LMFDB - Embedded newform 289.3.e.m.75.1

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 = [8,8,8,0,16] 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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			75.1
Root			$-0.382683 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	289.75
Dual form			289.3.e.m.158.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.15851 - 2.79690i) q^{2} +(0.451406 - 0.675577i) q^{3} +(-3.65205 - 3.65205i) q^{4} +(1.56645 + 7.87510i) q^{5} +(-1.36656 - 2.04520i) q^{6} +(-1.53233 + 7.70353i) q^{7} +(-3.25778 + 1.34942i) q^{8} +(3.19151 + 7.70500i) q^{9} +(23.8406 + 4.74219i) q^{10} +(6.71450 - 4.48649i) q^{11} +(-4.11580 + 0.818684i) q^{12} +(-0.798835 + 0.798835i) q^{13} +(19.7707 + 13.2104i) q^{14} +(6.02734 + 2.49661i) q^{15} -9.98414i q^{16} +25.2475 q^{18} +(-1.07647 + 2.59882i) q^{19} +(23.0395 - 34.4811i) q^{20} +(4.51262 + 4.51262i) q^{21} +(-4.76941 - 23.9774i) q^{22} +(4.76696 + 7.13426i) q^{23} +(-0.558947 + 2.81002i) q^{24} +(-36.4664 + 15.1049i) q^{25} +(1.30880 + 3.15972i) q^{26} +(13.8181 + 2.74858i) q^{27} +(33.7298 - 22.5376i) q^{28} +(3.01148 - 0.599020i) q^{29} +(13.9655 - 13.9655i) q^{30} +(-10.6746 - 7.13254i) q^{31} +(-40.9557 - 16.9644i) q^{32} -6.56139i q^{33} -63.0663 q^{35} +(16.4835 - 39.7946i) q^{36} +(-13.1509 + 19.6817i) q^{37} +(6.02153 + 6.02153i) q^{38} +(0.179075 + 0.900273i) q^{39} +(-15.7300 - 23.5416i) q^{40} +(4.26082 - 21.4206i) q^{41} +(17.8493 - 7.39341i) q^{42} +(8.89197 + 21.4671i) q^{43} +(-40.9066 - 8.13684i) q^{44} +(-55.6783 + 37.2030i) q^{45} +(25.4764 - 5.06757i) q^{46} +(55.6597 - 55.6597i) q^{47} +(-6.74505 - 4.50690i) q^{48} +(-11.7262 - 4.85715i) q^{49} +119.492i q^{50} +5.83478 q^{52} +(22.9922 - 55.5080i) q^{53} +(23.6959 - 35.4634i) q^{54} +(45.8495 + 45.8495i) q^{55} +(-5.40329 - 27.1642i) q^{56} +(1.26978 + 1.90036i) q^{57} +(1.81344 - 9.11677i) q^{58} +(25.3733 - 10.5100i) q^{59} +(-12.8944 - 31.1299i) q^{60} +(-35.7596 - 7.11302i) q^{61} +(-32.3156 + 21.5926i) q^{62} +(-64.2461 + 12.7793i) q^{63} +(-66.6561 + 66.6561i) q^{64} +(-7.54224 - 5.03957i) q^{65} +(-18.3515 - 7.60145i) q^{66} -117.219i q^{67} +6.97157 q^{69} +(-73.0632 + 176.390i) q^{70} +(-58.8738 + 88.1108i) q^{71} +(-20.7945 - 20.7945i) q^{72} +(-11.9073 - 59.8620i) q^{73} +(39.8122 + 59.5832i) q^{74} +(-6.25665 + 31.4543i) q^{75} +(13.4223 - 5.55971i) q^{76} +(24.2730 + 58.6001i) q^{77} +(2.72543 + 0.542122i) q^{78} +(79.2276 - 52.9382i) q^{79} +(78.6261 - 15.6397i) q^{80} +(-44.9799 + 44.9799i) q^{81} +(-54.9749 - 36.7331i) q^{82} +(109.791 + 45.4770i) q^{83} -32.9607i q^{84} +70.3428 q^{86} +(0.954715 - 2.30489i) q^{87} +(-15.8202 + 23.6767i) q^{88} +(-61.4534 - 61.4534i) q^{89} +(39.5490 + 198.826i) q^{90} +(-4.92977 - 7.37792i) q^{91} +(8.64551 - 43.4639i) q^{92} +(-9.63715 + 3.99184i) q^{93} +(-91.1920 - 220.157i) q^{94} +(-22.1522 - 4.40634i) q^{95} +(-29.9484 + 20.0109i) q^{96} +(-24.1185 + 4.79748i) q^{97} +(-27.1699 + 27.1699i) q^{98} +(55.9978 + 37.4165i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 16 q^{5} + 24 q^{6} - 8 q^{7} + 24 q^{8} + 16 q^{9} + 48 q^{10} + 48 q^{11} + 40 q^{12} + 16 q^{13} - 8 q^{14} + 16 q^{15} + 56 q^{18} + 32 q^{20} - 64 q^{21} + 56 q^{22} + 40 q^{23}+ \cdots + 272 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^3 + 16 * q^5 + 24 * q^6 - 8 * q^7 + 24 * q^8 + 16 * q^9 + 48 * q^10 + 48 * q^11 + 40 * q^12 + 16 * q^13 - 8 * q^14 + 16 * q^15 + 56 * q^18 + 32 * q^20 - 64 * q^21 + 56 * q^22 + 40 * q^23 + 104 * q^24 - 64 * q^25 - 176 * q^26 - 16 * q^27 + 56 * q^28 - 64 * q^29 + 16 * q^30 - 40 * q^31 - 88 * q^32 - 160 * q^35 + 128 * q^36 - 128 * q^37 - 120 * q^38 - 176 * q^39 + 16 * q^40 - 112 * q^41 - 16 * q^42 + 232 * q^43 - 24 * q^44 - 160 * q^45 + 136 * q^46 + 192 * q^47 + 8 * q^48 - 16 * q^49 - 384 * q^52 + 32 * q^53 + 224 * q^55 + 136 * q^56 - 72 * q^57 + 32 * q^58 + 48 * q^59 - 64 * q^60 + 64 * q^61 - 56 * q^62 - 168 * q^63 - 64 * q^64 + 96 * q^65 + 8 * q^66 + 240 * q^69 - 224 * q^70 - 88 * q^71 + 40 * q^72 - 48 * q^73 - 192 * q^74 - 80 * q^76 + 48 * q^77 - 304 * q^78 + 168 * q^79 + 112 * q^80 - 424 * q^81 - 136 * q^82 + 264 * q^83 + 832 * q^86 - 208 * q^87 + 320 * q^88 + 160 * q^89 - 144 * q^90 + 224 * q^91 + 184 * q^92 + 64 * q^93 - 32 * q^94 + 16 * q^95 - 232 * q^96 - 104 * q^97 - 120 * q^98 + 272 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{16}\right)$

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 $

$2$	1.15851	−	2.79690i	0.579256	−	1.39845i	−0.314225	−	0.949348i	$-0.601745\pi$
$2$	1.15851	−	2.79690i	0.579256	−	1.39845i	0.893481	−	0.449100i	$-0.148255\pi$
$3$	0.451406	−	0.675577i	0.150469	−	0.225192i	−0.748576	−	0.663049i	$-0.769262\pi$
$3$	0.451406	−	0.675577i	0.150469	−	0.225192i	0.899045	+	0.437857i	$0.144262\pi$
$4$	−3.65205	−	3.65205i	−0.913014	−	0.913014i
$5$	1.56645	+	7.87510i	0.313291	+	1.57502i	0.741255	+	0.671224i	$0.234231\pi$
$5$	1.56645	+	7.87510i	0.313291	+	1.57502i	−0.427964	+	0.903796i	$0.640769\pi$
$6$	−1.36656	−	2.04520i	−0.227760	−	0.340867i
$7$	−1.53233	+	7.70353i	−0.218904	+	1.10050i	0.702436	+	0.711746i	$0.252096\pi$
$7$	−1.53233	+	7.70353i	−0.218904	+	1.10050i	−0.921340	+	0.388757i	$0.872904\pi$
$8$	−3.25778	+	1.34942i	−0.407223	+	0.168677i
$9$	3.19151	+	7.70500i	0.354613	+	0.856111i
$10$	23.8406	+	4.74219i	2.38406	+	0.474219i
$11$	6.71450	−	4.48649i	0.610410	−	0.407863i	−0.211584	−	0.977360i	$-0.567862\pi$
$11$	6.71450	−	4.48649i	0.610410	−	0.407863i	0.821993	+	0.569497i	$0.192862\pi$
$12$	−4.11580	+	0.818684i	−0.342983	+	0.0682236i
$13$	−0.798835	+	0.798835i	−0.0614489	+	0.0614489i	−0.737163	−	0.675715i	$-0.763835\pi$
$13$	−0.798835	+	0.798835i	−0.0614489	+	0.0614489i	0.675715	+	0.737163i	$0.263835\pi$
$14$	19.7707	+	13.2104i	1.41220	+	0.943599i
$15$	6.02734	+	2.49661i	0.401823	+	0.166440i
$16$		−	9.98414i		−	0.624009i
$17$		0			0
$17$		0			0
$18$	25.2475			1.40264
$19$	−1.07647	+	2.59882i	−0.0566561	+	0.136780i	−0.949673	−	0.313244i	$-0.898584\pi$
$19$	−1.07647	+	2.59882i	−0.0566561	+	0.136780i	0.893017	+	0.450023i	$0.148584\pi$
$20$	23.0395	−	34.4811i	1.15198	−	1.72405i
$21$	4.51262	+	4.51262i	0.214887	+	0.214887i
$22$	−4.76941	−	23.9774i	−0.216791	−	1.08988i
$23$	4.76696	+	7.13426i	0.207259	+	0.310185i	0.920507	−	0.390727i	$-0.127776\pi$
$23$	4.76696	+	7.13426i	0.207259	+	0.310185i	−0.713247	+	0.700912i	$0.752776\pi$
$24$	−0.558947	+	2.81002i	−0.0232895	+	0.117084i
$25$	−36.4664	+	15.1049i	−1.45866	+	0.604195i
$26$	1.30880	+	3.15972i	0.0503384	+	0.121528i
$27$	13.8181	+	2.74858i	0.511780	+	0.101799i
$28$	33.7298	−	22.5376i	1.20464	−	0.804913i
$29$	3.01148	−	0.599020i	0.103844	−	0.0206559i	−0.142895	−	0.989738i	$-0.545641\pi$
$29$	3.01148	−	0.599020i	0.103844	−	0.0206559i	0.246739	+	0.969082i	$0.420641\pi$
$30$	13.9655	−	13.9655i	0.465517	−	0.465517i
$31$	−10.6746	−	7.13254i	−0.344342	−	0.230082i	0.371358	−	0.928490i	$-0.378892\pi$
$31$	−10.6746	−	7.13254i	−0.344342	−	0.230082i	−0.715700	+	0.698408i	$0.753892\pi$
$32$	−40.9557	−	16.9644i	−1.27987	−	0.530138i
$33$		−	6.56139i		−	0.198830i
$34$		0			0
$35$	−63.0663			−1.80190
$36$	16.4835	−	39.7946i	0.457875	−	1.10541i
$37$	−13.1509	+	19.6817i	−0.355429	+	0.531938i	−0.965498	−	0.260411i	$-0.916142\pi$
$37$	−13.1509	+	19.6817i	−0.355429	+	0.531938i	0.610068	+	0.792349i	$0.291142\pi$
$38$	6.02153	+	6.02153i	0.158461	+	0.158461i
$39$	0.179075	+	0.900273i	0.00459168	+	0.0230839i
$40$	−15.7300	−	23.5416i	−0.393249	−	0.588539i
$41$	4.26082	−	21.4206i	0.103922	−	0.522453i	−0.893396	−	0.449270i	$-0.851684\pi$
$41$	4.26082	−	21.4206i	0.103922	−	0.522453i	0.997319	−	0.0731833i	$-0.0233158\pi$
$42$	17.8493	−	7.39341i	0.424982	−	0.176034i
$43$	8.89197	+	21.4671i	0.206790	+	0.499235i	0.992914	−	0.118833i	$-0.0379154\pi$
$43$	8.89197	+	21.4671i	0.206790	+	0.499235i	−0.786124	+	0.618069i	$0.787915\pi$
$44$	−40.9066	−	8.13684i	−0.929696	−	0.184928i
$45$	−55.6783	+	37.2030i	−1.23729	+	0.826734i
$46$	25.4764	−	5.06757i	0.553834	−	0.110164i
$47$	55.6597	−	55.6597i	1.18425	−	1.18425i	0.205617	−	0.978632i	$-0.434080\pi$
$47$	55.6597	−	55.6597i	1.18425	−	1.18425i	0.978632	−	0.205617i	$-0.0659202\pi$
$48$	−6.74505	−	4.50690i	−0.140522	−	0.0938937i
$49$	−11.7262	−	4.85715i	−0.239310	−	0.0991254i
$50$			119.492i			2.38984i
$51$		0			0
$52$	5.83478			0.112207
$53$	22.9922	−	55.5080i	0.433815	−	1.04732i	−0.544232	−	0.838935i	$-0.683179\pi$
$53$	22.9922	−	55.5080i	0.433815	−	1.04732i	0.978047	−	0.208386i	$-0.0668212\pi$
$54$	23.6959	−	35.4634i	0.438813	−	0.656730i
$55$	45.8495	+	45.8495i	0.833627	+	0.833627i
$56$	−5.40329	−	27.1642i	−0.0964873	−	0.485074i
$57$	1.26978	+	1.90036i	0.0222768	+	0.0333396i
$58$	1.81344	−	9.11677i	0.0312662	−	0.157186i
$59$	25.3733	−	10.5100i	0.430057	−	0.178135i	−0.157146	−	0.987575i	$-0.550229\pi$
$59$	25.3733	−	10.5100i	0.430057	−	0.178135i	0.587202	+	0.809440i	$0.300229\pi$
$60$	−12.8944	−	31.1299i	−0.214907	−	0.518832i
$61$	−35.7596	−	7.11302i	−0.586223	−	0.116607i	−0.106937	−	0.994266i	$-0.534104\pi$
