LMFDB - Embedded newform 289.3.e.k.65.1

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			65.1
Root			$-0.923880 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	289.65
Dual form			289.3.e.k.249.1

$q$-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} +(-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} - 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 $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{9}{16}\right)$

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	0.449100	−	0.893481i	$-0.351745\pi$
$2$	2.79690	−	1.15851i	1.39845	−	0.579256i	0.949348	+	0.314225i	$0.101745\pi$
$3$	−0.158513	+	0.796897i	−0.0528376	+	0.265632i	−0.998170	−	0.0604771i	$-0.980738\pi$
$3$	−0.158513	+	0.796897i	−0.0528376	+	0.265632i	0.945332	+	0.326109i	$0.105738\pi$
$4$	3.65205	−	3.65205i	0.913014	−	0.913014i
$5$	−6.67619	+	4.46088i	−1.33524	+	0.892177i	−0.998773	−	0.0495193i	$-0.984231\pi$
$5$	−6.67619	+	4.46088i	−1.33524	+	0.892177i	−0.336464	+	0.941696i	$0.609231\pi$
$6$	0.479872	+	2.41248i	0.0799786	+	0.402080i
$7$	6.53073	+	4.36370i	0.932962	+	0.623385i	0.926379	−	0.376593i	$-0.122904\pi$
$7$	6.53073	+	4.36370i	0.932962	+	0.623385i	0.00658318	+	0.999978i	$0.497904\pi$
$8$	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	0.178542	−	0.983932i	$-0.442862\pi$
$11$	7.92030	−	1.57545i	0.720027	−	0.143222i	0.541486	+	0.840710i	$0.317862\pi$
$12$	2.33141	+	3.48921i	0.194285	+	0.290767i
$13$	0.798835	+	0.798835i	0.0614489	+	0.0614489i	0.737163	−	0.675715i	$-0.236165\pi$
$13$	0.798835	+	0.798835i	0.0614489	+	0.0614489i	−0.675715	+	0.737163i	$0.736165\pi$
$14$	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	−0.450023	−	0.893017i	$-0.648584\pi$
$19$	−2.59882	+	1.07647i	−0.136780	+	0.0566561i	0.313244	+	0.949673i	$0.398584\pi$
$20$	−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	0.927182	−	0.374611i	$-0.122224\pi$
$23$	−1.67393	−	8.41543i	−0.0727797	−	0.365888i	−0.999962	+	0.00872222i	$0.997224\pi$
$24$	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	0.800892	−	0.598809i	$-0.204359\pi$
$29$	−1.70587	−	2.55301i	−0.0588230	−	0.0880348i	−0.859715	+	0.510774i	$0.829359\pi$
$30$	−13.9655	−	13.9655i	−0.465517	−	0.465517i
$31$	−12.5915	−	2.50461i	−0.406179	−	0.0807940i	−0.0122273	−	0.999925i	$-0.503892\pi$
$31$	−12.5915	−	2.50461i	−0.406179	−	0.0807940i	−0.393951	+	0.919131i	$0.628892\pi$
$32$	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	−0.866848	−	0.498572i	$-0.833858\pi$
$37$	4.61798	−	23.2161i	0.124810	−	0.627463i	0.991659	−	0.128892i	$-0.0411420\pi$
$38$	−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	0.314045	−	0.949408i	$-0.398316\pi$
$41$	−18.1595	−	12.1338i	−0.442914	−	0.295946i	−0.756959	+	0.653462i	$0.773316\pi$
$42$	−7.39341	+	17.8493i	−0.176034	+	0.424982i
$43$	21.4671	+	8.89197i	0.499235	+	0.206790i	0.618069	−	0.786124i	$-0.287915\pi$
$43$	21.4671	+	8.89197i	0.499235	+	0.206790i	−0.118833	+	0.992914i	$0.537915\pi$
$44$	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	−0.978632	−	0.205617i	$-0.934080\pi$
$47$	−55.6597	−	55.6597i	−1.18425	−	1.18425i	−0.205617	−	0.978632i	$-0.565920\pi$
$48$	−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	0.208386	−	0.978047i	$-0.433179\pi$
$53$	55.5080	−	22.9922i	1.04732	−	0.433815i	0.838935	+	0.544232i	$0.183179\pi$
$54$	−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	−0.987575	−	0.157146i	$-0.949771\pi$
$59$	−10.5100	+	25.3733i	−0.178135	+	0.430057i	0.809440	+	0.587202i	$0.199771\pi$
$60$	−31.1299	−	12.8944i	−0.518832	−	0.214907i
$61$	20.2562	−	30.3155i	0.332068	−	0.496976i	−0.627436	−	0.778668i	$-0.715896\pi$
$61$	20.2562	−	30.3155i	0.332068	−	0.496976i	0.959505	+	0.281692i	$0.0908957\pi$
$62$	−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	$0.338985\pi$
$67$			117.219i			1.74953i	−0.484544	+	0.874767i	$0.661015\pi$
$68$		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	−0.507266	−	0.861789i	$-0.669344\pi$
$71$	20.6737	−	103.934i	0.291179	−	1.46386i	0.798446	−	0.602067i	$-0.205656\pi$
