−0.442914	+	0.295946i	0.314045	+	0.949408i	$0.398316\pi$
$42$	−7.39341	−	17.8493i	−0.176034	−	0.424982i
$43$	21.4671	−	8.89197i	0.499235	−	0.206790i	−0.118833	−	0.992914i	$-0.537915\pi$
$43$	21.4671	−	8.89197i	0.499235	−	0.206790i	0.618069	+	0.786124i	$0.287915\pi$
$44$	23.1717	+	34.6790i	0.526631	+	0.788158i
$45$	−65.6770	−	13.0640i	−1.45949	−	0.290310i
$46$	−14.4312	+	21.5978i	−0.313722	+	0.469518i
$47$	−55.6597	+	55.6597i	−1.18425	+	1.18425i	−0.205617	+	0.978632i	$0.565920\pi$
$47$	−55.6597	+	55.6597i	−1.18425	+	1.18425i	−0.978632	+	0.205617i	$0.934080\pi$
$48$	−7.95633	+	1.58261i	−0.165757	+	0.0329711i
$49$	4.85715	−	11.7262i	0.0991254	−	0.239310i
$50$			119.492i			2.38984i
$51$		0			0
$52$	5.83478			0.112207
$53$	55.5080	+	22.9922i	1.04732	+	0.433815i	0.838935	−	0.544232i	$-0.183179\pi$
$53$	55.5080	+	22.9922i	1.04732	+	0.433815i	0.208386	+	0.978047i	$0.433179\pi$
$54$	−8.32089	−	41.8320i	−0.154091	−	0.774666i
$55$	−45.8495	−	45.8495i	−0.833627	−	0.833627i
$56$	23.0287	+	15.3873i	0.411226	+	0.274772i
$57$	−0.445887	+	2.24162i	−0.00782257	+	0.0393267i
$58$	−7.72882	+	5.16424i	−0.133256	+	0.0890385i
$59$	−10.5100	−	25.3733i	−0.178135	−	0.430057i	0.809440	−	0.587202i	$-0.199771\pi$
$59$	−10.5100	−	25.3733i	−0.178135	−	0.430057i	−0.987575	+	0.157146i	$0.949771\pi$
$60$	−31.1299	+	12.8944i	−0.518832	+	0.214907i
$61$	20.2562	+	30.3155i	0.332068	+	0.496976i	0.959505	−	0.281692i	$-0.0908957\pi$
$61$	20.2562	+	30.3155i	0.332068	+	0.496976i	−0.627436	+	0.778668i	$0.715896\pi$
$62$	−38.1189	−	7.58231i	−0.614820	−	0.122295i
$63$	36.3925	−	54.4652i	0.577658	−	0.864527i
$64$	66.6561	−	66.6561i	1.04150	−	1.04150i
$65$	−8.89668	+	1.76966i	−0.136872	+	0.0272255i
$66$	7.60145	−	18.3515i	0.115174	−	0.278054i
$67$		−	117.219i		−	1.74953i	−0.484544	−	0.874767i	$-0.661015\pi$
$67$		−	117.219i		−	1.74953i	0.484544	−	0.874767i	$-0.338985\pi$
$68$		0			0
$69$	6.97157			0.101037
$70$	−176.390	−	73.0632i	−2.51986	−	1.04376i
$71$	20.6737	+	103.934i	0.291179	+	1.46386i	0.798446	+	0.602067i	$0.205656\pi$
$71$	20.6737	+	103.934i	0.291179	+	1.46386i	−0.507266	+	0.861789i	$0.669344\pi$
$72$	20.7945	+	20.7945i	0.288813	+	0.288813i
$73$	50.7486	+	33.9091i	0.695186	+	0.464508i	0.852287	−	0.523074i	$-0.175215\pi$
$73$	50.7486	+	33.9091i	0.695186	+	0.464508i	−0.157101	+	0.987583i	$0.550215\pi$
$74$	−13.9802	+	70.2832i	−0.188921	+	0.949772i
$75$	26.6657	−	17.8174i	0.355542	−	0.237566i
$76$	−5.55971	−	13.4223i	−0.0731541	−	0.176610i
$77$	58.6001	−	24.2730i	0.761041	−	0.315233i
$78$	−1.54383	−	2.31051i	−0.0197927	−	0.0296219i
$79$	93.4553	+	18.5894i	1.18298	+	0.235309i	0.747109	−	0.664701i	$-0.231441\pi$
$79$	93.4553	+	18.5894i	1.18298	+	0.235309i	0.435869	+	0.900010i	$0.356441\pi$
$80$	−44.5381	+	66.6560i	−0.556726	+	0.833200i
$81$	44.9799	−	44.9799i	0.555308	−	0.555308i
$82$	−64.8474	+	12.8989i	−0.790821	+	0.157304i
$83$	−45.4770	+	109.791i	−0.547916	+	1.32279i	0.371110	+	0.928589i	$0.378977\pi$
$83$	−45.4770	+	109.791i	−0.547916	+	1.32279i	−0.919026	+	0.394197i	$0.871023\pi$
$84$		−	32.9607i		−	0.392389i
$85$		0			0
$86$	70.3428			0.817939
$87$	2.30489	+	0.954715i	0.0264929	+	0.0109737i
$88$	5.55533	+	27.9285i	0.0631288	+	0.317370i
$89$	61.4534	+	61.4534i	0.690488	+	0.690488i	0.962339	−	0.271851i	$-0.0876359\pi$
$89$	61.4534	+	61.4534i	0.690488	+	0.690488i	−0.271851	+	0.962339i	$0.587636\pi$
$90$	−168.557	−	112.626i	−1.87286	−	1.25140i
$91$	1.73111	−	8.70285i	0.0190231	−	0.0956357i
$92$	−36.8469	+	24.6203i	−0.400510	+	0.267612i
$93$	3.99184	+	9.63715i	0.0429230	+	0.103625i
$94$	−220.157	+	91.1920i	−2.34210	+	0.970128i
$95$	12.5482	+	18.7797i	0.132086	+	0.197681i
$96$	−35.3266	−	7.02689i	−0.367985	−	0.0731968i
$97$	13.6621	−	20.4467i	0.140846	−	0.210791i	−0.754340	−	0.656484i	$-0.772043\pi$
$97$	13.6621	−	20.4467i	0.140846	−	0.210791i	0.895186	+	0.445693i	$0.147043\pi$
$98$	27.1699	−	27.1699i	0.277244	−	0.277244i
$99$	66.0539	−	13.1389i	0.667211	−	0.132717i
$100$	−78.0135	+	188.341i	−0.780135	+	1.88341i
$101$			7.70266i			0.0762640i	0.999273	+	0.0381320i	$0.0121407\pi$
$101$			7.70266i			0.0762640i	−0.999273	+	0.0381320i	$0.987859\pi$
$102$		0			0
$103$	41.5688			0.403581			0.201790	−	0.979429i	$-0.435324\pi$
$103$	41.5688			0.403581			0.201790	+	0.979429i	$0.435324\pi$
$104$	3.68039	+	1.52447i	0.0353884	+	0.0146584i
$105$	9.99681	+	50.2574i	0.0952078	+	0.478642i
$106$	128.614	+	128.614i	1.21333	+	1.21333i
$107$	−73.5122	−	49.1193i	−0.687030	−	0.459059i	0.162424	−	0.986721i	$-0.448069\pi$
$107$	−73.5122	−	49.1193i	−0.687030	−	0.459059i	−0.849454	+	0.527662i	$0.823069\pi$
$108$	14.1958	−	71.3673i	0.131443	−	0.660808i
$109$	−15.4932	+	10.3522i	−0.142139	+	0.0949743i	−0.624607	−	0.780940i	$-0.714741\pi$
$109$	−15.4932	+	10.3522i	−0.142139	+	0.0949743i	0.482467	+	0.875914i	$0.339741\pi$
$110$	−75.1191	−	181.354i	−0.682901	−	1.64867i
$111$	17.7689	−	7.36011i	0.160080	−	0.0663073i
$112$	−43.5678	−	65.2038i	−0.388998	−	0.582176i
$113$	−59.4768	−	11.8307i	−0.526343	−	0.104696i	−0.0752358	−	0.997166i	$-0.523971\pi$
$113$	−59.4768	−	11.8307i	−0.526343	−	0.104696i	−0.451108	+	0.892470i	$0.648971\pi$
$114$	−3.84405	+	5.75303i	−0.0337197	+	0.0504651i
$115$	48.7158	−	48.7158i	0.423615	−	0.423615i
$116$	−15.5536	+	3.09381i	−0.134083	+	0.0266708i
$117$	3.60553	−	8.70452i	0.0308165	−	0.0743976i
$118$		−	83.1426i		−	0.704598i
$119$		0			0
$120$	−23.0047			−0.191706
$121$	−51.5403	−	21.3487i	−0.425953	−	0.176436i
$122$	21.5335	+	108.256i	0.176504	+	0.887347i
$123$	12.5479	+	12.5479i	0.102015	+	0.102015i
$124$	−55.1320	−	36.8380i	−0.444613	−	0.297081i
$125$	22.6681	−	113.960i	0.181345	−	0.911682i
$126$	164.885	−	110.172i	1.30861	−	0.874384i
$127$	45.6333	+	110.168i	0.359317	+	0.867468i	0.995396	+	0.0958444i	$0.0305551\pi$
$127$	45.6333	+	110.168i	0.359317	+	0.867468i	−0.636079	+	0.771624i	$0.719445\pi$
$128$	99.8291	−	41.3506i	0.779915	−	0.323051i
$129$	−10.4888	−	15.6976i	−0.0813085	−	0.121687i
$130$	−26.9333	−	5.35736i	−0.207179	−	0.0412105i
$131$	95.1830	−	142.451i	0.726588	−	1.08742i	−0.265772	−	0.964036i	$-0.585627\pi$
$131$	95.1830	−	142.451i	0.726588	−	1.08742i	0.992360	−	0.123380i	$-0.0393733\pi$
$132$	23.9626	−	23.9626i	0.181534	−	0.181534i
$133$	−21.6696	+	4.31034i	−0.162929	+	0.0324086i
$134$	135.799	−	327.849i	1.01343	−	2.44663i
$135$			113.124i			0.837956i
$136$		0			0
$137$	−173.113			−1.26360			−0.631799	−	0.775132i	$-0.717683\pi$
$137$	−173.113			−1.26360			−0.631799	+	0.775132i	$0.717683\pi$
$138$	19.4988	+	8.07666i	0.141295	+	0.0585265i
$139$	−35.0323	−	176.119i	−0.252031	−	1.26705i	−0.874740	−	0.484593i	$-0.838968\pi$
$139$	−35.0323	−	176.119i	−0.252031	−	1.26705i	0.622709	−	0.782454i	$-0.286032\pi$
$140$	−230.322	−	230.322i	−1.64515	−	1.64515i
$141$	53.1779	+	35.5323i	0.377148	+	0.252002i
$142$	−62.5864	+	314.643i	−0.440749	+	2.21579i
$143$	7.58553	−	5.06849i	0.0530457	−	0.0354440i
$144$	−31.8645	−	76.9278i	−0.221281	−	0.534221i
$145$	22.7774	−	9.43469i	0.157085	−	0.0650668i
$146$	102.654	+	153.633i	0.703112	+	1.05228i
$147$	−10.1145	−	2.01190i	−0.0688060	−	0.0136864i
$148$	−67.9215	+	101.652i	−0.458929	+	0.686836i
$149$	−31.6842	+	31.6842i	−0.212646	+	0.212646i	−0.805391	−	0.592745i	$-0.798044\pi$
$149$	−31.6842	+	31.6842i	−0.212646	+	0.212646i	0.592745	+	0.805391i	$0.298044\pi$
$150$	95.2228	−	18.9410i	0.634819	−	0.126273i
$151$	−50.2789	+	121.384i	−0.332973	+	0.803868i	0.665380	+	0.746504i	$0.268269\pi$
$151$	−50.2789	+	121.384i	−0.332973	+	0.803868i	−0.998353	+	0.0573634i	$0.981731\pi$
$152$		−	9.91898i		−	0.0652565i
$153$		0			0
$154$	192.019			1.24688
$155$	95.2363	+	39.4482i	0.614428	+	0.254504i
$156$	−0.924886	−	4.64972i	−0.00592876	−	0.0298059i
$157$	−25.4694	−	25.4694i	−0.162225	−	0.162225i	0.621327	−	0.783552i	$-0.286594\pi$
$157$	−25.4694	−	25.4694i	−0.162225	−	0.162225i	−0.783552	+	0.621327i	$0.786594\pi$
$158$	239.849	+	160.262i	1.51803	+	1.01432i
$159$	9.52367	−	47.8787i	0.0598973	−	0.301124i
$160$	−295.956	+	197.752i	−1.84973	+	1.23595i
$161$	25.7904	+	62.2635i	0.160189	+	0.386730i
$162$	177.914	−	73.6944i	1.09823	−	0.454904i
$163$	88.7349	+	132.801i	0.544386	+	0.814731i	0.997034	−	0.0769579i	$-0.0245207\pi$
$163$	88.7349	+	132.801i	0.544386	+	0.814731i	−0.452648	+	0.891689i	$0.649521\pi$
$164$	−110.633	−	22.0062i	−0.674589	−	0.134184i