$61$	−35.7596	−	7.11302i	−0.586223	−	0.116607i	−0.479286	+	0.877659i	$0.659104\pi$
$62$	−32.3156	+	21.5926i	−0.521220	+	0.348268i
$63$	−64.2461	+	12.7793i	−1.01978	+	0.202847i
$64$	−66.6561	+	66.6561i	−1.04150	+	1.04150i
$65$	−7.54224	−	5.03957i	−0.116035	−	0.0775318i
$66$	−18.3515	−	7.60145i	−0.278054	−	0.115174i
$67$		−	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
$70$	−73.0632	+	176.390i	−1.04376	+	2.51986i
$71$	−58.8738	+	88.1108i	−0.829208	+	1.24100i	0.138861	+	0.990312i	$0.455656\pi$
$71$	−58.8738	+	88.1108i	−0.829208	+	1.24100i	−0.968069	+	0.250685i	$0.919344\pi$
$72$	−20.7945	−	20.7945i	−0.288813	−	0.288813i
$73$	−11.9073	−	59.8620i	−0.163114	−	0.820028i	−0.972527	−	0.232789i	$-0.925215\pi$
$73$	−11.9073	−	59.8620i	−0.163114	−	0.820028i	0.809414	−	0.587239i	$-0.199785\pi$
$74$	39.8122	+	59.5832i	0.538003	+	0.805178i
$75$	−6.25665	+	31.4543i	−0.0834220	+	0.419390i
$76$	13.4223	−	5.55971i	0.176610	−	0.0731541i
$77$	24.2730	+	58.6001i	0.315233	+	0.761041i
$78$	2.72543	+	0.542122i	0.0349414	+	0.00695029i
$79$	79.2276	−	52.9382i	1.00288	−	0.670103i	0.0582714	−	0.998301i	$-0.481441\pi$
$79$	79.2276	−	52.9382i	1.00288	−	0.670103i	0.944609	+	0.328197i	$0.106441\pi$
$80$	78.6261	−	15.6397i	0.982826	−	0.195496i
$81$	−44.9799	+	44.9799i	−0.555308	+	0.555308i
$82$	−54.9749	−	36.7331i	−0.670426	−	0.447964i
$83$	109.791	+	45.4770i	1.32279	+	0.547916i	0.928589	−	0.371110i	$-0.121023\pi$
$83$	109.791	+	45.4770i	1.32279	+	0.547916i	0.394197	+	0.919026i	$0.371023\pi$
$84$		−	32.9607i		−	0.392389i
$85$		0			0
$86$	70.3428			0.817939
$87$	0.954715	−	2.30489i	0.0109737	−	0.0264929i
$88$	−15.8202	+	23.6767i	−0.179776	+	0.269053i
$89$	−61.4534	−	61.4534i	−0.690488	−	0.690488i	0.271851	−	0.962339i	$-0.412364\pi$
$89$	−61.4534	−	61.4534i	−0.690488	−	0.690488i	−0.962339	+	0.271851i	$0.912364\pi$
$90$	39.5490	+	198.826i	0.439434	+	2.20918i
$91$	−4.92977	−	7.37792i	−0.0541733	−	0.0810761i
$92$	8.64551	−	43.4639i	0.0939729	−	0.472434i
$93$	−9.63715	+	3.99184i	−0.103625	+	0.0429230i
$94$	−91.1920	−	220.157i	−0.970128	−	2.34210i
$95$	−22.1522	−	4.40634i	−0.233181	−	0.0463826i
$96$	−29.9484	+	20.0109i	−0.311963	+	0.208447i
$97$	−24.1185	+	4.79748i	−0.248645	+	0.0494585i	−0.317839	−	0.948145i	$-0.602957\pi$
$97$	−24.1185	+	4.79748i	−0.248645	+	0.0494585i	0.0691943	+	0.997603i	$0.477957\pi$
$98$	−27.1699	+	27.1699i	−0.277244	+	0.277244i
$99$	55.9978	+	37.4165i	0.565635	+	0.377945i
$100$	188.341	+	78.0135i	1.88341	+	0.780135i
$101$			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	$0.435324\pi$
$104$	1.52447	−	3.68039i	0.0146584	−	0.0353884i
$105$	−28.4685	+	42.6061i	−0.271129	+	0.405773i
$106$	−128.614	−	128.614i	−1.21333	−	1.21333i
$107$	17.2484	+	86.7136i	0.161200	+	0.810407i	0.973768	+	0.227541i	$0.0730687\pi$
$107$	17.2484	+	86.7136i	0.161200	+	0.810407i	−0.812568	+	0.582866i	$0.801931\pi$
$108$	−40.4263	−	60.5023i	−0.374318	−	0.560206i
$109$	3.63521	−	18.2754i	0.0333506	−	0.167665i	−0.960521	−	0.278209i	$-0.910259\pi$
$109$	3.63521	−	18.2754i	0.0333506	−	0.167665i	0.993871	+	0.110544i	$0.0352593\pi$
$110$	181.354	−	75.1191i	1.64867	−	0.682901i
$111$	7.36011	+	17.7689i	0.0663073	+	0.160080i
$112$	76.9131	+	15.2990i	0.686724	+	0.136598i
$113$	−50.4220	+	33.6909i	−0.446212	+	0.298150i	−0.758302	−	0.651903i	$-0.773971\pi$
$113$	−50.4220	+	33.6909i	−0.446212	+	0.298150i	0.312090	+	0.950053i	$0.398971\pi$
$114$	6.78616	−	1.34985i	0.0595277	−	0.0118408i
$115$	−48.7158	+	48.7158i	−0.423615	+	0.423615i
$116$	−13.1857	−	8.81043i	−0.113670	−	0.0759520i
$117$	−8.70452	−	3.60553i	−0.0743976	−	0.0308165i
$118$		−	83.1426i		−	0.704598i
$119$		0			0
$120$	−23.0047			−0.191706
$121$	−21.3487	+	51.5403i	−0.176436	+	0.425953i
$122$	−61.3223	+	91.7753i	−0.502642	+	0.752257i
$123$	−12.5479	−	12.5479i	−0.102015	−	0.102015i
$124$	12.9358	+	65.0326i	0.104321	+	0.524456i
$125$	−64.5533	−	96.6108i	−0.516426	−	0.772886i
$126$	−38.6874	+	194.495i	−0.307043	+	1.54361i
$127$	−110.168	+	45.6333i	−0.867468	+	0.359317i	−0.771624	−	0.636079i	$-0.780555\pi$
$127$	−110.168	+	45.6333i	−0.867468	+	0.359317i	−0.0958444	+	0.995396i	$0.530555\pi$
$128$	41.3506	+	99.8291i	0.323051	+	0.779915i
$129$	18.5166	+	3.68317i	0.143539	+	0.0285517i
$130$	−22.8329	+	15.2565i	−0.175638	+	0.117358i
$131$	−168.033	+	33.4238i	−1.28269	+	0.255144i	−0.788947	−	0.614461i	$-0.789373\pi$
$131$	−168.033	+	33.4238i	−1.28269	+	0.255144i	−0.493748	+	0.869605i	$0.664373\pi$
$132$	−23.9626	+	23.9626i	−0.181534	+	0.181534i
$133$	−18.3706	−	12.2748i	−0.138125	−	0.0922919i
$134$	−327.849	−	135.799i	−2.44663	−	1.01343i
$135$			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	$0.717683\pi$
$138$	8.07666	−	19.4988i	0.0585265	−	0.141295i
$139$	99.7637	−	149.307i	0.717724	−	1.07415i	−0.275876	−	0.961193i	$-0.588968\pi$
$139$	99.7637	−	149.307i	0.717724	−	1.07415i	0.993600	−	0.112957i	$-0.0360322\pi$
$140$	230.322	+	230.322i	1.64515	+	1.64515i
$141$	−12.4773	−	62.7276i	−0.0884914	−	0.444876i
$142$	178.231	+	266.741i	1.25515	+	1.87846i
$143$	−1.77982	+	8.94775i	−0.0124463	+	0.0625717i
$144$	76.9278	−	31.8645i	0.534221	−	0.221281i
$145$	9.43469	+	22.7774i	0.0650668	+	0.157085i
$146$	−181.223	−	36.0474i	−1.24125	−	0.246900i
$147$	−8.57464	+	5.72939i	−0.0583309	+	0.0389755i
$148$	119.906	−	23.8509i	0.810178	−	0.161154i
$149$	31.6842	−	31.6842i	0.212646	−	0.212646i	−0.592745	−	0.805391i	$-0.701956\pi$
$149$	31.6842	−	31.6842i	0.212646	−	0.212646i	0.805391	+	0.592745i	$0.201956\pi$
$150$	80.7260	+	53.9394i	0.538173	+	0.359596i
$151$	121.384	+	50.2789i	0.803868	+	0.332973i	0.746504	−	0.665380i	$-0.231731\pi$
$151$	121.384	+	50.2789i	0.803868	+	0.332973i	0.0573634	+	0.998353i	$0.481731\pi$
$152$		−	9.91898i		−	0.0652565i
$153$		0			0
$154$	192.019			1.24688
$155$	39.4482	−	95.2363i	0.254504	−	0.614428i
$156$	2.63385	−	3.94184i	0.0168837	−	0.0252682i
$157$	25.4694	+	25.4694i	0.162225	+	0.162225i	0.783552	−	0.621327i	$-0.213406\pi$
$157$	25.4694	+	25.4694i	0.162225	+	0.162225i	−0.621327	+	0.783552i	$0.713406\pi$
$158$	−56.2765	−	282.921i	−0.356180	−	1.79064i
$159$	−27.1211	−	40.5896i	−0.170573	−	0.255281i
$160$	69.4412	−	349.104i	0.434007	−	2.18190i
$161$	−62.2635	+	25.7904i	−0.386730	+	0.160189i
$162$	73.6944	+	177.914i	0.454904	+	1.09823i
$163$	−156.650	−	31.1596i	−0.961041	−	0.191163i	−0.310449	−	0.950590i	$-0.600479\pi$
$163$	−156.650	−	31.1596i	−0.961041	−	0.191163i	−0.650592	+	0.759427i	$0.725479\pi$
$164$	−93.7898	+	62.6684i	−0.571889	+	0.382124i
$165$	51.6716	−	10.2781i	0.313161	−	0.0622916i
$166$	254.389	−	254.389i	1.53246	−	1.53246i
$167$	−92.0734	−	61.5214i	−0.551337	−	0.368392i	0.248478	−	0.968637i	$-0.420070\pi$
$167$	−92.0734	−	61.5214i	−0.551337	−	0.368392i	−0.799816	+	0.600246i	$0.795070\pi$
$168$	−20.7905	−	8.61173i	−0.123753	−	0.0512603i
$169$			167.724i			0.992448i
$170$		0			0
$171$	−23.4594			−0.137190
$172$	45.9251	−	110.873i	0.267006	−	0.644611i
$173$	98.9216	−	148.047i	0.571801	−	0.855761i	−0.427023	−	0.904241i	$-0.640438\pi$
$173$	98.9216	−	148.047i	0.571801	−	0.855761i	0.998824	+	0.0484797i	$0.0154376\pi$
$174$	−5.34048	−	5.34048i	−0.0306924	−	0.0306924i
$175$	−60.4824	−	304.066i	−0.345614	−	1.73752i
$176$	−44.7937	−	67.0386i	−0.254510	−	0.380901i
$177$	4.35338	−	21.8859i	0.0245954	−	0.123649i
$178$	−243.074	+	100.684i	−1.36558	+	0.565642i
$179$	−96.5028	−	232.978i	−0.539122	−	1.30155i	−0.925337	−	0.379146i	$-0.876218\pi$
$179$	−96.5028	−	232.978i	−0.539122	−	1.30155i	0.386215	−	0.922409i	$-0.373782\pi$
$180$	339.207	+	67.4725i	1.88449	+	0.374847i
$181$	250.563	−	167.421i	1.38433	−	0.924977i	0.384328	−	0.923197i	$-0.374433\pi$
$181$	250.563	−	167.421i	1.38433	−	0.924977i	0.999998	−	0.00178027i	$-0.000566678\pi$
$182$	−26.3465	+	5.24064i	−0.144761	+	0.0287947i
$183$	−20.9475	+	20.9475i	−0.114467	+	0.114467i
$184$	−25.1568	−	16.8092i	−0.136722	−	0.0913546i
$185$	−175.596	−	72.7341i	−0.949165	−	0.393157i
$186$			31.5787i			0.169778i
$187$		0			0
$188$	−406.545			−2.16247
$189$	−42.3476	+	102.236i	−0.224061	+	0.540931i
$190$	−37.9877	+	56.8526i	−0.199935	+	0.299224i
$191$	93.7287	+	93.7287i	0.490726	+	0.490726i	0.908535	−	0.417809i	$-0.137202\pi$
$191$	93.7287	+	93.7287i	0.490726	+	0.490726i	−0.417809	+	0.908535i	$0.637202\pi$
$192$	14.9423	+	75.1202i	0.0778247	+	0.391251i
$193$	−177.012	−	264.917i	−0.917161	−	1.37263i	−0.927957	−	0.372687i	$-0.878436\pi$
$193$	−177.012	−	264.917i	−0.917161	−	1.37263i	0.0107958	−	0.999942i	$-0.496564\pi$
$194$	−14.5236	+	73.0150i	−0.0748639	+	0.376366i
$195$	−6.80923	+	2.82047i	−0.0349191	+	0.0144640i
$196$	25.0861	+	60.5632i	0.127990	+	0.308996i
$197$	−113.442	−	22.5650i	−0.575847	−	0.114543i	−0.101429	−	0.994843i	$-0.532341\pi$
$197$	−113.442	−	22.5650i	−0.575847	−	0.114543i	−0.474418	+	0.880300i	$0.657341\pi$
$198$	169.524	−	113.273i	0.856184	−	0.572084i
$199$	290.161	−	57.7166i	1.45809	−	0.290033i	0.598547	−	0.801088i	$-0.295745\pi$
$199$	290.161	−	57.7166i	1.45809	−	0.290033i	0.859548	+	0.511055i	$0.170745\pi$