$72$	20.7945	−	20.7945i	0.288813	−	0.288813i
$73$	50.7486	−	33.9091i	0.695186	−	0.464508i	−0.157101	−	0.987583i	$-0.550215\pi$
$73$	50.7486	−	33.9091i	0.695186	−	0.464508i	0.852287	+	0.523074i	$0.175215\pi$
$74$	−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	0.435869	−	0.900010i	$-0.356441\pi$
$79$	93.4553	−	18.5894i	1.18298	−	0.235309i	0.747109	+	0.664701i	$0.231441\pi$
$80$	−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	−0.919026	−	0.394197i	$-0.871023\pi$
$83$	−45.4770	−	109.791i	−0.547916	−	1.32279i	0.371110	−	0.928589i	$-0.378977\pi$
$84$			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	−0.271851	−	0.962339i	$-0.587636\pi$
$89$	61.4534	−	61.4534i	0.690488	−	0.690488i	0.962339	+	0.271851i	$0.0876359\pi$
$90$	−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	0.895186	−	0.445693i	$-0.147043\pi$
$97$	13.6621	+	20.4467i	0.140846	+	0.210791i	−0.754340	+	0.656484i	$0.772043\pi$
$98$	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	$-0.987859\pi$
$101$		−	7.70266i		−	0.0762640i	0.999273	−	0.0381320i	$-0.0121407\pi$
$102$		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	−0.849454	−	0.527662i	$-0.823069\pi$
$107$	−73.5122	+	49.1193i	−0.687030	+	0.459059i	0.162424	+	0.986721i	$0.448069\pi$
$108$	14.1958	+	71.3673i	0.131443	+	0.660808i
$109$	−15.4932	−	10.3522i	−0.142139	−	0.0949743i	0.482467	−	0.875914i	$-0.339741\pi$
$109$	−15.4932	−	10.3522i	−0.142139	−	0.0949743i	−0.624607	+	0.780940i	$0.714741\pi$
$110$	−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	−0.451108	−	0.892470i	$-0.648971\pi$
$113$	−59.4768	+	11.8307i	−0.526343	+	0.104696i	−0.0752358	+	0.997166i	$0.523971\pi$
$114$	−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	−0.636079	−	0.771624i	$-0.719445\pi$
$127$	45.6333	−	110.168i	0.359317	−	0.867468i	0.995396	−	0.0958444i	$-0.0305551\pi$
$128$	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	0.992360	+	0.123380i	$0.0393733\pi$
$131$	95.1830	+	142.451i	0.726588	+	1.08742i	−0.265772	+	0.964036i	$0.585627\pi$
$132$	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	0.622709	+	0.782454i	$0.286032\pi$
$139$	−35.0323	+	176.119i	−0.252031	+	1.26705i	−0.874740	+	0.484593i	$0.838968\pi$
$140$	−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	0.592745	−	0.805391i	$-0.298044\pi$
$149$	−31.6842	−	31.6842i	−0.212646	−	0.212646i	−0.805391	+	0.592745i	$0.798044\pi$
$150$	95.2228	+	18.9410i	0.634819	+	0.126273i
$151$	−50.2789	−	121.384i	−0.332973	−	0.803868i	−0.998353	−	0.0573634i	$-0.981731\pi$
$151$	−50.2789	−	121.384i	−0.332973	−	0.803868i	0.665380	−	0.746504i	$-0.268269\pi$
$152$			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	−0.783552	−	0.621327i	$-0.786594\pi$
$157$	−25.4694	+	25.4694i	−0.162225	+	0.162225i	0.621327	+	0.783552i	$0.286594\pi$
$158$	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	−0.452648	−	0.891689i	$-0.649521\pi$
$163$	88.7349	−	132.801i	0.544386	−	0.814731i	0.997034	+	0.0769579i	$0.0245207\pi$
$164$	−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	−0.141117	−	0.989993i	$-0.545070\pi$
$167$	−108.608	−	21.6035i	−0.650347	−	0.129362i	−0.509229	+	0.860631i	$0.670070\pi$
$168$	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	0.740556	+	0.671995i	$0.234562\pi$
$173$	−34.7367	+	174.633i	−0.200790	+	1.00944i	−0.941346	+	0.337444i	$0.890438\pi$
$174$	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	−0.379146	−	0.925337i	$-0.623782\pi$
$179$	−232.978	−	96.5028i	−1.30155	−	0.539122i	−0.922409	+	0.386215i	$0.873782\pi$
$180$	−192.146	+	287.566i	−1.06748	+	1.59759i
$181$	295.559	−	58.7904i	1.63292	−	0.324809i	0.708365	−	0.705847i	$-0.249433\pi$
$181$	295.559	−	58.7904i	1.63292	−	0.324809i	0.924559	+	0.381038i	$0.124433\pi$
$182$	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	−0.908535	−	0.417809i	$-0.862798\pi$
$191$	−93.7287	+	93.7287i	−0.490726	+	0.490726i	0.417809	+	0.908535i	$0.362798\pi$
$192$	−63.6839	+	42.5522i	−0.331687	+	0.221626i
$193$	62.1584	+	312.491i	0.322064	+	1.61913i	0.714699	+	0.699432i	$0.246564\pi$