$165$	−29.2696	+	43.8051i	−0.177392	+	0.265485i
$166$	−254.389	+	254.389i	−1.53246	+	1.53246i
$167$	−108.608	+	21.6035i	−0.650347	+	0.129362i	−0.509229	−	0.860631i	$-0.670070\pi$
$167$	−108.608	+	21.6035i	−0.650347	+	0.129362i	−0.141117	+	0.989993i	$0.545070\pi$
$168$	8.61173	−	20.7905i	0.0512603	−	0.123753i
$169$			167.724i			0.992448i
$170$		0			0
$171$	−23.4594			−0.137190
$172$	110.873	+	45.9251i	0.644611	+	0.267006i
$173$	−34.7367	−	174.633i	−0.200790	−	1.00944i	−0.941346	−	0.337444i	$-0.890438\pi$
$173$	−34.7367	−	174.633i	−0.200790	−	1.00944i	0.740556	−	0.671995i	$-0.234562\pi$
$174$	5.34048	+	5.34048i	0.0306924	+	0.0306924i
$175$	257.774	+	172.239i	1.47300	+	0.984224i
$176$	15.7295	−	79.0774i	0.0893720	−	0.449303i
$177$	−18.5540	+	12.3974i	−0.104825	+	0.0700417i
$178$	100.684	+	243.074i	0.565642	+	1.36558i
$179$	−232.978	+	96.5028i	−1.30155	+	0.539122i	−0.922409	−	0.386215i	$-0.873782\pi$
$179$	−232.978	+	96.5028i	−1.30155	+	0.539122i	−0.379146	+	0.925337i	$0.623782\pi$
$180$	−192.146	−	287.566i	−1.06748	−	1.59759i
$181$	295.559	+	58.7904i	1.63292	+	0.324809i	0.924559	−	0.381038i	$-0.124433\pi$
$181$	295.559	+	58.7904i	1.63292	+	0.324809i	0.708365	+	0.705847i	$0.249433\pi$
$182$	14.9241	−	22.3355i	0.0820005	−	0.122722i
$183$	20.9475	−	20.9475i	0.114467	−	0.114467i
$184$	−29.6745	+	5.90262i	−0.161274	+	0.0320795i
$185$	72.7341	−	175.596i	0.393157	−	0.949165i
$186$			31.5787i			0.169778i
$187$		0			0
$188$	−406.545			−2.16247
$189$	−102.236	−	42.3476i	−0.540931	−	0.224061i
$190$	13.3395	+	67.0622i	0.0702079	+	0.352959i
$191$	−93.7287	−	93.7287i	−0.490726	−	0.490726i	0.417809	−	0.908535i	$-0.362798\pi$
$191$	−93.7287	−	93.7287i	−0.490726	−	0.490726i	−0.908535	+	0.417809i	$0.862798\pi$
$192$	−63.6839	−	42.5522i	−0.331687	−	0.221626i
$193$	62.1584	−	312.491i	0.322064	−	1.61913i	−0.392635	−	0.919694i	$-0.628436\pi$
$193$	62.1584	−	312.491i	0.322064	−	1.61913i	0.714699	−	0.699432i	$-0.246564\pi$
$194$	61.8991	−	41.3597i	0.319068	−	0.213194i
$195$	2.82047	+	6.80923i	0.0144640	+	0.0349191i
$196$	60.5632	−	25.0861i	0.308996	−	0.127990i
$197$	64.2597	+	96.1714i	0.326191	+	0.488180i	0.957930	−	0.287002i	$-0.0926585\pi$
$197$	64.2597	+	96.1714i	0.326191	+	0.488180i	−0.631739	+	0.775181i	$0.717659\pi$
$198$	199.968	+	39.7760i	1.00994	+	0.200889i
$199$	−164.363	+	245.987i	−0.825944	+	1.23611i	0.143218	+	0.989691i	$0.454255\pi$
$199$	−164.363	+	245.987i	−0.825944	+	1.23611i	−0.969163	+	0.246422i	$0.920745\pi$
$200$	−98.4168	+	98.4168i	−0.492084	+	0.492084i
$201$	−93.4113	+	18.5807i	−0.464733	+	0.0924411i
$202$	−8.92363	+	21.5436i	−0.0441764	+	0.106651i
$203$			24.1169i			0.118802i
$204$		0			0
$205$	175.364			0.855432
$206$	116.264	+	48.1580i	0.564387	+	0.233777i
$207$	13.9603	+	70.1833i	0.0674412	+	0.339050i
$208$	−7.97568	−	7.97568i	−0.0383446	−	0.0383446i
$209$	−18.8875	−	12.6202i	−0.0903708	−	0.0603839i
$210$	−30.2638	+	152.146i	−0.144113	+	0.724505i
$211$	191.021	−	127.636i	0.905315	−	0.604912i	−0.0133670	−	0.999911i	$-0.504255\pi$
$211$	191.021	−	127.636i	0.905315	−	0.604912i	0.918682	+	0.394999i	$0.129255\pi$
$212$	118.750	+	286.687i	0.560140	+	1.35230i
$213$	79.5475	−	32.9496i	0.373462	−	0.154693i
$214$	−148.701	−	222.546i	−0.694863	−	1.03994i
$215$	−182.985	−	36.3979i	−0.851091	−	0.169292i
$216$	27.6006	−	41.3072i	0.127781	−	0.191237i
$217$	−71.3026	+	71.3026i	−0.328584	+	0.328584i
$218$	−55.3260	+	11.0050i	−0.253789	+	0.0504817i
$219$	18.9778	−	45.8164i	0.0866565	−	0.209207i
$220$		−	334.890i		−	1.52223i
$221$		0			0
$222$	58.2245			0.262272
$223$	335.723	+	139.061i	1.50549	+	0.623593i	0.974621	−	0.223863i	$-0.0718669\pi$
$223$	335.723	+	139.061i	1.50549	+	0.623593i	0.530865	+	0.847456i	$0.321867\pi$
$224$	−67.9283	−	341.499i	−0.303251	−	1.52455i
$225$	232.766	+	232.766i	1.03452	+	1.03452i
$226$	−152.645	−	101.994i	−0.675418	−	0.451300i
$227$	−18.9088	+	95.0611i	−0.0832988	+	0.418772i	0.916525	+	0.399978i	$0.130982\pi$
$227$	−18.9088	+	95.0611i	−0.0832988	+	0.418772i	−0.999823	+	0.0187931i	$0.994018\pi$
$228$	−9.81493	+	6.55813i	−0.0430480	+	0.0287637i
$229$	−138.397	−	334.120i	−0.604353	−	1.45904i	−0.869059	−	0.494708i	$-0.835275\pi$
$229$	−138.397	−	334.120i	−0.604353	−	1.45904i	0.264706	−	0.964329i	$-0.414725\pi$
$230$	192.691	−	79.8152i	0.837786	−	0.347022i
$231$	−28.6319	−	42.8507i	−0.123948	−	0.185501i
$232$	−10.6191	−	2.11226i	−0.0457719	−	0.00910459i
$233$	155.642	−	232.935i	0.667991	−	0.999720i	−0.330445	−	0.943825i	$-0.607199\pi$
$233$	155.642	−	232.935i	0.667991	−	0.999720i	0.998437	−	0.0558946i	$-0.0178011\pi$
$234$	20.1686	−	20.1686i	0.0861905	−	0.0861905i
$235$	619.886	−	123.303i	2.63781	−	0.524694i
$236$	54.2818	−	131.048i	0.230008	−	0.555288i
$237$		−	77.4209i		−	0.326670i
$238$		0			0
$239$	328.551			1.37469			0.687345	−	0.726331i	$-0.258776\pi$
$239$	328.551			1.37469			0.687345	+	0.726331i	$0.258776\pi$
$240$	60.1778	+	24.9265i	0.250741	+	0.103860i
$241$	−47.2927	−	237.756i	−0.196235	−	0.986541i	−0.945835	−	0.324649i	$-0.894754\pi$
$241$	−47.2927	−	237.756i	−0.196235	−	0.986541i	0.749599	−	0.661892i	$-0.230246\pi$
$242$	−119.420	−	119.420i	−0.493472	−	0.493472i
$243$	−148.404	−	99.1602i	−0.610715	−	0.408067i
$244$	−36.7372	+	184.691i	−0.150562	+	0.756928i
$245$	−84.7364	+	56.6190i	−0.345863	+	0.231098i
$246$	20.5583	+	49.6320i	0.0835701	+	0.201756i
$247$	−2.93595	+	1.21611i	−0.0118864	+	0.00492352i
$248$	−25.1507	−	37.6407i	−0.101414	−	0.151777i
$249$	94.7010	+	18.8372i	0.380325	+	0.0756514i
$250$	195.425	−	292.474i	0.781699	−	1.16989i
$251$	155.463	−	155.463i	0.619375	−	0.619375i	−0.325996	−	0.945371i	$-0.605700\pi$
$251$	155.463	−	155.463i	0.619375	−	0.619375i	0.945371	+	0.325996i	$0.105700\pi$
$252$	331.817	−	66.0025i	1.31673	−	0.261915i
$253$	−26.5161	+	64.0155i	−0.104807	+	0.253026i
$254$			360.996i			1.42125i
$255$		0			0
$256$	−49.9468			−0.195105
$257$	−300.480	−	124.463i	−1.16918	−	0.484292i	−0.288261	−	0.957552i	$-0.593077\pi$
$257$	−300.480	−	124.463i	−1.16918	−	0.484292i	−0.880923	+	0.473260i	$0.843077\pi$
$258$	−11.1502	−	56.0559i	−0.0432179	−	0.217271i
$259$	131.467	+	131.467i	0.507595	+	0.507595i
$260$	−38.9541	−	26.0283i	−0.149823	−	0.100109i
$261$	−4.99573	+	25.1152i	−0.0191407	+	0.0962269i
$262$	431.249	−	288.151i	1.64599	−	1.09981i
$263$	53.0907	+	128.172i	0.201866	+	0.487347i	0.992099	−	0.125460i	$-0.0400405\pi$
$263$	53.0907	+	128.172i	0.201866	+	0.487347i	−0.790233	+	0.612806i	$0.790041\pi$
$264$	21.3756	−	8.85405i	0.0809681	−	0.0335381i
$265$	−268.016	−	401.115i	−1.01138	−	1.51364i
$266$	−65.6011	−	13.0489i	−0.246621	−	0.0490559i
$267$	39.2309	−	58.7132i	0.146932	−	0.219900i
$268$	428.089	−	428.089i	1.59735	−	1.59735i
$269$	−318.636	+	63.3806i	−1.18452	+	0.235615i	−0.747764	−	0.663965i	$-0.768872\pi$
$269$	−318.636	+	63.3806i	−1.18452	+	0.235615i	−0.436755	+	0.899580i	$0.643872\pi$
$270$	−131.056	+	316.396i	−0.485391	+	1.17184i
$271$			19.1867i			0.0707996i	0.999373	+	0.0353998i	$0.0112705\pi$
$271$			19.1867i			0.0707996i	−0.999373	+	0.0353998i	$0.988730\pi$
$272$		0			0
$273$	−7.20968			−0.0264091
$274$	−484.179	−	200.554i	−1.76708	−	0.731947i
$275$	62.1843	+	312.622i	0.226125	+	1.13681i
$276$	25.4606	+	25.4606i	0.0922484	+	0.0922484i
$277$	−256.095	−	171.117i	−0.924529	−	0.617751i	−0.000470113	−	1.00000i	$-0.500150\pi$
$277$	−256.095	−	171.117i	−0.924529	−	0.617751i	−0.924059	+	0.382249i	$0.875150\pi$
$278$	106.055	−	533.173i	0.381492	−	1.91789i
$279$	−89.0243	+	59.4841i	−0.319083	+	0.213205i
$280$	−85.1028	−	205.456i	−0.303939	−	0.733773i
$281$	79.9361	−	33.1106i	0.284470	−	0.117831i	−0.235886	−	0.971781i	$-0.575799\pi$
$281$	79.9361	−	33.1106i	0.284470	−	0.117831i	0.520356	+	0.853949i	$0.325799\pi$
$282$	107.568	+	160.987i	0.381448	+	0.570877i
$283$	7.33785	+	1.45959i	0.0259288	+	0.00515756i	0.208038	−	0.978121i	$-0.433292\pi$
$283$	7.33785	+	1.45959i	0.0259288	+	0.00515756i	−0.182109	+	0.983278i	$0.558292\pi$
$284$	−304.070	+	455.073i	−1.07067	+	1.60237i
$285$	12.9764	−	12.9764i	0.0455314	−	0.0455314i
$286$	27.0879	−	5.38811i	0.0947128	−	0.0188396i
$287$	−65.6466	+	158.485i	−0.228734	+	0.552213i
$288$		−	369.706i		−	1.28370i
$289$		0			0
$290$	74.6361			0.257366
$291$	−18.4595	−	7.64619i	−0.0634348	−	0.0262756i
$292$	61.4986	+	309.174i	0.210612	+	1.05882i