$200$	98.4168	−	98.4168i	0.492084	−	0.492084i
$201$	−79.1902	−	52.9132i	−0.393981	−	0.263250i
$202$	21.5436	+	8.92363i	0.106651	+	0.0441764i
$203$			24.1169i			0.118802i
$204$		0			0
$205$	175.364			0.855432
$206$	48.1580	−	116.264i	0.233777	−	0.564387i
$207$	−39.7556	+	59.4985i	−0.192056	+	0.287432i
$208$	7.97568	+	7.97568i	0.0383446	+	0.0383446i
$209$	4.43163	+	22.2793i	0.0212040	+	0.106600i
$210$	86.1839	+	128.983i	0.410399	+	0.614206i
$211$	−44.8199	+	225.325i	−0.212417	+	1.06789i	0.716495	+	0.697592i	$0.245745\pi$
$211$	−44.8199	+	225.325i	−0.212417	+	1.06789i	−0.928912	+	0.370300i	$0.879255\pi$
$212$	−286.687	+	118.750i	−1.35230	+	0.560140i
$213$	32.9496	+	79.5475i	0.154693	+	0.373462i
$214$	262.511	+	52.2168i	1.22669	+	0.244004i
$215$	−155.127	+	103.652i	−0.721520	+	0.482104i
$216$	−48.7252	+	9.69205i	−0.225580	+	0.0448706i
$217$	71.3026	−	71.3026i	0.328584	−	0.328584i
$218$	−46.9031	−	31.3396i	−0.215152	−	0.143760i
$219$	−45.8164	−	18.9778i	−0.209207	−	0.0866565i
$220$		−	334.890i		−	1.52223i
$221$		0			0
$222$	58.2245			0.262272
$223$	139.061	−	335.723i	0.623593	−	1.50549i	−0.223863	−	0.974621i	$-0.571867\pi$
$223$	139.061	−	335.723i	0.623593	−	1.50549i	0.847456	−	0.530865i	$-0.178133\pi$
$224$	193.443	−	289.509i	0.863587	−	1.29245i
$225$	−232.766	−	232.766i	−1.03452	−	1.03452i
$226$	35.8155	+	180.056i	0.158475	+	0.796710i
$227$	53.8478	+	80.5890i	0.237215	+	0.355017i	0.930908	−	0.365253i	$-0.119018\pi$
$227$	53.8478	+	80.5890i	0.237215	+	0.355017i	−0.693693	+	0.720271i	$0.744018\pi$
$228$	2.30291	−	11.5775i	0.0101005	−	0.0507785i
$229$	334.120	−	138.397i	1.45904	−	0.604353i	0.494708	−	0.869059i	$-0.335275\pi$
$229$	334.120	−	138.397i	1.45904	−	0.604353i	0.964329	+	0.264706i	$0.0852749\pi$
$230$	79.8152	+	192.691i	0.347022	+	0.837786i
$231$	50.5458	+	10.0542i	0.218813	+	0.0435246i
$232$	−9.00241	+	6.01522i	−0.0388035	+	0.0259277i
$233$	−274.765	+	54.6542i	−1.17925	+	0.234567i	−0.745525	−	0.666478i	$-0.767801\pi$
$233$	−274.765	+	54.6542i	−1.17925	+	0.234567i	−0.433725	+	0.901045i	$0.642801\pi$
$234$	−20.1686	+	20.1686i	−0.0861905	+	0.0861905i
$235$	525.514	+	351.137i	2.23623	+	1.49420i
$236$	−131.048	−	54.2818i	−0.555288	−	0.230008i
$237$		−	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	$0.258776\pi$
$240$	24.9265	−	60.1778i	0.103860	−	0.250741i
$241$	134.678	−	201.560i	0.558831	−	0.836349i	−0.439244	−	0.898368i	$-0.644754\pi$
$241$	134.678	−	201.560i	0.558831	−	0.836349i	0.998075	+	0.0620186i	$0.0197538\pi$
$242$	119.420	+	119.420i	0.493472	+	0.493472i
$243$	34.8204	+	175.054i	0.143294	+	0.720387i
$244$	104.619	+	156.573i	0.428765	+	0.641693i
$245$	19.8820	−	99.9534i	0.0811509	−	0.407973i
$246$	−49.6320	+	20.5583i	−0.201756	+	0.0835701i
$247$	−1.21611	−	2.93595i	−0.00492352	−	0.0118864i
$248$	44.4003	+	8.83176i	0.179033	+	0.0356119i
$249$	80.2836	−	53.6438i	0.322424	−	0.215437i
$250$	−344.996	+	68.6240i	−1.37999	+	0.274496i
$251$	−155.463	+	155.463i	−0.619375	+	0.619375i	−0.945371	−	0.325996i	$-0.894300\pi$
$251$	−155.463	+	155.463i	−0.619375	+	0.619375i	0.325996	+	0.945371i	$0.394300\pi$
$252$	281.301	+	187.959i	1.11627	+	0.745870i
$253$	64.0155	+	26.5161i	0.253026	+	0.104807i
$254$			360.996i			1.42125i
$255$		0			0
$256$	−49.9468			−0.195105
$257$	−124.463	+	300.480i	−0.484292	+	1.16918i	0.473260	+	0.880923i	$0.343077\pi$
$257$	−124.463	+	300.480i	−0.484292	+	1.16918i	−0.957552	+	0.288261i	$0.906923\pi$
$258$	31.7531	−	47.5219i	0.123074	−	0.184194i
$259$	−131.467	−	131.467i	−0.507595	−	0.507595i
$260$	9.13991	+	45.9494i	0.0351535	+	0.176729i
$261$	14.2266	+	21.2917i	0.0545082	+	0.0815772i
$262$	−101.185	+	508.693i	−0.386203	+	1.94158i
$263$	−128.172	+	53.0907i	−0.487347	+	0.201866i	−0.612806	−	0.790233i	$-0.709959\pi$
$263$	−128.172	+	53.0907i	−0.487347	+	0.201866i	0.125460	+	0.992099i	$0.459959\pi$
$264$	8.85405	+	21.3756i	0.0335381	+	0.0809681i
$265$	473.147	+	94.1149i	1.78546	+	0.355150i
$266$	−55.6139	+	37.1600i	−0.209075	+	0.139699i
$267$	−69.2570	+	13.7761i	−0.259389	+	0.0515957i
$268$	−428.089	+	428.089i	−1.59735	+	1.59735i
$269$	−270.126	−	180.493i	−1.00419	−	0.670976i	−0.0592547	−	0.998243i	$-0.518872\pi$
$269$	−270.126	−	180.493i	−1.00419	−	0.670976i	−0.944932	+	0.327267i	$0.893872\pi$
$270$	316.396	+	131.056i	1.17184	+	0.485391i
$271$			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
$274$	−200.554	+	484.179i	−0.731947	+	1.76708i
$275$	−177.086	+	265.028i	−0.643949	+	0.963738i
$276$	−25.4606	−	25.4606i	−0.0922484	−	0.0922484i
$277$	60.0883	+	302.084i	0.216925	+	1.09056i	0.923700	+	0.383118i	$0.125150\pi$
$277$	60.0883	+	302.084i	0.216925	+	1.09056i	−0.706774	+	0.707439i	$0.749850\pi$
$278$	−302.018	−	452.003i	−1.08640	−	1.62591i
$279$	20.8880	−	105.011i	0.0748676	−	0.376385i
$280$	205.456	−	85.1028i	0.733773	−	0.303939i
$281$	33.1106	+	79.9361i	0.117831	+	0.284470i	0.971781	−	0.235886i	$-0.0757992\pi$
$281$	33.1106	+	79.9361i	0.117831	+	0.284470i	−0.853949	+	0.520356i	$0.825799\pi$
$282$	−189.898	−	37.7730i	−0.673396	−	0.133947i
$283$	6.22073	−	4.15656i	0.0219814	−	0.0146875i	−0.544531	−	0.838741i	$-0.683292\pi$
$283$	6.22073	−	4.15656i	0.0219814	−	0.0146875i	0.566512	+	0.824053i	$0.308292\pi$
$284$	536.796	−	106.775i	1.89013	−	0.375969i
$285$	−12.9764	+	12.9764i	−0.0455314	+	0.0455314i
$286$	22.9640	+	15.3440i	0.0802937	+	0.0536505i
$287$	158.485	+	65.6466i	0.552213	+	0.228734i
$288$		−	369.706i		−	1.28370i
$289$		0			0
$290$	74.6361			0.257366
$291$	−7.64619	+	18.4595i	−0.0262756	+	0.0634348i
$292$	−175.133	+	262.105i	−0.599771	+	0.897621i
$293$	54.4583	+	54.4583i	0.185864	+	0.185864i	0.793906	−	0.608041i	$-0.208044\pi$
$293$	54.4583	+	54.4583i	0.185864	+	0.185864i	−0.608041	+	0.793906i	$0.708044\pi$
$294$	6.09069	+	30.6200i	0.0207166	+	0.104150i
$295$	122.513	+	183.354i	0.415300	+	0.621540i
$296$	16.2839	−	81.8647i	0.0550132	−	0.276570i
$297$	105.113	−	43.5392i	0.353915	−	0.146597i
$298$	−51.9110	−	125.324i	−0.174198	−	0.420551i
$299$	−9.50711	−	1.89108i	−0.0317964	−	0.00632469i
$300$	137.722	−	92.0231i	0.459075	−	0.306744i
$301$	−178.998	+	35.6049i	−0.594677	+	0.118289i
$302$	281.250	−	281.250i	0.931291	−	0.931291i
$303$	5.20374	+	3.47703i	0.0171741	+	0.0114753i
$304$	25.9470	+	10.7476i	0.0853519	+	0.0353539i
$305$		−	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	$0.583744\pi$
$308$	125.365	−	302.657i	0.407028	−	0.982653i
$309$	18.7644	−	28.0829i	0.0607262	−	0.0908832i
$310$	−220.665	−	220.665i	−0.711822	−	0.711822i
$311$	−64.9678	−	326.615i	−0.208900	−	1.05021i	−0.932825	−	0.360331i	$-0.882664\pi$
$311$	−64.9678	−	326.615i	−0.208900	−	1.05021i	0.723925	−	0.689879i	$-0.242336\pi$
$312$	−1.79823	−	2.69125i	−0.00576357	−	0.00862579i
$313$	76.9763	−	386.986i	0.245931	−	1.23638i	−0.638470	−	0.769647i	$-0.720432\pi$
$313$	76.9763	−	386.986i	0.245931	−	1.23638i	0.884400	−	0.466729i	$-0.154568\pi$
$314$	100.742	−	41.7286i	0.320834	−	0.132894i
$315$	−201.277	−	485.926i	−0.638975	−	1.54262i
$316$	−482.676	−	96.0103i	−1.52746	−	0.303830i
$317$	−115.654	+	77.2775i	−0.364839	+	0.243778i	−0.724454	−	0.689323i	$-0.757908\pi$
$317$	−115.654	+	77.2775i	−0.364839	+	0.243778i	0.359615	+	0.933101i	$0.382908\pi$
$318$	−144.945	+	28.8314i	−0.455802	+	0.0906647i
$319$	17.5331	−	17.5331i	0.0549627	−	0.0549627i
$320$	−629.337	−	420.509i	−1.96668	−	1.31409i
$321$	66.3677	+	27.4904i	0.206753	+	0.0856399i
$322$			204.023i			0.633612i
$323$		0			0
$324$	328.538			1.01401
$325$	17.0643	−	41.1970i	0.0525057	−	0.126760i
$326$	−268.631	+	402.034i	−0.824021	+	1.23323i
$327$	−10.7055	−	10.7055i	−0.0327385	−	0.0327385i
$328$	15.0245	+	75.5332i	0.0458064	+	0.230284i
$329$	343.487	+	514.065i	1.04403	+	1.56251i
$330$	31.1154	−	156.427i	0.0942890	−	0.474023i
$331$	−146.717	+	60.7720i	−0.443252	+	0.183601i	−0.593136	−	0.805103i	$-0.702110\pi$
$331$	−146.717	+	60.7720i	−0.443252	+	0.183601i	0.149883	+	0.988704i	$0.452110\pi$
$332$	−234.879	−	567.048i	−0.707467	−	1.70798i
$333$	−193.619	−	38.5132i	−0.581438	−	0.115655i
$334$	−278.737	+	186.246i	−0.834543	+	0.557624i
$335$	923.109	−	183.618i	2.75555	−	0.548113i
$336$	45.0546	−	45.0546i	0.134091	−	0.134091i
$337$	−401.062	−	267.981i	−1.19009	−	0.795195i	−0.207008	−	0.978339i	$-0.566372\pi$
$337$	−401.062	−	267.981i	−1.19009	−	0.795195i	−0.983086	+	0.183144i	$0.941372\pi$
$338$	469.106	+	194.310i	1.38789	+	0.574882i
$339$			49.2722i			0.145346i
$340$		0			0
$341$	−103.675			−0.304031
$342$	−27.1781	+	65.6136i	−0.0794680	+	0.191853i
$343$	−158.436	+	237.116i	−0.461912	+	0.691299i
$344$	−57.9362	−	57.9362i	−0.168419	−	0.168419i
$345$	10.9207	+	54.9018i	0.0316541	+	0.159136i
$346$	−299.469	−	448.188i	−0.865518	−	1.29534i
$347$	−3.86080	+	19.4096i	−0.0111262	+	0.0559353i	−0.985950	−	0.167043i	$-0.946578\pi$
$347$	−3.86080	+	19.4096i	−0.0111262	+	0.0559353i	0.974823	+	0.222979i	$0.0715780\pi$
$348$	−11.9042	+	4.93090i	−0.0342076	+	0.0141692i
$349$	149.801	+	361.651i	0.429229	+	1.03625i	0.979533	+	0.201286i	$0.0645120\pi$