$193$	62.1584	+	312.491i	0.322064	+	1.61913i	−0.392635	+	0.919694i	$0.628436\pi$
$194$	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	−0.631739	−	0.775181i	$-0.717659\pi$
$197$	64.2597	−	96.1714i	0.326191	−	0.488180i	0.957930	+	0.287002i	$0.0926585\pi$
$198$	199.968	−	39.7760i	1.00994	−	0.200889i
$199$	−164.363	−	245.987i	−0.825944	−	1.23611i	−0.969163	−	0.246422i	$-0.920745\pi$
$199$	−164.363	−	245.987i	−0.825944	−	1.23611i	0.143218	−	0.989691i	$-0.454255\pi$
$200$	−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	0.918682	−	0.394999i	$-0.129255\pi$
$211$	191.021	+	127.636i	0.905315	+	0.604912i	−0.0133670	+	0.999911i	$0.504255\pi$
$212$	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	0.530865	−	0.847456i	$-0.321867\pi$
$223$	335.723	−	139.061i	1.50549	−	0.623593i	0.974621	+	0.223863i	$0.0718669\pi$
$224$	−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	−0.999823	−	0.0187931i	$-0.994018\pi$
$227$	−18.9088	−	95.0611i	−0.0832988	−	0.418772i	0.916525	−	0.399978i	$-0.130982\pi$
$228$	−9.81493	−	6.55813i	−0.0430480	−	0.0287637i
$229$	−138.397	+	334.120i	−0.604353	+	1.45904i	0.264706	+	0.964329i	$0.414725\pi$
$229$	−138.397	+	334.120i	−0.604353	+	1.45904i	−0.869059	+	0.494708i	$0.835275\pi$
$230$	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	0.998437	+	0.0558946i	$0.0178011\pi$
$233$	155.642	+	232.935i	0.667991	+	0.999720i	−0.330445	+	0.943825i	$0.607199\pi$
$234$	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	0.749599	+	0.661892i	$0.230246\pi$
$241$	−47.2927	+	237.756i	−0.196235	+	0.986541i	−0.945835	+	0.324649i	$0.894754\pi$
$242$	−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	0.945371	−	0.325996i	$-0.105700\pi$
$251$	155.463	+	155.463i	0.619375	+	0.619375i	−0.325996	+	0.945371i	$0.605700\pi$
$252$	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	−0.880923	−	0.473260i	$-0.843077\pi$
$257$	−300.480	+	124.463i	−1.16918	+	0.484292i	−0.288261	+	0.957552i	$0.593077\pi$
$258$	−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	−0.790233	−	0.612806i	$-0.790041\pi$
$263$	53.0907	−	128.172i	0.201866	−	0.487347i	0.992099	+	0.125460i	$0.0400405\pi$
$264$	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	−0.436755	−	0.899580i	$-0.643872\pi$
$269$	−318.636	−	63.3806i	−1.18452	−	0.235615i	−0.747764	+	0.663965i	$0.768872\pi$
$270$	−131.056	−	316.396i	−0.485391	−	1.17184i
$271$		−	19.1867i		−	0.0707996i	−0.999373	−	0.0353998i	$-0.988730\pi$
$271$		−	19.1867i		−	0.0707996i	0.999373	−	0.0353998i	$-0.0112705\pi$
$272$		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	−0.924059	−	0.382249i	$-0.875150\pi$
$277$	−256.095	+	171.117i	−0.924529	+	0.617751i	−0.000470113		1.00000i	$0.500150\pi$
$278$	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	0.520356	−	0.853949i	$-0.325799\pi$
$281$	79.9361	+	33.1106i	0.284470	+	0.117831i	−0.235886	+	0.971781i	$0.575799\pi$
$282$	107.568	−	160.987i	0.381448	−	0.570877i
$283$	7.33785	−	1.45959i	0.0259288	−	0.00515756i	−0.182109	−	0.983278i	$-0.558292\pi$
$283$	7.33785	−	1.45959i	0.0259288	−	0.00515756i	0.208038	+	0.978121i	$0.433292\pi$
$284$	−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	−0.793906	−	0.608041i	$-0.791956\pi$
$293$	−54.4583	+	54.4583i	−0.185864	+	0.185864i	0.608041	+	0.793906i	$0.291956\pi$
$294$	−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	−0.0240745	−	0.999710i	$-0.507664\pi$
$311$	276.891	−	185.013i	0.890324	−	0.594896i	0.914399	+	0.404814i	$0.132664\pi$
$312$	0.631456	+	3.17454i	0.00202390	+	0.0101748i
$313$	−328.071	−	219.210i	−1.04815	−	0.700351i	−0.0927565	−	0.995689i	$-0.529568\pi$
$313$	−328.071	−	219.210i	−1.04815	−	0.700351i	−0.955393	+	0.295338i	$0.904568\pi$
$314$	−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	−0.405516	−	0.914088i	$-0.632908\pi$
$317$	−136.423	+	27.1362i	−0.430357	+	0.0856033i	−0.0248412	+	0.999691i	$0.507908\pi$
$318$	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	−0.805103	−	0.593136i	$-0.797890\pi$