$293$	−54.4583	−	54.4583i	−0.185864	−	0.185864i	0.608041	−	0.793906i	$-0.291956\pi$
$293$	−54.4583	−	54.4583i	−0.185864	−	0.185864i	−0.793906	+	0.608041i	$0.791956\pi$
$294$	−25.9584	−	17.3448i	−0.0882937	−	0.0589960i
$295$	−43.0210	+	216.281i	−0.145834	+	0.733156i
$296$	−69.4016	+	46.3726i	−0.234465	+	0.156664i
$297$	−43.5392	−	105.113i	−0.146597	−	0.353915i
$298$	−125.324	+	51.9110i	−0.420551	+	0.174198i
$299$	5.38535	+	8.05974i	0.0180112	+	0.0269557i
$300$	162.455	+	32.3142i	0.541515	+	0.107714i
$301$	101.394	−	151.747i	0.336858	−	0.504143i
$302$	−281.250	+	281.250i	−0.931291	+	0.931291i
$303$	6.13823	−	1.22097i	0.0202582	−	0.00402960i
$304$	−10.7476	+	25.9470i	−0.0353539	+	0.0853519i
$305$		−	292.752i		−	0.959844i
$306$		0			0
$307$	−159.680			−0.520132			−0.260066	−	0.965591i	$-0.583744\pi$
$307$	−159.680			−0.520132			−0.260066	+	0.965591i	$0.583744\pi$
$308$	302.657	+	125.365i	0.982653	+	0.407028i
$309$	−6.58918	−	33.1261i	−0.0213242	−	0.107204i
$310$	220.665	+	220.665i	0.711822	+	0.711822i
$311$	276.891	+	185.013i	0.890324	+	0.594896i	0.914399	−	0.404814i	$-0.132664\pi$
$311$	276.891	+	185.013i	0.890324	+	0.594896i	−0.0240745	+	0.999710i	$0.507664\pi$
$312$	0.631456	−	3.17454i	0.00202390	−	0.0101748i
$313$	−328.071	+	219.210i	−1.04815	+	0.700351i	−0.955393	−	0.295338i	$-0.904568\pi$
$313$	−328.071	+	219.210i	−1.04815	+	0.700351i	−0.0927565	+	0.995689i	$0.529568\pi$
$314$	−41.7286	−	100.742i	−0.132894	−	0.320834i
$315$	−485.926	+	201.277i	−1.54262	+	0.638975i
$316$	273.414	+	409.193i	0.865235	+	1.29492i
$317$	−136.423	−	27.1362i	−0.430357	−	0.0856033i	−0.0248412	−	0.999691i	$-0.507908\pi$
$317$	−136.423	−	27.1362i	−0.430357	−	0.0856033i	−0.405516	+	0.914088i	$0.632908\pi$
$318$	82.1048	−	122.879i	0.258191	−	0.386411i
$319$	−17.5331	+	17.5331i	−0.0549627	+	0.0549627i
$320$	−742.353	+	147.663i	−2.31985	+	0.461448i
$321$	−27.4904	+	66.3677i	−0.0856399	+	0.206753i
$322$			204.023i			0.633612i
$323$		0			0
$324$	328.538			1.01401
$325$	41.1970	+	17.0643i	0.126760	+	0.0525057i
$326$	94.3306	+	474.232i	0.289358	+	1.45470i
$327$	10.7055	+	10.7055i	0.0327385	+	0.0327385i
$328$	−64.0340	−	42.7861i	−0.195225	−	0.130445i
$329$	−120.617	+	606.381i	−0.366616	+	1.84310i
$330$	−132.613	+	88.6090i	−0.401857	+	0.268512i
$331$	60.7720	+	146.717i	0.183601	+	0.443252i	0.988704	−	0.149883i	$-0.0478898\pi$
$331$	60.7720	+	146.717i	0.183601	+	0.443252i	−0.805103	+	0.593136i	$0.797890\pi$
$332$	−567.048	+	234.879i	−1.70798	+	0.707467i
$333$	109.676	+	164.142i	0.329358	+	0.492919i
$334$	−328.793	−	65.4010i	−0.984410	−	0.195811i
$335$	−522.899	+	782.574i	−1.56089	+	2.33604i
$336$	−45.0546	+	45.0546i	−0.134091	+	0.134091i
$337$	−473.084	+	94.1023i	−1.40381	+	0.279235i	−0.838167	−	0.545414i	$-0.816372\pi$
$337$	−473.084	+	94.1023i	−1.40381	+	0.279235i	−0.565644	+	0.824649i	$0.691372\pi$
$338$	−194.310	+	469.106i	−0.574882	+	1.38789i
$339$			49.2722i			0.145346i
$340$		0			0
$341$	−103.675			−0.304031
$342$	−65.6136	−	27.1781i	−0.191853	−	0.0794680i
$343$	55.6352	+	279.697i	0.162202	+	0.815443i
$344$	57.9362	+	57.9362i	0.168419	+	0.168419i
$345$	−46.5435	−	31.0994i	−0.134909	−	0.0901431i
$346$	105.160	−	528.673i	0.303930	−	1.52796i
$347$	16.4546	−	10.9946i	0.0474197	−	0.0316848i	−0.531634	−	0.846974i	$-0.678422\pi$
$347$	16.4546	−	10.9946i	0.0474197	−	0.0316848i	0.579054	+	0.815289i	$0.303422\pi$
$348$	4.93090	+	11.9042i	0.0141692	+	0.0342076i
$349$	361.651	−	149.801i	1.03625	−	0.429229i	0.201286	−	0.979533i	$-0.435488\pi$
$349$	361.651	−	149.801i	1.03625	−	0.429229i	0.834965	+	0.550304i	$0.185488\pi$
$350$	521.427	+	780.370i	1.48979	+	2.22963i
$351$	−15.6106	−	3.10514i	−0.0444746	−	0.00884655i
$352$	198.887	−	297.655i	0.565019	−	0.845611i
$353$	−138.024	+	138.024i	−0.391003	+	0.391003i	−0.875045	−	0.484042i	$-0.839168\pi$
$353$	−138.024	+	138.024i	−0.391003	+	0.391003i	0.484042	+	0.875045i	$0.339168\pi$
$354$	−66.2561	+	13.1792i	−0.187164	+	0.0372293i
$355$	325.615	−	786.104i	0.917226	−	2.21438i
$356$			448.863i			1.26085i
$357$		0			0
$358$	−763.416			−2.13245
$359$	−328.726	−	136.163i	−0.915672	−	0.379284i	−0.125447	−	0.992100i	$-0.540036\pi$
$359$	−328.726	−	136.163i	−0.915672	−	0.379284i	−0.790225	+	0.612817i	$0.790036\pi$
$360$	−46.0661	−	231.590i	−0.127961	−	0.643306i
$361$	−249.670	−	249.670i	−0.691608	−	0.691608i
$362$	758.539	+	506.840i	2.09541	+	1.40011i
$363$	−8.84292	+	44.4564i	−0.0243607	+	0.122469i
$364$	38.1054	−	25.4612i	0.104685	−	0.0699484i
$365$	−187.542	−	452.767i	−0.513814	−	1.24046i
$366$	82.8558	−	34.3200i	0.226382	−	0.0937705i
$367$	−45.4052	−	67.9537i	−0.123720	−	0.185160i	0.764439	−	0.644696i	$-0.223016\pi$
$367$	−45.4052	−	67.9537i	−0.123720	−	0.185160i	−0.888159	+	0.459536i	$0.848016\pi$
$368$	84.0209	+	16.7128i	0.228318	+	0.0454152i
$369$	−101.194	+	151.447i	−0.274238	+	0.410426i
$370$	406.859	−	406.859i	1.09962	−	1.09962i
$371$	462.839	−	92.0644i	1.24754	−	0.248152i
$372$	−20.6170	+	49.7738i	−0.0554220	+	0.133801i
$373$			76.8209i			0.205954i	0.994684	+	0.102977i	$0.0328368\pi$
$373$			76.8209i			0.205954i	−0.994684	+	0.102977i	$0.967163\pi$
$374$		0			0
$375$	−94.4077			−0.251754
$376$	−256.436	−	106.219i	−0.682009	−	0.282498i
$377$	0.676727	+	3.40214i	0.00179503	+	0.00902424i
$378$	−236.883	−	236.883i	−0.626676	−	0.626676i
$379$	−489.954	−	327.377i	−1.29275	−	0.863791i	−0.296914	−	0.954904i	$-0.595957\pi$
$379$	−489.954	−	327.377i	−1.29275	−	0.863791i	−0.995841	+	0.0911132i	$0.970957\pi$
$380$	−22.7578	+	114.411i	−0.0598890	+	0.301082i
$381$	80.5594	−	53.8281i	0.211442	−	0.141281i
$382$	−153.564	−	370.735i	−0.401999	−	0.970511i
$383$	215.834	−	89.4016i	0.563537	−	0.233424i	−0.0826832	−	0.996576i	$-0.526349\pi$
$383$	215.834	−	89.4016i	0.563537	−	0.233424i	0.646220	+	0.763151i	$0.276349\pi$
$384$	−48.7763	−	72.9989i	−0.127022	−	0.190101i
$385$	−499.504	−	99.3576i	−1.29741	−	0.258072i
$386$	535.876	−	801.995i	1.38828	−	2.07771i
$387$	137.025	−	137.025i	0.354070	−	0.354070i
$388$	124.567	−	24.7779i	0.321049	−	0.0638606i
$389$	154.467	−	372.916i	0.397087	−	0.958653i	−0.591266	−	0.806477i	$-0.701372\pi$
$389$	154.467	−	372.916i	0.397087	−	0.958653i	0.988353	−	0.152177i	$-0.0486283\pi$
$390$			22.3123i			0.0572109i
$391$		0			0
$392$	44.7557			0.114173
$393$	−128.607	−	53.2707i	−0.327244	−	0.135549i
$394$	68.3119	+	343.427i	0.173380	+	0.871642i
$395$	−541.000	−	541.000i	−1.36962	−	1.36962i
$396$	289.217	+	193.248i	0.730345	+	0.488001i
$397$	51.4626	−	258.720i	0.129629	−	0.651688i	−0.860262	−	0.509853i	$-0.829700\pi$
$397$	51.4626	−	258.720i	0.129629	−	0.651688i	0.989890	−	0.141835i	$-0.0453002\pi$
$398$	−744.685	+	497.582i	−1.87107	+	1.25021i
$399$	6.86980	+	16.5852i	0.0172175	+	0.0415668i
$400$	364.086	−	150.809i	0.910214	−	0.377023i
$401$	132.942	+	198.962i	0.331526	+	0.496164i	0.959361	−	0.282183i	$-0.0910586\pi$
$401$	132.942	+	198.962i	0.331526	+	0.496164i	−0.627835	+	0.778347i	$0.716059\pi$
$402$	−282.788	−	56.2499i	−0.703452	−	0.139925i
$403$	−8.05779	+	12.0593i	−0.0199945	+	0.0299239i
$404$	−28.1305	+	28.1305i	−0.0696300	+	0.0696300i
$405$	−500.945	+	99.6441i	−1.23690	+	0.246035i
$406$	−27.9397	+	67.4525i	−0.0688171	+	0.166139i
$407$			191.154i			0.469666i
$408$		0			0
$409$	259.903			0.635461			0.317730	−	0.948181i	$-0.397079\pi$
$409$	259.903			0.635461			0.317730	+	0.948181i	$0.397079\pi$
$410$	490.474	+	203.161i	1.19628	+	0.495514i
$411$	27.4406	+	137.953i	0.0667654	+	0.335652i
$412$	151.812	+	151.812i	0.368475	+	0.368475i
$413$	−179.360	−	119.844i	−0.434285	−	0.290180i
$414$	−42.2626	+	212.469i	−0.102084	+	0.513209i
$415$	793.379	−	530.119i	1.91176	−	1.27740i
$416$	−19.1651	−	46.2687i	−0.0460700	−	0.111223i
$417$	−134.796	+	55.8343i	−0.323252	+	0.133895i
$418$	−38.2057	−	57.1789i	−0.0914012	−	0.136792i
$419$	−168.255	−	33.4680i	−0.401563	−	0.0798758i	−0.00982284	−	0.999952i	$-0.503127\pi$
$419$	−168.255	−	33.4680i	−0.401563	−	0.0798758i	−0.391740	+	0.920076i	$0.628127\pi$
$420$	−147.034	+	220.052i	−0.350080	+	0.523932i
$421$	−443.214	+	443.214i	−1.05276	+	1.05276i	−0.0542356	+	0.998528i	$0.517272\pi$
$421$	−443.214	+	443.214i	−1.05276	+	1.05276i	−0.998528	+	0.0542356i	$0.982728\pi$
$422$	682.136	−	135.685i	1.61644	−	0.321529i
$423$	−251.219	+	606.497i	−0.593899	+	1.43380i