$349$	149.801	+	361.651i	0.429229	+	1.03625i	−0.550304	+	0.834965i	$0.685488\pi$
$350$	−920.510	−	183.101i	−2.63003	−	0.523145i
$351$	−13.2340	+	8.84268i	−0.0377037	+	0.0251928i
$352$	−351.108	+	69.8398i	−0.997466	+	0.198408i
$353$	138.024	−	138.024i	0.391003	−	0.391003i	−0.484042	−	0.875045i	$-0.660832\pi$
$353$	138.024	−	138.024i	0.391003	−	0.391003i	0.875045	+	0.484042i	$0.160832\pi$
$354$	−56.1692	−	37.5311i	−0.158670	−	0.106020i
$355$	−786.104	−	325.615i	−2.21438	−	0.917226i
$356$			448.863i			1.26085i
$357$		0			0
$358$	−763.416			−2.13245
$359$	−136.163	+	328.726i	−0.379284	+	0.915672i	0.612817	+	0.790225i	$0.290036\pi$
$359$	−136.163	+	328.726i	−0.379284	+	0.915672i	−0.992100	+	0.125447i	$0.959964\pi$
$360$	131.185	−	196.333i	0.364403	−	0.545368i
$361$	249.670	+	249.670i	0.691608	+	0.691608i
$362$	−177.978	−	894.758i	−0.491653	−	2.47171i
$363$	25.1825	+	37.6883i	0.0693733	+	0.103824i
$364$	−8.94078	+	44.9484i	−0.0245626	+	0.123485i
$365$	452.767	−	187.542i	1.24046	−	0.513814i
$366$	34.3200	+	82.8558i	0.0937705	+	0.226382i
$367$	80.1568	+	15.9442i	0.218411	+	0.0434446i	0.303083	−	0.952964i	$-0.401984\pi$
$367$	80.1568	+	15.9442i	0.218411	+	0.0434446i	−0.0846717	+	0.996409i	$0.526984\pi$
$368$	71.2294	−	47.5940i	0.193558	−	0.129331i
$369$	178.644	−	35.5345i	0.484130	−	0.0962994i
$370$	−406.859	+	406.859i	−1.09962	+	1.09962i
$371$	392.376	+	262.177i	1.05762	+	0.706677i
$372$	49.7738	+	20.6170i	0.133801	+	0.0554220i
$373$			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
$376$	−106.219	+	256.436i	−0.282498	+	0.682009i
$377$	−1.92716	+	2.88419i	−0.00511182	+	0.00765038i
$378$	236.883	+	236.883i	0.626676	+	0.626676i
$379$	114.959	+	577.940i	0.303323	+	1.52491i	0.768592	+	0.639739i	$0.220957\pi$
$379$	114.959	+	577.940i	0.303323	+	1.52491i	−0.465269	+	0.885169i	$0.654043\pi$
$380$	64.8088	+	96.9932i	0.170549	+	0.255245i
$381$	−18.9019	+	95.0264i	−0.0496113	+	0.249413i
$382$	370.735	−	153.564i	0.970511	−	0.401999i
$383$	89.4016	+	215.834i	0.233424	+	0.563537i	0.996576	−	0.0826832i	$-0.0263490\pi$
$383$	89.4016	+	215.834i	0.233424	+	0.563537i	−0.763151	+	0.646220i	$0.776349\pi$
$384$	86.1081	+	17.1280i	0.224240	+	0.0446041i
$385$	−423.459	+	282.946i	−1.09989	+	0.734926i
$386$	−946.017	+	188.175i	−2.45082	+	0.487499i
$387$	−137.025	+	137.025i	−0.354070	+	0.354070i
$388$	105.603	+	70.5616i	0.272172	+	0.181860i
$389$	−372.916	−	154.467i	−0.958653	−	0.397087i	−0.152177	−	0.988353i	$-0.548628\pi$
$389$	−372.916	−	154.467i	−0.958653	−	0.397087i	−0.806477	+	0.591266i	$0.798628\pi$
$390$			22.3123i			0.0572109i
$391$		0			0
$392$	44.7557			0.114173
$393$	−53.2707	+	128.607i	−0.135549	+	0.327244i
$394$	−194.536	+	291.143i	−0.493746	+	0.738943i
$395$	541.000	+	541.000i	1.36962	+	1.36962i
$396$	−67.8598	−	341.154i	−0.171363	−	0.861501i
$397$	−146.553	−	219.332i	−0.369151	−	0.552474i	0.599666	−	0.800251i	$-0.295300\pi$
$397$	−146.553	−	219.332i	−0.369151	−	0.552474i	−0.968817	+	0.247776i	$0.920300\pi$
$398$	174.728	−	878.415i	0.439014	−	2.20707i
$399$	−16.5852	+	6.86980i	−0.0415668	+	0.0172175i
$400$	150.809	+	364.086i	0.377023	+	0.910214i
$401$	−234.691	−	46.6830i	−0.585265	−	0.116416i	−0.106428	−	0.994320i	$-0.533941\pi$
$401$	−234.691	−	46.6830i	−0.585265	−	0.116416i	−0.478837	+	0.877904i	$0.658941\pi$
$402$	−239.736	+	160.186i	−0.596358	+	0.398473i
$403$	14.2250	−	2.82952i	0.0352977	−	0.00702114i
$404$	28.1305	−	28.1305i	0.0696300	−	0.0696300i
$405$	−424.680	−	283.762i	−1.04859	−	0.700648i
$406$	67.4525	+	27.9397i	0.166139	+	0.0688171i
$407$			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	$0.397079\pi$
$410$	203.161	−	490.474i	0.495514	−	1.19628i
$411$	−78.1442	+	116.951i	−0.190132	+	0.284552i
$412$	−151.812	−	151.812i	−0.368475	−	0.368475i
$413$	42.0837	+	211.569i	0.101898	+	0.512274i
$414$	120.354	+	180.122i	0.290710	+	0.435078i
$415$	−186.153	+	935.855i	−0.448562	+	2.25507i
$416$	46.2687	−	19.1651i	0.111223	−	0.0460700i
$417$	−55.8343	−	134.796i	−0.133895	−	0.323252i
$418$	67.4471	+	13.4161i	0.161357	+	0.0320958i
$419$	−142.640	+	95.3087i	−0.340429	+	0.227467i	−0.714018	−	0.700127i	$-0.753127\pi$
$419$	−142.640	+	95.3087i	−0.340429	+	0.227467i	0.373590	+	0.927594i	$0.378127\pi$
$420$	259.569	−	51.6314i	0.618020	−	0.122932i
$421$	443.214	−	443.214i	1.05276	−	1.05276i	0.0542356	−	0.998528i	$-0.482728\pi$
$421$	443.214	−	443.214i	1.05276	−	1.05276i	0.998528	−	0.0542356i	$-0.0172722\pi$
$422$	578.287	+	386.399i	1.37035	+	0.915637i
$423$	606.497	+	251.219i	1.43380	+	0.593899i
$424$			211.859i			0.499668i
$425$		0			0
$426$	260.659			0.611875
$427$	109.591	−	264.575i	0.256653	−	0.619614i
$428$	253.691	−	379.675i	0.592735	−	0.887090i
$429$	5.24147	+	5.24147i	0.0122179	+	0.0122179i
$430$	110.189	+	553.956i	0.256253	+	1.28827i
$431$	423.447	+	633.734i	0.982477	+	1.47038i	0.879616	+	0.475684i	$0.157799\pi$
$431$	423.447	+	633.734i	0.982477	+	1.47038i	0.102860	+	0.994696i	$0.467201\pi$
$432$	27.4422	−	137.961i	0.0635237	−	0.319355i
$433$	−87.4681	+	36.2305i	−0.202005	+	0.0836732i	−0.481392	−	0.876505i	$-0.659869\pi$
$433$	−87.4681	+	36.2305i	−0.202005	+	0.0836732i	0.279387	+	0.960179i	$0.409869\pi$
$434$	−116.821	−	282.031i	−0.269173	−	0.649841i
$435$	19.6467	+	3.90798i	0.0451649	+	0.00898385i
$436$	−80.0189	+	53.4669i	−0.183530	+	0.122630i
$437$	−23.6721	+	4.70868i	−0.0541696	+	0.0107750i
$438$	−106.158	+	106.158i	−0.242369	+	0.242369i
$439$	−30.7465	−	20.5441i	−0.0700375	−	0.0467976i	0.520059	−	0.854131i	$-0.325910\pi$
$439$	−30.7465	−	20.5441i	−0.0700375	−	0.0467976i	−0.590096	+	0.807333i	$0.700910\pi$
$440$	−211.238	−	87.4976i	−0.480086	−	0.198858i
$441$		−	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	$0.753911\pi$
$444$	38.0134	−	91.7724i	0.0856157	−	0.206695i
$445$	387.688	−	580.216i	0.871209	−	1.30386i
$446$	−777.880	−	777.880i	−1.74412	−	1.74412i
$447$	−7.10268	−	35.7076i	−0.0158897	−	0.0798828i
$448$	−411.348	−	615.626i	−0.918187	−	1.37416i
$449$	86.1959	−	433.336i	0.191973	−	0.965114i	−0.757874	−	0.652400i	$-0.773762\pi$
$449$	86.1959	−	433.336i	0.191973	−	0.965114i	0.949848	−	0.312713i	$-0.101238\pi$
$450$	−920.685	+	381.360i	−2.04597	+	0.847468i
$451$	−67.4939	−	162.945i	−0.149654	−	0.361296i
$452$	307.185	+	61.1029i	0.679613	+	0.135183i
$453$	88.7607	−	59.3080i	0.195940	−	0.130923i
$454$	287.782	−	57.2435i	0.633882	−	0.126087i
$455$	50.3796	−	50.3796i	0.110724	−	0.110724i
$456$	−6.70103	−	4.47749i	−0.0146953	−	0.00981905i
$457$	−246.501	−	102.104i	−0.539390	−	0.223423i	0.0963202	−	0.995350i	$-0.469293\pi$
$457$	−246.501	−	102.104i	−0.539390	−	0.223423i	−0.635710	+	0.771928i	$0.719293\pi$
$458$		−	1094.83i		−	2.39046i
$459$		0			0
$460$	355.825			0.773533
$461$	−172.768	+	417.100i	−0.374769	+	0.904772i	0.618159	+	0.786053i	$0.287879\pi$
$461$	−172.768	+	417.100i	−0.374769	+	0.904772i	−0.992928	+	0.118719i	$0.962121\pi$
$462$	86.6785	−	129.724i	0.187616	−	0.280787i
$463$	−57.1171	−	57.1171i	−0.123363	−	0.123363i	0.642730	−	0.766093i	$-0.277802\pi$
$463$	−57.1171	−	57.1171i	−0.123363	−	0.123363i	−0.766093	+	0.642730i	$0.777802\pi$
$464$	−5.98070	−	30.0670i	−0.0128894	−	0.0647996i
$465$	−46.5323	−	69.6405i	−0.100069	−	0.149764i
$466$	−165.457	+	831.808i	−0.355058	+	1.78499i
$467$	−76.1879	+	31.5580i	−0.163143	+	0.0675761i	−0.462760	−	0.886483i	$-0.653141\pi$
$467$	−76.1879	+	31.5580i	−0.163143	+	0.0675761i	0.299617	+	0.954059i	$0.403141\pi$
$468$	18.6218	+	44.9569i	0.0397901	+	0.0960619i
$469$	902.998	+	179.617i	1.92537	+	0.382979i
$470$	1590.91	−	1063.01i	3.38492	−	2.26173i
$471$	28.7035	−	5.70949i	0.0609417	−	0.0121221i
$472$	−68.4785	+	68.4785i	−0.145082	+	0.145082i
$473$	156.017	+	104.247i	0.329846	+	0.220396i
$474$	−216.538	−	89.6931i	−0.456832	−	0.189226i
$475$		−	111.029i		−	0.233746i
$476$		0			0
$477$	501.069			1.05046
$478$	380.630	−	918.923i	0.796298	−	1.92243i
$479$	−255.775	+	382.794i	−0.533977	+	0.799153i	−0.996153	−	0.0876357i	$-0.972069\pi$
$479$	−255.775	+	382.794i	−0.533977	+	0.799153i	0.462176	+	0.886788i	$0.347069\pi$
$480$	−204.501	−	204.501i	−0.426043	−	0.426043i
$481$	−5.21704	−	26.2278i	−0.0108462	−	0.0545277i
$482$	−407.717	−	610.191i	−0.845885	−	1.26596i
$483$	−10.6827	+	53.7057i	−0.0221174	+	0.111192i
$484$	266.195	−	110.261i	0.549989	−	0.227813i
$485$	−75.5612	−	182.421i	−0.155796	−	0.376125i
$486$	529.948	+	105.413i	1.09043	+	0.216900i
$487$	434.982	−	290.646i	0.893187	−	0.596809i	−0.0220352	−	0.999757i	$-0.507015\pi$
$487$	434.982	−	290.646i	0.893187	−	0.596809i	0.915223	+	0.402948i	$0.132015\pi$
$488$	126.095	−	25.0819i	0.258392	−	0.0513974i
$489$	−91.7633	+	91.7633i	−0.187655	+	0.187655i
$490$	−256.526	−	171.405i	−0.523522	−	0.349806i
$491$	451.862	+	187.167i	0.920289	+	0.381196i	0.791986	−	0.610539i	$-0.209047\pi$
$491$	451.862	+	187.167i	0.920289	+	0.381196i	0.128303	+	0.991735i	$0.459047\pi$
$492$			91.6511i			0.186283i
$493$		0			0
$494$	−9.62041			−0.0194745
$495$	−206.941	+	499.600i	−0.418063	+	1.00929i
$496$	−71.2122	+	106.577i	−0.143573	+	0.214872i