$331$	60.7720	−	146.717i	0.183601	−	0.443252i	0.988704	+	0.149883i	$0.0478898\pi$
$332$	−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	−0.565644	−	0.824649i	$-0.691372\pi$
$337$	−473.084	−	94.1023i	−1.40381	−	0.279235i	−0.838167	+	0.545414i	$0.816372\pi$
$338$	−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	0.579054	−	0.815289i	$-0.303422\pi$
$347$	16.4546	+	10.9946i	0.0474197	+	0.0316848i	−0.531634	+	0.846974i	$0.678422\pi$
$348$	4.93090	−	11.9042i	0.0141692	−	0.0342076i
$349$	361.651	+	149.801i	1.03625	+	0.429229i	0.834965	−	0.550304i	$-0.185488\pi$
$349$	361.651	+	149.801i	1.03625	+	0.429229i	0.201286	+	0.979533i	$0.435488\pi$
$350$	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	0.484042	−	0.875045i	$-0.339168\pi$
$353$	−138.024	−	138.024i	−0.391003	−	0.391003i	−0.875045	+	0.484042i	$0.839168\pi$
$354$	−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	−0.790225	−	0.612817i	$-0.790036\pi$
$359$	−328.726	+	136.163i	−0.915672	+	0.379284i	−0.125447	+	0.992100i	$0.540036\pi$
$360$	−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	−0.888159	−	0.459536i	$-0.848016\pi$
$367$	−45.4052	+	67.9537i	−0.123720	+	0.185160i	0.764439	+	0.644696i	$0.223016\pi$
$368$	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	$-0.967163\pi$
$373$		−	76.8209i		−	0.205954i	0.994684	−	0.102977i	$-0.0328368\pi$
$374$		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	−0.995841	−	0.0911132i	$-0.970957\pi$
$379$	−489.954	+	327.377i	−1.29275	+	0.863791i	−0.296914	+	0.954904i	$0.595957\pi$
$380$	−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	0.646220	−	0.763151i	$-0.276349\pi$
$383$	215.834	+	89.4016i	0.563537	+	0.233424i	−0.0826832	+	0.996576i	$0.526349\pi$
$384$	−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	0.988353	+	0.152177i	$0.0486283\pi$
$389$	154.467	+	372.916i	0.397087	+	0.958653i	−0.591266	+	0.806477i	$0.701372\pi$
$390$		−	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	0.989890	+	0.141835i	$0.0453002\pi$
$397$	51.4626	+	258.720i	0.129629	+	0.651688i	−0.860262	+	0.509853i	$0.829700\pi$
$398$	−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	−0.627835	−	0.778347i	$-0.716059\pi$
$401$	132.942	−	198.962i	0.331526	−	0.496164i	0.959361	+	0.282183i	$0.0910586\pi$
$402$	−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	−0.391740	−	0.920076i	$-0.628127\pi$
$419$	−168.255	+	33.4680i	−0.401563	+	0.0798758i	−0.00982284	+	0.999952i	$0.503127\pi$
$420$	−147.034	−	220.052i	−0.350080	−	0.523932i
$421$	−443.214	−	443.214i	−1.05276	−	1.05276i	−0.998528	−	0.0542356i	$-0.982728\pi$
$421$	−443.214	−	443.214i	−1.05276	−	1.05276i	−0.0542356	−	0.998528i	$-0.517272\pi$
$422$	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	−0.630623	−	0.776089i	$-0.717201\pi$
$431$	−148.695	−	747.540i	−0.345000	−	1.73443i	0.285623	−	0.958342i	$-0.407799\pi$
$432$	−116.958	−	78.1489i	−0.270736	−	0.180900i
$433$	36.2305	−	87.4681i	0.0836732	−	0.202005i	−0.876505	−	0.481392i	$-0.840131\pi$
$433$	36.2305	−	87.4681i	0.0836732	−	0.202005i	0.960179	+	0.279387i	$0.0901313\pi$
$434$	−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	0.153610	−	0.988132i	$-0.450910\pi$
$439$	−36.2679	−	7.21414i	−0.0826149	−	0.0164331i	−0.236225	+	0.971698i	$0.575910\pi$
$440$	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	0.0745814	−	0.997215i	$-0.476238\pi$
$449$	−367.365	−	245.465i	−0.818184	−	0.546693i	−0.892765	+	0.450522i	$0.851238\pi$
$450$	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	0.995350	−	0.0963202i	$-0.0307073\pi$
$457$	102.104	+	246.501i	0.223423	+	0.539390i	−0.771928	+	0.635710i	$0.780707\pi$
$458$			1094.83i			2.39046i
$459$		0			0
$460$	355.825			0.773533
$461$	−417.100	+	172.768i	−0.904772	+	0.374769i	−0.786053	−	0.618159i	$-0.787879\pi$
$461$	−417.100	+	172.768i	−0.904772	+	0.374769i	−0.118719	+	0.992928i	$0.537879\pi$
$462$	−30.4375	+	153.019i	−0.0658819	+	0.331211i
$463$	57.1171	−	57.1171i	0.123363	−	0.123363i	−0.642730	−	0.766093i	$-0.722198\pi$