$424$			211.859i			0.499668i
$425$		0			0
$426$	260.659			0.611875
$427$	264.575	+	109.591i	0.619614	+	0.256653i
$428$	−89.0843	−	447.857i	−0.208141	−	1.04639i
$429$	−5.24147	−	5.24147i	−0.0122179	−	0.0122179i
$430$	−469.621	−	313.791i	−1.09214	−	0.729747i
$431$	−148.695	+	747.540i	−0.345000	+	1.73443i	0.285623	+	0.958342i	$0.407799\pi$
$431$	−148.695	+	747.540i	−0.345000	+	1.73443i	−0.630623	+	0.776089i	$0.717201\pi$
$432$	−116.958	+	78.1489i	−0.270736	+	0.180900i
$433$	36.2305	+	87.4681i	0.0836732	+	0.202005i	0.960179	−	0.279387i	$-0.0901313\pi$
$433$	36.2305	+	87.4681i	0.0836732	+	0.202005i	−0.876505	+	0.481392i	$0.840131\pi$
$434$	−282.031	+	116.821i	−0.649841	+	0.269173i
$435$	−11.1290	−	16.6557i	−0.0255839	−	0.0382889i
$436$	−94.3887	−	18.7751i	−0.216488	−	0.0430621i
$437$	13.4092	−	20.0682i	0.0306846	−	0.0459228i
$438$	106.158	−	106.158i	0.242369	−	0.242369i
$439$	−36.2679	+	7.21414i	−0.0826149	+	0.0164331i	−0.236225	−	0.971698i	$-0.575910\pi$
$439$	−36.2679	+	7.21414i	−0.0826149	+	0.0164331i	0.153610	+	0.988132i	$0.450910\pi$
$440$	87.4976	−	211.238i	0.198858	−	0.480086i
$441$		−	105.852i		−	0.240027i
$442$		0			0
$443$	−634.146			−1.43148			−0.715740	−	0.698367i	$-0.753911\pi$
$443$	−634.146			−1.43148			−0.715740	+	0.698367i	$0.753911\pi$
$444$	91.7724	+	38.0134i	0.206695	+	0.0856157i
$445$	−136.138	−	684.411i	−0.305928	−	1.53800i
$446$	777.880	+	777.880i	1.74412	+	1.74412i
$447$	30.2714	+	20.2267i	0.0677213	+	0.0452499i
$448$	144.446	−	726.180i	0.322424	−	1.62094i
$449$	−367.365	+	245.465i	−0.818184	+	0.546693i	−0.892765	−	0.450522i	$-0.851238\pi$
$449$	−367.365	+	245.465i	−0.818184	+	0.546693i	0.0745814	+	0.997215i	$0.476238\pi$
$450$	381.360	+	920.685i	0.847468	+	2.04597i
$451$	−162.945	+	67.4939i	−0.361296	+	0.149654i
$452$	−174.006	−	260.419i	−0.384970	−	0.576148i
$453$	104.700	+	20.8262i	0.231127	+	0.0459740i
$454$	−163.016	+	243.970i	−0.359065	+	0.537379i
$455$	−50.3796	+	50.3796i	−0.110724	+	0.110724i
$456$	−7.90441	+	1.57228i	−0.0173342	+	0.00344799i
$457$	102.104	−	246.501i	0.223423	−	0.539390i	−0.771928	−	0.635710i	$-0.780707\pi$
$457$	102.104	−	246.501i	0.223423	−	0.539390i	0.995350	+	0.0963202i	$0.0307073\pi$
$458$		−	1094.83i		−	2.39046i
$459$		0			0
$460$	355.825			0.773533
$461$	−417.100	−	172.768i	−0.904772	−	0.374769i	−0.118719	−	0.992928i	$-0.537879\pi$
$461$	−417.100	−	172.768i	−0.904772	−	0.374769i	−0.786053	+	0.618159i	$0.787879\pi$
$462$	−30.4375	−	153.019i	−0.0658819	−	0.331211i
$463$	57.1171	+	57.1171i	0.123363	+	0.123363i	0.766093	−	0.642730i	$-0.222198\pi$
$463$	57.1171	+	57.1171i	0.123363	+	0.123363i	−0.642730	+	0.766093i	$0.722198\pi$
$464$	25.4896	+	17.0316i	0.0549345	+	0.0367060i
$465$	16.3400	−	82.1465i	0.0351397	−	0.176659i
$466$	705.172	−	471.181i	1.51325	−	1.01112i
$467$	31.5580	+	76.1879i	0.0675761	+	0.163143i	0.954059	−	0.299617i	$-0.0968590\pi$
$467$	31.5580	+	76.1879i	0.0675761	+	0.163143i	−0.886483	+	0.462760i	$0.846859\pi$
$468$	44.9569	−	18.6218i	0.0960619	−	0.0397901i
$469$	−511.507	−	765.524i	−1.09063	−	1.63225i
$470$	1876.61	+	373.280i	3.99278	+	0.794213i
$471$	−16.2592	+	24.3337i	−0.0345207	+	0.0516638i
$472$	68.4785	−	68.4785i	0.145082	−	0.145082i
$473$	184.035	−	36.6068i	0.389080	−	0.0773928i
$474$	89.6931	−	216.538i	0.189226	−	0.456832i
$475$		−	111.029i		−	0.233746i
$476$		0			0
$477$	501.069			1.05046
$478$	918.923	+	380.630i	1.92243	+	0.796298i
$479$	89.8162	+	451.536i	0.187508	+	0.942665i	0.953862	+	0.300246i	$0.0970689\pi$
$479$	89.8162	+	451.536i	0.187508	+	0.942665i	−0.766354	+	0.642418i	$0.777931\pi$
$480$	204.501	+	204.501i	0.426043	+	0.426043i
$481$	22.2349	+	14.8569i	0.0462264	+	0.0308875i
$482$	143.171	−	719.769i	0.297035	−	1.49330i
$483$	45.5295	−	30.4218i	0.0942639	−	0.0629852i
$484$	−110.261	−	266.195i	−0.227813	−	0.549989i
$485$	−182.421	+	75.5612i	−0.376125	+	0.155796i
$486$	−300.192	−	449.268i	−0.617678	−	0.924421i
$487$	513.097	+	102.061i	1.05359	+	0.209571i	0.691354	−	0.722516i	$-0.257015\pi$
$487$	513.097	+	102.061i	1.05359	+	0.209571i	0.362233	+	0.932088i	$0.382015\pi$
$488$	−71.4273	+	106.898i	−0.146367	+	0.219054i
$489$	91.7633	−	91.7633i	0.187655	−	0.187655i
$490$	−302.593	+	60.1894i	−0.617536	+	0.122836i
$491$	−187.167	+	451.862i	−0.381196	+	0.920289i	0.610539	+	0.791986i	$0.290953\pi$
$491$	−187.167	+	451.862i	−0.381196	+	0.920289i	−0.991735	+	0.128303i	$0.959047\pi$
$492$			91.6511i			0.186283i
$493$		0			0
$494$	−9.62041			−0.0194745
$495$	−499.600	−	206.941i	−1.00929	−	0.418063i
$496$	25.0064	+	125.716i	0.0504161	+	0.253459i
$497$	588.550	+	588.550i	1.18421	+	1.18421i
$498$	243.046	+	162.398i	0.488044	+	0.326100i
$499$	−98.9237	+	497.323i	−0.198244	+	0.996639i	0.745637	+	0.666353i	$0.232145\pi$
$499$	−98.9237	+	497.323i	−0.198244	+	0.996639i	−0.943881	+	0.330287i	$0.892855\pi$
$500$	498.974	−	333.404i	0.997948	−	0.666807i
$501$	34.4315	+	83.1249i	0.0687255	+	0.165918i
$502$	614.921	−	254.709i	1.22494	−	0.507388i
$503$	−374.700	−	560.779i	−0.744931	−	1.11487i	−0.989401	−	0.145211i	$-0.953614\pi$
$503$	−374.700	−	560.779i	−0.744931	−	1.11487i	0.244470	−	0.969657i	$-0.421386\pi$
$504$	226.544	+	45.0625i	0.449493	+	0.0894097i
$505$	34.3607	−	51.4244i	0.0680410	−	0.101831i
$506$	−148.326	+	148.326i	−0.293134	+	0.293134i
$507$	133.659	−	26.5863i	0.263626	−	0.0524385i
$508$	−235.686	+	568.996i	−0.463949	+	1.12007i
$509$		−	349.504i		−	0.686648i	−0.939217	−	0.343324i	$-0.888447\pi$
$509$		−	349.504i		−	0.686648i	0.939217	−	0.343324i	$-0.111553\pi$
$510$		0			0
$511$	479.395			0.938150
$512$	−539.012	−	223.266i	−1.05276	−	0.436067i
$513$	7.73160	+	38.8694i	0.0150713	+	0.0757688i
$514$	−696.221	−	696.221i	−1.35451	−	1.35451i
$515$	−277.521	−	185.434i	−0.538876	−	0.360065i
$516$	19.0228	−	95.6341i	0.0368659	−	0.185337i
$517$	−528.531	+	353.153i	−1.02230	+	0.683081i
$518$	215.393	+	520.006i	0.415818	+	1.00387i
$519$	−133.658	+	55.3631i	−0.257530	+	0.106673i
$520$	−17.7705	−	26.5954i	−0.0341741	−	0.0511451i
$521$	−309.333	−	61.5301i	−0.593729	−	0.118100i	−0.110925	−	0.993829i	$-0.535381\pi$
$521$	−309.333	−	61.5301i	−0.593729	−	0.118100i	−0.482803	+	0.875729i	$0.660381\pi$
$522$	−43.0688	+	64.4571i	−0.0825074	+	0.123481i
$523$	145.221	−	145.221i	0.277669	−	0.277669i	−0.554509	−	0.832178i	$-0.687094\pi$
$523$	145.221	−	145.221i	0.277669	−	0.277669i	0.832178	+	0.554509i	$0.187094\pi$
$524$	867.854	−	172.627i	1.65621	−	0.329441i
$525$	96.3965	−	232.722i	0.183612	−	0.443279i
$526$			419.991i			0.798461i
$527$		0			0
$528$	−65.5098			−0.124072
$529$	420.715	+	174.266i	0.795302	+	0.329425i
$530$	−284.918	−	1432.38i	−0.537580	−	2.70260i
$531$	−161.959	−	161.959i	−0.305007	−	0.305007i
$532$	−94.8800	−	63.3968i	−0.178346	−	0.119167i
$533$	−4.81355	+	24.1993i	−0.00903104	+	0.0454021i
$534$	177.745	−	118.765i	0.332855	−	0.222407i
$535$	271.666	+	655.859i	0.507786	+	1.22590i
$536$	381.873	−	158.177i	0.712450	−	0.295106i
$537$	113.833	+	170.363i	0.211979	+	0.317249i
$538$	−964.618	−	191.874i	−1.79297	−	0.356644i
$539$	56.9440	−	85.2227i	0.105648	−	0.158113i
$540$	−413.135	+	413.135i	−0.765065	+	0.765065i
$541$	775.493	−	154.255i	1.43344	−	0.285130i	0.583547	−	0.812079i	$-0.301664\pi$
$541$	775.493	−	154.255i	1.43344	−	0.285130i	0.849897	+	0.526949i	$0.176664\pi$
$542$	−22.2280	+	53.6632i	−0.0410111	+	0.0990096i
$543$		−	244.849i		−	0.450919i
$544$		0			0
$545$	149.615			0.274523
$546$	−20.1647	−	8.35251i	−0.0369317	−	0.0152976i
$547$	−183.920	−	924.626i	−0.336233	−	1.69036i	−0.665723	−	0.746199i	$-0.731877\pi$
$547$	−183.920	−	924.626i	−0.336233	−	1.69036i	0.329490	−	0.944159i	$-0.393123\pi$
$548$	−632.218	−	632.218i	−1.15368	−	1.15368i
$549$	252.826	+	168.933i	0.460521	+	0.307710i
$550$	−188.253	+	946.412i	−0.342278	+	1.72075i
$551$	7.18146	−	4.79850i	0.0130335	−	0.00870871i
$552$	9.40756	+	22.7119i	0.0170427	+	0.0411447i
$553$	691.450	−	286.408i	1.25036	−	0.517917i
$554$	−518.029	−	775.285i	−0.935071	−	1.39943i
$555$	−151.461	−	30.1274i	−0.272902	−	0.0542837i
$556$	515.258	−	771.138i	0.926723	−	1.38694i
$557$	303.284	−	303.284i	0.544495	−	0.544495i	−0.380348	−	0.924843i	$-0.624196\pi$
$557$	303.284	−	303.284i	0.544495	−	0.544495i	0.924843	+	0.380348i	$0.124196\pi$
$558$	−317.905	+	63.2352i	−0.569722	+	0.113325i
$559$	10.0455	−	24.2519i	0.0179704	−	0.0433844i