$497$	−588.550	−	588.550i	−1.18421	−	1.18421i
$498$	−57.0266	−	286.692i	−0.114511	−	0.575687i
$499$	281.711	+	421.610i	0.564551	+	0.844910i	0.998427	−	0.0560623i	$-0.0178545\pi$
$499$	281.711	+	421.610i	0.564551	+	0.844910i	−0.433876	+	0.900972i	$0.642855\pi$
$500$	−117.076	+	588.580i	−0.234152	+	1.17716i
$501$	−83.1249	+	34.4315i	−0.165918	+	0.0687255i
$502$	254.709	+	614.921i	0.507388	+	1.22494i
$503$	661.484	+	131.577i	1.31508	+	0.261585i	0.802292	−	0.596932i	$-0.203614\pi$
$503$	661.484	+	131.577i	1.31508	+	0.261585i	0.512785	+	0.858517i	$0.328614\pi$
$504$	192.055	−	128.327i	0.381062	−	0.254617i
$505$	−60.6592	+	12.0659i	−0.120117	+	0.0238928i
$506$	148.326	−	148.326i	0.293134	−	0.293134i
$507$	113.310	+	75.7115i	0.223492	+	0.149332i
$508$	568.996	+	235.686i	1.12007	+	0.463949i
$509$		−	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
$512$	−223.266	+	539.012i	−0.436067	+	1.05276i
$513$	−22.0177	+	32.9519i	−0.0429196	+	0.0642337i
$514$	696.221	+	696.221i	1.35451	+	1.35451i
$515$	65.1157	+	327.358i	0.126438	+	0.635648i
$516$	−54.1724	−	81.0747i	−0.104985	−	0.157121i
$517$	124.011	−	623.444i	0.239866	−	1.20589i
$518$	−520.006	+	215.393i	−1.00387	+	0.415818i
$519$	−55.3631	−	133.658i	−0.106673	−	0.257530i
$520$	31.3715	+	6.24017i	0.0603297	+	0.0120003i
$521$	−262.240	+	175.223i	−0.503339	+	0.336320i	−0.781179	−	0.624307i	$-0.785381\pi$
$521$	−262.240	+	175.223i	−0.503339	+	0.336320i	0.277840	+	0.960627i	$0.410381\pi$
$522$	76.0323	−	15.1238i	0.145656	−	0.0289727i
$523$	−145.221	+	145.221i	−0.277669	+	0.277669i	−0.832178	−	0.554509i	$-0.812906\pi$
$523$	−145.221	+	145.221i	−0.277669	+	0.277669i	0.554509	+	0.832178i	$0.312906\pi$
$524$	735.731	+	491.600i	1.40407	+	0.938168i
$525$	−232.722	−	96.3965i	−0.443279	−	0.183612i
$526$			419.991i			0.798461i
$527$		0			0
$528$	−65.5098			−0.124072
$529$	174.266	−	420.715i	0.329425	−	0.795302i
$530$	811.377	−	1214.31i	1.53090	−	2.29115i
$531$	161.959	+	161.959i	0.305007	+	0.305007i
$532$	22.2620	+	111.919i	0.0418459	+	0.210373i
$533$	13.7078	+	20.5152i	0.0257182	+	0.0384901i
$534$	−41.7048	+	209.664i	−0.0780989	+	0.392630i
$535$	−655.859	+	271.666i	−1.22590	+	0.507786i
$536$	158.177	+	381.873i	0.295106	+	0.712450i
$537$	−200.957	−	39.9728i	−0.374221	−	0.0744372i
$538$	−817.764	+	546.412i	−1.52001	+	1.01564i
$539$	−100.527	+	19.9961i	−0.186507	+	0.0370985i
$540$	413.135	−	413.135i	0.765065	−	0.765065i
$541$	657.431	+	439.282i	1.21522	+	0.811981i	0.986857	−	0.161596i	$-0.0516642\pi$
$541$	657.431	+	439.282i	1.21522	+	0.811981i	0.228358	+	0.973577i	$0.426664\pi$
$542$	53.6632	+	22.2280i	0.0990096	+	0.0410111i
$543$		−	244.849i		−	0.450919i
$544$		0			0
$545$	149.615			0.274523
$546$	−8.35251	+	20.1647i	−0.0152976	+	0.0369317i
$547$	523.758	−	783.860i	0.957511	−	1.43302i	0.0569051	−	0.998380i	$-0.481877\pi$
$547$	523.758	−	783.860i	0.957511	−	1.43302i	0.900606	−	0.434637i	$-0.143123\pi$
$548$	632.218	+	632.218i	1.15368	+	1.15368i
$549$	−59.3214	−	298.229i	−0.108054	−	0.543222i
$550$	536.099	+	802.330i	0.974726	+	1.45878i
$551$	−1.68501	+	8.47111i	−0.00305809	+	0.0153741i
$552$	−22.7119	+	9.40756i	−0.0411447	+	0.0170427i
$553$	286.408	+	691.450i	0.517917	+	1.25036i
$554$	914.512	+	181.908i	1.65074	+	0.328353i
$555$	−128.402	+	85.7957i	−0.231356	+	0.154587i
$556$	−909.619	+	180.934i	−1.63601	+	0.325422i
$557$	−303.284	+	303.284i	−0.544495	+	0.544495i	−0.924843	−	0.380348i	$-0.875804\pi$
$557$	−303.284	+	303.284i	−0.544495	+	0.544495i	0.380348	+	0.924843i	$0.375804\pi$
$558$	−269.507	−	180.079i	−0.482987	−	0.322722i
$559$	−24.2519	−	10.0455i	−0.0433844	−	0.0179704i
$560$			629.663i			1.12440i
$561$		0			0
$562$	261.932			0.466071
$563$	264.879	−	639.473i	0.470477	−	1.13583i	−0.493476	−	0.869759i	$-0.664274\pi$
$563$	264.879	−	639.473i	0.470477	−	1.13583i	0.963953	−	0.266072i	$-0.0857260\pi$
$564$	−183.517	+	274.652i	−0.325384	+	0.486972i
$565$	−344.303	−	344.303i	−0.609386	−	0.609386i
$566$	−4.41867	−	22.2142i	−0.00780684	−	0.0392476i
$567$	−277.580	−	415.428i	−0.489559	−	0.732677i
$568$	72.8996	−	366.491i	0.128344	−	0.645231i
$569$	370.173	−	153.331i	0.650567	−	0.269474i	−0.0328958	−	0.999459i	$-0.510473\pi$
$569$	370.173	−	153.331i	0.650567	−	0.269474i	0.683463	+	0.729985i	$0.260473\pi$
$570$	21.2604	+	51.3272i	0.0372990	+	0.0900477i
$571$	−639.187	−	127.142i	−1.11942	−	0.222666i	−0.399505	−	0.916731i	$-0.630818\pi$
$571$	−639.187	−	127.142i	−1.11942	−	0.222666i	−0.719912	+	0.694065i	$0.755818\pi$
$572$	39.1776	−	26.1777i	0.0684924	−	0.0457651i
$573$	105.631	−	21.0112i	0.184347	−	0.0366688i
$574$	367.214	−	367.214i	0.639745	−	0.639745i
$575$	−281.596	−	188.156i	−0.489732	−	0.327229i
$576$	−726.319	−	300.851i	−1.26097	−	0.522311i
$577$			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
$580$	48.7281	−	117.640i	0.0840140	−	0.202828i
$581$	−518.569	+	776.094i	−0.892546	+	1.33579i
$582$	42.7712	+	42.7712i	0.0734900	+	0.0734900i
$583$	−94.6550	−	475.863i	−0.162359	−	0.816232i
$584$	119.570	+	178.950i	0.204744	+	0.306420i
$585$	14.7587	−	74.1968i	0.0252285	−	0.126832i
$586$	215.405	−	89.2236i	0.367585	−	0.152259i
$587$	141.750	+	342.216i	0.241483	+	0.582991i	0.997430	−	0.0716408i	$-0.0228235\pi$
$587$	141.750	+	342.216i	0.241483	+	0.582991i	−0.755948	+	0.654632i	$0.772824\pi$
$588$	52.2391	+	10.3910i	0.0888420	+	0.0176718i
$589$	30.0270	−	20.0634i	0.0509796	−	0.0340635i
$590$	654.756	−	130.239i	1.10976	−	0.220744i
$591$	−66.4527	+	66.4527i	−0.112441	+	0.112441i
$592$	196.505	+	131.300i	0.331934	+	0.221791i
$593$	−585.245	−	242.416i	−0.986922	−	0.408797i	−0.169937	−	0.985455i	$-0.554356\pi$
$593$	−585.245	−	242.416i	−0.986922	−	0.408797i	−0.816985	+	0.576658i	$0.804356\pi$
$594$		−	344.431i		−	0.579850i
$595$		0			0
$596$	−231.425			−0.388297
$597$	91.9883	−	222.080i	0.154084	−	0.371992i
$598$	−16.3033	+	24.3996i	−0.0272630	+	0.0408020i
$599$	315.855	+	315.855i	0.527304	+	0.527304i	0.919768	−	0.392463i	$-0.128377\pi$
$599$	315.855	+	315.855i	0.527304	+	0.527304i	−0.392463	+	0.919768i	$0.628377\pi$
$600$	−22.0622	−	110.914i	−0.0367703	−	0.184857i
$601$	−242.067	−	362.279i	−0.402774	−	0.602794i	0.573533	−	0.819182i	$-0.305572\pi$
$601$	−242.067	−	362.279i	−0.402774	−	0.602794i	−0.976307	+	0.216388i	$0.930572\pi$
$602$	−107.788	+	541.887i	−0.179050	+	0.900145i
$603$	903.170	−	374.105i	1.49779	−	0.620407i
$604$	−259.680	−	626.922i	−0.429933	−	1.03795i
$605$	−439.327	−	87.3876i	−0.726160	−	0.144442i
$606$	15.7535	−	10.5261i	0.0259958	−	0.0173699i
$607$	−622.400	+	123.803i	−1.02537	+	0.203959i	−0.679000	−	0.734139i	$-0.737586\pi$
$607$	−622.400	+	123.803i	−1.02537	+	0.203959i	−0.346371	+	0.938098i	$0.612586\pi$
$608$	88.1749	−	88.1749i	0.145025	−	0.145025i
$609$	16.2928	+	10.8865i	0.0267534	+	0.0178760i
$610$	−818.798	−	339.157i	−1.34229	−	0.555996i
$611$			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	$0.691040\pi$
$614$	−184.992	+	446.610i	−0.301290	+	0.727377i
$615$	79.1601	−	118.472i	0.128716	−	0.192637i
$616$	−158.152	−	158.152i	−0.256740	−	0.256740i
$617$	−52.3292	−	263.077i	−0.0848124	−	0.426381i	−0.999741	−	0.0227645i	$-0.992753\pi$
$617$	−52.3292	−	263.077i	−0.0848124	−	0.426381i	0.914928	−	0.403616i	$-0.132247\pi$
$618$	−56.8062	−	85.0165i	−0.0919195	−	0.137567i
$619$	−30.5428	+	153.549i	−0.0493422	+	0.248060i	−0.997582	−	0.0694940i	$-0.977862\pi$
$619$	−30.5428	+	153.549i	−0.0493422	+	0.248060i	0.948240	+	0.317554i	$0.102862\pi$
$620$	−491.875	+	203.741i	−0.793346	+	0.328615i
$621$	46.2610	+	111.684i	0.0744944	+	0.179845i
$622$	−988.775	−	196.680i	−1.58967	−	0.316205i
$623$	567.575	−	379.241i	0.911035	−	0.608734i
$624$	8.98845	−	1.78791i	0.0144046	−	0.00286525i
$625$	−38.0547	+	38.0547i	−0.0608875	+	0.0608875i
$626$	−993.182	−	663.623i	−1.58655	−	1.06010i
$627$	17.0519	+	7.06311i	0.0271959	+	0.0112649i
$628$		−	186.031i		−	0.296228i
$629$		0			0
$630$	−1592.27			−2.52741
$631$	119.803	−	289.230i	0.189862	−	0.458368i	−0.800071	−	0.599906i	$-0.795205\pi$
$631$	119.803	−	289.230i	0.189862	−	0.458368i	0.989933	+	0.141538i	$0.0452048\pi$
$632$	−186.670	+	279.372i	−0.295365	+	0.442044i
$633$	131.992	+	131.992i	0.208519	+	0.208519i
$634$	82.1506	+	412.999i	0.129575	+	0.651418i
$635$	−531.940	−	796.105i	−0.837701	−	1.25371i
$636$	−49.1877	+	247.283i	−0.0773392	+	0.388810i
$637$	13.2473	−	5.48723i	0.0207965	−	0.00861418i
$638$	−28.7259	−	69.3506i	−0.0450250	−	0.108700i
$639$	−866.790	−	172.415i	−1.35648	−	0.269820i
$640$	−721.390	+	482.018i	−1.12717	+	0.753153i
$641$	363.011	−	72.2074i	0.566320	−	0.112648i	0.0963771	−	0.995345i	$-0.469275\pi$
$641$	363.011	−	72.2074i	0.566320	−	0.112648i	0.469943	+	0.882697i	$0.344275\pi$
$642$	153.776	−	153.776i	0.239526	−	0.239526i
$643$	−182.915	−	122.220i	−0.284471	−	0.190077i	0.405146	−	0.914252i	$-0.367221\pi$
$643$	−182.915	−	122.220i	−0.284471	−	0.190077i	−0.689616	+	0.724175i	$0.742221\pi$
$644$	321.577	+	133.202i	0.499344	+	0.206835i
$645$			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	$0.297407\pi$