$463$	57.1171	−	57.1171i	0.123363	−	0.123363i	0.766093	+	0.642730i	$0.222198\pi$
$464$	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	−0.886483	−	0.462760i	$-0.846859\pi$
$467$	31.5580	−	76.1879i	0.0675761	−	0.163143i	0.954059	+	0.299617i	$0.0968590\pi$
$468$	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	−0.766354	−	0.642418i	$-0.777931\pi$
$479$	89.8162	−	451.536i	0.187508	−	0.942665i	0.953862	−	0.300246i	$-0.0970689\pi$
$480$	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	0.362233	−	0.932088i	$-0.382015\pi$
$487$	513.097	−	102.061i	1.05359	−	0.209571i	0.691354	+	0.722516i	$0.257015\pi$
$488$	−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	−0.991735	−	0.128303i	$-0.959047\pi$
$491$	−187.167	−	451.862i	−0.381196	−	0.920289i	0.610539	−	0.791986i	$-0.290953\pi$
$492$		−	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	−0.943881	−	0.330287i	$-0.892855\pi$
$499$	−98.9237	−	497.323i	−0.198244	−	0.996639i	0.745637	−	0.666353i	$-0.232145\pi$
$500$	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	0.244470	+	0.969657i	$0.421386\pi$
$503$	−374.700	+	560.779i	−0.744931	+	1.11487i	−0.989401	+	0.145211i	$0.953614\pi$
$504$	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	$0.111553\pi$
$509$			349.504i			0.686648i	−0.939217	+	0.343324i	$0.888447\pi$
$510$		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	−0.482803	−	0.875729i	$-0.660381\pi$
$521$	−309.333	+	61.5301i	−0.593729	+	0.118100i	−0.110925	+	0.993829i	$0.535381\pi$
$522$	−43.0688	−	64.4571i	−0.0825074	−	0.123481i
$523$	145.221	+	145.221i	0.277669	+	0.277669i	0.832178	−	0.554509i	$-0.187094\pi$
$523$	145.221	+	145.221i	0.277669	+	0.277669i	−0.554509	+	0.832178i	$0.687094\pi$
$524$	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	0.849897	−	0.526949i	$-0.176664\pi$
$541$	775.493	+	154.255i	1.43344	+	0.285130i	0.583547	+	0.812079i	$0.301664\pi$
$542$	−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	0.329490	+	0.944159i	$0.393123\pi$
$547$	−183.920	+	924.626i	−0.336233	+	1.69036i	−0.665723	+	0.746199i	$0.731877\pi$
$548$	−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	0.924843	−	0.380348i	$-0.124196\pi$
$557$	303.284	+	303.284i	0.544495	+	0.544495i	−0.380348	+	0.924843i	$0.624196\pi$
$558$	−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	0.266072	−	0.963953i	$-0.414274\pi$
$563$	639.473	−	264.879i	1.13583	−	0.470477i	0.869759	+	0.493476i	$0.164274\pi$
$564$	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	−0.999459	−	0.0328958i	$-0.989527\pi$
$569$	−153.331	+	370.173i	−0.269474	+	0.650567i	0.729985	+	0.683463i	$0.239527\pi$
$570$	51.3272	+	21.2604i	0.0900477	+	0.0372990i
$571$	362.070	−	541.876i	0.634098	−	0.948995i	−0.365734	−	0.930719i	$-0.619182\pi$
$571$	362.070	−	541.876i	0.634098	−	0.948995i	0.999833	−	0.0182762i	$-0.00581782\pi$
$572$	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	$-0.798017\pi$
$577$		−	684.109i		−	1.18563i	0.805339	−	0.592815i	$-0.201983\pi$
$578$		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	0.654632	−	0.755948i	$-0.272824\pi$
$587$	342.216	+	141.750i	0.582991	+	0.241483i	−0.0716408	+	0.997430i	$0.522824\pi$
$588$	−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	0.985455	+	0.169937i	$0.0543564\pi$
$593$	242.416	+	585.245i	0.408797	+	0.986922i	−0.576658	+	0.816985i	$0.695644\pi$
$594$			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	−0.919768	−	0.392463i	$-0.871623\pi$
$599$	−315.855	+	315.855i	−0.527304	+	0.527304i	0.392463	+	0.919768i	$0.371623\pi$
$600$	94.0284	−	62.8278i	0.156714	−	0.104713i
$601$	85.0027	+	427.337i	0.141435	+	0.711044i	0.984799	+	0.173700i	$0.0555723\pi$
$601$	85.0027	+	427.337i	0.141435	+	0.711044i	−0.843363	+	0.537344i	$0.819428\pi$
$602$	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	0.999240	−	0.0389892i	$-0.0124138\pi$
$607$	352.561	+	527.645i	0.580826	+	0.869267i	−0.418414	+	0.908257i	$0.637414\pi$
$608$	−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	−0.361553	−	0.932352i	$-0.617753\pi$