$560$			629.663i			1.12440i
$561$		0			0
$562$	261.932			0.466071
$563$	639.473	+	264.879i	1.13583	+	0.470477i	0.869759	−	0.493476i	$-0.164274\pi$
$563$	639.473	+	264.879i	1.13583	+	0.470477i	0.266072	+	0.963953i	$0.414274\pi$
$564$	64.4425	+	323.974i	0.114260	+	0.574423i
$565$	344.303	+	344.303i	0.609386	+	0.609386i
$566$	18.8323	+	12.5833i	0.0332725	+	0.0222320i
$567$	97.4731	−	490.031i	0.171910	−	0.864251i
$568$	−310.696	+	207.601i	−0.547000	+	0.365494i
$569$	−153.331	−	370.173i	−0.269474	−	0.650567i	0.729985	−	0.683463i	$-0.239527\pi$
$569$	−153.331	−	370.173i	−0.269474	−	0.650567i	−0.999459	+	0.0328958i	$0.989527\pi$
$570$	51.3272	−	21.2604i	0.0900477	−	0.0372990i
$571$	362.070	+	541.876i	0.634098	+	0.948995i	0.999833	+	0.0182762i	$0.00581782\pi$
$571$	362.070	+	541.876i	0.634098	+	0.948995i	−0.365734	+	0.930719i	$0.619182\pi$
$572$	46.2132	+	9.19237i	0.0807923	+	0.0160706i
$573$	−59.8349	+	89.5493i	−0.104424	+	0.156281i
$574$	−367.214	+	367.214i	−0.639745	+	0.639745i
$575$	−332.165	+	66.0718i	−0.577679	+	0.114907i
$576$	300.851	−	726.319i	0.522311	−	1.26097i
$577$			684.109i			1.18563i	0.805339	+	0.592815i	$0.201983\pi$
$577$			684.109i			1.18563i	−0.805339	+	0.592815i	$0.798017\pi$
$578$		0			0
$579$	−258.876			−0.447109
$580$	117.640	+	48.7281i	0.202828	+	0.0840140i
$581$	182.097	+	915.465i	0.313421	+	1.57567i
$582$	−42.7712	−	42.7712i	−0.0734900	−	0.0734900i
$583$	403.417	+	269.555i	0.691968	+	0.462358i
$584$	−41.9875	+	211.085i	−0.0718964	+	0.361448i
$585$	−62.9010	+	42.0291i	−0.107523	+	0.0718446i
$586$	−89.2236	−	215.405i	−0.152259	−	0.367585i
$587$	342.216	−	141.750i	0.582991	−	0.241483i	−0.0716408	−	0.997430i	$-0.522824\pi$
$587$	342.216	−	141.750i	0.582991	−	0.241483i	0.654632	+	0.755948i	$0.272824\pi$
$588$	−29.5911	−	44.2862i	−0.0503250	−	0.0753166i
$589$	35.4193	+	7.04533i	0.0601346	+	0.0119615i
$590$	−370.890	+	555.075i	−0.628626	+	0.940806i
$591$	66.4527	−	66.4527i	0.112441	−	0.112441i
$592$	231.793	−	46.1065i	0.391543	−	0.0778827i
$593$	242.416	−	585.245i	0.408797	−	0.986922i	−0.576658	−	0.816985i	$-0.695644\pi$
$593$	242.416	−	585.245i	0.408797	−	0.986922i	0.985455	−	0.169937i	$-0.0543564\pi$
$594$		−	344.431i		−	0.579850i
$595$		0			0
$596$	−231.425			−0.388297
$597$	222.080	+	91.9883i	0.371992	+	0.154084i
$598$	5.72495	+	28.7813i	0.00957349	+	0.0481292i
$599$	−315.855	−	315.855i	−0.527304	−	0.527304i	0.392463	−	0.919768i	$-0.371623\pi$
$599$	−315.855	−	315.855i	−0.527304	−	0.527304i	−0.919768	+	0.392463i	$0.871623\pi$
$600$	94.0284	+	62.8278i	0.156714	+	0.104713i
$601$	85.0027	−	427.337i	0.141435	−	0.711044i	−0.843363	−	0.537344i	$-0.819428\pi$
$601$	85.0027	−	427.337i	0.141435	−	0.711044i	0.984799	−	0.173700i	$-0.0555723\pi$
$602$	459.390	−	306.955i	0.763106	−	0.509891i
$603$	−374.105	−	903.170i	−0.620407	−	1.49779i
$604$	−626.922	+	259.680i	−1.03795	+	0.429933i
$605$	248.859	+	372.443i	0.411337	+	0.615609i
$606$	18.5825	+	3.69629i	0.0306642	+	0.00609949i
$607$	352.561	−	527.645i	0.580826	−	0.869267i	−0.418414	−	0.908257i	$-0.637414\pi$
$607$	352.561	−	527.645i	0.580826	−	0.869267i	0.999240	+	0.0389892i	$0.0124138\pi$
$608$	−88.1749	+	88.1749i	−0.145025	+	0.145025i
$609$	19.2187	−	3.82283i	0.0315578	−	0.00627723i
$610$	339.157	−	818.798i	0.555996	−	1.34229i
$611$			88.9259i			0.145542i
$612$		0			0
$613$	−692.422			−1.12956			−0.564782	−	0.825240i	$-0.691040\pi$
$613$	−692.422			−1.12956			−0.564782	+	0.825240i	$0.691040\pi$
$614$	−446.610	−	184.992i	−0.727377	−	0.301290i
$615$	−27.7973	−	139.747i	−0.0451989	−	0.227230i
$616$	158.152	+	158.152i	0.256740	+	0.256740i
$617$	223.026	+	149.021i	0.361468	+	0.241525i	0.723021	−	0.690827i	$-0.242753\pi$
$617$	223.026	+	149.021i	0.361468	+	0.241525i	−0.361553	+	0.932352i	$0.617753\pi$
$618$	19.9477	−	100.284i	0.0322778	−	0.162272i
$619$	130.173	−	86.9787i	0.210295	−	0.140515i	−0.445962	−	0.895052i	$-0.647138\pi$
$619$	130.173	−	86.9787i	0.210295	−	0.140515i	0.656258	+	0.754537i	$0.272138\pi$
$620$	203.741	+	491.875i	0.328615	+	0.793346i
$621$	111.684	−	46.2610i	0.179845	−	0.0744944i
$622$	560.096	+	838.243i	0.900476	+	1.34766i
$623$	669.500	+	133.172i	1.07464	+	0.213759i
$624$	−5.09155	+	7.62004i	−0.00815953	+	0.0122116i
$625$	38.0547	−	38.0547i	0.0608875	−	0.0608875i
$626$	−1171.54	+	233.033i	−1.87147	+	0.372258i
$627$	−7.06311	+	17.0519i	−0.0112649	+	0.0271959i
$628$		−	186.031i		−	0.296228i
$629$		0			0
$630$	−1592.27			−2.52741
$631$	289.230	+	119.803i	0.458368	+	0.189862i	0.599906	−	0.800071i	$-0.295205\pi$
$631$	289.230	+	119.803i	0.458368	+	0.189862i	−0.141538	+	0.989933i	$0.545205\pi$
$632$	65.5499	+	329.542i	0.103718	+	0.521427i
$633$	−131.992	−	131.992i	−0.208519	−	0.208519i
$634$	−350.124	−	233.945i	−0.552246	−	0.368999i
$635$	186.793	−	939.070i	0.294162	−	1.47885i
$636$	209.637	−	140.075i	0.329617	−	0.220243i
$637$	−5.48723	−	13.2473i	−0.00861418	−	0.0207965i
$638$	−69.3506	+	28.7259i	−0.108700	+	0.0450250i
$639$	490.997	+	734.829i	0.768384	+	1.14997i
$640$	−850.938	−	169.262i	−1.32959	−	0.264472i
$641$	−205.629	+	307.746i	−0.320794	+	0.480103i	−0.956461	−	0.291861i	$-0.905725\pi$
$641$	−205.629	+	307.746i	−0.320794	+	0.480103i	0.635666	+	0.771964i	$0.280725\pi$
$642$	−153.776	+	153.776i	−0.239526	+	0.239526i
$643$	−215.763	+	42.9179i	−0.335556	+	0.0667463i	−0.359993	−	0.932955i	$-0.617221\pi$
$643$	−215.763	+	42.9179i	−0.335556	+	0.0667463i	0.0244365	+	0.999701i	$0.492221\pi$
$644$	−133.202	+	321.577i	−0.206835	+	0.499344i
$645$			151.589i			0.235022i
$646$		0			0
$647$	769.098			1.18871			0.594357	−	0.804201i	$-0.297407\pi$
$647$	769.098			1.18871			0.594357	+	0.804201i	$0.297407\pi$
$648$	207.231	+	85.8381i	0.319802	+	0.132466i
$649$	−43.2679	−	217.522i	−0.0666686	−	0.335165i
$650$	95.4544	+	95.4544i	0.146853	+	0.146853i
$651$	68.1232	+	45.5185i	0.104644	+	0.0699209i
$652$	−160.932	+	809.062i	−0.246829	+	1.24089i
$653$	35.2838	−	23.5759i	0.0540334	−	0.0361040i	−0.528260	−	0.849083i	$-0.677155\pi$
$653$	35.2838	−	23.5759i	0.0540334	−	0.0361040i	0.582294	+	0.812979i	$0.302155\pi$
$654$	17.5397	+	42.3446i	0.0268192	+	0.0647472i
$655$	−1270.92	+	526.432i	−1.94033	+	0.803713i
$656$	121.145	+	181.307i	0.184673	+	0.276382i
$657$	499.239	+	99.3048i	0.759877	+	0.151149i
$658$	−1039.85	+	1556.25i	−1.58032	+	2.36512i
$659$	−472.719	+	472.719i	−0.717328	+	0.717328i	−0.968057	−	0.250729i	$-0.919330\pi$
$659$	−472.719	+	472.719i	−0.717328	+	0.717328i	0.250729	+	0.968057i	$0.419330\pi$
$660$	−266.873	+	53.0843i	−0.404352	+	0.0804307i
$661$	−157.467	+	380.158i	−0.238225	+	0.575126i	−0.997099	−	0.0761113i	$-0.975750\pi$
$661$	−157.467	+	380.158i	−0.238225	+	0.575126i	0.758874	+	0.651237i	$0.225750\pi$
$662$			480.756i			0.726218i
$663$		0			0
$664$	−419.043			−0.631089
$665$	163.898	+	67.8888i	0.246463	+	0.102088i
$666$	116.592	+	586.150i	0.175064	+	0.880104i
$667$	−18.6292	−	18.6292i	−0.0279298	−	0.0279298i
$668$	−475.539	−	317.745i	−0.711885	−	0.475666i
$669$	57.6010	−	289.580i	0.0861002	−	0.432855i
$670$	−2369.12	+	1582.99i	−3.53600	+	2.36268i
$671$	112.675	+	272.020i	0.167920	+	0.405395i
$672$	−261.372	+	108.264i	−0.388946	+	0.161107i
$673$	9.00950	+	13.4837i	0.0133871	+	0.0200352i	0.838103	−	0.545512i	$-0.183665\pi$
$673$	9.00950	+	13.4837i	0.0133871	+	0.0200352i	−0.824716	+	0.565547i	$0.808665\pi$
$674$	−1432.19	−	284.880i	−2.12491	−	0.422670i
$675$	308.951	−	462.378i	0.457705	−	0.685004i
$676$	−612.536	+	612.536i	−0.906119	+	0.906119i
$677$	−1008.45	+	200.593i	−1.48958	+	0.296297i	−0.871726	−	0.489993i	$-0.836999\pi$
$677$	−1008.45	+	200.593i	−1.48958	+	0.296297i	−0.617858	+	0.786290i	$0.711999\pi$
$678$	−57.0825	+	137.809i	−0.0841924	+	0.203258i
$679$		−	193.149i		−	0.284461i
$680$		0			0
$681$	78.7512			0.115641
$682$	−289.967	−	120.108i	−0.425172	−	0.176112i
$683$	44.1583	+	221.999i	0.0646534	+	0.325035i	0.999554	−	0.0298760i	$-0.00951125\pi$
$683$	44.1583	+	221.999i	0.0646534	+	0.325035i	−0.934900	+	0.354911i	$0.884511\pi$
$684$	−85.6752	−	85.6752i	−0.125256	−	0.125256i
$685$	1155.73	+	772.237i	1.68720	+	1.12735i
$686$	−168.427	+	846.738i	−0.245520	+	1.23431i
$687$	−244.321	+	163.250i	−0.355635	+	0.237628i
$688$	−88.7787	−	214.331i	−0.129039	−	0.311527i
$689$	62.7087	−	25.9748i	0.0910141	−	0.0376993i
$690$	−94.1484	−	140.903i	−0.136447	−	0.204207i