$648$	85.8381	−	207.231i	0.132466	−	0.319802i
$649$	123.217	−	184.407i	0.189856	−	0.284140i
$650$	−95.4544	−	95.4544i	−0.146853	−	0.146853i
$651$	−15.9840	−	80.3568i	−0.0245529	−	0.123436i
$652$	458.297	+	685.889i	0.702909	+	1.05198i
$653$	−8.27876	+	41.6201i	−0.0126780	+	0.0637368i	−0.986606	−	0.163119i	$-0.947845\pi$
$653$	−8.27876	+	41.6201i	−0.0126780	+	0.0637368i	0.973928	+	0.226856i	$0.0728446\pi$
$654$	−42.3446	+	17.5397i	−0.0647472	+	0.0268192i
$655$	−526.432	−	1270.92i	−0.803713	−	1.94033i
$656$	−213.866	−	42.5406i	−0.326015	−	0.0648485i
$657$	423.234	−	282.796i	0.644192	−	0.430436i
$658$	1835.72	−	365.148i	2.78985	−	0.554936i
$659$	472.719	−	472.719i	0.717328	−	0.717328i	−0.250729	−	0.968057i	$-0.580670\pi$
$659$	472.719	−	472.719i	0.717328	−	0.717328i	0.968057	+	0.250729i	$0.0806703\pi$
$660$	−226.244	−	151.171i	−0.342793	−	0.229047i
$661$	380.158	+	157.467i	0.575126	+	0.238225i	0.651237	−	0.758874i	$-0.274250\pi$
$661$	380.158	+	157.467i	0.575126	+	0.238225i	−0.0761113	+	0.997099i	$0.524250\pi$
$662$			480.756i			0.726218i
$663$		0			0
$664$	−419.043			−0.631089
$665$	67.8888	−	163.898i	0.102088	−	0.246463i
$666$	−332.027	+	496.914i	−0.498539	+	0.746116i
$667$	18.6292	+	18.6292i	0.0279298	+	0.0279298i
$668$	111.577	+	560.937i	0.167032	+	0.839725i
$669$	−164.034	−	245.494i	−0.245193	−	0.366957i
$670$	555.873	−	2794.56i	0.829662	−	4.17099i
$671$	−272.020	+	112.675i	−0.405395	+	0.167920i
$672$	−108.264	−	261.372i	−0.161107	−	0.388946i
$673$	−15.9051	−	3.16371i	−0.0236331	−	0.00470091i	0.183260	−	0.983065i	$-0.441335\pi$
$673$	−15.9051	−	3.16371i	−0.0236331	−	0.00470091i	−0.206893	+	0.978364i	$0.566335\pi$
$674$	−1214.15	+	811.269i	−1.80141	+	1.20366i
$675$	−545.412	+	108.489i	−0.808018	+	0.160725i
$676$	612.536	−	612.536i	0.906119	−	0.906119i
$677$	−854.921	−	571.240i	−1.26281	−	0.843782i	−0.269926	−	0.962881i	$-0.586999\pi$
$677$	−854.921	−	571.240i	−1.26281	−	0.843782i	−0.992882	+	0.119099i	$0.961999\pi$
$678$	137.809	+	57.0825i	0.203258	+	0.0841924i
$679$		−	193.149i		−	0.284461i
$680$		0			0
$681$	78.7512			0.115641
$682$	−120.108	+	289.967i	−0.176112	+	0.425172i
$683$	−125.752	+	188.201i	−0.184117	+	0.275551i	−0.912034	−	0.410114i	$-0.865489\pi$
$683$	−125.752	+	188.201i	−0.184117	+	0.275551i	0.727917	+	0.685666i	$0.240489\pi$
$684$	85.6752	+	85.6752i	0.125256	+	0.125256i
$685$	−271.173	−	1363.28i	−0.395874	−	1.99019i
$686$	479.639	+	717.830i	0.699181	+	1.04640i
$687$	57.3259	−	288.197i	0.0834438	−	0.419500i
$688$	214.331	−	88.7787i	0.311527	−	0.129039i
$689$	25.9748	+	62.7087i	0.0376993	+	0.0910141i
$690$	166.206	+	33.0605i	0.240879	+	0.0479138i
$691$	−32.4851	+	21.7058i	−0.0470117	+	0.0314122i	−0.578854	−	0.815431i	$-0.696500\pi$
$691$	−32.4851	+	21.7058i	−0.0470117	+	0.0314122i	0.531842	+	0.846843i	$0.321500\pi$
$692$	−901.942	+	179.407i	−1.30338	+	0.259259i
$693$	−374.046	+	374.046i	−0.539749	+	0.539749i
$694$	49.8138	+	33.2845i	0.0717778	+	0.0479604i
$695$	1332.08	+	551.766i	1.91666	+	0.793908i
$696$			8.79713i			0.0126395i
$697$		0			0
$698$	1185.05			1.69778
$699$	−87.1075	+	210.296i	−0.124617	+	0.300853i
$700$	−889.579	+	1331.35i	−1.27083	+	1.90193i
$701$	−401.261	−	401.261i	−0.572412	−	0.572412i	0.360390	−	0.932802i	$-0.382644\pi$
$701$	−401.261	−	401.261i	−0.572412	−	0.572412i	−0.932802	+	0.360390i	$0.882644\pi$
$702$	9.40031	+	47.2585i	0.0133908	+	0.0673198i
$703$	−36.9927	−	55.3634i	−0.0526212	−	0.0787531i
$704$	−148.511	+	746.614i	−0.210953	+	1.06053i
$705$	474.441	−	196.520i	0.672965	−	0.278751i
$706$	−226.136	−	545.941i	−0.320306	−	0.773288i
$707$	−59.3377	−	11.8030i	−0.0839288	−	0.0166945i
$708$	−95.8273	+	64.0298i	−0.135349	+	0.0904375i
$709$	−279.901	+	55.6759i	−0.394783	+	0.0785273i	−0.388490	−	0.921453i	$-0.627003\pi$
$709$	−279.901	+	55.6759i	−0.394783	+	0.0785273i	−0.00629329	+	0.999980i	$0.502003\pi$
$710$	−1821.42	+	1821.42i	−2.56539	+	2.56539i
$711$	660.744	+	441.495i	0.929317	+	0.620950i
$712$	283.128	+	117.276i	0.397652	+	0.164713i
$713$		−	110.156i		−	0.154496i
$714$		0			0
$715$	−73.2524			−0.102451
$716$	−498.416	+	1203.28i	−0.696112	+	1.68056i
$717$	148.310	−	221.961i	0.206848	−	0.309569i
$718$	761.667	+	761.667i	1.06082	+	1.06082i
$719$	119.674	+	601.644i	0.166446	+	0.836779i	0.970291	+	0.241941i	$0.0777839\pi$
$719$	119.674	+	601.644i	0.166446	+	0.836779i	−0.803845	+	0.594838i	$0.797216\pi$
$720$	371.440	+	555.899i	0.515889	+	0.772083i
$721$	−63.6970	+	320.226i	−0.0883453	+	0.444142i
$722$	987.549	−	409.056i	1.36780	−	0.566560i
$723$	−75.3748	−	181.971i	−0.104253	−	0.251689i
$724$	−1526.50	−	303.640i	−2.10842	−	0.419392i
$725$	−100.770	+	67.3322i	−0.138993	+	0.0928719i
$726$	134.585	−	26.7705i	0.185378	−	0.0368740i
$727$	244.413	−	244.413i	0.336194	−	0.336194i	−0.518739	−	0.854933i	$-0.673598\pi$
$727$	244.413	−	244.413i	0.336194	−	0.336194i	0.854933	+	0.518739i	$0.173598\pi$
$728$	26.0160	+	17.3833i	0.0357363	+	0.0238782i
$729$	−394.941	−	163.590i	−0.541758	−	0.224403i
$730$		−	1483.61i		−	2.03235i
$731$		0			0
$732$	153.003			0.209020
$733$	−516.266	+	1246.38i	−0.704319	+	1.70038i	0.00941053	+	0.999956i	$0.497004\pi$
$733$	−516.266	+	1246.38i	−0.704319	+	1.70038i	−0.713730	+	0.700421i	$0.752996\pi$
$734$	137.457	−	205.719i	0.187271	−	0.280271i
$735$	−58.5513	−	58.5513i	−0.0796617	−	0.0796617i
$736$	−74.2058	−	373.058i	−0.100823	−	0.506872i
$737$	−525.901	−	787.066i	−0.713569	−	1.06793i
$738$	107.575	−	540.816i	0.145766	−	0.732813i
$739$	−602.925	+	249.740i	−0.815866	+	0.337943i	−0.751292	−	0.659970i	$-0.770569\pi$
$739$	−602.925	+	249.740i	−0.815866	+	0.337943i	−0.0645741	+	0.997913i	$0.520569\pi$
$740$	375.656	+	906.913i	0.507643	+	1.22556i
$741$	−2.53241	−	0.503729i	−0.00341756	−	0.000679796i
$742$	1187.86	−	793.700i	1.60088	−	1.06968i
$743$	218.711	−	43.5044i	0.294362	−	0.0585523i	−0.0456999	−	0.998955i	$-0.514552\pi$
$743$	218.711	−	43.5044i	0.294362	−	0.0585523i	0.340062	+	0.940403i	$0.389552\pi$
$744$	26.0091	−	26.0091i	0.0349584	−	0.0349584i
$745$	299.149	+	199.885i	0.401542	+	0.268302i
$746$	214.860	+	88.9980i	0.288016	+	0.119300i
$747$			991.082i			1.32675i
$748$		0			0
$749$	−694.430			−0.927143
$750$	−109.373	+	264.049i	−0.145830	+	0.352065i
$751$	249.467	−	373.353i	0.332180	−	0.497142i	−0.627355	−	0.778734i	$-0.715862\pi$
$751$	249.467	−	373.353i	0.332180	−	0.497142i	0.959534	+	0.281592i	$0.0908624\pi$
$752$	−555.715	−	555.715i	−0.738982	−	0.738982i
$753$	34.8503	+	175.204i	0.0462820	+	0.232675i
$754$	5.83416	+	8.73143i	0.00773761	+	0.0115802i
$755$	−205.809	+	1034.67i	−0.272595	+	1.37043i
$756$	528.027	−	218.716i	0.698449	−	0.289307i
$757$	17.6369	+	42.5792i	0.0232984	+	0.0562473i	0.935101	−	0.354382i	$-0.115309\pi$
$757$	17.6369	+	42.5792i	0.0232984	+	0.0562473i	−0.911802	+	0.410630i	$0.865309\pi$
$758$	1749.62	+	348.021i	2.30821	+	0.459131i
$759$	46.8107	−	31.2779i	0.0616741	−	0.0412093i
$760$	78.1130	−	15.5376i	0.102780	−	0.0204443i
$761$	−552.081	+	552.081i	−0.725467	+	0.725467i	−0.969713	−	0.244246i	$-0.921460\pi$
$761$	−552.081	+	552.081i	−0.725467	+	0.725467i	0.244246	+	0.969713i	$0.421460\pi$
$762$	243.881	+	162.956i	0.320054	+	0.213853i
$763$	135.215	+	56.0079i	0.177215	+	0.0734048i
$764$		−	684.604i		−	0.896079i
$765$		0			0
$766$	707.240			0.923289
$767$	−11.8734	+	28.6649i	−0.0154803	+	0.0373727i
$768$	−22.5463	+	33.7429i	−0.0293571	+	0.0439360i
$769$	−625.504	−	625.504i	−0.813400	−	0.813400i	0.171742	−	0.985142i	$-0.445060\pi$
$769$	−625.504	−	625.504i	−0.813400	−	0.813400i	−0.985142	+	0.171742i	$0.945060\pi$
$770$	300.789	+	1512.17i	0.390635	+	1.96386i
$771$	146.814	+	219.723i	0.190420	+	0.284984i
$772$	−321.035	+	1613.95i	−0.415848	+	2.09061i
$773$	−1123.75	+	465.474i	−1.45376	+	0.602166i	−0.963090	−	0.269181i	$-0.913247\pi$
$773$	−1123.75	+	465.474i	−1.45376	+	0.602166i	−0.490667	+	0.871347i	$0.663247\pi$
$774$	224.500	+	541.991i	0.290052	+	0.700247i
$775$	497.000	+	98.8595i	0.641291	+	0.127561i
$776$	72.0992	−	48.1751i	0.0929113	−	0.0620813i
$777$	−148.161	+	29.4711i	−0.190683	+	0.0379293i
$778$	−864.056	+	864.056i	−1.11061	+	1.11061i
$779$	51.0816	+	34.1316i	0.0655733	+	0.0438146i
$780$	35.1682	+	14.5671i	0.0450874	+	0.0186758i
$781$			855.757i			1.09572i
$782$		0			0
$783$	43.2592			0.0552481
$784$	−48.4944	+	117.076i	−0.0618551	+	0.149331i
$785$	−160.677	+	240.470i	−0.204684	+	0.306332i
$786$	297.985	+	297.985i	0.379116	+	0.379116i
$787$	−37.8601	−	190.336i	−0.0481069	−	0.241850i	0.949249	−	0.314527i	$-0.101846\pi$
$787$	−37.8601	−	190.336i	−0.0481069	−	0.241850i	−0.997356	+	0.0726771i	$0.976846\pi$
$788$	331.887	+	496.704i	0.421177	+	0.630336i
$789$	−21.9909	+	110.556i	−0.0278718	+	0.140121i
$790$	2139.88	−	886.365i	2.70870	−	1.12198i
$791$	−182.276	−	440.053i	−0.230437	−	0.556324i
$792$	−232.919	−	46.3305i	−0.294090	−	0.0584981i
$793$	34.2481	−	22.8839i	0.0431881	−	0.0288573i
$794$	−783.233	+	155.795i	−0.986440	+	0.196215i
$795$	277.163	−	277.163i	0.348633	−	0.348633i