$617$	223.026	−	149.021i	0.361468	−	0.241525i	0.723021	+	0.690827i	$0.242753\pi$
$618$	19.9477	+	100.284i	0.0322778	+	0.162272i
$619$	130.173	+	86.9787i	0.210295	+	0.140515i	0.656258	−	0.754537i	$-0.272138\pi$
$619$	130.173	+	86.9787i	0.210295	+	0.140515i	−0.445962	+	0.895052i	$0.647138\pi$
$620$	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	−0.141538	−	0.989933i	$-0.545205\pi$
$631$	289.230	−	119.803i	0.458368	−	0.189862i	0.599906	+	0.800071i	$0.295205\pi$
$632$	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	0.635666	−	0.771964i	$-0.280725\pi$
$641$	−205.629	−	307.746i	−0.320794	−	0.480103i	−0.956461	+	0.291861i	$0.905725\pi$
$642$	−153.776	−	153.776i	−0.239526	−	0.239526i
$643$	−215.763	−	42.9179i	−0.335556	−	0.0667463i	0.0244365	−	0.999701i	$-0.492221\pi$
$643$	−215.763	−	42.9179i	−0.335556	−	0.0667463i	−0.359993	+	0.932955i	$0.617221\pi$
$644$	−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	0.582294	−	0.812979i	$-0.302155\pi$
$653$	35.2838	+	23.5759i	0.0540334	+	0.0361040i	−0.528260	+	0.849083i	$0.677155\pi$
$654$	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	0.250729	−	0.968057i	$-0.419330\pi$
$659$	−472.719	−	472.719i	−0.717328	−	0.717328i	−0.968057	+	0.250729i	$0.919330\pi$
$660$	−266.873	−	53.0843i	−0.404352	−	0.0804307i
$661$	−157.467	−	380.158i	−0.238225	−	0.575126i	0.758874	−	0.651237i	$-0.225750\pi$
$661$	−157.467	−	380.158i	−0.238225	−	0.575126i	−0.997099	+	0.0761113i	$0.975750\pi$
$662$		−	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	−0.824716	−	0.565547i	$-0.808665\pi$
$673$	9.00950	−	13.4837i	0.0133871	−	0.0200352i	0.838103	+	0.545512i	$0.183665\pi$
$674$	−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	−0.617858	−	0.786290i	$-0.711999\pi$
$677$	−1008.45	−	200.593i	−1.48958	−	0.296297i	−0.871726	+	0.489993i	$0.836999\pi$
$678$	−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	−0.934900	−	0.354911i	$-0.884511\pi$
$683$	44.1583	−	221.999i	0.0646534	−	0.325035i	0.999554	+	0.0298760i	$0.00951125\pi$
$684$	−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	−0.222739	−	0.974878i	$-0.571500\pi$
$691$	−38.3188	+	7.62208i	−0.0554541	+	0.0110305i	0.167285	+	0.985909i	$0.446500\pi$
$692$	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	−0.360390	−	0.932802i	$-0.617356\pi$
$701$	401.261	−	401.261i	0.572412	−	0.572412i	0.932802	+	0.360390i	$0.117356\pi$
$702$	−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	0.926270	−	0.376862i	$-0.122997\pi$
$709$	158.551	+	237.289i	0.223627	+	0.334681i	−0.702643	+	0.711543i	$0.747997\pi$
$710$	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	−0.857177	−	0.515022i	$-0.827784\pi$
$719$	−510.049	+	340.804i	−0.709387	+	0.473997i	0.147790	+	0.989019i	$0.452784\pi$
$720$	−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	0.518739	−	0.854933i	$-0.326402\pi$
$727$	−244.413	−	244.413i	−0.336194	−	0.336194i	−0.854933	+	0.518739i	$0.826402\pi$
$728$	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	−0.999956	−	0.00941053i	$-0.997004\pi$
$733$	−1246.38	+	516.266i	−1.70038	+	0.704319i	−0.700421	+	0.713730i	$0.747004\pi$
$734$	−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	−0.659970	−	0.751292i	$-0.729431\pi$
$739$	249.740	−	602.925i	0.337943	−	0.815866i	0.997913	−	0.0645741i	$-0.0205689\pi$
$740$	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	0.738683	−	0.674053i	$-0.235448\pi$
$743$	−123.890	−	185.415i	−0.166743	−	0.249548i	−0.905426	+	0.424505i	$0.860448\pi$
$744$	−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	0.877609	+	0.479378i	$0.159138\pi$
$751$	−87.6011	+	440.400i	−0.116646	+	0.586419i	−0.994255	+	0.107041i	$0.965862\pi$
$752$	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	0.410630	−	0.911802i	$-0.365309\pi$
$757$	42.5792	+	17.6369i	0.0562473	+	0.0232984i	−0.354382	+	0.935101i	$0.615309\pi$
$758$	−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	0.969713	−	0.244246i	$-0.0785404\pi$
$761$	552.081	+	552.081i	0.725467	+	0.725467i	−0.244246	+	0.969713i	$0.578540\pi$