$691$	−38.3188	−	7.62208i	−0.0554541	−	0.0110305i	0.167285	−	0.985909i	$-0.446500\pi$
$691$	−38.3188	−	7.62208i	−0.0554541	−	0.0110305i	−0.222739	+	0.974878i	$0.571500\pi$
$692$	510.909	−	764.629i	0.738308	−	1.10496i
$693$	374.046	−	374.046i	0.539749	−	0.539749i
$694$	58.7593	−	11.6880i	0.0846676	−	0.0168414i
$695$	−551.766	+	1332.08i	−0.793908	+	1.91666i
$696$			8.79713i			0.0126395i
$697$		0			0
$698$	1185.05			1.69778
$699$	−210.296	−	87.1075i	−0.300853	−	0.124617i
$700$	312.379	+	1570.43i	0.446255	+	2.24348i
$701$	401.261	+	401.261i	0.572412	+	0.572412i	0.932802	−	0.360390i	$-0.117356\pi$
$701$	401.261	+	401.261i	0.572412	+	0.572412i	−0.360390	+	0.932802i	$0.617356\pi$
$702$	−40.0639	−	26.7698i	−0.0570710	−	0.0381336i
$703$	12.9901	−	65.3056i	0.0184781	−	0.0928956i
$704$	632.949	−	422.923i	0.899075	−	0.600743i
$705$	−196.520	−	474.441i	−0.278751	−	0.672965i
$706$	−545.941	+	226.136i	−0.773288	+	0.320306i
$707$	33.6121	+	50.3040i	0.0475418	+	0.0711514i
$708$	−113.036	−	22.4843i	−0.159655	−	0.0317574i
$709$	158.551	−	237.289i	0.223627	−	0.334681i	−0.702643	−	0.711543i	$-0.747997\pi$
$709$	158.551	−	237.289i	0.223627	−	0.334681i	0.926270	+	0.376862i	$0.122997\pi$
$710$	1821.42	−	1821.42i	2.56539	−	2.56539i
$711$	779.401	−	155.033i	1.09620	−	0.218049i
$712$	−117.276	+	283.128i	−0.164713	+	0.397652i
$713$		−	110.156i		−	0.154496i
$714$		0			0
$715$	−73.2524			−0.102451
$716$	−1203.28	−	498.416i	−1.68056	−	0.696112i
$717$	−52.0795	−	261.821i	−0.0726353	−	0.365162i
$718$	−761.667	−	761.667i	−1.06082	−	1.06082i
$719$	−510.049	−	340.804i	−0.709387	−	0.473997i	0.147790	−	0.989019i	$-0.452784\pi$
$719$	−510.049	−	340.804i	−0.709387	−	0.473997i	−0.857177	+	0.515022i	$0.827784\pi$
$720$	−130.432	+	655.728i	−0.181156	+	0.910733i
$721$	271.475	−	181.394i	0.376525	−	0.251586i
$722$	−409.056	−	987.549i	−0.566560	−	1.36780i
$723$	−181.971	+	75.3748i	−0.251689	+	0.104253i
$724$	864.693	+	1294.10i	1.19433	+	1.78744i
$725$	−118.866	−	23.6439i	−0.163953	−	0.0326123i
$726$	−76.2360	+	114.095i	−0.105008	+	0.157156i
$727$	−244.413	+	244.413i	−0.336194	+	0.336194i	−0.854933	−	0.518739i	$-0.826402\pi$
$727$	−244.413	+	244.413i	−0.336194	+	0.336194i	0.518739	+	0.854933i	$0.326402\pi$
$728$	30.6880	−	6.10422i	0.0421538	−	0.00838492i
$729$	163.590	−	394.941i	0.224403	−	0.541758i
$730$		−	1483.61i		−	2.03235i
$731$		0			0
$732$	153.003			0.209020
$733$	−1246.38	−	516.266i	−1.70038	−	0.704319i	−0.700421	−	0.713730i	$-0.747004\pi$
$733$	−1246.38	−	516.266i	−1.70038	−	0.704319i	−0.999956	+	0.00941053i	$0.997004\pi$
$734$	−48.2685	−	242.662i	−0.0657608	−	0.330602i
$735$	58.5513	+	58.5513i	0.0796617	+	0.0796617i
$736$	316.263	+	211.320i	0.429705	+	0.287120i
$737$	184.672	−	928.407i	0.250572	−	1.25971i
$738$	−458.482	+	306.348i	−0.621249	+	0.415105i
$739$	249.740	+	602.925i	0.337943	+	0.815866i	0.997913	+	0.0645741i	$0.0205689\pi$
$739$	249.740	+	602.925i	0.337943	+	0.815866i	−0.659970	+	0.751292i	$0.729431\pi$
$740$	906.913	−	375.656i	1.22556	−	0.507643i
$741$	1.43450	+	2.14688i	0.00193589	+	0.00289727i
$742$	1401.17	+	278.710i	1.88837	+	0.375620i
$743$	−123.890	+	185.415i	−0.166743	+	0.249548i	−0.905426	−	0.424505i	$-0.860448\pi$
$743$	−123.890	+	185.415i	−0.166743	+	0.249548i	0.738683	+	0.674053i	$0.235448\pi$
$744$	−26.0091	+	26.0091i	−0.0349584	+	0.0349584i
$745$	352.870	−	70.1902i	0.473651	−	0.0942150i
$746$	−88.9980	+	214.860i	−0.119300	+	0.288016i
$747$			991.082i			1.32675i
$748$		0			0
$749$	−694.430			−0.927143
$750$	−264.049	−	109.373i	−0.352065	−	0.145830i
$751$	−87.6011	−	440.400i	−0.116646	−	0.586419i	−0.994255	−	0.107041i	$-0.965862\pi$
$751$	−87.6011	−	440.400i	−0.116646	−	0.586419i	0.877609	−	0.479378i	$-0.159138\pi$
$752$	555.715	+	555.715i	0.738982	+	0.738982i
$753$	−148.531	−	99.2453i	−0.197252	−	0.131800i
$754$	−2.04868	+	10.2994i	−0.00271709	+	0.0136597i
$755$	877.152	−	586.094i	1.16179	−	0.776283i
$756$	−218.716	−	528.027i	−0.289307	−	0.698449i
$757$	42.5792	−	17.6369i	0.0562473	−	0.0232984i	−0.354382	−	0.935101i	$-0.615309\pi$
$757$	42.5792	−	17.6369i	0.0562473	−	0.0232984i	0.410630	+	0.911802i	$0.365309\pi$
$758$	−991.081	−	1483.26i	−1.30749	−	1.95680i
$759$	55.2169	+	10.9833i	0.0727496	+	0.0144708i
$760$	−44.2475	+	66.2210i	−0.0582203	+	0.0871329i
$761$	552.081	−	552.081i	0.725467	−	0.725467i	−0.244246	−	0.969713i	$-0.578540\pi$
$761$	552.081	−	552.081i	0.725467	−	0.725467i	0.969713	+	0.244246i	$0.0785404\pi$
$762$	287.677	−	57.2225i	0.377529	−	0.0750952i
$763$	−56.0079	+	135.215i	−0.0734048	+	0.177215i
$764$		−	684.604i		−	0.896079i
$765$		0			0
$766$	707.240			0.923289
$767$	−28.6649	−	11.8734i	−0.0373727	−	0.0154803i
$768$	7.91719	+	39.8024i	0.0103088	+	0.0518261i
$769$	625.504	+	625.504i	0.813400	+	0.813400i	0.985142	−	0.171742i	$-0.0549396\pi$
$769$	625.504	+	625.504i	0.813400	+	0.813400i	−0.171742	+	0.985142i	$0.554940\pi$
$770$	−1281.95	−	856.575i	−1.66488	−	1.11243i
$771$	−51.5543	+	259.181i	−0.0668668	+	0.336162i
$772$	1368.24	−	914.229i	1.77233	−	1.18424i
$773$	465.474	+	1123.75i	0.602166	+	1.45376i	0.871347	+	0.490667i	$0.163247\pi$
$773$	465.474	+	1123.75i	0.602166	+	1.45376i	−0.269181	+	0.963090i	$0.586753\pi$
$774$	541.991	−	224.500i	0.700247	−	0.290052i
$775$	−281.528	−	421.336i	−0.363262	−	0.543660i
$776$	85.0468	+	16.9169i	0.109596	+	0.0218001i
$777$	83.9265	−	125.605i	0.108013	−	0.161654i
$778$	864.056	−	864.056i	1.11061	−	1.11061i
$779$	60.2548	−	11.9854i	0.0773489	−	0.0153857i
$780$	−14.5671	+	35.1682i	−0.0186758	+	0.0450874i
$781$			855.757i			1.09572i
$782$		0			0
$783$	43.2592			0.0552481
$784$	−117.076	−	48.4944i	−0.149331	−	0.0618551i
$785$	56.4223	+	283.654i	0.0718755	+	0.361343i
$786$	−297.985	−	297.985i	−0.379116	−	0.379116i
$787$	161.359	+	107.816i	0.205030	+	0.136997i	0.653846	−	0.756627i	$-0.273154\pi$
$787$	161.359	+	107.816i	0.205030	+	0.136997i	−0.448816	+	0.893624i	$0.648154\pi$
$788$	−116.543	+	585.903i	−0.147898	+	0.743532i
$789$	93.7245	−	62.6247i	0.118789	−	0.0793723i
$790$	−886.365	−	2139.88i	−1.12198	−	2.70870i
$791$	−440.053	+	182.276i	−0.556324	+	0.230437i
$792$	131.938	+	197.459i	0.166589	+	0.249317i
$793$	40.3984	+	8.03575i	0.0509438	+	0.0101334i
$794$	443.666	−	663.993i	0.558773	−	0.836263i
$795$	−277.163	+	277.163i	−0.348633	+	0.348633i
$796$	−1498.62	+	298.094i	−1.88269	+	0.374490i
$797$	49.1164	−	118.577i	0.0616266	−	0.148780i	−0.890066	−	0.455831i	$-0.849342\pi$
$797$	49.1164	−	118.577i	0.0616266	−	0.148780i	0.951693	+	0.307051i	$0.0993422\pi$
$798$			54.3457i			0.0681024i
$799$		0			0
$800$	1749.75			2.18719
$801$	669.628	+	277.369i	0.835990	+	0.346278i
$802$	141.325	+	710.490i	0.176216	+	0.885898i
$803$	348.522	+	348.522i	0.434025	+	0.434025i
$804$	−409.001	−	273.285i	−0.508707	−	0.339907i
$805$	105.569	−	530.731i	0.131141	−	0.659293i
$806$	−36.5077	+	24.3937i	−0.0452949	+	0.0302651i
$807$	101.016	+	243.873i	0.125174	+	0.302197i
$808$	−25.0936	+	10.3941i	−0.0310564	+	0.0128640i
$809$	193.960	+	290.282i	0.239753	+	0.358816i	0.931760	−	0.363075i	$-0.118273\pi$
$809$	193.960	+	290.282i	0.239753	+	0.358816i	−0.692007	+	0.721891i	$0.743273\pi$
$810$	−1516.53	−	301.656i	−1.87226	−	0.372415i
$811$	103.131	−	154.347i	0.127166	−	0.190317i	−0.762423	−	0.647078i	$-0.775991\pi$
$811$	103.131	−	154.347i	0.127166	−	0.190317i	0.889589	+	0.456761i	$0.150991\pi$
$812$	−88.0762	+	88.0762i	−0.108468	+	0.108468i
$813$	15.2898	−	3.04133i	0.0188067	−	0.00374088i
$814$	−221.455	+	534.639i	−0.272057	+	0.656804i
$815$		−	1282.44i		−	1.57355i
$816$		0			0
$817$	−65.3610			−0.0800013
$818$	726.923	+	301.101i	0.888659	+	0.368095i
$819$	−14.4371	−	72.5803i	−0.0176277	−	0.0886206i
$820$	640.437	+	640.437i	0.781021	+	0.781021i
$821$	−1310.45	−	875.613i	−1.59616	−	1.06652i	−0.953939	−	0.300001i	$-0.903013\pi$
$821$	−1310.45	−	875.613i	−1.59616	−	1.06652i	−0.642221	−	0.766519i	$-0.721987\pi$
$822$	−83.0720	+	417.631i	−0.101061	+	0.508067i
$823$	−836.137	+	558.689i	−1.01596	+	0.678844i	−0.947812	−	0.318831i	$-0.896710\pi$
$823$	−836.137	+	558.689i	−1.01596	+	0.678844i	−0.0681507	+	0.997675i	$0.521710\pi$
$824$	56.0937	+	135.422i	0.0680749	+	0.164347i
$825$	239.270	−	99.1090i	0.290025	−	0.120132i
$826$	−362.809	−	542.982i	−0.439236	−	0.657363i