$796$	−1270.47	−	848.899i	−1.59606	−	1.06646i
$797$	−118.577	−	49.1164i	−0.148780	−	0.0616266i	0.307051	−	0.951693i	$-0.400658\pi$
$797$	−118.577	−	49.1164i	−0.148780	−	0.0616266i	−0.455831	+	0.890066i	$0.650658\pi$
$798$			54.3457i			0.0681024i
$799$		0			0
$800$	1749.75			2.18719
$801$	277.369	−	669.628i	0.346278	−	0.835990i
$802$	−402.460	+	602.324i	−0.501821	+	0.751028i
$803$	−348.522	−	348.522i	−0.434025	−	0.434025i
$804$	95.9651	+	482.449i	0.119360	+	0.600061i
$805$	−300.635	−	449.932i	−0.373459	−	0.558921i
$806$	8.56592	−	43.0638i	0.0106277	−	0.0534290i
$807$	−243.873	+	101.016i	−0.302197	+	0.125174i
$808$	−10.3941	−	25.0936i	−0.0128640	−	0.0310564i
$809$	−342.411	−	68.1098i	−0.423253	−	0.0841902i	−0.0211316	−	0.999777i	$-0.506727\pi$
$809$	−342.411	−	68.1098i	−0.423253	−	0.0841902i	−0.402121	+	0.915587i	$0.631727\pi$
$810$	−1285.65	+	859.045i	−1.58722	+	1.06055i
$811$	−182.065	+	36.2150i	−0.224494	+	0.0446547i	−0.306056	−	0.952014i	$-0.599009\pi$
$811$	−182.065	+	36.2150i	−0.224494	+	0.0446547i	0.0815613	+	0.996668i	$0.474009\pi$
$812$	88.0762	−	88.0762i	0.108468	−	0.108468i
$813$	12.9621	+	8.66099i	0.0159435	+	0.0106531i
$814$	534.639	+	221.455i	0.656804	+	0.272057i
$815$		−	1282.44i		−	1.57355i
$816$		0			0
$817$	−65.3610			−0.0800013
$818$	301.101	−	726.923i	0.368095	−	0.888659i
$819$	41.1134	−	61.5306i	0.0501996	−	0.0751290i
$820$	−640.437	−	640.437i	−0.781021	−	0.781021i
$821$	307.474	+	1545.78i	0.374512	+	1.88280i	0.462404	+	0.886669i	$0.346987\pi$
$821$	307.474	+	1545.78i	0.374512	+	1.88280i	−0.0878920	+	0.996130i	$0.528013\pi$
$822$	236.569	+	354.051i	0.287797	+	0.430718i
$823$	196.185	−	986.291i	0.238378	−	1.19841i	−0.657273	−	0.753653i	$-0.728290\pi$
$823$	196.185	−	986.291i	0.238378	−	1.19841i	0.895651	−	0.444757i	$-0.146710\pi$
$824$	−135.422	+	56.0937i	−0.164347	+	0.0680749i
$825$	99.1090	+	239.270i	0.120132	+	0.290025i
$826$	640.491	+	127.402i	0.775413	+	0.154239i
$827$	−1321.52	+	883.014i	−1.59797	+	1.06773i	−0.645216	+	0.764001i	$0.723232\pi$
$827$	−1321.52	+	883.014i	−1.59797	+	1.06773i	−0.952758	+	0.303731i	$0.901768\pi$
$828$	362.481	−	72.1020i	0.437780	−	0.0870798i
$829$	−269.747	+	269.747i	−0.325388	+	0.325388i	−0.850830	−	0.525442i	$-0.823900\pi$
$829$	−269.747	+	269.747i	−0.325388	+	0.325388i	0.525442	+	0.850830i	$0.323900\pi$
$830$	2401.83	+	1604.85i	2.89377	+	1.93355i
$831$	231.205	+	95.7684i	0.278225	+	0.115245i
$832$		−	106.494i		−	0.127998i
$833$		0			0
$834$	−441.695			−0.529611
$835$	340.259	−	821.457i	0.407495	−	0.983781i
$836$	65.1807	−	97.5499i	0.0779674	−	0.116686i
$837$	−127.898	−	127.898i	−0.152805	−	0.152805i
$838$	101.319	+	509.365i	0.120906	+	0.607834i
$839$	20.5664	+	30.7798i	0.0245130	+	0.0366862i	0.843524	−	0.537092i	$-0.180477\pi$
$839$	20.5664	+	30.7798i	0.0245130	+	0.0366862i	−0.819011	+	0.573778i	$0.805477\pi$
$840$	35.2507	−	177.217i	0.0419652	−	0.210973i
$841$	−768.273	+	318.229i	−0.913523	+	0.378393i
$842$	−726.154	−	1753.09i	−0.862416	−	2.08206i
$843$	68.9493	+	13.7149i	0.0817904	+	0.0162691i
$844$	986.584	−	659.215i	1.16894	−	0.781060i
$845$	−1320.84	+	262.732i	−1.56313	+	0.310925i
$846$	1405.27	−	1405.27i	1.66107	−	1.66107i
$847$	−364.329	−	243.437i	−0.430141	−	0.287411i
$848$	−554.200	−	229.557i	−0.653538	−	0.270704i
$849$		−	6.07887i		−	0.00716004i
$850$		0			0
$851$	−203.104			−0.238665
$852$	170.178	−	410.846i	0.199739	−	0.482213i
$853$	43.8137	−	65.5718i	0.0513642	−	0.0768720i	−0.804899	−	0.593412i	$-0.797780\pi$
$853$	43.8137	−	65.5718i	0.0513642	−	0.0768720i	0.856263	+	0.516540i	$0.172780\pi$
$854$	−613.028	−	613.028i	−0.717831	−	0.717831i
$855$	−36.7481	−	184.745i	−0.0429803	−	0.216077i
$856$	−173.204	−	259.219i	−0.202342	−	0.302825i
$857$	−129.947	+	653.288i	−0.151630	+	0.762297i	0.827880	+	0.560905i	$0.189547\pi$
$857$	−129.947	+	653.288i	−0.151630	+	0.762297i	−0.979511	+	0.201392i	$0.935453\pi$
$858$	20.7322	−	8.58754i	0.0241634	−	0.0100088i
$859$	530.649	+	1281.10i	0.617752	+	1.49138i	0.854308	+	0.519767i	$0.173981\pi$
$859$	530.649	+	1281.10i	0.617752	+	1.49138i	−0.236556	+	0.971618i	$0.576019\pi$
$860$	945.076	+	187.987i	1.09893	+	0.218590i
$861$	115.890	−	77.4355i	0.134600	−	0.0899367i
$862$	2263.06	−	450.150i	2.62536	−	0.522216i
$863$	−375.548	+	375.548i	−0.435166	+	0.435166i	−0.890381	−	0.455215i	$-0.849562\pi$
$863$	−375.548	+	375.548i	−0.435166	+	0.435166i	0.455215	+	0.890381i	$0.349562\pi$
$864$	−519.301	−	346.986i	−0.601042	−	0.401604i
$865$	1320.84	+	547.109i	1.52698	+	0.632496i
$866$			286.613i			0.330962i
$867$		0			0
$868$	−520.802			−0.600002
$869$	294.467	−	710.907i	0.338858	−	0.818075i
$870$	33.6912	−	50.4224i	0.0387255	−	0.0579568i
$871$	93.6384	+	93.6384i	0.107507	+	0.107507i
$872$	12.8185	+	64.4428i	0.0147001	+	0.0739023i
$873$	−113.939	−	170.522i	−0.130515	−	0.195329i
$874$	−14.2548	+	71.6635i	−0.0163098	+	0.0819949i
$875$	843.160	−	349.249i	0.963612	−	0.399141i
$876$	98.0161	+	236.632i	0.111891	+	0.270128i
$877$	243.780	+	48.4908i	0.277970	+	0.0552917i	0.332107	−	0.943242i	$-0.392241\pi$
$877$	243.780	+	48.4908i	0.277970	+	0.0552917i	−0.0541366	+	0.998534i	$0.517241\pi$
$878$	−93.0800	+	62.1940i	−0.106014	+	0.0708360i
$879$	61.3735	−	12.2080i	0.0698220	−	0.0138885i
$880$	457.768	−	457.768i	0.520191	−	0.520191i
$881$	−121.777	−	81.3688i	−0.138226	−	0.0923595i	0.484535	−	0.874772i	$-0.338989\pi$
$881$	−121.777	−	81.3688i	−0.138226	−	0.0923595i	−0.622761	+	0.782412i	$0.713989\pi$
$882$	−296.057	−	122.631i	−0.335665	−	0.139037i
$883$			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
$886$	−734.666	+	1773.64i	−0.829194	+	2.00185i
$887$	34.9202	−	52.2618i	0.0393689	−	0.0589197i	−0.811263	−	0.584681i	$-0.801220\pi$
$887$	34.9202	−	52.2618i	0.0393689	−	0.0589197i	0.850632	+	0.525762i	$0.176220\pi$
$888$	−47.9552	−	47.9552i	−0.0540037	−	0.0540037i
$889$	−182.723	−	918.610i	−0.205538	−	1.03331i
$890$	−1173.66	−	1756.51i	−1.31872	−	1.97361i
$891$	−100.216	+	503.820i	−0.112476	+	0.565454i
$892$	−1733.94	+	718.221i	−1.94388	+	0.805180i
$893$	84.7337	+	204.565i	0.0948866	+	0.229077i
$894$	−108.099	−	21.5022i	−0.120916	−	0.0240517i
$895$	1683.56	−	1124.92i	1.88107	−	1.25689i
$896$	−832.399	+	165.574i	−0.929016	+	0.184793i
$897$	−5.56914	+	5.56914i	−0.00620863	+	0.00620863i
$898$	−1112.14	−	743.106i	−1.23846	−	0.827513i
$899$	−36.4189	−	15.0852i	−0.0405104	−	0.0167800i
$900$			1700.15i			1.88905i
$901$		0			0
$902$	−533.932			−0.591942
$903$	−56.7469	+	136.999i	−0.0628426	+	0.151715i
$904$	118.801	−	177.798i	0.131417	−	0.196679i
$905$	1710.95	+	1710.95i	1.89055	+	1.89055i
$906$	−63.0480	−	316.964i	−0.0695894	−	0.349850i
$907$	122.120	+	182.765i	0.134641	+	0.201505i	0.892663	−	0.450724i	$-0.148834\pi$
$907$	122.120	+	182.765i	0.134641	+	0.201505i	−0.758022	+	0.652229i	$0.773834\pi$
$908$	97.6601	−	490.970i	0.107555	−	0.540716i
$909$	−59.3490	+	24.5832i	−0.0652904	+	0.0270442i
$910$	−82.5412	−	199.272i	−0.0907046	−	0.218980i
$911$	−495.652	−	98.5913i	−0.544074	−	0.108223i	−0.0846014	−	0.996415i	$-0.526962\pi$
$911$	−495.652	−	98.5913i	−0.544074	−	0.108223i	−0.459473	+	0.888192i	$0.651962\pi$
$912$	18.9734	−	12.6776i	0.0208042	−	0.0139009i
$913$	941.226	−	187.221i	1.03092	−	0.205062i
$914$	−571.150	+	571.150i	−0.624890	+	0.624890i
$915$	−197.777	−	132.150i	−0.216149	−	0.144426i
$916$	−1725.66	−	714.790i	−1.88390	−	0.780338i
$917$		−	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	$0.668910\pi$
$920$	92.9674	−	224.443i	0.101052	−	0.243960i
$921$	−72.0807	+	107.876i	−0.0782635	+	0.117130i
$922$	966.431	+	966.431i	1.04819	+	1.04819i
$923$	−23.3556	−	117.416i	−0.0253040	−	0.127212i
$924$	−147.878	−	221.315i	−0.160041	−	0.239518i
$925$	182.276	−	916.364i	0.197055	−	0.990663i
$926$	−225.922	+	93.5798i	−0.243976	+	0.101058i
$927$	132.667	+	320.288i	0.143115	+	0.345510i
$928$	−133.499	−	26.5547i	−0.143857	−	0.0286150i
$929$	954.224	−	637.592i	1.02715	−	0.686321i	0.0766557	−	0.997058i	$-0.475576\pi$
$929$	954.224	−	637.592i	1.02715	−	0.686321i	0.950496	+	0.310737i	$0.100576\pi$
$930$	−248.685	+	49.4666i	−0.267404	+	0.0531899i
$931$	25.2457	−	25.2457i	0.0271167	−	0.0271167i
$932$	1203.06	+	803.857i	1.29083	+	0.862508i
$933$	−249.980	−	103.545i	−0.267932	−	0.110981i
$934$			249.650i			0.267291i
$935$		0			0
$936$	33.2228			0.0354944
$937$	−517.380	+	1249.07i	−0.552166	+	1.33305i	0.363682	+	0.931523i	$0.381519\pi$
$937$	−517.380	+	1249.07i	−0.552166	+	1.33305i	−0.915848	+	0.401524i	$0.868481\pi$
$938$	1548.51	−	2317.50i	1.65086	−	2.47068i
$939$	−226.691	−	226.691i	−0.241418	−	0.241418i
$940$	−636.834	−	3201.58i	−0.677483	−	3.40594i
$941$	1022.11	+	1529.70i	1.08620	+	1.62561i	0.718291	+	0.695743i	$0.244925\pi$
$941$	1022.11	+	1529.70i	1.08620	+	1.62561i	0.367905	+	0.929864i	$0.380075\pi$
$942$	17.2846	−	86.8953i	0.0183488	−	0.0922455i
$943$	173.131	−	71.7133i	0.183596	−	0.0760480i
$944$	−104.933	−	253.331i	−0.111158	−	0.268359i
$945$	−871.454	−	173.343i	−0.922174	−	0.183432i
$946$	472.317	−	315.592i	0.499278	−	0.333607i