$762$	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	−0.171742	−	0.985142i	$-0.554940\pi$
$769$	625.504	−	625.504i	0.813400	−	0.813400i	0.985142	+	0.171742i	$0.0549396\pi$
$770$	−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	−0.269181	−	0.963090i	$-0.586753\pi$
$773$	465.474	−	1123.75i	0.602166	−	1.45376i	0.871347	−	0.490667i	$-0.163247\pi$
$774$	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	−0.448816	−	0.893624i	$-0.648154\pi$
$787$	161.359	−	107.816i	0.205030	−	0.136997i	0.653846	+	0.756627i	$0.273154\pi$
$788$	−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	0.951693	−	0.307051i	$-0.0993422\pi$
$797$	49.1164	+	118.577i	0.0616266	+	0.148780i	−0.890066	+	0.455831i	$0.849342\pi$
$798$		−	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	−0.692007	−	0.721891i	$-0.743273\pi$
$809$	193.960	−	290.282i	0.239753	−	0.358816i	0.931760	+	0.363075i	$0.118273\pi$
$810$	−1516.53	+	301.656i	−1.87226	+	0.372415i
$811$	103.131	+	154.347i	0.127166	+	0.190317i	0.889589	−	0.456761i	$-0.150991\pi$
$811$	103.131	+	154.347i	0.127166	+	0.190317i	−0.762423	+	0.647078i	$0.775991\pi$
$812$	−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	−0.642221	+	0.766519i	$0.721987\pi$
$821$	−1310.45	+	875.613i	−1.59616	+	1.06652i	−0.953939	+	0.300001i	$0.903013\pi$
$822$	−83.0720	−	417.631i	−0.101061	−	0.508067i
$823$	−836.137	−	558.689i	−1.01596	−	0.678844i	−0.0681507	−	0.997675i	$-0.521710\pi$
$823$	−836.137	−	558.689i	−1.01596	−	0.678844i	−0.947812	+	0.318831i	$0.896710\pi$
$824$	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	−0.996466	−	0.0839938i	$-0.973232\pi$
$827$	−1558.84	+	310.073i	−1.88494	+	0.374937i	−0.888472	+	0.458931i	$0.848232\pi$
$828$	−205.329	−	307.297i	−0.247982	−	0.371132i
$829$	269.747	+	269.747i	0.325388	+	0.325388i	0.850830	−	0.525442i	$-0.176100\pi$
$829$	269.747	+	269.747i	0.325388	+	0.325388i	−0.525442	+	0.850830i	$0.676100\pi$
$830$	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	0.976243	−	0.216680i	$-0.0695228\pi$
$839$	−7.22195	−	36.3072i	−0.00860781	−	0.0432744i	−0.984850	+	0.173406i	$0.944523\pi$
$840$	−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	−0.988755	−	0.149543i	$-0.952220\pi$
$853$	−15.3853	+	77.3472i	−0.0180367	+	0.0906767i	0.970718	+	0.240220i	$0.0772196\pi$
$854$	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	0.835024	−	0.550213i	$-0.185453\pi$
$857$	553.831	+	370.058i	0.646244	+	0.431806i	−0.188780	+	0.982019i	$0.560453\pi$
$858$	−8.58754	+	20.7322i	−0.0100088	+	0.0241634i
$859$	1281.10	+	530.649i	1.49138	+	0.617752i	0.971618	−	0.236556i	$-0.0760187\pi$
$859$	1281.10	+	530.649i	1.49138	+	0.617752i	0.519767	+	0.854308i	$0.326019\pi$
$860$	−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	0.890381	−	0.455215i	$-0.150438\pi$
$863$	375.548	+	375.548i	0.435166	+	0.435166i	−0.455215	+	0.890381i	$0.650438\pi$
$864$	−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	−0.901808	−	0.432138i	$-0.857759\pi$
$877$	−138.090	+	206.666i	−0.157457	+	0.235652i	0.744350	+	0.667789i	$0.232759\pi$
$878$	−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	0.112891	−	0.993607i	$-0.463989\pi$
$881$	−143.646	−	28.5729i	−0.163048	−	0.0324324i	−0.275939	+	0.961175i	$0.588989\pi$
$882$	122.631	+	296.057i	0.139037	+	0.335665i
$883$		−	322.505i		−	0.365237i	−0.983184	−	0.182619i	$-0.941543\pi$
$883$		−	322.505i		−	0.365237i	0.983184	−	0.182619i	$-0.0584574\pi$
$884$		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	−0.987082	−	0.160218i	$-0.948780\pi$
$887$	−12.2623	+	61.6470i	−0.0138245	+	0.0695005i	0.973257	+	0.229718i	$0.0737804\pi$
$888$	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	0.949918	−	0.312498i	$-0.101166\pi$
$907$	−42.8827	−	215.586i	−0.0472797	−	0.237691i	−0.997198	+	0.0748072i	$0.976166\pi$
$908$	−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	−0.644750	−	0.764394i	$-0.723038\pi$
$911$	280.764	−	420.193i	0.308193	−	0.461244i	0.952943	+	0.303150i	$0.0980383\pi$
$912$	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	0.452378	−	0.891826i	$-0.350576\pi$