$827$	−1558.84	−	310.073i	−1.88494	−	0.374937i	−0.888472	−	0.458931i	$-0.848232\pi$
$827$	−1558.84	−	310.073i	−1.88494	−	0.374937i	−0.996466	+	0.0839938i	$0.973232\pi$
$828$	−205.329	+	307.297i	−0.247982	+	0.371132i
$829$	269.747	−	269.747i	0.325388	−	0.325388i	−0.525442	−	0.850830i	$-0.676100\pi$
$829$	269.747	−	269.747i	0.325388	−	0.325388i	0.850830	+	0.525442i	$0.176100\pi$
$830$	2833.15	−	563.548i	3.41343	−	0.678974i
$831$	−95.7684	+	231.205i	−0.115245	+	0.278225i
$832$		−	106.494i		−	0.127998i
$833$		0			0
$834$	−441.695			−0.529611
$835$	821.457	+	340.259i	0.983781	+	0.407495i
$836$	−22.8884	−	115.068i	−0.0273785	−	0.137641i
$837$	127.898	+	127.898i	0.152805	+	0.152805i
$838$	−431.818	−	288.532i	−0.515297	−	0.344310i
$839$	−7.22195	+	36.3072i	−0.00860781	+	0.0432744i	−0.984850	−	0.173406i	$-0.944523\pi$
$839$	−7.22195	+	36.3072i	−0.00860781	+	0.0432744i	0.976243	+	0.216680i	$0.0695228\pi$
$840$	−150.238	+	100.386i	−0.178854	+	0.119507i
$841$	318.229	+	768.273i	0.378393	+	0.913523i
$842$	−1753.09	+	726.154i	−2.08206	+	0.862416i
$843$	−39.0566	−	58.4524i	−0.0463305	−	0.0693386i
$844$	1163.76	+	231.485i	1.37886	+	0.274272i
$845$	748.196	−	1119.75i	0.885439	−	1.32515i
$846$	−1405.27	+	1405.27i	−1.66107	+	1.66107i
$847$	−429.755	+	85.4837i	−0.507385	+	0.100925i
$848$	229.557	−	554.200i	0.270704	−	0.653538i
$849$		−	6.07887i		−	0.00716004i
$850$		0			0
$851$	−203.104			−0.238665
$852$	410.846	+	170.178i	0.482213	+	0.199739i
$853$	−15.3853	−	77.3472i	−0.0180367	−	0.0906767i	0.970718	−	0.240220i	$-0.0772196\pi$
$853$	−15.3853	−	77.3472i	−0.0180367	−	0.0906767i	−0.988755	+	0.149543i	$0.952220\pi$
$854$	613.028	+	613.028i	0.717831	+	0.717831i
$855$	156.620	+	104.650i	0.183181	+	0.122398i
$856$	60.8213	−	305.769i	0.0710529	−	0.357207i
$857$	553.831	−	370.058i	0.646244	−	0.431806i	−0.188780	−	0.982019i	$-0.560453\pi$
$857$	553.831	−	370.058i	0.646244	−	0.431806i	0.835024	+	0.550213i	$0.185453\pi$
$858$	−8.58754	−	20.7322i	−0.0100088	−	0.0241634i
$859$	1281.10	−	530.649i	1.49138	−	0.617752i	0.519767	−	0.854308i	$-0.326019\pi$
$859$	1281.10	−	530.649i	1.49138	−	0.617752i	0.971618	+	0.236556i	$0.0760187\pi$
$860$	−535.342	−	801.196i	−0.622491	−	0.931624i
$861$	136.702	+	27.1917i	0.158771	+	0.0315816i
$862$	−1281.92	+	1918.53i	−1.48714	+	2.22567i
$863$	375.548	−	375.548i	0.435166	−	0.435166i	−0.455215	−	0.890381i	$-0.650438\pi$
$863$	375.548	−	375.548i	0.435166	−	0.435166i	0.890381	+	0.455215i	$0.150438\pi$
$864$	−612.557	+	121.845i	−0.708978	+	0.141024i
$865$	−547.109	+	1320.84i	−0.632496	+	1.52698i
$866$			286.613i			0.330962i
$867$		0			0
$868$	−520.802			−0.600002
$869$	710.907	+	294.467i	0.818075	+	0.338858i
$870$	−11.8308	−	59.4773i	−0.0135986	−	0.0683647i
$871$	−93.6384	−	93.6384i	−0.107507	−	0.107507i
$872$	−54.6320	−	36.5039i	−0.0626513	−	0.0418623i
$873$	40.0101	−	201.145i	0.0458306	−	0.230406i
$874$	60.7534	−	40.5941i	0.0695119	−	0.0464464i
$875$	−349.249	−	843.160i	−0.399141	−	0.963612i
$876$	236.632	−	98.0161i	0.270128	−	0.111891i
$877$	−138.090	−	206.666i	−0.157457	−	0.235652i	0.744350	−	0.667789i	$-0.232759\pi$
$877$	−138.090	−	206.666i	−0.157457	−	0.235652i	−0.901808	+	0.432138i	$0.857759\pi$
$878$	−109.795	−	21.8396i	−0.125052	−	0.0248743i
$879$	−34.7653	+	52.0300i	−0.0395510	+	0.0591922i
$880$	−457.768	+	457.768i	−0.520191	+	0.520191i
$881$	−143.646	+	28.5729i	−0.163048	+	0.0324324i	−0.275939	−	0.961175i	$-0.588989\pi$
$881$	−143.646	+	28.5729i	−0.163048	+	0.0324324i	0.112891	+	0.993607i	$0.463989\pi$
$882$	122.631	−	296.057i	0.139037	−	0.335665i
$883$			322.505i			0.365237i	0.983184	+	0.182619i	$0.0584574\pi$
$883$			322.505i			0.365237i	−0.983184	+	0.182619i	$0.941543\pi$
$884$		0			0
$885$	179.173			0.202455
$886$	−1773.64	−	734.666i	−2.00185	−	0.829194i
$887$	−12.2623	−	61.6470i	−0.0138245	−	0.0695005i	0.973257	−	0.229718i	$-0.0737804\pi$
$887$	−12.2623	−	61.6470i	−0.0138245	−	0.0695005i	−0.987082	+	0.160218i	$0.948780\pi$
$888$	47.9552	+	47.9552i	0.0540037	+	0.0540037i
$889$	778.760	+	520.351i	0.875996	+	0.585322i
$890$	412.136	−	2071.95i	0.463074	−	2.32803i
$891$	427.118	−	285.391i	0.479369	−	0.320304i
$892$	718.221	+	1733.94i	0.805180	+	1.94388i
$893$	204.565	−	84.7337i	0.229077	−	0.0948866i
$894$	61.2332	+	91.6419i	0.0684935	+	0.102508i
$895$	1985.89	+	395.019i	2.21888	+	0.441362i
$896$	471.516	−	705.674i	0.526246	−	0.787582i
$897$	5.56914	−	5.56914i	0.00620863	−	0.00620863i
$898$	−1311.86	+	260.944i	−1.46086	+	0.290584i
$899$	15.0852	−	36.4189i	0.0167800	−	0.0405104i
$900$			1700.15i			1.88905i
$901$		0			0
$902$	−533.932			−0.591942
$903$	−136.999	−	56.7469i	−0.151715	−	0.0628426i
$904$	−41.7173	−	209.727i	−0.0461474	−	0.231999i
$905$	−1710.95	−	1710.95i	−1.89055	−	1.89055i
$906$	268.709	+	179.546i	0.296588	+	0.198174i
$907$	−42.8827	+	215.586i	−0.0472797	+	0.237691i	−0.997198	−	0.0748072i	$-0.976166\pi$
$907$	−42.8827	+	215.586i	−0.0472797	+	0.237691i	0.949918	+	0.312498i	$0.101166\pi$
$908$	−416.225	+	278.112i	−0.458397	+	0.306291i
$909$	24.5832	+	59.3490i	0.0270442	+	0.0652904i
$910$	−199.272	+	82.5412i	−0.218980	+	0.0907046i
$911$	280.764	+	420.193i	0.308193	+	0.461244i	0.952943	−	0.303150i	$-0.0980383\pi$
$911$	280.764	+	420.193i	0.308193	+	0.461244i	−0.644750	+	0.764394i	$0.723038\pi$
$912$	22.3807	+	4.45180i	0.0245402	+	0.00488135i
$913$	−533.162	+	797.933i	−0.583967	+	0.873968i
$914$	571.150	−	571.150i	0.624890	−	0.624890i
$915$	−233.294	+	46.4050i	−0.254966	+	0.0507158i
$916$	714.790	−	1725.66i	0.780338	−	1.88390i
$917$		−	1345.66i		−	1.46746i
$918$		0			0
$919$	−930.196			−1.01218			−0.506091	−	0.862480i	$-0.668910\pi$
$919$	−930.196			−1.01218			−0.506091	+	0.862480i	$0.668910\pi$
$920$	224.443	+	92.9674i	0.243960	+	0.101052i
$921$	25.3114	+	127.249i	0.0274825	+	0.138164i
$922$	−966.431	−	966.431i	−1.04819	−	1.04819i
$923$	99.5409	+	66.5111i	0.107845	+	0.0720597i
$924$	51.9277	−	261.058i	0.0561988	−	0.282531i
$925$	−776.855	+	519.078i	−0.839844	+	0.561166i
$926$	93.5798	+	225.922i	0.101058	+	0.243976i
$927$	320.288	−	132.667i	0.345510	−	0.143115i
$928$	75.6213	+	113.175i	0.0814885	+	0.121956i
$929$	1125.58	+	223.893i	1.21161	+	0.241004i	0.759230	−	0.650822i	$-0.225576\pi$
$929$	1125.58	+	223.893i	1.21161	+	0.241004i	0.452378	+	0.891826i	$0.350576\pi$
$930$	140.869	−	210.825i	0.151472	−	0.226694i
$931$	−25.2457	+	25.2457i	−0.0271167	+	0.0271167i
$932$	1419.10	−	282.277i	1.52264	−	0.302872i
$933$	103.545	−	249.980i	0.110981	−	0.267932i
$934$			249.650i			0.267291i
$935$		0			0
$936$	33.2228			0.0354944
$937$	−1249.07	−	517.380i	−1.33305	−	0.552166i	−0.401524	−	0.915848i	$-0.631519\pi$
$937$	−1249.07	−	517.380i	−1.33305	−	0.552166i	−0.931523	+	0.363682i	$0.881519\pi$
$938$	−543.763	−	2733.68i	−0.579704	−	2.91437i
$939$	226.691	+	226.691i	0.241418	+	0.241418i
$940$	2714.17	+	1813.55i	2.88741	+	1.92931i
$941$	−358.917	+	1804.40i	−0.381421	+	1.91753i	0.0159438	+	0.999873i	$0.494925\pi$
$941$	−358.917	+	1804.40i	−0.381421	+	1.91753i	−0.397365	+	0.917661i	$0.630075\pi$
$942$	−73.6663	+	49.2222i	−0.0782020	+	0.0522529i
$943$	−71.7133	−	173.131i	−0.0760480	−	0.183596i
$944$	−253.331	+	104.933i	−0.268359	+	0.111158i
$945$	493.639	+	738.783i	0.522370	+	0.781781i
$946$	557.136	+	110.821i	0.588938	+	0.117147i
$947$	−21.8620	+	32.7188i	−0.0230855	+	0.0345499i	−0.842833	−	0.538175i	$-0.819114\pi$
$947$	−21.8620	+	32.7188i	−0.0230855	+	0.0345499i	0.819747	+	0.572725i	$0.194114\pi$
$948$	282.745	−	282.745i	0.298255	−	0.298255i
$949$	67.6275	−	13.4520i	0.0712619	−	0.0141749i
$950$	128.629	−	310.538i	0.135399	−	0.326882i
$951$			113.017i			0.118840i
$952$		0			0
$953$	183.445			0.192492			0.0962458	−	0.995358i	$-0.469317\pi$
$953$	183.445			0.192492			0.0962458	+	0.995358i	$0.469317\pi$
$954$	1401.44	+	580.495i	1.46901	+	0.608485i
$955$	207.637	+	1043.86i	0.217421	+	1.09305i
$956$	1199.89	+	1199.89i	1.25511	+	1.25511i
$957$	16.7513	+	11.1929i	0.0175040	+	0.0116958i
$958$	−271.904	+	1366.95i	−0.283825	+	1.42688i
$959$	−1130.55	+	755.412i	−1.17889	+	0.787708i
$960$	235.345	+	568.173i	0.245151	+	0.591847i
$961$	−735.574	+	304.685i	−0.765426	+	0.317050i
$962$	44.9768	+	67.3125i	0.0467534	+	0.0699714i
$963$	−723.176	−	143.849i	−0.750962	−	0.149376i
$964$	695.584	−	1041.01i	0.721560	−	1.07989i
$965$	−1808.97	+	1808.97i	−1.87458	+	1.87458i