$947$	38.5945	−	7.67691i	0.0407544	−	0.00810656i	−0.174671	−	0.984627i	$-0.555886\pi$
$947$	38.5945	−	7.67691i	0.0407544	−	0.00810656i	0.215425	+	0.976520i	$0.430886\pi$
$948$	−282.745	+	282.745i	−0.298255	+	0.298255i
$949$	57.3319	+	38.3079i	0.0604129	+	0.0403666i
$950$	−310.538	−	128.629i	−0.326882	−	0.135399i
$951$			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	$0.469317\pi$
$954$	580.495	−	1401.44i	0.608485	−	1.46901i
$955$	−591.301	+	884.944i	−0.619163	+	0.926643i
$956$	−1199.89	−	1199.89i	−1.25511	−	1.25511i
$957$	−3.93041	−	19.7595i	−0.00410701	−	0.0206473i
$958$	774.317	+	1158.85i	0.808264	+	1.20965i
$959$	265.266	−	1333.58i	0.276606	−	1.39059i
$960$	−568.173	+	235.345i	−0.591847	+	0.245151i
$961$	−304.685	−	735.574i	−0.317050	−	0.765426i
$962$	−79.4005	−	15.7937i	−0.0825369	−	0.0164176i
$963$	−613.079	+	409.646i	−0.636635	+	0.425386i
$964$	−1227.96	+	244.257i	−1.27382	+	0.253378i
$965$	1808.97	−	1808.97i	1.87458	−	1.87458i
$966$	137.833	+	92.0972i	0.142684	+	0.0953387i
$967$	−1181.69	−	489.471i	−1.22201	−	0.506175i	−0.323965	−	0.946069i	$-0.605016\pi$
$967$	−1181.69	−	489.471i	−1.22201	−	0.506175i	−0.898050	+	0.439894i	$0.855016\pi$
$968$		−	196.715i		−	0.203218i
$969$		0			0
$970$	−597.751			−0.616238
$971$	349.777	−	844.437i	0.360224	−	0.869657i	−0.635043	−	0.772477i	$-0.719018\pi$
$971$	349.777	−	844.437i	0.360224	−	0.869657i	0.995267	−	0.0971803i	$-0.0309823\pi$
$972$	512.141	−	766.473i	0.526894	−	0.788553i
$973$	997.319	+	997.319i	1.02499	+	1.02499i
$974$	−308.974	−	1553.32i	−0.317222	−	1.59478i
$975$	−20.1288	−	30.1248i	−0.0206449	−	0.0308972i
$976$	−71.0174	+	357.029i	−0.0727637	+	0.365808i
$977$	408.510	−	169.210i	0.418126	−	0.173194i	−0.163694	−	0.986511i	$-0.552341\pi$
$977$	408.510	−	169.210i	0.418126	−	0.173194i	0.581820	+	0.813318i	$0.302341\pi$
$978$	150.343	+	362.961i	0.153725	+	0.371126i
$979$	−688.340	−	136.919i	−0.703105	−	0.139856i
$980$	−437.645	+	292.425i	−0.446577	+	0.298393i
$981$	152.414	−	30.3170i	0.155366	−	0.0309042i
$982$	1046.98	−	1046.98i	1.06617	−	1.06617i
$983$	553.287	+	369.695i	0.562856	+	0.376088i	0.804207	−	0.594350i	$-0.202590\pi$
$983$	553.287	+	369.695i	0.562856	+	0.376088i	−0.241351	+	0.970438i	$0.577590\pi$
$984$	57.8106	+	23.9459i	0.0587506	+	0.0243353i
$985$		−	928.713i		−	0.942856i
$986$		0			0
$987$	502.343			0.508959
$988$	−6.28094	+	15.1635i	−0.00635723	+	0.0153477i
$989$	−110.764	+	165.770i	−0.111996	+	0.167614i
$990$	1157.59	+	1157.59i	1.16928	+	1.16928i
$991$	−305.291	−	1534.80i	−0.308063	−	1.54874i	−0.755939	−	0.654642i	$-0.772819\pi$
$991$	−305.291	−	1534.80i	−0.308063	−	1.54874i	0.447876	−	0.894096i	$-0.352181\pi$
$992$	316.187	+	473.207i	0.318736	+	0.477023i
$993$	−25.1726	+	126.551i	−0.0253500	+	0.127443i
$994$	−2327.96	+	964.271i	−2.34201	+	0.970092i
$995$	909.048	+	2194.64i	0.913616	+	2.20566i
$996$	−489.110	−	97.2901i	−0.491075	−	0.0976808i
$997$	−1280.55	+	855.639i	−1.28441	+	0.858213i	−0.995086	−	0.0990189i	$-0.968430\pi$
$997$	−1280.55	+	855.639i	−1.28441	+	0.858213i	−0.289321	+	0.957232i	$0.593430\pi$
$998$	1505.57	−	299.476i	1.50858	−	0.300076i
$999$	−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.m.75.1		8
17.2	even	8		289.3.e.k.249.1		8
17.3	odd	16		289.3.e.c.131.1		8
17.4	even	4		17.3.e.a.10.1	✓	8
17.5	odd	16	inner	289.3.e.m.158.1		8
17.6	odd	16		289.3.e.l.65.1		8
17.7	odd	16		289.3.e.d.224.1		8
17.8	even	8		289.3.e.d.40.1		8
17.9	even	8		289.3.e.b.40.1		8
17.10	odd	16		289.3.e.b.224.1		8
17.11	odd	16		289.3.e.k.65.1		8
17.12	odd	16		289.3.e.i.158.1		8
17.13	even	4		289.3.e.c.214.1		8
17.14	odd	16		17.3.e.a.12.1	yes	8
17.15	even	8		289.3.e.l.249.1		8
17.16	even	2		289.3.e.i.75.1		8
51.14	even	16		153.3.p.b.46.1		8
51.38	odd	4		153.3.p.b.10.1		8
68.31	even	16		272.3.bh.c.97.1		8
68.55	odd	4		272.3.bh.c.129.1		8
85.4	even	4		425.3.u.b.401.1		8
85.14	odd	16		425.3.u.b.301.1		8
85.38	odd	4		425.3.t.c.299.1		8
85.48	even	16		425.3.t.a.199.1		8
85.72	odd	4		425.3.t.a.299.1		8
85.82	even	16		425.3.t.c.199.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.10.1	✓	8	17.4	even	4
17.3.e.a.12.1	yes	8	17.14	odd	16
153.3.p.b.10.1		8	51.38	odd	4
153.3.p.b.46.1		8	51.14	even	16
272.3.bh.c.97.1		8	68.31	even	16
272.3.bh.c.129.1		8	68.55	odd	4
289.3.e.b.40.1		8	17.9	even	8
289.3.e.b.224.1		8	17.10	odd	16
289.3.e.c.131.1		8	17.3	odd	16
289.3.e.c.214.1		8	17.13	even	4
289.3.e.d.40.1		8	17.8	even	8
289.3.e.d.224.1		8	17.7	odd	16
289.3.e.i.75.1		8	17.16	even	2
289.3.e.i.158.1		8	17.12	odd	16
289.3.e.k.65.1		8	17.11	odd	16
289.3.e.k.249.1		8	17.2	even	8
289.3.e.l.65.1		8	17.6	odd	16
289.3.e.l.249.1		8	17.15	even	8
289.3.e.m.75.1		8	1.1	even	1	trivial
289.3.e.m.158.1		8	17.5	odd	16	inner
425.3.t.a.199.1		8	85.48	even	16
425.3.t.a.299.1		8	85.72	odd	4
425.3.t.c.199.1		8	85.82	even	16
425.3.t.c.299.1		8	85.38	odd	4
425.3.u.b.301.1		8	85.14	odd	16
425.3.u.b.401.1		8	85.4	even	4

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+(1.15851 - 2.79690i) q^{2} +(0.451406 - 0.675577i) q^{3} +(-3.65205 - 3.65205i) q^{4} +(1.56645 + 7.87510i) q^{5} +(-1.36656 - 2.04520i) q^{6} +(-1.53233 + 7.70353i) q^{7} +(-3.25778 + 1.34942i) q^{8} +(3.19151 + 7.70500i) q^{9} +(23.8406 + 4.74219i) q^{10} +(6.71450 - 4.48649i) q^{11} +(-4.11580 + 0.818684i) q^{12} +(-0.798835 + 0.798835i) q^{13} +(19.7707 + 13.2104i) q^{14} +(6.02734 + 2.49661i) q^{15} -9.98414i q^{16} +25.2475 q^{18} +(-1.07647 + 2.59882i) q^{19} +(23.0395 - 34.4811i) q^{20} +(4.51262 + 4.51262i) q^{21} +(-4.76941 - 23.9774i) q^{22} +(4.76696 + 7.13426i) q^{23} +(-0.558947 + 2.81002i) q^{24} +(-36.4664 + 15.1049i) q^{25} +(1.30880 + 3.15972i) q^{26} +(13.8181 + 2.74858i) q^{27} +(33.7298 - 22.5376i) q^{28} +(3.01148 - 0.599020i) q^{29} +(13.9655 - 13.9655i) q^{30} +(-10.6746 - 7.13254i) q^{31} +(-40.9557 - 16.9644i) q^{32} -6.56139i q^{33} -63.0663 q^{35} +(16.4835 - 39.7946i) q^{36} +(-13.1509 + 19.6817i) q^{37} +(6.02153 + 6.02153i) q^{38} +(0.179075 + 0.900273i) q^{39} +(-15.7300 - 23.5416i) q^{40} +(4.26082 - 21.4206i) q^{41} +(17.8493 - 7.39341i) q^{42} +(8.89197 + 21.4671i) q^{43} +(-40.9066 - 8.13684i) q^{44} +(-55.6783 + 37.2030i) q^{45} +(25.4764 - 5.06757i) q^{46} +(55.6597 - 55.6597i) q^{47} +(-6.74505 - 4.50690i) q^{48} +(-11.7262 - 4.85715i) q^{49} +119.492i q^{50} +5.83478 q^{52} +(22.9922 - 55.5080i) q^{53} +(23.6959 - 35.4634i) q^{54} +(45.8495 + 45.8495i) q^{55} +(-5.40329 - 27.1642i) q^{56} +(1.26978 + 1.90036i) q^{57} +(1.81344 - 9.11677i) q^{58} +(25.3733 - 10.5100i) q^{59} +(-12.8944 - 31.1299i) q^{60} +(-35.7596 - 7.11302i) q^{61} +(-32.3156 + 21.5926i) q^{62} +(-64.2461 + 12.7793i) q^{63} +(-66.6561 + 66.6561i) q^{64} +(-7.54224 - 5.03957i) q^{65} +(-18.3515 - 7.60145i) q^{66} -117.219i q^{67} +6.97157 q^{69} +(-73.0632 + 176.390i) q^{70} +(-58.8738 + 88.1108i) q^{71} +(-20.7945 - 20.7945i) q^{72} +(-11.9073 - 59.8620i) q^{73} +(39.8122 + 59.5832i) q^{74} +(-6.25665 + 31.4543i) q^{75} +(13.4223 - 5.55971i) q^{76} +(24.2730 + 58.6001i) q^{77} +(2.72543 + 0.542122i) q^{78} +(79.2276 - 52.9382i) q^{79} +(78.6261 - 15.6397i) q^{80} +(-44.9799 + 44.9799i) q^{81} +(-54.9749 - 36.7331i) q^{82} +(109.791 + 45.4770i) q^{83} -32.9607i q^{84} +70.3428 q^{86} +(0.954715 - 2.30489i) q^{87} +(-15.8202 + 23.6767i) q^{88} +(-61.4534 - 61.4534i) q^{89} +(39.5490 + 198.826i) q^{90} +(-4.92977 - 7.37792i) q^{91} +(8.64551 - 43.4639i) q^{92} +(-9.63715 + 3.99184i) q^{93} +(-91.1920 - 220.157i) q^{94} +(-22.1522 - 4.40634i) q^{95} +(-29.9484 + 20.0109i) q^{96} +(-24.1185 + 4.79748i) q^{97} +(-27.1699 + 27.1699i) q^{98} +(55.9978 + 37.4165i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 16 q^{5} + 24 q^{6} - 8 q^{7} + 24 q^{8} + 16 q^{9} + 48 q^{10} + 48 q^{11} + 40 q^{12} + 16 q^{13} - 8 q^{14} + 16 q^{15} + 56 q^{18} + 32 q^{20} - 64 q^{21} + 56 q^{22} + 40 q^{23}+ \cdots + 272 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 16 * q^5 + 24 * q^6 - 8 * q^7 + 24 * q^8 + 16 * q^9 + 48 * q^10 + 48 * q^11 + 40 * q^12 + 16 * q^13 - 8 * q^14 + 16 * q^15 + 56 * q^18 + 32 * q^20 - 64 * q^21 + 56 * q^22 + 40 * q^23 + 104 * q^24 - 64 * q^25 - 176 * q^26 - 16 * q^27 + 56 * q^28 - 64 * q^29 + 16 * q^30 - 40 * q^31 - 88 * q^32 - 160 * q^35 + 128 * q^36 - 128 * q^37 - 120 * q^38 - 176 * q^39 + 16 * q^40 - 112 * q^41 - 16 * q^42 + 232 * q^43 - 24 * q^44 - 160 * q^45 + 136 * q^46 + 192 * q^47 + 8 * q^48 - 16 * q^49 - 384 * q^52 + 32 * q^53 + 224 * q^55 + 136 * q^56 - 72 * q^57 + 32 * q^58 + 48 * q^59 - 64 * q^60 + 64 * q^61 - 56 * q^62 - 168 * q^63 - 64 * q^64 + 96 * q^65 + 8 * q^66 + 240 * q^69 - 224 * q^70 - 88 * q^71 + 40 * q^72 - 48 * q^73 - 192 * q^74 - 80 * q^76 + 48 * q^77 - 304 * q^78 + 168 * q^79 + 112 * q^80 - 424 * q^81 - 136 * q^82 + 264 * q^83 + 832 * q^86 - 208 * q^87 + 320 * q^88 + 160 * q^89 - 144 * q^90 + 224 * q^91 + 184 * q^92 + 64 * q^93 - 32 * q^94 + 16 * q^95 - 232 * q^96 - 104 * q^97 - 120 * q^98 + 272 * q^99

Introduction

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