$929$	1125.58	−	223.893i	1.21161	−	0.241004i	0.759230	+	0.650822i	$0.225576\pi$
$930$	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	−0.931523	−	0.363682i	$-0.881519\pi$
$937$	−1249.07	+	517.380i	−1.33305	+	0.552166i	−0.401524	+	0.915848i	$0.631519\pi$
$938$	−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	−0.397365	−	0.917661i	$-0.630075\pi$
$941$	−358.917	−	1804.40i	−0.381421	−	1.91753i	0.0159438	−	0.999873i	$-0.494925\pi$
$942$	−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	0.819747	−	0.572725i	$-0.194114\pi$
$947$	−21.8620	−	32.7188i	−0.0230855	−	0.0345499i	−0.842833	+	0.538175i	$0.819114\pi$
$948$	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	0.946069	+	0.323965i	$0.105016\pi$
$967$	489.471	+	1181.69i	0.506175	+	1.22201i	−0.439894	+	0.898050i	$0.644984\pi$
$968$			196.715i			0.203218i
$969$		0			0
$970$	−597.751			−0.616238
$971$	844.437	−	349.777i	0.869657	−	0.360224i	0.0971803	−	0.995267i	$-0.469018\pi$
$971$	844.437	−	349.777i	0.869657	−	0.360224i	0.772477	+	0.635043i	$0.219018\pi$
$972$	−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	−0.986511	−	0.163694i	$-0.947659\pi$
$977$	−169.210	+	408.510i	−0.173194	+	0.418126i	0.813318	+	0.581820i	$0.197659\pi$
$978$	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	0.515542	−	0.856864i	$-0.327590\pi$
$983$	652.647	+	129.820i	0.663934	+	0.132065i	0.148391	+	0.988929i	$0.452590\pi$
$984$	−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	0.315525	−	0.948917i	$-0.397819\pi$
$991$	1301.14	−	869.394i	1.31296	−	0.877289i	0.997431	+	0.0716278i	$0.0228194\pi$
$992$	−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	−0.881446	−	0.472284i	$-0.843430\pi$
$997$	−1510.52	+	300.460i	−1.51506	+	0.301364i	−0.633615	+	0.773649i	$0.718430\pi$
$998$	−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.65.1		8
17.2	even	8		289.3.e.m.158.1		8
17.3	odd	16		289.3.e.i.75.1		8
17.4	even	4		289.3.e.b.224.1		8
17.5	odd	16		17.3.e.a.10.1	✓	8
17.6	odd	16		289.3.e.l.249.1		8
17.7	odd	16		289.3.e.b.40.1		8
17.8	even	8		289.3.e.c.131.1		8
17.9	even	8		17.3.e.a.12.1	yes	8
17.10	odd	16		289.3.e.d.40.1		8
17.11	odd	16	inner	289.3.e.k.249.1		8
17.12	odd	16		289.3.e.c.214.1		8
17.13	even	4		289.3.e.d.224.1		8
17.14	odd	16		289.3.e.m.75.1		8
17.15	even	8		289.3.e.i.158.1		8
17.16	even	2		289.3.e.l.65.1		8
51.5	even	16		153.3.p.b.10.1		8
51.26	odd	8		153.3.p.b.46.1		8
68.39	even	16		272.3.bh.c.129.1		8
68.43	odd	8		272.3.bh.c.97.1		8
85.9	even	8		425.3.u.b.301.1		8
85.22	even	16		425.3.t.a.299.1		8
85.39	odd	16		425.3.u.b.401.1		8
85.43	odd	8		425.3.t.a.199.1		8
85.73	even	16		425.3.t.c.299.1		8
85.77	odd	8		425.3.t.c.199.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.10.1	✓	8	17.5	odd	16
17.3.e.a.12.1	yes	8	17.9	even	8
153.3.p.b.10.1		8	51.5	even	16
153.3.p.b.46.1		8	51.26	odd	8
272.3.bh.c.97.1		8	68.43	odd	8
272.3.bh.c.129.1		8	68.39	even	16
289.3.e.b.40.1		8	17.7	odd	16
289.3.e.b.224.1		8	17.4	even	4
289.3.e.c.131.1		8	17.8	even	8
289.3.e.c.214.1		8	17.12	odd	16
289.3.e.d.40.1		8	17.10	odd	16
289.3.e.d.224.1		8	17.13	even	4
289.3.e.i.75.1		8	17.3	odd	16
289.3.e.i.158.1		8	17.15	even	8
289.3.e.k.65.1		8	1.1	even	1	trivial
289.3.e.k.249.1		8	17.11	odd	16	inner
289.3.e.l.65.1		8	17.16	even	2
289.3.e.l.249.1		8	17.6	odd	16
289.3.e.m.75.1		8	17.14	odd	16
289.3.e.m.158.1		8	17.2	even	8
425.3.t.a.199.1		8	85.43	odd	8
425.3.t.a.299.1		8	85.22	even	16
425.3.t.c.199.1		8	85.77	odd	8
425.3.t.c.299.1		8	85.73	even	16
425.3.u.b.301.1		8	85.9	even	8
425.3.u.b.401.1		8	85.39	odd	16

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+(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 16 q^{5} - 8 q^{6} + 40 q^{7} + 40 q^{8} - 8 q^{9} - 48 q^{10} - 8 q^{11} + 72 q^{12} - 16 q^{13} + 104 q^{14} + 56 q^{18} + 48 q^{19} - 16 q^{20} + 64 q^{21} - 24 q^{22} + 56 q^{23} + 24 q^{24}+ \cdots + 128 q^{99}+O(q^{100}) \) 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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