$966$	162.585	−	32.3402i	0.168308	−	0.0334785i
$967$	489.471	−	1181.69i	0.506175	−	1.22201i	−0.439894	−	0.898050i	$-0.644984\pi$
$967$	489.471	−	1181.69i	0.506175	−	1.22201i	0.946069	−	0.323965i	$-0.105016\pi$
$968$		−	196.715i		−	0.203218i
$969$		0			0
$970$	−597.751			−0.616238
$971$	844.437	+	349.777i	0.869657	+	0.360224i	0.772477	−	0.635043i	$-0.219018\pi$
$971$	844.437	+	349.777i	0.869657	+	0.360224i	0.0971803	+	0.995267i	$0.469018\pi$
$972$	−179.840	−	904.117i	−0.185021	−	0.930161i
$973$	−997.319	−	997.319i	−1.02499	−	1.02499i
$974$	1316.84	+	879.884i	1.35199	+	0.903371i
$975$	7.06828	−	35.5346i	0.00724952	−	0.0364458i
$976$	302.674	−	202.240i	0.310117	−	0.207214i
$977$	−169.210	−	408.510i	−0.173194	−	0.418126i	0.813318	−	0.581820i	$-0.197659\pi$
$977$	−169.210	−	408.510i	−0.173194	−	0.418126i	−0.986511	+	0.163694i	$0.947659\pi$
$978$	362.961	−	150.343i	0.371126	−	0.153725i
$979$	389.913	+	583.546i	0.398277	+	0.596063i
$980$	−516.238	−	102.686i	−0.526773	−	0.104782i
$981$	−86.3356	+	129.210i	−0.0880078	+	0.131713i
$982$	−1046.98	+	1046.98i	−1.06617	+	1.06617i
$983$	652.647	−	129.820i	0.663934	−	0.132065i	0.148391	−	0.988929i	$-0.452590\pi$
$983$	652.647	−	129.820i	0.663934	−	0.132065i	0.515542	+	0.856864i	$0.327590\pi$
$984$	−23.9459	+	57.8106i	−0.0243353	+	0.0587506i
$985$		−	928.713i		−	0.942856i
$986$		0			0
$987$	502.343			0.508959
$988$	−15.1635	−	6.28094i	−0.0153477	−	0.00635723i
$989$	38.8953	+	195.540i	0.0393279	+	0.197714i
$990$	−1157.59	−	1157.59i	−1.16928	−	1.16928i
$991$	1301.14	+	869.394i	1.31296	+	0.877289i	0.997431	−	0.0716278i	$-0.0228194\pi$
$991$	1301.14	+	869.394i	1.31296	+	0.877289i	0.315525	+	0.948917i	$0.397819\pi$
$992$	−111.030	+	558.185i	−0.111925	+	0.562687i
$993$	107.285	−	71.6854i	0.108041	−	0.0721908i
$994$	964.271	+	2327.96i	0.970092	+	2.34201i
$995$	2194.64	−	909.048i	2.20566	−	0.913616i
$996$	277.059	+	414.648i	0.278171	+	0.416313i
$997$	−1510.52	−	300.460i	−1.51506	−	0.301364i	−0.633615	−	0.773649i	$-0.718430\pi$
$997$	−1510.52	−	300.460i	−1.51506	−	0.301364i	−0.881446	+	0.472284i	$0.843430\pi$
$998$	−852.835	+	1276.36i	−0.854544	+	1.27891i
$999$	235.817	−	235.817i	0.236053	−	0.236053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.3.e.k.249.1		8
17.2	even	8		17.3.e.a.10.1	✓	8
17.3	odd	16		289.3.e.l.65.1		8
17.4	even	4		289.3.e.d.40.1		8
17.5	odd	16		289.3.e.b.224.1		8
17.6	odd	16		289.3.e.i.158.1		8
17.7	odd	16		17.3.e.a.12.1	yes	8
17.8	even	8		289.3.e.i.75.1		8
17.9	even	8		289.3.e.m.75.1		8
17.10	odd	16		289.3.e.c.131.1		8
17.11	odd	16		289.3.e.m.158.1		8
17.12	odd	16		289.3.e.d.224.1		8
17.13	even	4		289.3.e.b.40.1		8
17.14	odd	16	inner	289.3.e.k.65.1		8
17.15	even	8		289.3.e.c.214.1		8
17.16	even	2		289.3.e.l.249.1		8
51.2	odd	8		153.3.p.b.10.1		8
51.41	even	16		153.3.p.b.46.1		8
68.7	even	16		272.3.bh.c.97.1		8
68.19	odd	8		272.3.bh.c.129.1		8
85.2	odd	8		425.3.t.a.299.1		8
85.7	even	16		425.3.t.c.199.1		8
85.19	even	8		425.3.u.b.401.1		8
85.24	odd	16		425.3.u.b.301.1		8
85.53	odd	8		425.3.t.c.299.1		8
85.58	even	16		425.3.t.a.199.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.10.1	✓	8	17.2	even	8
17.3.e.a.12.1	yes	8	17.7	odd	16
153.3.p.b.10.1		8	51.2	odd	8
153.3.p.b.46.1		8	51.41	even	16
272.3.bh.c.97.1		8	68.7	even	16
272.3.bh.c.129.1		8	68.19	odd	8
289.3.e.b.40.1		8	17.13	even	4
289.3.e.b.224.1		8	17.5	odd	16
289.3.e.c.131.1		8	17.10	odd	16
289.3.e.c.214.1		8	17.15	even	8
289.3.e.d.40.1		8	17.4	even	4
289.3.e.d.224.1		8	17.12	odd	16
289.3.e.i.75.1		8	17.8	even	8
289.3.e.i.158.1		8	17.6	odd	16
289.3.e.k.65.1		8	17.14	odd	16	inner
289.3.e.k.249.1		8	1.1	even	1	trivial
289.3.e.l.65.1		8	17.3	odd	16
289.3.e.l.249.1		8	17.16	even	2
289.3.e.m.75.1		8	17.9	even	8
289.3.e.m.158.1		8	17.11	odd	16
425.3.t.a.199.1		8	85.58	even	16
425.3.t.a.299.1		8	85.2	odd	8
425.3.t.c.199.1		8	85.7	even	16
425.3.t.c.299.1		8	85.53	odd	8
425.3.u.b.301.1		8	85.24	odd	16
425.3.u.b.401.1		8	85.19	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(2.79690 + 1.15851i) q^{2} +(-0.158513 - 0.796897i) q^{3} +(3.65205 + 3.65205i) q^{4} +(-6.67619 - 4.46088i) q^{5} +(0.479872 - 2.41248i) q^{6} +(6.53073 - 4.36370i) q^{7} +(1.34942 + 3.25778i) q^{8} +(7.70500 - 3.19151i) q^{9} +O(q^{10})\)	\(q+(2.79690 + 1.15851i) q^{2} +(-0.158513 - 0.796897i) q^{3} +(3.65205 + 3.65205i) q^{4} +(-6.67619 - 4.46088i) q^{5} +(0.479872 - 2.41248i) q^{6} +(6.53073 - 4.36370i) q^{7} +(1.34942 + 3.25778i) q^{8} +(7.70500 - 3.19151i) q^{9} +(-13.5046 - 20.2111i) q^{10} +(7.92030 + 1.57545i) q^{11} +(2.33141 - 3.48921i) q^{12} +(0.798835 - 0.798835i) q^{13} +(23.3212 - 4.63887i) q^{14} +(-2.49661 + 6.02734i) q^{15} -9.98414i q^{16} +25.2475 q^{18} +(-2.59882 - 1.07647i) q^{19} +(-8.09040 - 40.6732i) q^{20} +(-4.51262 - 4.51262i) q^{21} +(20.3271 + 13.5821i) q^{22} +(-1.67393 + 8.41543i) q^{23} +(2.38222 - 1.59175i) q^{24} +(15.1049 + 36.4664i) q^{25} +(3.15972 - 1.30880i) q^{26} +(-7.82730 - 11.7144i) q^{27} +(39.7870 + 7.91414i) q^{28} +(-1.70587 + 2.55301i) q^{29} +(-13.9655 + 13.9655i) q^{30} +(-12.5915 + 2.50461i) q^{31} +(16.9644 - 40.9557i) q^{32} -6.56139i q^{33} -63.0663 q^{35} +(39.7946 + 16.4835i) q^{36} +(4.61798 + 23.2161i) q^{37} +(-6.02153 - 6.02153i) q^{38} +(-0.763215 - 0.509964i) q^{39} +(5.52363 - 27.7692i) q^{40} +(-18.1595 + 12.1338i) q^{41} +(-7.39341 - 17.8493i) q^{42} +(21.4671 - 8.89197i) q^{43} +(23.1717 + 34.6790i) q^{44} +(-65.6770 - 13.0640i) q^{45} +(-14.4312 + 21.5978i) q^{46} +(-55.6597 + 55.6597i) q^{47} +(-7.95633 + 1.58261i) q^{48} +(4.85715 - 11.7262i) q^{49} +119.492i q^{50} +5.83478 q^{52} +(55.5080 + 22.9922i) q^{53} +(-8.32089 - 41.8320i) q^{54} +(-45.8495 - 45.8495i) q^{55} +(23.0287 + 15.3873i) q^{56} +(-0.445887 + 2.24162i) q^{57} +(-7.72882 + 5.16424i) q^{58} +(-10.5100 - 25.3733i) q^{59} +(-31.1299 + 12.8944i) q^{60} +(20.2562 + 30.3155i) q^{61} +(-38.1189 - 7.58231i) q^{62} +(36.3925 - 54.4652i) q^{63} +(66.6561 - 66.6561i) q^{64} +(-8.89668 + 1.76966i) q^{65} +(7.60145 - 18.3515i) q^{66} -117.219i q^{67} +6.97157 q^{69} +(-176.390 - 73.0632i) q^{70} +(20.6737 + 103.934i) q^{71} +(20.7945 + 20.7945i) q^{72} +(50.7486 + 33.9091i) q^{73} +(-13.9802 + 70.2832i) q^{74} +(26.6657 - 17.8174i) q^{75} +(-5.55971 - 13.4223i) q^{76} +(58.6001 - 24.2730i) q^{77} +(-1.54383 - 2.31051i) q^{78} +(93.4553 + 18.5894i) q^{79} +(-44.5381 + 66.6560i) q^{80} +(44.9799 - 44.9799i) q^{81} +(-64.8474 + 12.8989i) q^{82} +(-45.4770 + 109.791i) q^{83} -32.9607i q^{84} +70.3428 q^{86} +(2.30489 + 0.954715i) q^{87} +(5.55533 + 27.9285i) q^{88} +(61.4534 + 61.4534i) q^{89} +(-168.557 - 112.626i) q^{90} +(1.73111 - 8.70285i) q^{91} +(-36.8469 + 24.6203i) q^{92} +(3.99184 + 9.63715i) q^{93} +(-220.157 + 91.1920i) q^{94} +(12.5482 + 18.7797i) q^{95} +(-35.3266 - 7.02689i) q^{96} +(13.6621 - 20.4467i) q^{97} +(27.1699 - 27.1699i) q^{98} +(66.0539 - 13.1389i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 16 q^{5} - 8 q^{6} + 40 q^{7} + 40 q^{8} - 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 - 16 * q^5 - 8 * q^6 + 40 * q^7 + 40 * q^8 - 8 * q^9	\( 8 q + 8 q^{2} - 16 q^{5} - 8 q^{6} + 40 q^{7} + 40 q^{8} - 8 q^{9} - 48 q^{10} - 8 q^{11} + 72 q^{12} - 16 q^{13} + 104 q^{14} + 56 q^{18} + 48 q^{19} - 16 q^{20} + 64 q^{21} - 24 q^{22} + 56 q^{23} + 24 q^{24} + 32 q^{25} + 48 q^{26} - 24 q^{27} + 8 q^{28} - 128 q^{29} - 16 q^{30} - 40 q^{31} + 88 q^{32} - 160 q^{35} + 24 q^{36} - 96 q^{37} + 120 q^{38} - 96 q^{39} + 112 q^{40} - 48 q^{41} - 128 q^{42} + 112 q^{43} + 120 q^{44} - 112 q^{45} + 72 q^{46} - 192 q^{47} - 136 q^{48} + 80 q^{49} - 384 q^{52} + 128 q^{53} - 64 q^{54} - 224 q^{55} + 200 q^{56} + 48 q^{57} + 120 q^{59} - 48 q^{60} + 288 q^{61} + 8 q^{62} - 120 q^{63} + 64 q^{64} - 64 q^{65} + 96 q^{66} + 240 q^{69} - 480 q^{70} + 344 q^{71} - 40 q^{72} + 200 q^{73} - 208 q^{74} - 104 q^{75} - 160 q^{76} - 80 q^{77} - 512 q^{78} + 328 q^{79} + 64 q^{80} + 424 q^{81} - 64 q^{82} - 336 q^{83} + 832 q^{86} + 80 q^{87} + 8 q^{88} - 160 q^{89} - 224 q^{90} - 544 q^{91} + 24 q^{92} + 208 q^{93} - 432 q^{94} - 192 q^{95} + 64 q^{96} + 240 q^{97} + 120 q^{98} + 128 q^{99}+O(q^{100}) \) 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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